tag:blogger.com,1999:blog-81379881368609413982024-03-18T02:48:04.858-07:00SprachlogikA philosophy blog with a focus on logic and language.Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.comBlogger165125tag:blogger.com,1999:blog-8137988136860941398.post-9129710627539569682024-03-14T23:03:00.000-07:002024-03-14T23:11:45.644-07:00In what sense can classical logic be wrong?<p><span style="font-size: 11pt; white-space-collapse: preserve;"><span style="font-family: georgia;">Failing to capture stuff is not being wrong, so for e.g. indicative conditionals not being material conditionals does not mean that classical logic is wrong, only that it doesn’t by itself handle the validity or otherwise of arguments involving indicative conditionals.</span></span></p><span id="docs-internal-guid-4e0dee21-7fff-f32f-1384-1fad21951db1"><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span style="font-family: georgia;">But the threat from truth-theoretic considerations, gaps and gluts, is different here.</span></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span style="font-family: georgia;">Also the threat from the more general idea that there’s a relevant sense of logical consequence whereby explosion (ex falso quodiblet) isn’t valid. </span></span></p><span style="font-family: georgia;"><br /></span><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span style="font-family: georgia;">In both cases things come to a head with: this argument is valid according to classical logic but really isn’t.</span></span></p><span style="font-family: georgia;"><br /></span><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: georgia;"><span style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">With the first threat, the problem is </span><span style="font-size: 11pt; font-style: italic; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">not</span><span style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"> in the notion of validity—that can stay. With the second, the frame of mind is that of wanting a conception of consequence/validity in which explosion simply lacks that status, isn’t sort of pseudo-valid, i.e. valid in a stronger pseudo-logic where we ignore some real possibilities. </span></span></p><span style="font-family: georgia;"><br /></span><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span style="font-family: georgia;">With the first, you can say: explosion instances are often good arguments in some sense, even if not strictly valid. They’re truth-preserving w.r.t. all cases not involving dialetheia. Not, of course, good arguments in the sense that you’d ever follow them from premise to conclusion! But we can say yep, anything “follows from” a contradiction if we ignore models in which dialtheia occur. Provided you know you have no dialethia in the mix, you have your guarantee that you’re not gonna be led from truth to falsity. </span></span></p><span style="font-family: georgia;"><br /></span><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span style="font-family: georgia;">On this first conception, i.e. the dialethic one, how does classical logic err? Where does it go wrong? </span></span></p><span style="font-family: georgia;"><br /></span><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: georgia;"><span style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">‘You say it is not possible for P&~P to be true while Q is false. But it </span><span style="font-size: 11pt; font-style: italic; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">is</span><span style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"> possible, because, when you interpret P, sometimes your classical model which corresponds to reality, while it rightly captures the fact that P is true (false), goes wrong in not also capturing the fact that P is false (true). Well, actually, in these cases, two of your classical models will correspond to reality.’ (One fix, make the valuation function a relation—on that implementation, we can say the classical model rightly maps P to T (F) but fails to also map it to F (T). Another, add a third truth value representing the dialethic status - but that’s a different mode of presentation and so you don’t get the perspicuous sense in which the classical model just leaves something out. — In the relation mode of presentation, you can take a classical model with one letter and get two full models - the one where you do nothing, and the one where you also map it to the other value. But with the three-value mode of presentation, while a classical model is straightforwardly still a special case of one of these full-story models, it is no longer the case that you can take a classical model of a situation and make it correct by only adding something (or doing nothing)-if you have a dialethia, you have to </span><span style="font-size: 11pt; font-style: italic; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">un</span><span style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">map it from T and instead map it to X. So that makes it look like the classical model has said something wrong — and of course we can look at a classical model what way, if we treat T as “true and true only” or regard the model as making an implicit claim to telling the whole story about which letters have which of the two properties truth and falsity. </span><span style="font-size: 11pt; font-style: italic; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">But here the principle of charity, and general good sense, should tell us to not regard that as part of classical logic itself</span><span style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">. So let’s put that aside.</span></span></p><span style="font-family: georgia;"><br /></span><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span style="font-family: georgia;">From this point of view, classical logic knows what validity is alright, and doesn’t get any individual thing wrong semantically, but the semantics is incomplete—the models lack information sometimes (and the way the notion of model is set up precludes putting it in). And this leads to cases where counterexamples fail to show up, because the classical models miss parts of the picture without which the picture doesn’t show a counterexample. </span></span></p><div><span face="Arial, sans-serif" style="font-size: 11pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><br /></span></div></span>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com0tag:blogger.com,1999:blog-8137988136860941398.post-23615011947847159292022-09-09T22:18:00.004-07:002022-09-09T22:26:57.145-07:00Notes on Modal Issues Regarding the Ontology of Propositions<span id="docs-internal-guid-1de521e5-7fff-3bc4-6c06-d4e69d4696a0"><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial;"><span style="font-size: 14.6667px; white-space: pre-wrap;"><a href="https://sprachlogik.substack.com/p/notes-on-modal-issues-regarding-the?sd=pf">Cross-posted here.</a></span></span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">A true sentence like ‘John is here in this room’, and its Twin Earth counterpart, express different propositions, since they are about distinct people. And that means that propositions sometimes constitutively involve particular external things that they are about.</span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">What, in light of this, should we say about how, if at all, what propositions there are—what claims exist—varies across possible worlds?</span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">One side of this issue is: could propositions like the ones expressed by a normal true use of ‘John is here in this room’ have failed to exist? Do they fail to exist in (or </span><span style="font-family: Arial; font-size: 11pt; font-style: italic; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">with respect to</span><span style="font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">, perhaps?) all worlds in which John does not exist? (I set aside Williamsonian necessitarianism about what there is.)</span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">My notion of the </span><span style="font-family: Arial; font-size: 11pt; font-style: italic; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">internal meaning</span><span style="font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> of a sentence, or the way it is used, gives me a way of agreeing that there’s </span><span style="font-family: Arial; font-size: 11pt; font-style: italic; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">something</span><span style="font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> right about the idea that the meanings of sentences are just there and exist necessarily. Given a normal occurrence of ‘John is here in this room’, the way the sentence is being used—which it has in common with its Twin Earth counterpart—may be regarded as a pure abstract object, like a way of dancing, which we can say is just there and could in no sense have failed to exist.</span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Here is another question we might ask: propositions about particular people and physical things—suppose they do exist in some possible worlds apart from the actual world. But do they themselves have different properties in worlds where the things they are about have different properties? A way of using a sentence, we might say, is just what it is and doesn’t have different </span><span style="font-family: Arial; font-size: 11pt; font-style: italic; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">intrinsic</span><span style="font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> properties at any rate in different worlds—it will of course have different extrinsic properties such as ‘having been instantiated by someone wearing a blue hat’. But if a claim constitutively involves the object it is about, is the object with respect to the claim like a diamond set in a piece of jewellry, so that the piece’s properties change whenever the diamond’s do, since the diamond is </span><span style="font-family: Arial; font-size: 11pt; font-style: italic; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">part</span><span style="font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> of it? I think perhaps this need not be so. We could instead use the model of something which needs to be tied to something else, and which disappears, or at least ceases to be that thing, if we cut the tie or remove the something else.</span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">A tremendous complicating factor is that there are undoubtedly, in some sense, claims about things that do not in fact exist. We cannot here follow Kripke in </span><span style="font-family: Arial; font-size: 11pt; font-style: italic; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Reference and Existence</span><span style="font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> into the view that these sentences do not in fact express propositions, anymore than we should follow him in analyzing particular existential statements as talking about whether there is such-and-such a proposition. (That theory is I think clearly tortured but this is not the place to mount objections but see Postscript.) And recall there that even Kripke was keen to avoid the seeming absurdity of having to hold that the correct analysis of a statement can depend on whether it is true or false. However! It seems to me there is one thing in this general vicinity which we </span><span style="font-family: Arial; font-size: 11pt; font-style: italic; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">might</span><span style="font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> indeed have to come to terms with. Namely, that the modal profiles and identity conditions of propositions expressed by statements involving names that happen to be empty differ from those of propositions expressed by statements </span><span style="font-family: Arial; font-size: 11pt; font-style: italic; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">which are being used in exactly the same way</span><span style="font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> but where the names aren’t empty. </span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Someone might want to say: just because we can’t pick out particular propositions about physical objects and people etc. that do not actually exist, doesn’t mean they don’t exist. (Anymore than the fact that non-actual people can’t pick out our propositions means that </span><span style="font-family: Arial; font-size: 11pt; font-style: italic; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">they</span><span style="font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> don’t exist.) But this is only really correct given something like Lewisian modal realism.</span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">‘What if Vulcan</span><span style="font-family: Arial; font-size: 11pt; font-style: italic; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> had </span><span style="font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">existed?’—Are we to follow Kripke in his view of unicorns and apply that even to the case of names, i.e. say that there is no particular possibility in question at all here? A lot of what I am otherwise tending toward does seem to be leading me that way—but I suspect that here the shoe might really pinch, and that dwelling on this part of the issue and trying to do it justice will lead to a breakthrough—-a better view. A kind of more nuanced view which, </span><span style="font-family: Arial; font-size: 11pt; font-style: italic; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">pace</span><span style="font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> recent Williamson, would not be a case of overfitting.</span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">‘What if the claims made by some astronomers about Vulcan had been true? I don’t mean what if they had been right when they spoke. I mean, consider the claims they expressed about Vulcan. What if those claims had been true? Is there a possible world in which they are true?’</span></p><br /><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 11pt; font-style: italic; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Postscript.</span><span style="font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> It seems a very important objection to Kripke’s analysis of negative existentials in R&E that he is kicking the can down the road. For how does it get to be true that ‘There is no such proposition as that Vulcan exists’ expresses a true proposition? If we interpret it metalinguistically, it’s wrong as an analysis. So then how do we interpret it? The ‘no such’ has a soothing effect and as it were shrouds the occurrence of ‘Vulcan’ in a haze. But we still need to account for what it’s doing there and how we get different statements when we pop in different empty names.</span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: Arial; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><i>This post is dedicated to the memory of the late Queen Elizabeth II.</i></span></p></span>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com1tag:blogger.com,1999:blog-8137988136860941398.post-50940690168622568652022-06-28T22:06:00.003-07:002022-06-28T22:06:44.027-07:00Meaning and Metaphysical Necessity - now out with Routledge<p> </p><div class="separator" style="clear: both; text-align: center;"><a href="https://philpapers.org/rec/HAZMAM-2" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1200" data-original-width="785" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEgUzRw6DRgdB3rmCyrwRjuqKhpfldQEPBeAo_z3CFKjege58x4_9Tbstps_T-Pz7v5bi-khctwVoMiApnlSREK6p1Z66VQXpu4KXSKP7bYVnu43lfW_flOCPmgG7CFQphJxqkXUJ3dHzGynxw6yzO4CBhV9DTf2m-5WDe4kou4oh78V_4ZbM9wx7iQ7" width="157" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><span style="font-family: georgia;">My book <i>Meaning and Metaphysical Necessity </i>is now out with Routledge. I began seriously developing the ideas in it in 2011 when I began my PhD, which is also the year this blog started. Many of the posts here over the years were devoted to working out the views in the book.</span></div><br /><p></p>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com2tag:blogger.com,1999:blog-8137988136860941398.post-22275381610985220582021-12-03T16:24:00.005-08:002021-12-03T16:27:09.969-08:00The Threefold Root of the How-Question About Mathematical Knowledge<p>Platonism is the default, almost obviously correct view about mathematical objects. One of the major things that puts pressure on Platonism is the question 'How do we know about mathematical objects, then?'. What gives this question its power? I think three things conspire and that the third might be under-appreciated:</p><p>1. <i>Real justificatory demands internal to mathematical discourse</i>. For particular mathematical claims, there are very real 'How do we know?' questions, and they have substantive mathematical answers. The impulse to ask the question then gets generalized to mathematical knowledge in general, except that then there's no substantial answer.</p><p>2. <i>A feeling of impossibility engendered by a causal theory of knowledge.</i> If you only think about certain kinds of knowledge, it can seem plausible that, in general, the way we get to know about things is via their causal impacts on us. This then makes mathematical knowledge seem impossible.<br /><br />3. <i>Our deeply-ingrained habit of giving reasons.</i> The social impulse to justify one's claims to another is hacked by a monster: the philosophical question at the heart of the epistemology of mathematics.<br /><br />If it were just 1 and 2 getting tangled up with each other, the how-question would not be so persistent. With existing philosophical understanding we'd be able to see our way past it. But 3 hasn't been excavated yet and that keeps the whole thing going.</p>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com18tag:blogger.com,1999:blog-8137988136860941398.post-46670669435408273322021-11-20T17:19:00.000-08:002021-11-20T17:19:59.126-08:00A Puzzle about Abbreviation and Self-Reference<p>Let us use 'ONE' as an abbreviation of 'This sentence token contains more than one word token'. Now consider whether the following is true:<br /><br /><span> ONE</span></p>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com13tag:blogger.com,1999:blog-8137988136860941398.post-34140484029807297422021-11-05T01:36:00.003-07:002021-11-05T01:36:29.039-07:00Major Inaccuracies in Misak's review of Journey to the Edge of Reason, a new Gödel Biography<p>In the Times Literary Supplement there is a <a href="https://www.the-tls.co.uk/articles/journey-to-the-edge-of-reason-kurt-godel-stephen-budianksy-book-review-cheryl-misak/">review</a> of a new biography of Gödel biography by philosopher Cheryl Misak. The review is called 'What are the limits of logic? How a groundbreaking logician lost control'. This paragraph contains two major inaccuracies:<br /></p><p><span style="color: #292929; font-family: "Publico Text 400 Roman", serif; font-size: 18px;">Gödel proved that if a statement in first-order logic is well formed (that is to say, it follows the syntactic rules for the formal language correctly), then there is a formal proof of it. But his second doctorate, or </span><i style="box-sizing: border-box; color: #292929; font-family: "Publico Text 400 Roman", serif; font-size: 18px;">Habilitation</i><span style="color: #292929; font-family: "Publico Text 400 Roman", serif; font-size: 18px;">, published in 1931, showed that in any formal system that includes arithmetic, there will always be statements that are both true and unprovable. The answer to the </span><i style="box-sizing: border-box; color: #292929; font-family: "Publico Text 400 Roman", serif; font-size: 18px;">Entscheidungsproblem </i><span style="color: #292929; font-family: "Publico Text 400 Roman", serif; font-size: 18px;">was, therefore, negative.</span></p><p>The first one is that being well formed is like being grammatically correct - among the well formed formulas of first-order logic, there are formulas that are false no matter what (false on all models or interpretations), formulas that can go either way, and formulas that are true no matter what (these ones are often called logical truths, or logically valid formulas). What Gödel showed is that for every logical truth, there is a proof that it's a logical truth. </p><p>The second major inaccuracy is that the answer to the decision problem (Entscheidungsproblem) is not shown to be negative by the incompleteness theorem that Misak alludes to. The negative answer became known only in 1936, when Alonzo Church and Alan Turing independently showed it.</p>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com27tag:blogger.com,1999:blog-8137988136860941398.post-48500257866960091162021-10-21T19:04:00.003-07:002021-10-21T19:04:50.209-07:00Reversing Logical Nihilism - Forthcoming in Synthese<p>Final draft available <a href="https://philpapers.org/rec/HAZRLN">on PhilPapers</a>.</p><p>Abstract: <span style="font-size: 12pt; white-space: pre-wrap;">Gillian Russell has recently proposed counterexamples to such elementary argument forms as Conjunction Introduction (e.g. ‘Snow is white. Grass is green. Therefore, snow is white and grass is green’) and Identity (e.g. ‘Snow is white. Therefore, snow is white’). These purported counterexamples involve expressions that are sensitive to linguistic context—for example, a sentence which is true when it appears alone but false when embedded in a larger sentence. If they are genuine counterexamples, it looks as though logical nihilism—the view that there are no valid argument forms—might be true. In this paper, I argue that the purported counterexamples are not genuine, on the grounds that they equivocate. Having defused the threat of logical nihilism, I argue that the kind of linguistic context sensitivity at work in Russell’s purported counterexamples, if taken seriously, far from leading to logical nihilism, reveals new, previously undreamt-of valid forms. By way of proof of concept I present a simple logic, Solo-Only Propositional Logic (SOPL), designed to capture some of them. Along the way, some interesting subtleties about the fallacy of equivocation are revealed.</span></p><p><span style="font-size: 12pt; white-space: pre-wrap;"></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://lh3.googleusercontent.com/-O3zmhs35EQQ/YXIcOxhfxKI/AAAAAAAABQI/V34eGNq4soweOBFa4a08VsS2DNk268vcACLcBGAsYHQ/image.png" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="504" data-original-width="650" height="240" src="https://lh3.googleusercontent.com/-O3zmhs35EQQ/YXIcOxhfxKI/AAAAAAAABQI/V34eGNq4soweOBFa4a08VsS2DNk268vcACLcBGAsYHQ/image.png" width="310" /></a></div><br /><br /><p></p><p><span style="font-size: 12pt; white-space: pre-wrap;"><br /></span></p>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com21tag:blogger.com,1999:blog-8137988136860941398.post-967981692947068342021-08-28T19:54:00.003-07:002021-08-28T19:54:47.543-07:00Validity as (Material!) Truth-Preservation in Virtue of Form<p>Forthcoming in <i>Analytic Philosophy </i>and available <a href="https://philpapers.org/rec/HAZVAM">on PhilPapers.</a><br /><br />Abstract:</p><p><span style="background-color: white; color: #333333; font-family: "Open Sans", sans-serif; font-size: 14px;">According to a standard story, part of what we have in mind when we say that an argument is valid is that it is necessarily truth preserving: if the premises are true, the conclusion must also be true. But—the story continues—that’s not enough, since ‘Roses are red, therefore roses are coloured’ for example, while it may be necessarily truth-preserving, is not so in virtue of form. Thus we arrive at a standard contemporary characterisation of validity: an argument is valid when it is NTP in virtue of form. Here I argue that we can and should drop the N; the resulting account is simpler, less problematic, and performs just as well with examples.</span></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://lh3.googleusercontent.com/-fqTa0mvHJa0/YSr277fTtRI/AAAAAAAABOo/JR1O4crhhgcnrNo1QWo-YFaiCKVRONDyACLcBGAsYHQ/image.png" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="270" data-original-width="186" height="240" src="https://lh3.googleusercontent.com/-fqTa0mvHJa0/YSr277fTtRI/AAAAAAAABOo/JR1O4crhhgcnrNo1QWo-YFaiCKVRONDyACLcBGAsYHQ/image.png" width="165" /></a></div><br /><br /><p></p>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com30tag:blogger.com,1999:blog-8137988136860941398.post-34078013822835802032021-06-18T19:55:00.004-07:002021-06-18T19:55:32.621-07:00Sprachlogik on Substack<p><a href="http://sprachlogik.substack.com">Here.</a></p>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com66tag:blogger.com,1999:blog-8137988136860941398.post-23397869942966656432021-06-06T20:49:00.004-07:002021-06-06T20:50:43.872-07:00Dialetheism and Transition States<p><span style="font-size: medium;">I've been thinking recently about an argument given by Graham Priest for the view that, when you're on your way out of a room, there's a point in time at which you're both in the room and not in the room. </span></p><p><span style="font-size: medium;">For those who believe in true contradictions (<i>dialethias</i>) already because of Liar-like phenomena, whether or not this kind of example also exist may not seem like such an urgent issue. But if, like me, you are drawn to a gappy rather than a glutty response to Liar-like paradoxes, this sort of argument becomes more important, since it may take you from not believing in true contradictions to believing in them.</span></p><p><span style="font-size: medium;">Priest's argument appears on p. 415 of his 'What is So Bad About Contradictions?' and is discussed in Section 3.4. of the <a href="https://plato.stanford.edu/entries/dialetheism/#OtheMotiForDial">SEP article on dialetheism</a>. From the latter:</span></p><p><span style="font-size: medium;"><em style="background-color: white; color: #1a1a1a; font-family: serif;"></em></span></p><blockquote><span style="font-size: medium;"><em style="background-color: white; color: #1a1a1a; font-family: serif;">Transition states</em><span style="background-color: white; color: #1a1a1a; font-family: serif;">: when I exit the room, I am inside the room at one time, and outside of it at another. Given the continuity of motion, there must be a precise instant in time, call it </span><span class="mjx-chtml MathJax_CHTML" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>" id="MathJax-Element-44-Frame" role="presentation" style="background-color: white; border: 0px; color: #1a1a1a; direction: ltr; display: inline-block; float: none; font-family: serif; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; white-space: nowrap;" tabindex="0"><span aria-hidden="true" class="mjx-math" id="MJXc-Node-233" style="border-collapse: separate; border-spacing: 0px; display: inline-block;"><span class="mjx-mrow" id="MJXc-Node-234" style="box-sizing: content-box; display: inline-block;"><span class="mjx-mi" id="MJXc-Node-235" style="box-sizing: content-box; display: inline-block;"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.303em; padding-top: 0.423em; white-space: pre;">t</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML">t</math></span></span><span style="background-color: white; color: #1a1a1a; font-family: serif;">, at which I leave the room. Am I inside the room or outside at time </span><span class="mjx-chtml MathJax_CHTML" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math>" id="MathJax-Element-45-Frame" role="presentation" style="background-color: white; border: 0px; color: #1a1a1a; direction: ltr; display: inline-block; float: none; font-family: serif; line-height: 0; margin: 0px; max-height: none; max-width: none; min-height: 0px; min-width: 0px; overflow-wrap: normal; padding: 1px 0px; position: relative; white-space: nowrap;" tabindex="0"><span aria-hidden="true" class="mjx-math" id="MJXc-Node-236" style="border-collapse: separate; border-spacing: 0px; display: inline-block;"><span class="mjx-mrow" id="MJXc-Node-237" style="box-sizing: content-box; display: inline-block;"><span class="mjx-mi" id="MJXc-Node-238" style="box-sizing: content-box; display: inline-block;"><span class="mjx-char MJXc-TeX-math-I" face="MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw" style="box-sizing: content-box; display: block; padding-bottom: 0.303em; padding-top: 0.423em; white-space: pre;">t</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation" style="border: 0px; clip: rect(1px, 1px, 1px, 1px); display: block; height: 1px; left: 0px; overflow: hidden; padding: 1px 0px 0px; position: absolute; top: 0px; user-select: none; width: 1px;"><math xmlns="http://www.w3.org/1998/Math/MathML">t</math></span></span><span style="background-color: white; color: #1a1a1a; font-family: serif;">? Four answers are available: (a) I am inside; (b) I am outside; (c) I am both; and (d) I am neither. There is a strong intuition that (a) and (b) are ruled out by symmetry considerations: choosing either would be completely arbitrary. (This intuition is not at all unique to dialetheists: see the article on </span><a href="https://plato.stanford.edu/entries/boundary/" style="background-color: white; color: #8c1515; font-family: serif; text-decoration: inherit;">boundaries</a><span style="background-color: white; color: #1a1a1a; font-family: serif;"> in general.) As for (d): if I am neither inside not outside the room, then I am not inside and not-not inside; therefore, I am either inside and not inside (option (c)), or not inside and not-not inside (which follows from option (d)); in both cases, a dialetheic situation. Or so it has been argued. For a recent description of inconsistent boundaries using formal mereology, see Weber and Cotnoir 2015.</span></span></blockquote><span style="background-color: white; color: #1a1a1a; font-family: serif; font-size: medium;"></span><p></p><p><span style="font-size: medium;">I will now outline what I think we should say in response. </span></p><p><span style="font-size: medium;">The appeal to 'symmetry considerations' is where the trouble is in this argument. Let us assume for a moment that there are no true contradictions and see what we can say that is consistent with that commonsense view. On pain of contradiction, the notion of being 'inside' a room is not both true of me and false of me in this case. Now, we can grant that any notion of being 'inside' which is true of me in this case is in a sense <i>biased</i> in favour of insideness, and any notion of being 'inside' which is false of me in this case is biased against insideness. But probably, our normal notion of 'inside' as applied to rooms is just not determinate here; our linguistic behaviour doesn't make it the case that we are using the inside-biased notion rather than the outside-biased notion, nor does it make the opposite the case. But if we need to, we can just pick one of these notions, and everything will be OK as long as this is understood by speakers and hearers.</span></p><p><span style="font-size: medium;">To me, this seems highly plausible. And it lets us maintain that there are no true contradictions. Let's grant Priest that it's bad philosophy to just reject outright the idea that there might be true contradictions. But if we haven't already adopted dialetheism, which is a pretty radical view, then other things equal, we should look for less drastic ways to make sense of examples like this. And that's what I've sketched above.</span></p>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com27tag:blogger.com,1999:blog-8137988136860941398.post-16023544722088196182021-04-15T21:38:00.006-07:002021-04-15T21:41:02.999-07:00Forthcoming in Philosophical Studies: A Simple Theory of Rigidity<p> </p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://lh3.googleusercontent.com/--q0ynIteuOE/YHkT4rV7SDI/AAAAAAAABJE/Cgcf3N36e7YidS01uXMaapy6ToIk59GMACLcBGAsYHQ/image.png" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="232" data-original-width="153" height="240" src="https://lh3.googleusercontent.com/--q0ynIteuOE/YHkT4rV7SDI/AAAAAAAABJE/Cgcf3N36e7YidS01uXMaapy6ToIk59GMACLcBGAsYHQ/image.png" width="158" /></a></div><br /><p></p><div style="text-align: left;"><span style="font-size: medium;">After <a href="http://sprachlogik.blogspot.com/2019/01/rigidity-and-general-terms-two.html">wrestling inconclusively</a> with this topic a couple of years ago on this blog, I came to a much clearer view about rigidity, which I set forth in this paper:</span></div><div style="text-align: left;"><span style="font-size: medium;"><br /></span></div><div style="text-align: left;"><b><span style="font-size: medium;">A Simple Theory of Rigidity</span></b></div><p><span id="docs-internal-guid-b34257d2-7fff-e0c8-353c-45c3c6367b2f" style="font-size: medium;"><span style="font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">The notion of rigidity looms large in philosophy of language, but is beset by difficulties. This paper proposes a simple theory of rigidity, according to which an expression has a world-relative semantic property rigidly when it has that property at, or with respect to, all worlds. Just as names, and certain descriptions like </span><span style="font-style: italic; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">The square root of 4</span><span style="font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">, rigidly designate their referents, so too are necessary truths rigidly true, and so too does </span><span style="font-style: italic; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">cat</span><span style="font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> rigidly have only animals in its extension. After spelling out the theory, I argue that it enables us to avoid the headaches that attend the misbegotten desire to have a simple rigid/non-rigid distinction that applies to expressions, giving us a simple solution to the problem of generalizing the notion of rigidity beyond singular terms.</span></span></p><div style="text-align: left;"><a href="https://philpapers.org/rec/HAZAST"><span style="font-size: medium;">Pre-print available at PhilPapers</span></a></div>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com122tag:blogger.com,1999:blog-8137988136860941398.post-46664695233054420882020-10-17T19:36:00.000-07:002020-10-17T19:36:52.636-07:00On the Failures of Nonsense-Policing and Ordinary Language Philosophy<p><i><span style="font-family: arial;">In this post I reflect on the failures of nonsense-policing and ordinary language philosophy, and the fact that notwithstanding these failures, paying critical attention to semantic issues is of central importance in philosophy, and in metaphysics as well as philosophy of language. </span></i></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: arial;"><span id="docs-internal-guid-81f80a32-7fff-02c2-c7e3-6961dc8322f0"></span></span></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: arial;">The early Twentieth Century saw a surge of interest in the idea that the apparently intractable problems of philosophy come from misunderstanding language, and that philosophical questions are often unanswerable not because they are too difficult for us, but because they fail to make sense, or we fail to understand them properly.</span></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: arial;"><br /></span></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: arial;">This idea took various forms. The logical positivists attempted to give general criteria of meaningfulness using the notion of verification, the early Wittgenstein aims at a comprehensive, general theory of how language represent which leaves no place for genuine philosophical propositions, and more specific doctrines in logic and philosophy of language were used to dissolve particular problems.</span></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: arial;"><br /></span></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: arial;">Logical positivists attempted to formulate a criterion of meaningfulness in terms of the notion of verifiability. The basic idea is that a meaningful sentence must either be analytic (i.e. true in virtue of meaning) or verifiable in principle by experience. Philosophical sentences which are neither analytic nor verifiable experientially are therefore meaningless if this idea is correct, and works of metaphysics appear to be full of such sentences. As powerful as this idea seemed to the logical positivists, attempts to work it out in detail ran into trouble. There are also serious problems affecting even the basic idea; what about statements about minute happenings in the distant past, or events outside our light cone? (Such cases are more or less worrying depending on how one thinks about ‘verifiability in principle’.) And what about competing theoretical claims that do not appear to be analytic but where the contest does not appear to be settled by any possible experience? These arise in science as well as philosophy and we seem to decide about them on the basis of things like theoretical virtues rather than empirical tests. Thus the whole idea of experiential verifiability as a criterion of meaningfulness has been largely abandoned (at least in academic philosophy; it enjoys a vigorous half-life, along with Popper’s idea that truly scientific theories must be falsifiable, in the wider intellectual culture).</span></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: arial;"><br /></span></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: arial;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Wittgenstein in the </span><span style="font-size: 11pt; font-style: italic; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Tractatus</span><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> (a source of inspiration for the verificationists) attempts to say in general how meaningful propositions are constructed. In numbered, often cryptic remarks, we are given a beautiful, austere picture of how language represents. Elementary propositions are constructed out of names, and more complex propositions are constructed from them by simple logical operations. Anything which can’t be constructed in this way is not a genuine proposition. And many sentences in philosophical works fail to be genuine propositions. Wittgenstein’s proposal is that, with theses and questions in metaphysical philosophy, something akin to what is wrong with the sentence ‘Mortality is Socrates’ has gone wrong, only more subtly so.</span></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: arial;"><br /></span></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: arial;">(Wittgenstein’s later work is also replete with denials of sense, although it is up for debate what these come to and what they are based on. Assessing expressions for sense becomes a looser, more occasion-sensitive affair in the later work, as opposed to being based on some general theory of meaningfulness. Sense-denying aspects of Wittgenstein’s work, and interpreters of his work who emphasise them (e.g. P.M.S. Hacker), have come in for extensive criticism, and are seldom echoed in more recent contemporary philosophy. I see them as an unfortunate holdover from the early work, and as marking a place where Wittgenstein’s ideas require both revision and further development.)</span></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: arial;"><br /></span></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: arial;">Apart from general criteria of meaningfulness and overarching theories of what can be said, logical doctrines about particular parts of language have also been used to dispense with philosophical problems by denying sense. A famous example is the doctrine, defended by Bertrand Russell and wielded by many later writers (a prominent example being Rudolph Carnap), that ‘exists’ cannot be used with proper names. This is a kind of modern logical version of Kant’s doctrine that existence is not a predicate. From a contemporary point of view, this seems hopelessly revisionary. What we ordinarily call ‘proper names’ can meaningfully be put together with ‘exists’, and logically minded philosophers must accommodate this fact as best they can. </span></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: arial;"><br /></span></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: arial;">The above views have in common that they are supposed to be based on the technical foundation of modern logic. Another influential Twentieth Century development of the idea that a better understanding of linguistic meaning is methodologically crucial is the Ordinary Language Philosophy (OLP) movement, as spearheaded by J.L. Austin. In a way it involves a kind of nonsense policing, but there is no general, technical policy that is being enforced; the OLP nonsense police, if that’s what they are, know that they’re operating in a complicated society and will require good judgement. This no doubt enhanced OLP’s plausibility in the wake of logical positivism’s failure.</span></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: arial;"><br /></span></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: arial;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">I once heard from a mentor that in the 1960’s there was a feeling in the air that the traditional problems of philosophy would soon be cleared up by means of OLP. That this hasn’t happened should be uncontroversial. Why it hasn’t happened is more controversial, but we can speculate. One factor seems to be that the urge to use language in extraordinary ways is deep-rooted. No amount of attention to ordinary usage can stop it. Metaphysicians have become more self-conscious about the fact that their use of key terminology may depart from ordinary usage, and have found ways to persist in it nonetheless.</span><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> (For example, in response to arguments by Eli Hirsch to the effect that non-commonsensical claims in ontology simply couldn’t be true, since they fly in the face of metasemantic wisdom - charity demands that we interpret natural language sentences so they aren’t radically false - Theodore Sider has argued that non-commonsensical metaphysical views should be regarded as being stated in Ontologese, a special non-ordinary language. For the Hirsch-Sider debate, see (in dialectical order) Hirsch (2010) (a collection of essays), Sider (2009), Hirsch (2008) and Sider (2014).)</span></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: arial;"><br /></span></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: arial;">Another factor may be a lack of technical sophistication: philosophy can get quite technical, but OLP tends not to come along for the ride. (Perhaps proponents of OLP could have done better here, either by coming along for the ride in some fashion or by forestalling misguided research programmes.) OLP at its most interesting can also become quite idiosyncratic and fragile, in contrast to a more recent trend of international and interpersonal cooperation. One of the most intriguing developments of OLP, the work of Stanley Cavell, typifies this tendency: you see all this sophistication, all these interesting scruples, but you have to be a special kind of person in a special kind of culture to appreciate it. Interesting as it may be, such work can be difficult to make use of in the sort of thing that Bertrand Russell called ‘technical philosophy’. Above all, the ordinary language philosophy of the mid Twentieth Century has simply been sidelined by more vital developments in connection with which it appears at least to have little to offer. Quine, Putnam, Kripke, Lewis and many others come on the scene, we get a whole raft of topics and problems to work on, and ordinary language philosophy falls by the wayside. </span></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: arial;"><br /></span></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-family: arial;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">The failures of nonsense-policing and ordinary language philosophy have had the unfortunate consequence of leading to </span><span style="font-size: 11pt; font-style: italic; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">complacency about sense</span><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"> in contemporary philosophy; a kind of presumption of innocence, where once basic standards of clarity have been met, we tend to take it for granted that philosophers’ utterances are meaningful and that we understand well enough what they mean. According to this way of thinking, the important work in philosophy tends to consist, not in inquiring not into the sense of expressions, but rather into which claims are true.</span></span></p><p dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: arial;"><br /></span></span></p><p dir="ltr" style="-webkit-text-stroke-width: 0px; color: black; font-size: medium; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; orphans: 2; text-align: left; text-decoration-color: initial; text-decoration-style: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><span style="font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: arial;">But the failure of nonsense-policing should not be taken to suggest that the analysis of meaning is not of central importance in philosophy. There may not be much of a future for denying meaning to animating words and phrases, but there remains a need to be critical and inquisitive about what they do mean. We are often being critical in this way even if we aren’t explicitly talking about meaning, or aren’t doing so systematically. But to get further we need to be able to be self-conscious and systematic, without losing crucial data that doesn’t fit well with the kind of thin, reference-based conception of meaning that now seems to hold sway again in philosophy.</span></span></p><p dir="ltr" style="-webkit-text-stroke-width: 0px; color: black; font-size: medium; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; letter-spacing: normal; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; orphans: 2; text-align: left; text-decoration-color: initial; text-decoration-style: initial; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"><br /></p><p dir="ltr" style="line-height: 2.4; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: white; color: black; font-variant: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><i><b><span style="font-family: arial; font-size: x-small;">References</span></b></i></span></p><span style="font-family: arial; font-size: x-small;"><br />Hirsch, Eli (2010). Quantifier Variance and Realism: Essays in Metaontology. Oxford University Press.<br /><br />Hirsch, Eli (2008). Language, ontology, and structure. Noûs 42 (3):509-528.<br /><br />Sider, Theodore (2009). Ontological realism. In David John Chalmers, David Manley & Ryan Wasserman (eds.), Metametaphysics: New Essays on the Foundations of Ontology. Oxford University Press. pp. 384-423.<br /><br />Sider, Theodore (2014). Hirsch's Attack on Ontologese. Noûs 48 (3):565-572.</span>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com18tag:blogger.com,1999:blog-8137988136860941398.post-10317563591672730622020-09-17T23:27:00.003-07:002020-09-17T23:31:57.883-07:00On the Need to Distinguish Knowledge of Essential Properties from the Knowledge That They Are Essential<p><span style="font-family: georgia;">In one of my favourite papers about modal metaphysics, Rosen's 'The Limits of Contingency', Rosen develops the idea that there are two sets of modal notions which are apt to be conflated under the heading 'metaphysical modality'. Roughly: a correct conceivability modality, and a more properly metaphysical modality on which some things which are correctly conceivable are in any case not <i>really </i>possible.</span></p><p><span style="font-family: georgia;"><br /></span></p><p><span style="font-family: georgia;">In a recent paper, 'Correct Conceivability and its Role in the Epistemology of Modality' whichin a new book <i>Les Principes Métaphysiques </i>published by the College de France, Robert Michels considers an objection to Rosen's idea of a correct conceivability modality construed as giving an account of how considerrations about conceivability can takes us from non-modal to modal knowledge. I think this objection is based on a misunderstanding, as I will explain in this post. </span></p><p><span style="font-family: georgia;"><br /></span></p><p><span style="font-family: georgia;">Let me quote from Michels, first to set the scene, and then to see the objection and the main responses Michels considers.</span></p><h1 class="texte" style="background-color: white; box-sizing: border-box; color: #004c93; font-family: Georgia, "Times New Roman", Times, serif; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: normal; line-height: 1.3em; margin: 1em 0px 0px; padding: 0px;"><a href="https://books.openedition.org/cdf/8079#tocfrom1n2" id="tocto1n2" style="box-sizing: border-box; color: #004c93; overflow-wrap: break-word; text-decoration-line: none; word-break: break-word;">Correct Conceivability</a></h1><h2 class="texte" style="background-color: white; box-sizing: border-box; color: #004c93; font-family: Georgia, "Times New Roman", Times, serif; font-size: 1.667em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: normal; line-height: 1.3em; margin: 1em 0px 0px; padding: 0px;"><a href="https://books.openedition.org/cdf/8079#tocfrom2n1" id="tocto2n1" style="box-sizing: border-box; color: #004c93; overflow-wrap: break-word; text-decoration-line: none; word-break: break-word;">The basic idea</a></h2><p class="texte" style="background-color: white; box-sizing: border-box; color: #353535; font-family: "Lucida Sans Unicode", "Lucida Grande", "Lucida Sans", sans-serif; font-size: 14.004px; margin: 0.5em 0px; padding: 0px; position: relative; text-align: justify; word-break: break-word;"><span class="paranumber" style="box-sizing: border-box; color: #bbbbbb; font-family: Georgia, "Times New Roman", Times, serif; font-size: 1em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.5em; margin-left: -3.8em; position: absolute; text-align: center; width: 5em; z-index: -1;">10</span>The correct conceivability-approach presupposes the Kripkean standard view of metaphysical modality and accordingly has to rule out modal errors, cases in which a state of affairs is conceivable, but not metaphysically possible. How this is done is nicely explained in the following mock-quote of Rosen’s “others”:</p><blockquote style="background-color: white; box-sizing: border-box; font-family: "Lucida Sans Unicode", "Lucida Grande", "Lucida Sans", sans-serif; font-size: 14.004px; margin: 0px; padding: 0px; text-align: justify;"><p class="citation" style="box-sizing: border-box; color: #333333; font-size: 0.929em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.5em; margin: 0.5em 0px; padding: 0px 0px 0px 3.5em; position: relative; word-break: break-word;">If the ancients could conceive a world in which water is an element, this is only because they were ignorant of certain facts about the natures of things. In particular, it is because they did not know what it is to be water. They did not know that to be water just is to be a certain compound of hydrogen and oxygen – that to be a sample of water just is to be a quantity of matter predominantly composed of molecules of H2O. This is not to say that they did not understand their word for water. But it’s one thing to understand a word, another to know the nature of its referent. The ancients could see no contradiction in the supposition that water is an element because they did not know that water is a compound by its very nature. But we know this; and given that we do, we can see that to suppose a world in which water is an element is to suppose a world in which a substance that is by nature a compound is not a compound. And that’s absurd. (Rosen 2006, p. 22-23)</p></blockquote><p class="texte" style="background-color: white; box-sizing: border-box; color: #353535; font-family: "Lucida Sans Unicode", "Lucida Grande", "Lucida Sans", sans-serif; font-size: 14.004px; margin: 0.5em 0px; padding: 0px; position: relative; text-align: justify; word-break: break-word;"><span class="paranumber" style="box-sizing: border-box; color: #bbbbbb; font-family: Georgia, "Times New Roman", Times, serif; font-size: 1em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.5em; margin-left: -3.8em; position: absolute; text-align: center; width: 5em; z-index: -1;">11</span>The idea is hence that in order to avoid modal error, conceivability needs to be supplemented by knowledge of the natures, or equivalently, essences of relevant entities, in this case the essence of (the property of being) water. Equipped with this knowledge, the conceiver is able to detect that the assumption that water is an element together with essential truths about the relevant entity entails an absurdity.</p><p class="texte" style="background-color: white; box-sizing: border-box; color: #353535; font-family: "Lucida Sans Unicode", "Lucida Grande", "Lucida Sans", sans-serif; font-size: 14.004px; margin: 0.5em 0px; padding: 0px; position: relative; text-align: justify; word-break: break-word;"><span class="paranumber" style="box-sizing: border-box; color: #bbbbbb; font-family: Georgia, "Times New Roman", Times, serif; font-size: 1em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.5em; margin-left: -3.8em; position: absolute; text-align: center; width: 5em; z-index: -1;">12</span>The correct conceivability-approach hence gives us a simple and elegant explanation of why we are apt to make modal errors and a recipe for ruling them out. We tend to commit modal errors because we can conceive of states of affairs which are ruled out by relevant essences. To avoid these errors, we have to let our ability to conceive be guided by knowledge of the essences of relevant entities.</p><h2 class="texte" style="background-color: white; box-sizing: border-box; color: #004c93; font-family: Georgia, "Times New Roman", Times, serif; font-size: 1.667em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-weight: normal; line-height: 1.3em; margin: 1em 0px 0px; padding: 0px;"><a href="https://books.openedition.org/cdf/8079#tocfrom2n2" id="tocto2n2" style="box-sizing: border-box; color: #004c93; overflow-wrap: break-word; text-decoration-line: none; word-break: break-word;">An objection to essence-based conceivability approaches and how it can be addressed</a></h2><p class="texte" style="background-color: white; box-sizing: border-box; color: #353535; font-family: "Lucida Sans Unicode", "Lucida Grande", "Lucida Sans", sans-serif; font-size: 14.004px; margin: 0.5em 0px; padding: 0px; position: relative; text-align: justify; word-break: break-word;"><span class="paranumber" style="box-sizing: border-box; color: #bbbbbb; font-family: Georgia, "Times New Roman", Times, serif; font-size: 1em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.5em; margin-left: -3.8em; position: absolute; text-align: center; width: 5em; z-index: -1;">13</span>There is a rather obvious objection to the correct conceivability-approach which should be mentioned: The approach crucially relies the conceiver having knowledge of essence, but essence itself is a modal notion. Doesn’t this mean that the notion of correct conceivability cannot answer the core question of modal epistemology, the question of how we can acquire modal knowledge?</p><div class="textandnotes" style="background-color: white; box-sizing: border-box; font-family: "Lucida Sans Unicode", "Lucida Grande", "Lucida Sans", sans-serif; font-size: 14.004px; margin: 0px; padding: 0px; position: relative; text-align: justify;"><ul class="sidenotes" style="box-sizing: border-box; color: #353535; font-family: Verdana, sans-serif; font-size: 0.917em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.167em; list-style-image: initial; list-style-position: initial; margin: 0px; overflow: visible; padding: 0px; position: absolute; right: -15.5em; text-align: left; top: 0px; width: 14em;"><li style="background: none; box-sizing: border-box; color: #777777; font-size: 0.929em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.44em; list-style-type: none; margin: 0.2em 0px 1.44em; padding: 0px; text-align: left;"><span class="num" style="box-sizing: border-box; color: #004c93; font-weight: bold;">5</span> See for example Lowe (2012), Hale (2013, ch. 11), Tahko (2016), Tahko (2017). For a recent critical <a href="https://books.openedition.org/cdf/8079#ftn5" style="box-sizing: border-box; color: #004c93; overflow-wrap: break-word; text-decoration-line: none; word-break: break-word;">(...)</a></li></ul><p class="texte" style="box-sizing: border-box; color: #353535; margin: 0.5em 0px; padding: 0px; position: relative; word-break: break-word;"><span class="paranumber" style="box-sizing: border-box; color: #bbbbbb; font-family: Georgia, "Times New Roman", Times, serif; font-size: 1em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.5em; margin-left: -3.8em; position: absolute; text-align: center; width: 5em; z-index: -1;">14</span><span class="paranumber" style="box-sizing: border-box; color: #bbbbbb; font-family: Georgia, "Times New Roman", Times, serif; font-size: 1em; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: 1.5em; margin-left: -3.8em; position: absolute; text-align: center; width: 5em; z-index: -1;"><br /></span></p></div><div class="textandnotes" style="box-sizing: border-box; margin: 0px; padding: 0px; position: relative;"><p class="texte" style="background-color: white; box-sizing: border-box; color: #353535; font-family: "Lucida Sans Unicode", "Lucida Grande", "Lucida Sans", sans-serif; font-size: 14.004px; margin: 0.5em 0px; padding: 0px; position: relative; word-break: break-word;"><br /></p><p class="texte" style="background-color: white; box-sizing: border-box; color: #353535; margin: 0.5em 0px; padding: 0px; position: relative; word-break: break-word;"><span style="font-family: georgia;">(End of quote.) </span></p><p class="texte" style="background-color: white; box-sizing: border-box; color: #353535; margin: 0.5em 0px; padding: 0px; position: relative; word-break: break-word;"><span style="font-family: georgia;"><br /></span></p><p class="texte" style="background-color: white; box-sizing: border-box; color: #353535; margin: 0.5em 0px; padding: 0px; position: relative; word-break: break-word;"><span style="font-family: georgia;">Michels considers a number of responses, but not the following simple one which I think is correct.</span></p><p class="texte" style="background-color: white; box-sizing: border-box; color: #353535; margin: 0.5em 0px; padding: 0px; position: relative; word-break: break-word;"><span style="font-family: georgia;"><br /></span></p><p class="texte" style="background-color: white; box-sizing: border-box; color: #353535; margin: 0.5em 0px; padding: 0px; position: relative; word-break: break-word;"><span style="font-family: georgia;">Yes, the approach relies on the conceiver knowing that some thing has a property, where arguably that property is in fact an essential property of the thing. But the approach does not rely on the conceiver knowing that the thing essentially has that property.<br /><br />The idea is not that people learned that water is <i>essentially</i> H2O and then on that basis, saw that water being simply an element is not correctly conceivable. Rather, they just learned that water is H2O, and then on the basis of their grasp of how the concept of water works, saw that water being an element is not correctly conceivable. The knowledge of essence, just like the knowledge of necessity (Fine taught us to disinguish the two), may perhaps also be accounted for along similar lines. But that's by the by. This objection simply doesn't get off the ground as far as I can see. </span></p><p class="texte" style="background-color: white; box-sizing: border-box; color: #353535; margin: 0.5em 0px; padding: 0px; position: relative; word-break: break-word;"><span style="font-family: georgia;"><br /></span></p><p class="texte" style="background-color: white; box-sizing: border-box; color: #353535; margin: 0.5em 0px; padding: 0px; position: relative; word-break: break-word;"><span style="font-family: georgia;">This sort of confusion is not unique to Michels's paper. </span><span style="font-family: georgia;">Phrases like 'knowledge of essence' and 'knowledge of necessity' are apt to blur this important sort of distinction, leading to mistakes in the epistemology of modality. </span></p><span style="font-family: georgia;"><br /><i>References</i></span></div><div class="textandnotes" style="box-sizing: border-box; margin: 0px; padding: 0px; position: relative;"><span style="font-family: georgia;"><i><br /></i>Michels, Robert. Correct Conceivability and its Role in the Epistemology of Modality In : Les principes métaphysiques [en ligne]. Paris : Collège de France, 2020 (généré le 18 septembre 2020). Disponible sur Internet : <http://books.openedition.org/cdf/8079>. ISBN : 9782722605350. DOI : https://doi.org/10.4000/books.cdf.8079.<br /><br />Rosen, Gideon (2006). The limits of contingency. In Fraser MacBride (ed.), Identity and Modality. Oxford University Press. pp. 13--39.</span></div>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com52tag:blogger.com,1999:blog-8137988136860941398.post-15504585369456787232020-05-14T23:11:00.000-07:002020-05-16T05:40:07.299-07:00On Family Resemblance Concepts<span style="font-family: "georgia" , "times new roman" , serif;">I want to clarify some aspects of the celebrated Wittgensteinian idea of a family resemblance concept.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<i><span style="font-family: "georgia" , "times new roman" , serif;">Are all family resemblance concepts such that no single feature is shared by all the things to which the concept applies?</span></i><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">Some of Wittgenstein's formulations, and explanations based upon them, would suggest an affirmative answer. But I think that a more general, useful notion of a family resemblance concept should not require this.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">It should disqualify a concept for family resemblance status that some feature happens to be common to all the things that fall under the concept. It may be that this feature does not sufficiently characterise the things as falling under the concept. That is, just because you can give necessary conditions for the application of a concept, does not mean its application is not based on the kind of criss-crossing network of similarities that Wittgenstein has us imagine. This passage gets it right:</span><br />
<blockquote class="tr_bq">
<span style="font-family: "georgia" , "times new roman" , serif;"><span style="background-color: white; color: #202122;">we extend our concept of number as in spinning a thread we twist fibre on fibre. And the strength of the thread does not reside in the fact that some one fibre runs through its whole length, but in the overlapping of many fibres. (PI </span><span style="background-color: white; color: #202122;">§67)</span></span></blockquote>
<span style="font-family: "georgia" , "times new roman" , serif;">This makes it clear that there may still be a single fibre running through the thread. It's just that that alone isn't responsible for the strength of the thread.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<i><span style="font-family: "georgia" , "times new roman" , serif;">Are all concepts which do not admit of non-trivial analysis in terms of necessary and sufficient conditions family resemblance concepts?</span></i><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">It seems to be a necessary condition on family resemblance concepts that they do not admit of non-trivial analysis in terms of necessary and sufficient conditions. But it doesn't seem to be a sufficient condition. That is, it seems that there are concepts which do not admit of this sort of analysis and yet are not what we would think of as family resemblance concepts. For example:</span><br />
<br />
<ul>
<li><span style="font-family: "georgia" , "times new roman" , serif;">Certain primitive, i.e. undefined, concepts in theoretical use are not family resemblance concepts. For example, the concept of a lever (insofar as it isn't defined).</span></li>
<li><span style="font-family: "georgia" , "times new roman" , serif;">A concept that is undefined but very closely tied to experience, e.g. the concept of red.</span></li>
<li><span style="font-family: "georgia" , "times new roman" , serif;">Concepts which by design only apply to one thing, such as the concept of God - or, for that matter, just your concept of some particular person you know. (The whole idea of 'individual concepts' is a bit neglected though, and may not strike the reader as being in good standing.)</span></li>
</ul>
<br />
<span style="font-family: "georgia" , "times new roman" , serif;">These do not seem to count as family resemblance concepts, because while they do not admit of non-trivial airtight definitions, there does not seem to be the sort of heterogeneity among the things that they apply to that characterises family resemblance concepts as discussed by Wittgenstein.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">This last category, however, invites another question...</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<i><span style="font-family: "georgia" , "times new roman" , serif;">Diachronic family resemblance concepts?</span></i><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><i><br /></i>
It would seem that the concept of a particular person can't be a family resemblance concept in the sense of many different things falling under it not because of a common feature but because of overlapping similarities, because at most one thing does fall under it. But if we consider the individual through time, we start to see the possibility for something like the family resemblance idea applying to the concept of a particular person.</span><br />
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<i><span style="font-family: "georgia" , "times new roman" , serif;">Is 'family resemblance concept' a family resemblance concept?</span></i><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">I think there's potential for a negative answer. At least, it seems to me we can give a precisified version of the idea that is not itself a family resemblance concept. On the other hand, perhaps such a thing would fail to capture the idea in full.</span>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com22tag:blogger.com,1999:blog-8137988136860941398.post-24293842286243494742020-03-20T21:06:00.000-07:002020-03-20T23:28:36.389-07:00Opportunism and Fastidiousness in Language<span style="font-family: "georgia" , "times new roman" , serif;">Many, probably most, intelligent speakers and thinkers are linguistic opportunists. They treat words and phrases as tools to convey things that they are already thinking in proto-linguistic or rough linguistic form, and if some construction seems likely to do the conveying job, they use it. </span><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">Linguistic opportunism is higher in private communication than in public, and higher in informal writing than in formal writing. The opposite of linguistic opportunism is linguistic fastidiousness. Analytic philosophy is characterised by high linguistic fastidiousness, while other types of philosophy are often linguistically opportunistic.</span><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">Certain moves that may at first seem like moves of fastidiousness belie an underlying opportunism. For example, an linguistic opportunist may abandon a formulation and self-correct to a formulation which lets their underlying message come through clearly, where a stickler may take the time and effort to clarify the sense in which what they said was correct although potentially misleading.</span><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">(I heard an example of this in an episode of Dan Carlin's Hardcore History podcast, but I can't remember the details. Carlin is an interesting example of a fairly fastidious opportunist. As I see it, his underlying goal makes him fundamentally an opportunist. His goal is to paint pictures with words, to move the listener, and to convey history. But he often becomes self-conscious about language. Nevertheless, this is all kept in the service of the goal, and so does not go into niceties that the true stickler would go into.)</span><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">What drives the stickler? In large part and in many cases, their motivation takes the form of an intrinsic interest in language and fine distinctions. (But remember, one may ask why such an interest should ever arise in the first place.) As someone with marked stickler tendencies myself - tendencies which have at certain points in my development reached nearly pathological levels - there are many times when I have become interested in some linguistic or conceptual issue raised by some construction that has been used, where this definitely only detracts from the task of staying on-message. But sticklerhood is not always like this. Sometimes it is motivated by real, felt concern with the <i>ongoing</i> adequacy of the linguistic resources to the task at hand. </span><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">Even the purer form of sticklerhood, which unambiguously cuts against the grain of achieving the purpose of the discourse from which it arises, may have a justification beyond the intrinsic interest of reflecting on language and concepts. The stickler may be seen as concerning themselves with utility too. Not with having the right tools for the task at hand, but with maintaining a large, powerful toolkit for whatever may come next. And sometimes this goal may be in conflict with an opportunistic strategy which would work well for current purposes.</span><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">It may seem self-evident that the linguistic opportunist is a friend of linguistic innovation, the fastidious stickler a foe. But this is too quick. By maintaining order and consistency, the stickler helps to cultivate an environment in which buildings can be erected which, if the opportunist held sway, would crumble into confusion. </span>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com16tag:blogger.com,1999:blog-8137988136860941398.post-59757612007659444992020-01-10T20:34:00.000-08:002020-01-10T20:36:31.239-08:00Forthcoming in Thought: The Accident of Logical Constants<div style="text-align: center;">
<img alt="View Table of Contents for Thought: A Journal of Philosophy volume 8 issue 4" height="200" src="https://onlinelibrary.wiley.com/cms/attachment/47621c94-7410-453a-a3a3-28145e00377b/tht3.v8.4.cover.gif" width="138" /></div>
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<span style="font-family: "georgia" , "times new roman" , serif;">The Accident of Logical Constants</span><br />
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<span style="background-color: white; color: #555555; font-size: 14px;"><span style="font-family: "arial" , "helvetica" , sans-serif;">Work on the nature and scope of formal logic has focused unduly on the distinction between logical and extra-logical vocabulary; which argument forms a logical theory countenances depends not only on its stock of logical terms, but also on its range of grammatical categories and modes of composition. Furthermore, there is a sense in which logical terms are unnecessary. Alexandra Zinke has recently pointed out that propositional logic can be done without logical terms. By defining a logical-term-free language with the full expressive power of first-order logic with identity, I show that this is true of logic more generally. Furthermore, having, in a logical theory, non-trivial valid forms that do not involve logical terms is not merely a technical possibility. As the case of adverbs shows, issues about the range of argument forms logic should countenance can quite naturally arise in such a way that they do not turn on whether we countenance certain terms as logical.</span></span><br />
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<a href="https://philpapers.org/rec/HAZTAO-5"><span style="font-family: "georgia" , "times new roman" , serif;">Pre-print available at PhilPapers</span></a>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com5tag:blogger.com,1999:blog-8137988136860941398.post-38826358023599618952019-12-13T21:25:00.000-08:002019-12-13T21:54:55.686-08:00Tractarian Propositions and Taking the 'X in Y' Construction Seriously<div>
<i><span style="font-family: Georgia, Times New Roman, serif;">This is a sequel to the previous post, in which I continue to react to interesting recent "cognitive act theories" of propositions championed by Soames and Hanks, and work out my own views in relation to them.</span></i></div>
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<span style="font-family: Georgia, Times New Roman, serif;">In Soames's recent article on the <i>Tractatus</i>, he argues that Wittgenstein's conception of a proposition - that it is a propositional sign <i>in its projective relation to the world </i>- is incoherent. Soames's idea is that this doesn't actually specify a thing over and above the propositional sign. Just as Soames-in-relation-to-his-wife (one of his examples) isn't actually a separate thing or person from Soames, a propositional sign in its projective relation to the world isn't actually something other than the propositional sign. It is not some "larger" entity which includes the propositional sign as a part.</span><br />
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<span style="font-family: Georgia, Times New Roman, serif;">This then leads Soames to propose, on the basis also of a remark in the Tractatus that our thinking the sense of a proposition is our putting it in relation to the world, that Wittgenstein would have been better off identifying propositions as propositional signs together with cognitive acts. And this is similar to his own recent theory of propositions, on which they are just cognitive acts in abstraction from any particular signs. </span></div>
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<span style="font-family: Georgia, Times New Roman, serif;">In this way, Soames presents Wittgenstein as groping toward a better view of the nature of propositions - better than those of Frege and Russell, for whom propositions were Platonic things independent of language use - and offering a more coherent way of doing this.</span></div>
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<span style="font-family: Georgia, Times New Roman, serif;">Recently Peter Hanks has argued that there is another way here: that we can instead look at the (to me confusing and confused) idea in the Tractatus that a propositional sign <i>is a fact</i>. (This is something Wittgenstein later came to think of as a category mistake - but the new act theorists of propositions are generally disposed to be less keen to convict philosophers of category mistakes. After all, the view that a proposition is an act - a thing done - itself sounds like a category mistake. So we're in a pocket of philosophy where there's a fair amount of tolerance of what can seem like category mistakes, being explained away in terms of unimportant intuitions that should be overcome as we better systematise out thinking.) Looking at it that way, Hanks argues that the propositional sign <i>in its relation to the world</i> may be seen as a "larger" fact which involves the fact that is the propositional sign, but where the elements of that sign/fact that are related to one another are also related to further elements, things out in the world. </span></div>
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<span style="font-family: Georgia, Times New Roman, serif;">I share Hanks's sense that Soames's argument against the coherence of Wittgenstein's conception of propositions and how they relate to propositional signs is surmountable. But I confess that the idea of a sign as a fact has never appealed to me, and really does seem like a category mistake. </span></div>
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<span style="font-family: Georgia, Times New Roman, serif;">I think there's a third way to understand this talk of a proposition being a propositional sign in its projective relation to the world. It may even be more faithful to the <i>Tractatus</i>, but maybe not. I think it probably is more faithful to Wittgenstein's ideas as they developed after the <i>Tractatus</i> though. More importantly, I think it may be the best way of thinking about these matters.</span></div>
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<span style="font-family: Georgia, Times New Roman, serif;">Soames complains that a thing in some relation isn't actually a separate thing. And this is meant to be an objection to the Tractarian notion of a proposition, the idea being that propositions are meant to be distinct things from propositional signs. </span></div>
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<span style="font-family: Georgia, Times New Roman, serif;">But who said they had to be? The objection I have to both Soames's and Hanks's reconstructions of the Tractarian idea is that they both look for a way to avoid taking the 'X in Y' construction seriously, whereas part of what makes it a truly radical and fruitful idea may get lost that way. (The new act theorists want propositions to be inherently representational things. But perhaps part of Wittgenstein's thinking is that really we have signs, and we use them, and it is only in those uses that they bear representational properties and properties like truth. And so looking for a further object over and above the sign is unnecessary, and even a mistake.)</span></div>
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<span style="font-family: Georgia, Times New Roman, serif;">Now, there are different ways to think about how this conception can be expressed, and how expressions of it can be decomposed. You might think of it this way: there's a complex sign, which may get used in two different language systems. Then you might think that this sign is true in one of its projective relations to the world, and false in another. Here the 'in projective relation R' becomes part of the predicate, like 'true-in-L' in discussions of Tarski. But you can also put it into the subject, 'The sign in relation R' and then predicate truth of the sign in that relation. Is this a further entity over and above the sign? You can think of it that way, but perhaps there's another way here, where we just have the property of truth - not some more complicated projective-relation-involving predicate - and we just have the sign as our main entity. But we nevertheless predicate truth not of the sign simpliciter but we predicate it of the sign <i>in a particular projective relation to the world</i>. On this conception, it's not that we have an augmented predicate or a thing over and above the sign, rather we're just using a logical form which isn't just a simple subject-predicate proposition of the sort whose truth conditions can be given as: the proposition is true iff the property expressed by the predicate is possessed by the entity denoted by the subject. To squeeze the Tractarian conception of propositions into that form is to water it down. In particular, it is to water down its ability to get around the problem laying at the foundation of the new act-based theories of propositions - the problem about propositions needing to be inherently representational. Taking the Tractarian idea of a proposition more seriously, we don't have to find a thing that is inherently representational and then put that at the basis of our theories. We may insist that the primary truth bearers really are signs, but that these signs only bear truth <i>in use, </i>and that a given sign can bear truth in one use and falsity in another. </span></div>
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<b><i><span style="font-family: Georgia, Times New Roman, serif;">References</span></i></b></div>
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<b><i><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></i></b></div>
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<span style="font-family: Georgia, Times New Roman, serif;">Hanks, Peter (2019). Soames on the <i>Tractatus</i>. <i>Philosophical Studies</i> 176 (5):1367-1376.</span></div>
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<span style="font-family: Georgia, Times New Roman, serif;">Soames, Scott (2016). Propositions, The <i>Tractatus</i>, and "The Single Great Problem of Philosophy". <i>Critica</i> 48 (143):3-19.</span></div>
Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com5tag:blogger.com,1999:blog-8137988136860941398.post-1740913677850275972019-12-08T17:19:00.001-08:002019-12-13T17:57:42.794-08:00Against Inherently Representational Anything<span style="font-family: "georgia" , "times new roman" , serif;">Soames, in his fascinating recent work <i>Rethinking Language, Mind, and Meaning</i>, begins by posing a problem for the study of meaning and language as developed by philosophers and logicians in the Twentieth Century.</span><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">For propositions to play the theoretical roles assigned to them - such as being the primary bearers of truth, being the objects of propositional attitudes like belief and desire, being the contents of mental and perceptual states, and being the meanings of some sentences - they, Soames says, must be inherently representational. That is, they must impose conditions on the world off their own bat, so to speak. </span><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">But, argues Soames, the sorts of things that traditionally play the proposition role in modern theories do not seem to be inherently representational. Soames provides 'reasons to believe that no set-theoretic
construction of objects, properties, world-states or other denizens of Plato’s
heaven, could ever be inherently representational bearers of truth conditions
in this sense' (<i>Rethinking</i>, Ch. 2).</span><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">This leads Soames to his new theory of propositions, on which they are cognitive acts of a certain kind. ('Suppose, however, we start at the other end, taking it as an uncontested certainty that agents represent things as being certain ways when they think of them as being those ways' (<i>Rethinking</i>, Ch. 2).) For example, the proposition that snow is white, on Soames's theory, is the act of predicating whiteness of snow. These cognitive acts, according to Soames, <i>are</i> inherently representational, which means that they could be able to play the role of propositions. </span><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">(Soames says that, at bottom, it is language users that represent things as being certain ways, and they do this by performing cognitive acts, which acts may derivatively be said to represent. But although, in this way, they represent in a derivative sense, they do so <i>inherently</i> - and that is the crucial point for Soames, that makes cognitive acts fit to play the role of propositions.)</span><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">I am very heartened to see Soames realising that his earlier, broadly Russellian conception of propositions won't do and looking for an alternative. But his cognitive acts seem a bit mysterious to me. In this note I won't try to refute Soames's new theory of propositions, but let me say something briefly about what worries me. It's not so much that I think that there's no such thing as the cognitive act of predicating whiteness of snow, but I don't feel like this is the sort of thing that is fit to play the sort of basic explanatory role that Soames wants it to play. It feels too much like a black box containing important workings for that. Treated as something basic, it feels occult or magical. (Wittgenstein in the <i>Investigations</i> seems very concerned to avoid positing mental goings-on that are meant to play this kind of foundational role in explaining representation. This has influenced me and I think there's something right about Wittgenstein's conviction that this is not the way forward.)</span><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">There is another conception of propositions, on which they are sentences (of a certain kind) <i>in use</i> (or a certain kind of use). For instance, in the <i>Tractatus</i> Wittgenstein said that a proposition is a propositional sign in a projective relation to the world. (In a <a href="https://philpapers.org/rec/HAZPMA">recent paper</a> I sketch an account of propositions that treats them similarly.)</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">(Of course, it is nice to be able to say what two synonymous sentences in different languages have in common, and often it is said that they 'express the same proposition'. On the present approach, they may be said to have the same use, the same meaning. But ultimately it is not just the use or the meaning that represents - it is a sign in use, a sign with meaning, that does this. The "proposition" or "statement" or whatever you call it that two different sentences express is an abstraction from the particular propositions that are alike in meaning.)</span><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">It seems to me that this fundamental logical move of treating propositions not as things by themselves, as it were, but a certain kind of thing <i>in a certain kind of context</i> is very important, and constitutes the right way to avoid the twin pitfalls of having propositions be things that don't themselves represent, and of having them be explanatorily basic cognitive acts. </span><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">Admittedly, sentences in use can't just be slotted in to all the roles Soames delineates without further ado. For instance, we probably don't want to say that if you believe something - perhaps without even representing it to yourself linguistically - the thing you believe <i>is</i> a sentence in a particular use. Soames's theory may have an advantage over my approach here in having this one kind of thing - propositions - playing all of these roles (although I doubt it, since Soames's theory has predictions which sound like category-mistakes, such as that one may 'perform a proposition', propositions being acts according to this theory). But I think that ultimately such a theory with one single sort of thing playing all these diverse roles will not be attractive overall, and that we may have to refine the picture somewhat of how these things like sentence meaning and the objects of belief relate to each other. I am focusing for now on linguistic meaning.</span><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">Sentences in use, you might say are 'inherently representational': but the whole idea of inherence doesn't really fit here. The whole point is that sentences are not inherently representational, but used in certain ways, they are. If you want to treat the sentence-in-use as a sort of <i>thing by itself</i>, then this is a kind of abstraction. Such a logical construction may be useful, but the resulting entity is not explanatorily basic: underneath, you have the sentence and you have all the stuff about how it is used. And so, at the base level, you don't have anything inherently representational.</span><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">This approach fits naturally with the ideas of representing and of a representation. Fundamentally, a representation itself is just a concrete thing - like a drawing or a sentence. And it represents not inherently, but by being used in a certain way. People represent things as being certain ways by putting representations to use.</span><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">This approach also furnishes a kind of explanation of the feeling of occultness or suspiciousness in theories which posit inherently representational entities in their explanatory base: they feel unsatisfactory because they hide the contextual rabbit in the hat of some posited object. If we are forced to treat this object as basic, we can never see under the hat.</span><br />
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<b><i><span style="font-family: "georgia" , "times new roman" , serif;">References</span></i></b><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">Haze, Tristan Grøtvedt (2018). Propositions, Meaning, and Names. <i>Philosophical Forum</i> 49 (3):335-362.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">Soames, Scott (2015). <i>Rethinking Language, Mind, and Meaning</i>. Princeton University Press.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">Wittgenstein, Ludwig (1922). <i>Tractatus Logico-Philosophicus</i>. Routledge & Kegan Paul.</span>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com8tag:blogger.com,1999:blog-8137988136860941398.post-85304859298306889352019-11-02T15:54:00.000-07:002019-11-09T23:36:06.701-08:00‘Two Recent Theories of Conditionals’ vs. Two Recent Theories of Conditionals<html><head><style type="text/css">ul.lst-kix_uqm7f689vdz-4{list-style-type:none}.lst-kix_1bkib659zo4w-5>li:before{content:"- "}ul.lst-kix_uqm7f689vdz-5{list-style-type:none}ul.lst-kix_vltoi2uupdh6-0{list-style-type:none}ul.lst-kix_uqm7f689vdz-6{list-style-type:none}.lst-kix_1bkib659zo4w-4>li:before{content:"- "}.lst-kix_1bkib659zo4w-6>li:before{content:"- "}.lst-kix_bqh166gv9ol9-8>li:before{content:"- "}.lst-kix_uqm7f689vdz-0>li:before{content:"- "}.lst-kix_uqm7f689vdz-2>li:before{content:"- 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class="c29"><div>
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<div class="c7">
<span class="c0"><i>The tide is beginning to turn against counterintuitive theories of indicative conditionals which either deny them truth-values or give them apparently wrong ones, but a deductive argument in Gibbard’s 1981 paper ‘Two Recent Theories of Conditionals’ appears to show that those unhappy options are the only viable ones. Here I summarise some fascinating recent technical work on an escape route and argue that Gibbard’s reason for not taking that route stemmed from a (forgivable) failure of theoretical imagination and a too-narrow view of the motivation for granting truth-values to indicatives.</i></span></div>
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<span class="c0"></span></div>
<div class="c7">
<span class="c2">Introduction</span></div>
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<span class="c6 c4 c5"></span></div>
<div class="c7">
<span class="c0">Indicative conditionals seem to have truth-values. Just as ‘I will not eat a grapefruit tomorrow’ and ‘You are a horse’ are true and false respectively, so it seems that ‘If I have breakfast tomorrow, it won’t be a grapefruit’ and ‘If tomorrow someone tells you you’re a horse, you’ll become a horse’ are true and false respectively.</span></div>
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<span class="c0"></span></div>
<div class="c7">
<span class="c0">It also seems that an indicative conditional does not always have the same truth-value as the corresponding material conditional (which is true in all cases except when the antecedent is true and the consequent false). For example, both ‘If you die tonight, you’ll be alive tomorrow’ and ‘If you die tonight, the French Government will collapse tomorrow’ seem false - the first due to the nature of life and death, the second due to the way the world is organized - even though ‘You will die tonight ⊃ you’ll be alive tomorrow’ and ‘You will die tonight ⊃ the French Government will collapse tomorrow’ are both true provided that you don’t die tonight. </span></div>
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<span class="c6 c15"></span></div>
<div class="c7">
<span class="c4">An ingenious deductive argument from Allan Gibbard’s 1981 paper ‘Two Recent Theories of Conditionals’ appears to show that these two seemings cannot both be right. </span><span class="c4 c5">Gibbard’s</span><span class="c4"> </span><span class="c4 c5">collapse argument</span><span class="c0"> is so called because threatens to collapse any truth-conditions that an indicative conditional might have down to those of the corresponding material conditional.</span></div>
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<span class="c0"></span></div>
<div class="c7">
<span class="c4">But Gibbard’s argument does not by itself demonstrate collapse, and the larger context of Gibbard (1981) shows that he was aware of that fact. Indeed, he identified an escape route - one which takes some noticing, and may not be noticed by many who encounter this much-discussed argument outside the context of Gibbard’s paper. However, upon identifying the escape route Gibbard gave what may seem like a compelling reason not to take it. Having also rejected the material conditional account of indicatives, Gibbard ends up adopting the </span><span class="c4 c5">NTV thesis </span><span class="c0">- the view that indicative conditionals lack truth-values.</span></div>
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<span class="c0"></span></div>
<div class="c7">
<span class="c0">Subsequently, theories which take the escape route Gibbard identified have been pursued in earnest anyway, with impressive results. After a period in which the NTV thesis was beginning to look like the dominant view, the tide is finally beginning to turn.</span></div>
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<span class="c0"></span></div>
<div class="c7">
<span class="c0">The purpose of this article is to contribute to turning the tide by confronting and neutralizing Gibbard’s reason for not taking the escape route, and along the way to provide a high-level summary of some recent relevant work (some of which can be highly technical). We will see that by drawing on this work we can uphold, in a principled way, the intuitive view that indicative conditionals do indeed have truth-values, and ones which can differ from those of the corresponding material conditionals.</span></div>
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<span class="c0"></span></div>
<div class="c7">
<span class="c6 c2">1. Gibbard’s Collapse Argument</span></div>
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<span class="c6 c2"></span></div>
<div class="c7">
<span class="c0">I begin with a reader-friendly reconstruction of Gibbard’s collapse argument.</span></div>
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<span class="c0"></span></div>
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<span class="c17 c4 c11">Assumptions:</span></div>
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<span class="c0"></span></div>
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<span class="c4 c5">If Implies Hook</span><span class="c0">: An indicative conditional ‘If A then C’ always implies ‘A ⊃ C’, i.e. indicatives are at least as strong as material conditionals.</span></div>
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<span class="c0"></span></div>
<div class="c7">
<span class="c4 c5">Conditional Conjunction Elimination</span><span class="c4">: All indicative conditionals of the form ‘If (A & C) then C’ are logical truths.</span><sup class="c4"><a href="https://www.blogger.com/blogger.g?blogID=8137988136860941398#ftnt1" id="ftnt_ref1">[1]</a></sup></div>
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<span class="c0"></span></div>
<div class="c7">
<span class="c4 c5">Import-Export</span><span class="c0">: In any arbitrary context, all pairs of indicative conditionals of the forms ‘If A then (if B then C)’ and ‘If (A & B) then C’ are logically equivalent. </span></div>
<div class="c3">
<span class="c0"></span></div>
<div class="c7">
<span class="c4 c5">Equivalent Antecedents</span><span class="c0">: In any arbitrary context, all pairs of indicative conditionals which share the same consequent, and whose antecedents are logically equivalent, are themselves logically equivalent.</span></div>
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<span class="c0"></span></div>
<div class="c7">
<span class="c4 c11 c17">Reasoning:</span></div>
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<span class="c0"></span></div>
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<span class="c0">Consider any arbitrary indicative conditional ‘If A then C’ in an arbitrary context and its corresponding ‘A ⊃ C’.</span></div>
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<span class="c0"></span></div>
<div class="c7">
<span class="c4">By </span><span class="c4 c5">Conditional Conjunction Elimination</span><span class="c0">, ‘If (A & C) then C’ is a logical truth.</span></div>
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<span class="c0"></span></div>
<div class="c7">
<span class="c4">By </span><span class="c4 c5">Equivalent Antecedents</span><span class="c0">, ‘If ((A ⊃ C) & A) then C’ is then also a logical truth, since ‘A & C’ is logically equivalent to ‘(A ⊃ C) & A’ by propositional logic.</span></div>
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<span class="c0"></span></div>
<div class="c7">
<span class="c4">By </span><span class="c4 c5">Import-Export</span><span class="c4">, ‘If (A ⊃ C) then (if A then C)’ is then also a logical truth. (Here ‘(A ⊃ C)’ plays the ‘A’ role in </span><span class="c4 c5">Import-Export</span><span class="c4"> as stated above, ‘A’ plays the ‘B’ role, and ‘C’ plays the ‘C’ role.)</span></div>
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<span class="c0"></span></div>
<div class="c7">
<span class="c4">By </span><span class="c4 c5">If Implies Hook</span><span class="c0">, ‘(A ⊃ C) ⊃ (if A then C)’ is then also a logical truth, since the implications of logical truths are logical truths.</span></div>
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<span class="c0"></span></div>
<div class="c7">
<span class="c4">By </span><span class="c4 c5">If Implies Hook</span><span class="c0"> again, ‘(If A then C) ⊃ (A ⊃ C)’ is a logical truth.</span></div>
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<span class="c0"></span></div>
<div class="c7">
<span class="c0">By propositional logic applied to the last two sentences, ‘(If A then C) ≡ (A ⊃ C)’ is a logical truth. Hence, any arbitrary indicative conditional in any arbitrary context is logically equivalent to its corresponding material conditional. QED.</span></div>
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<span class="c0"></span></div>
<div class="c7">
<span class="c0">If we accept the reasoning and want to maintain that indicatives have truth-values that don’t always agree with the corresponding material conditional, we need to reject one of the assumptions of the argument - either one of the explicit ones listed above, or some auxiliary assumption.</span></div>
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<span class="c0"></span></div>
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<span class="c2">2. The State of the Art of Resisting Collapse</span></div>
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<span class="c0"></span></div>
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<span class="c4">Some have suspected </span><span class="c4 c5">Import-Export</span><span class="c0">. For instance, a detailed axiomatic analysis of Gibbard’s proof leads Fitelson to conclude as follows:</span></div>
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<span class="c0"></span></div>
<div class="c7 c16">
<span class="c0">The only axioms that seem plausibly deniable (to me — in the context of a sentential logic containing only conditionals and conjunctions) are [...] the import-export laws, and they seem to be the most suspect of the bunch. I find it difficult to see how any of the other axioms could (plausibly) be denied (but I won’t argue for that claim here). (Fitelson (2013), p. 184.)</span></div>
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<span class="c0"></span></div>
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<span class="c4">However, </span><span class="c4 c5">Import-Export</span><span class="c0"> has proven difficult to reject. It strikes many as plausible, and counterexamples have been elusive. Edgington, for instance, finds them plausible in the abstract, and suggests that any example one tries seems to obey the principle:</span></div>
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<span class="c0"></span></div>
<div class="c19 c16">
<span class="c23 c4 c22">Here are two sentence forms instances of which are, intuitively, equivalent:</span></div>
<div class="c1">
<span class="c4 c22">(i) If (</span><span class="c4 c22 c5">A</span><span class="c4 c22">&</span><span class="c4 c22 c5">B</span><span class="c4 c22">), </span><span class="c4 c22 c5">C</span><span class="c4 c22 c23">. </span></div>
<div class="c1">
<span class="c4 c22">(ii) If </span><span class="c4 c22 c5">A</span><span class="c4 c22">, then if </span><span class="c4 c22 c5">B</span><span class="c4 c22">, </span><span class="c4 c22 c5">C</span><span class="c23 c4 c22">.</span></div>
<div class="c16 c19">
<span class="c4 c24">(Following Vann McGee (1985) I'll call the principle that (i) and (ii) are equivalent the Import-Export Principle, or “Import-Export” for short.) Try any example: “If Mary comes then if John doesn't have to leave early we will play Bridge”; “If Mary comes and John doesn't have to leave early we will play Bridge”. “If they were outside and it rained, they got wet”; “If they were outside, then if it rained, they got wet”. (Edgington (2014), </span><span class="c0">Sec. 2.5.)</span></div>
<div class="c7">
<span class="c0">There is one notable attempt at a counterexample in the literature, due to Kaufmann (2005, pp. 213 - 214). In Fitelson’s (2016) presentation:</span></div>
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<span class="c0"></span></div>
<div class="c7 c16">
<span class="c0">Suppose that the probability that a given match ignites if struck is low, and consider a situation in which it is very likely that the match is not struck but instead is tossed into a campfire, where it ignites without being struck. Now, consider the following two indicative conditionals.</span></div>
<div class="c7 c16 c20">
<span class="c0">(a) If the match will ignite, then it will ignite if struck. </span></div>
<div class="c7 c16 c20">
<span class="c0">(b) If the match is struck and it will ignite, then it will ignite.</span></div>
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<span class="c0"></span></div>
<div class="c7">
<span class="c4">It seems like it is possible to understand (a) and (b) in such a way that (a) expresses a logical truth and (b) does not, suggesting that they may not be equivalent, making for a counterexample to </span><span class="c4 c5">Import-Export</span><span class="c0">. But this has been challenged. Khoo and Mandelkern (forthcoming) write:</span></div>
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<span class="c0"></span></div>
<div class="c7 c16">
<span class="c4">However, we suspect the intuitive grip of this example rests on an equivocation in ‘will’ between a broadly dispositional meaning and a temporal meaning. We can disambiguate these readings by replacing ‘will ignite’ with ‘is ignitable’, to select for the dispositional meaning, and by replacing ‘will ignite’ with ‘will ignite at </span><span class="c4 c5">t</span><span class="c4">’, to select for the temporal meaning. (We also replace ‘struck’ with ‘struck at t</span><span class="c4 c12">0</span><span class="c0">’, to thoroughly regiment the readings.) We suspect that the reading on which (a) and (b) strike us as inequivalent is:</span></div>
<div class="c3 c16">
<span class="c0"></span></div>
<div class="c7 c16 c20">
<span class="c4">(a’) If the match is ignitable, then it will ignite at t if struck at t</span><span class="c4 c12">0</span><span class="c0">. </span></div>
<div class="c7 c16 c20">
<span class="c4">(b’) If the match is struck at t</span><span class="c4 c12">0</span><span class="c0"> and it will ignite at t, then it will ignite at t.</span></div>
<div class="c3 c16 c20">
<span class="c0"></span></div>
<div class="c7 c16">
<span class="c0">(b’) does indeed strike us as a logical truth, while (a’) certainly does not. But this pair is of course no longer a counterexample to the pattern we are exploring; we would only get a counterexample if we were to disambiguate (a) and (b) in a uniform way. But no matter how we do this, the resulting sentences strike us as equivalent. (Khoo & Mandelkern (forthcoming), pp. 8 - 9 in online version). </span></div>
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<span class="c4 c11">In view of the fact that even the most suspect of </span><span class="c4">Gibbard’s</span><span class="c4 c11"> explicitly stated principles has proven difficult to reject, it is not surprising that some have rejected auxiliary assumptions not directly appealed to in the derivation. According to Kratzer (1986, 2012</span><span class="c4">, p. 105 in latter</span><span class="c4 c11">) - whose syntactically distinctive theory of indicatives was inspired by Lewis (1975) - the problem with Gibbard’s argument is that it relies on the assumption that indicative conditionals are propositions formed by an operator, ‘if’, which takes two propositions and yields a proposition. If instead we follow Kratzer and treat ‘if’ as a restrictor, and regard ordinary indicative conditionals as containing an unvoiced necessity operator restricted by ‘if’, the conclusion of Gibbard’s argument no longer leads to the result that indicative conditionals, if they have truth-conditions at all, are truth-functional. For Gibbard’s conclusion is that </span><span class="c4 c11 c5">if</span><span class="c0"> indicative conditionals are propositions in which a two-place propositional operator is applied to two propositions, then their truth-conditions collapse to those of the material conditional.</span></div>
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<div class="c7">
<span class="c4 c11">However, as Khoo (</span><span class="c4">2013</span><span class="c4 c11">) has shown in detail, an analogous argument can be given directly in terms of the semantic values of sentence-schemas, without assuming that ‘if’ is a two-place propositional operator. But it turns out that Kratzer’s theory is nevertheless able, in another way, to block both the original and the analogous argument. Kratzer’s theory predicts subtle counterexamples to the principle that whenever an indicative conditional is true, so is the corresponding material conditional, thus invalidating the</span><span class="c4 c11 c5"> If Impl</span><span class="c4 c5">ies Hook</span><span class="c4"> assumption of Gibbard’s argument. So too does Gillies’ (2009) theory, on which ‘if’ is a two-place operator, but one which is able to shift the index and context</span><sup class="c4"><a href="https://www.blogger.com/blogger.g?blogID=8137988136860941398#ftnt2" id="ftnt_ref2">[2]</a></sup><span class="c4"> against which the consequent of an indicative conditional is evaluated (in the course of the evaluation of the conditional containing it).</span></div>
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<span class="c0"></span></div>
<div class="c7">
<span class="c4">On</span><span class="c4 c11"> Khoo’s </span><span class="c4">analy</span><span class="c4 c11">sis, Kratzer’s alternative view of the syntax of indicative conditionals is orthogonal to the collapse issue. Both her theory, on which ‘if’ is a restrictor, and Gillies’ theory, on which ‘if’ is a “shifty” two-place propositional operator, avoid Gibbard’s conclusion. But in consequence of </span><span class="c4">how</span><span class="c4 c11"> they avoid Gibbard’s conclusion</span><span class="c4"> - by invalidating </span><span class="c4 c5">If Implies Hook</span><span class="c4"> -</span><span class="c0"> both theories predict counterexamples to modus ponens construed as a semantic thesis according to which ‘C’ is true whenever ‘A’ and ‘If A then C’ are both true.</span></div>
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<span class="c4 c11">Completely </span><span class="c4">invalidating</span><span class="c4 c11"> modus ponens would be a serious issue and would naturally cast doubt on these theories. But, like McGee’s (1985) independently-motivated counterexample to modus ponens, the main conditionals in the predicted counterexamples feature indicative conditionals in their consequents. That the predicted counterexamples are in this way similar to </span><span class="c4">independently-motivated one</span><span class="c4 c11">s suggests that they are not mere artefacts of faulty theories. Furthermore, while modus ponens construed as a semantic thesis as explained above turns out to be invalid on these theories, modus ponens as a practical inference rule remains unaffected, insofar as asserting or supposing som</span><span class="c4">ething</span><span class="c4 c11"> has the effect of restricting the range of possibilities against which conditionals are evaluated to ones in which </span><span class="c4">that</span><span class="c4 c11"> thing holds. In this way, both theories are compatible with modus ponens being “dynamically valid” (for details see Khoo (</span><span class="c4">2013</span><span class="c4 c11">)). </span><span class="c4">I</span><span class="c0">t seems reasonable to suppose that this is all the modus ponens we need.</span></div>
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<div class="c7">
<span class="c4 c11">Although the whole of this intricate story could not have been imagined by Gibbard, he certainly was aware in the abstract that theories which, like Kratzer’s and Gillies’, allow</span><span class="c4"> embedded</span><span class="c0"> indicative conditionals’ semantic values to differ from the semantic values they would get if taken alone, have the resources to avoid his conclusion.</span></div>
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<div class="c7">
<span class="c0">This possibility, now realised in detail by existing theories, was the very escape route that Gibbard identified and gave reason not to take. The assumption that a given indicative conditional sentence in a given context always gets the same semantic value, regardless of whether it is embedded in a larger conditional, is thus an auxiliary assumption of Gibbard’s proof.</span></div>
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<span class="c2">3. Why Gibbard Wouldn’t Take the Escape Route</span></div>
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<span class="c0">Gibbard’s identification of this auxiliary assumption and his argument against rejecting it are contained in the following passage:</span></div>
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<div class="c7 c16">
<span class="c0">One other possibility remains: that → always represents a propositional function, but that what that function is depends not only on the utterer's epistemic state, but on the place of the connective in the sentence. In a → (b → c), for instance, we might suppose that the two different arrows represent two different propositional functions. Nothing we have seen rules that out.</span></div>
<div class="c3 c16">
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<div class="c7 c16">
<span class="c0">The pursuit of such a theory, though, has now lost its advantage. A theory of indicative conditionals as propositions was supposed to give, at no extra cost, a general theory of sentences with indicative conditional components: simply add the theory of conditionals to our extant theory of the ways truth-conditions of sentences depend on the truth-conditions of their components. The alternative was to develop a new theory to account for each way indicative conditionals might be embedded in longer sentences, and that seemed costly. Now it turns out that for each way indicative conditionals might be embedded in longer sentences, a propositional theory will have to account for their propositional content, and do so in a way that is sensitive to the place of each indicative conditional in its sentence. In a → (b → c), the right and left arrows must be treated separately. What must be done with the left and right arrow in (a → b) → c or with the arrows in a & (b → c) and a ∨ (b → c) we do not yet know. Thus, for instance, no account of sentences of the form (a → b) → c will fall out of a simple general account of indicative conditionals as propositions; rather the account of indicative conditionals itself will have to confront separately the way left-embedded arrows work. A propositional theory would not save labor; instead it would demand all the labor that would have to be done without it. (Gibbard (1981), pp. 236-237)</span></div>
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<span class="c4 c11">The way Gibbard puts it, the assumption at issue is that ‘→ is a fixed propositional function’ (Gibbard (1981, p. 236)), but for present purposes it is the ‘fixed’ part that is relevant, and in view of the possibility of a Kratzerian treatment of the syntax of indicatives, we should separate the ‘fixed’ part out and state it in a way that does not presuppose that ‘→’ is syntactically a two-place propositional operator. Hence our statement of it at the end of the previous section: a given indicative conditional sentence in a given context always gets the same semantic value, regardless of whether it is embedded in a larger conditional. Or in other words again, the assumption is that in a given context, there is no more than one indicative conditional with one set of truth-conditions per pair of antecedent and consequent. </span><span class="c4">Henceforth l</span><span class="c4 c11">et’s call this </span><span class="c4 c11 c5">the fixity assumption</span><span class="c0">.</span></div>
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<span class="c2">4. The Escape Route is Open</span></div>
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<span class="c4 c11">I will give a four-pronged argument against Gibbard’s </span><span class="c4">defense of the fixity assumption. If it is successful, we are left free to abandon the fixity assumption and thus to resist the collapse of indicative conditionals into material conditionals while maintaining a truth-conditional approach to indivatives.</span></div>
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<span class="c4 c11 c5">Prong 1.</span><span class="c4 c11"> Gibbard’s description of the extra work </span><span class="c4">we must do if we abandon the fixity assumption in the pursuit of truth-conditions for indicatives</span><span class="c4 c11"> </span><span class="c4">overplays the amount of extra work required, due to what appears to be a (forgivable) failure of theoretical imagination on his part</span><span class="c0">. </span></div>
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<span class="c0">Gibbard says that if we give up fixity, then ‘for each way indicative conditionals might be embedded in longer sentences, a propositional theory will have to account for their propositional content, and do so in a way that is sensitive to the place of each indicative conditional in its sentence’. This may be strictly correct, but it doesn’t follow that such a theory has to confront each form of embedding separately, or that this sensitivity to place cannot come about in an elegant, systematic way.</span></div>
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<div class="c7">
<span class="c4">Indeed, the sensitivity to place of indicatives-inside-indicatives that we need in order to block Gibbard’s collapse argument </span><span class="c4 c5">does</span><span class="c0"> come about in an elegant, systematic way on both of the theories we have been discussing. On Kratzer’s theory, it stems from the fact that ‘if’ restricts a modal and that such restriction may occur more than once in a single sentence. On Gillies’, it stems from the fact that ‘if’ shifts index and context, and that such shifting may occur multiple times in a single sentence.</span></div>
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<span class="c4">Thus, when Gibbard says that ‘no account of sentences of the form (a → b) → c will fall out of a simple general account of indicative conditionals as propositions; rather the account of indicative conditionals itself will have to confront separately the way left-embedded arrows work’, this - provided that Kratzer’s and Gillies’ theories qualify as ‘simple’ - is simply false. An account of sentences of that form does fall out of both accounts.</span></div>
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<span class="c4">Krazter’s and Gillies’ theories </span><span class="c4 c11">deliver, in an elegant way, different semantic values for conditionals depending on where they are in a sentence</span><span class="c4">. And it seems to me that there is a good sense in which these theories </span><span class="c4 c5">are</span><span class="c4"> such that we can ‘simply add the theory of conditionals to our extant theory of the ways truth-conditions of sentences depend on the truth-conditions of their components’.</span></div>
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<span class="c4 c11 c5">Prong 2.</span><span class="c0"> Following Gibbard in embracing the NTV thesis creates special work of its own, which does not have to be done if we hold that they have truth-values.</span></div>
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<span class="c4 c11">For one thing, there is an irony in his complaint that if we give up the fixity assumption ‘we do not know’ what to do with the arrow in a sentence of the form ‘a ∨ (b → c)’. </span><span class="c4">In keeping with what w</span><span class="c4 c11">e saw in the previous prong, the fixity-denying theories we now have do not encounter any special difficulty in handling such sentences, and we do not have to consider such forms of embedding on a one-by-one basis. Now we may observe further that, if anything, it is the NTV route that leads to issues with such a form; if we deny truth-values to indicative conditionals, we don’t know what to do with the </span><span class="c4 c11 c5">wedge</span><span class="c4 c11"> in such a sentence. That is, we face the </span><span class="c4">extra work</span><span class="c4 c11"> of making sense of, or denying sense to, embeddings of allegedly truth-valueless sentences in what appear to be truth-functional contexts. (See, howeve</span><span class="c4">r, Edgington (1995) for a classic defense of the view that such embeddings are not problematic after all.)</span></div>
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<span class="c0">That is one sort of extra work the NTV theorist seems to be saddled with. And there is another, quite different sort. Namely, the work of explaining what is going on when people appear to ascribe truth-values to indicatives. A truth-value-granting view of indicatives such as Kratzer’s or Gillies’ lets us take these ascriptions at face value, and to allow that they are often correct. An NTV view must either reinterpret these ascriptions so that they aren’t all incorrect, or explain why people so often say these incorrect things. So if we want to avoid extra work, it may be that we do better to uphold truth-value-granting theories like Kratzer’s and Gillies’.</span></div>
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<div class="c7">
<span class="c4 c11 c5">Prong 3.</span><span class="c4 c11"> It’s not all about extra work! The issue is whether we should or should not respond to the collapse argument by denying that indicatives have truth-values. To proceed as though this issue turns just on whether we save labor by maintaining that indicatives have truth-values is too narro</span><span class="c4">w</span><span class="c4 c11">. Labor-saving patently </span><span class="c4 c11 c5">isn’t</span><span class="c4 c11"> the only reason why we might want to maintain that indicatives have truth-values. A distinct and arguably very important reason is that </span><span class="c4 c11 c5">they seem to have truth-values</span><span class="c0">! (How compelling you find this will depend on your philosophical orientation, but if you think that what pre-theoretically seems to be the case is an important guide in philosophy, it should count for quite a bit.)</span></div>
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<span class="c4 c11 c5">Prong 4.</span><span class="c4 c11"> Gibbard’s argument against abandoning the fixity assumption obscures the fact that, when you think about it, it makes sense to expect the assumption to be false. Rejecting the assumption is presented by Gibbard as</span><span class="c4"> a last resort</span><span class="c0">. But rejecting the fixity assumption is not, on reflection, some intuitively unpalatable thing which we get forced into doing just so that we can uphold a prejudice. </span></div>
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<span class="c4">There are well-developed, intuitively motivated views which enable us to</span><span class="c4 c11"> think of indicative conditionals, schematically, as saying something like ‘In all relevant possibilities in which the antecedent holds, the consequent holds’. And it is quite natural to think that what is </span><span class="c4">known</span><span class="c4 c11"> to be true, or what is being supposed to be true, can affect what possibilities are relevant. </span><span class="c4">F</span><span class="c0">urthermore, it is quite natural to think of the antecedents of conditionals, for example, as introducing a supposition. Putting these last two things together, it is quite natural to think that the possibilities relevant for the ‘if B then C’ in ‘If A, then if B then C’ may differ from the possibilities relevant for an unembedded ‘If B then C’. In particular, it is natural to think that only A-possibilities will be relevant to the embedded conditional, while not-A-possibilities may still be relevant to the unembedded one.</span></div>
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<div class="c7">
<span class="c4 c11">So, the negation of the fixity assumption is something which has quite a bit of plausibility. At the very least, it seems plausible from within the general way of looking at indicatives which the collapse argument is supposed to threaten. Namely, a perspective according to which indicatives have truth-values and in some sense deal with ranges of relevant possibilities. And </span><span class="c4">obviously,</span><span class="c0"> such a perspective has much to recommend it besides helping us to resist Gibbard’s argument.</span></div>
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<span class="c2">5. </span><span class="c6 c2">Conclusion</span></div>
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<div class="c7">
<span class="c4">Starting from the intuitiveness of the view that indicative conditionals have truth-values which can differ from those of the corresponding material conditional, we looked at how Gibbard’s collapse argument threatens that view, and how </span><span class="c4 c5">Import-Export</span><span class="c4">, flagged as suspicious by Fitelson, is hard to fault. Drawing on work by </span><span class="c4 c11">Khoo, we then saw that both Kratzer’s and Gillies’ independently</span><span class="c4">-</span><span class="c4 c11">motivated theories of indicative conditionals block Gibbard’s argument</span><span class="c4"> at the cost of invalidating</span><span class="c4 c11"> modus ponens construed as a general semantic thesis</span><span class="c4">,</span><span class="c4 c11"> but that the predicted counterexamples coincide with McGee’s</span><span class="c4"> </span><span class="c4 c11">independently</span><span class="c4">-</span><span class="c4 c11">motivated ones</span><span class="c4"> and</span><span class="c4 c11"> leave modus ponens unscathed as a form of dynamically valid inference. </span><span class="c4">We then looked at </span><span class="c4 c11">Gibbard’s</span><span class="c4"> argument</span><span class="c4 c11"> against truth-va</span><span class="c4">lue-granting theories of indicatives which, like Kratzer’s and Gillies’, </span><span class="c4 c11">reject</span><span class="c4"> </span><span class="c4 c11">the fixity assumption</span><span class="c4">, and saw that</span><span class="c4 c11"> th</span><span class="c4">e</span><span class="c4 c11"> threat is not serious</span><span class="c4">. Gibbard’s refusal to abandon fixity in pursuit of truth-conditions for indicatives </span><span class="c4 c11">stemmed from a failure of theoretical imagination and a too-narrow view of the motivations for non-material, truth-value-granting accounts of indicatives</span><span class="c4">. The prospects for such accounts appear to be brightening.</span></div>
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<span class="c0"></span></div>
<div class="c7">
<span class="c2">References</span></div>
<div class="c3">
<span class="c8 c4"></span></div>
<div class="c7">
<span class="c4 c13">Edgington, Dorothy (1995). On conditionals. </span><span class="c4 c5 c13">Mind</span><span class="c8 c4"> 104 (414):235-329.</span></div>
<div class="c3">
<span class="c8 c4"></span></div>
<div class="c7">
<span class="c4 c13">Edgington, Dorothy (2014). Indicative Conditionals. In </span><span class="c4 c5 c13">The Stanford Encyclopedia of Philosophy </span><span class="c4 c13">(Winter 2014 Edition), ed. Edward N. Zalta. </span><span class="c4 c13">https://plato.stanford.edu/archives/win2014/entries/conditionals/</span></div>
<div class="c3">
<span class="c8 c4"></span></div>
<div class="c7">
<span class="c4 c13">Fitelson, Branden (2013). Gibbard's Collapse Theorem for the Indicative Conditional: An Axiomatic Approach. In </span><span class="c4 c5 c13">Automated Reasoning and Mathematics: Essays in Memory of William W. McCune</span><span class="c8 c4">, M.P. Bonacina and M. Stickel (eds.), Springer.</span></div>
<div class="c3">
<span class="c8 c4"></span></div>
<div class="c7">
<span class="c4 c13">Fitelson, Branden (2016). Two new(ish) triviality results for the indicative conditional. Lecture Notes. </span><span class="c4 c13">http://fitelson.org/triviality_handout.pdf</span></div>
<div class="c3">
<span class="c8 c4"></span></div>
<div class="c7">
<span class="c4 c13">Gibbard, Allan (1981). Two Recent Theories of Conditionals. In William Harper, Robert C. Stalnaker & Glenn Pearce (eds.), </span><span class="c4 c5 c13">Ifs</span><span class="c8 c4">. Reidel. pp. 211-247.</span></div>
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<span class="c8 c4"></span></div>
<div class="c7">
<span class="c4 c13">Gillies, Anthony S. (2009). On truth-conditions for if (but not quite only if ). </span><span class="c4 c5 c13">Philosophical Review</span><span class="c8 c4"> 118 (3):325-349.</span></div>
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<span class="c8 c4"></span></div>
<div class="c7">
<span class="c4 c9">Kaufmann, Stefan (2005). Conditional predictions. </span><span class="c4 c9 c5">Linguistics and Philosophy</span><span class="c4 c9"> 28 (2):181 - 231.</span></div>
<div class="c3">
<span class="c8 c4"></span></div>
<div class="c7">
<span class="c4 c9">Khoo, Justin (2013). A note on Gibbard's proof. </span><span class="c4 c9 c5">Philosophical Studies</span><span class="c8 c4"> 166 (S1):153-164.</span></div>
<div class="c3">
<span class="c8 c4"></span></div>
<div class="c7">
<span class="c4 c9">Khoo, Justin & Mandelkern, Matthew (forthcoming). Triviality results and the relationship between logical and natural languages. </span><span class="c4 c9 c5">Mind</span><span class="c8 c4">.</span></div>
<div class="c3">
<span class="c8 c4"></span></div>
<div class="c7">
<span class="c4 c9">Kratzer, A. (1986). Conditionals. </span><span class="c4 c9 c5">Chicago Linguistics Society</span><span class="c8 c4">, 22(2), 1–15.</span></div>
<div class="c3">
<span class="c8 c4"></span></div>
<div class="c7">
<span class="c4 c9">Kratzer, A. (2012). </span><span class="c4 c5 c9">Collected papers on modals and conditionals</span><span class="c8 c4">. Oxford: Oxford University Press.</span></div>
<div class="c3">
<span class="c8 c4"></span></div>
<div class="c7">
<span class="c8 c4">Lewis, D. (1975). Adverbs of quantification. In: E. L. Keenan (Ed.). Formal semantics of natural</span></div>
<div class="c7">
<span class="c8 c4">language. Cambridge, MA: Cambridge University Press.</span></div>
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<hr class="c28" />
<div>
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<a href="https://www.blogger.com/blogger.g?blogID=8137988136860941398#ftnt_ref1" id="ftnt1">[1]</a><span class="c6 c14"> Gibbard leaves the notion of ‘logical truth’ unexplicated in his proof, but the arguments in the present article do not turn on any particular understanding of it.</span></div>
</div>
<div>
<div class="c7">
<a href="https://www.blogger.com/blogger.g?blogID=8137988136860941398#ftnt_ref2" id="ftnt2">[2]</a><span class="c14 c6"> Contexts, whatever they are, should be thought of as determining ranges or sets of possibilities relevant to the evaluation of conditionals in that context. Cf. Gillies (2009), p. 329 (incl. f.n. 5). Note also that the use of ‘possibilities’ here should not be taken to imply that the possibilities in question are all metaphysical possibilities.</span></div>
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</body></html>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com6tag:blogger.com,1999:blog-8137988136860941398.post-19724338074197822642019-08-17T19:41:00.000-07:002019-08-18T07:10:24.125-07:00Imaginary Foundations, the Zombie Argument, and Modal Inertness<span style="font-family: "georgia" , "times new roman" , serif;">Recently published work by Wolfgang Schwarz, to an extent I'd thought impossible, offers an explanation of why there seem to be facts of phenomenal consciousness that we can know for sure. 'Red looks like <i>this</i>!', one says, as one inwardly points at the sensation, and one feels there is an indubitable fact here.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">The basic idea, as I understand it, is that by having a cognitive architecture that allows us to keep track of sensation by means of belief-like things that we have full credence in, we can do things more efficiently than without such a mechanism. That's only a very rough explanation, but see:</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">- <a href="https://www.umsu.de/papers/imaginary.pdf">The main paper of Schwarz's on this, 'Imaginary Foundations'.</a></span><br />
<span style="font-family: "georgia" , "times new roman" , serif;">- <a href="https://www.umsu.de/papers/sensorfacts.pdf">A second paper outlining some of the ideas from 'Imaginary Foundations' in a more basic way.</a> </span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">Schwarz's explanation of the seeming existence of phenomenal facts that we know with certainty leaves room for various metaphysical views about whether there are facts of phenomenal consciousness, and whether or not they're reducible to non-phenomenal facts. But Schwarz leans towards a sophisticated sort of eliminativism; it's not wrong to call phenomenal reports 'true', but really they don't state facts about the world. Nor do they seem to state <i>a priori</i> necessary facts, like mathematical sentences seem to - these apparent phenomenal facts have the flavour of <i>a posteriori</i> contingent matters, as Schwarz clarified for me in an exchange on his blog (link below). And so we might think there really aren't any facts here.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">- See <a href="https://www.umsu.de/wo/2019/691">here</a> for a blog post of Schwarz's, and the comments where he clarifies why it doesn't seem right to think of them as like non-external-worldly facts, the way we might think of mathematical facts. </span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">Now, one thing I'd like to do is explore the prospects of sticking with Schwarz's explanation of the seeming existence of phenomenal facts, but drawing a different metaphysical moral (or perhaps being critical of the very framework in which the apparent metaphysical options appear).</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">But another thing I'd like to do is run with the whole Schwarz package - the explanation of the seeming as well as the sophisticated eliminativism about phenomenal facts - and see what adopting this package might enable us to say about the Zombie Argument against materialism, the relationship between conceivability and metaphysical possibility, and the like.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">Schwarz has already indicated briefly, in 'Imaginary Foundations' how his explanation of the seeming can explain why a philosophical zombie (p-zombie) - a being just like us but without any inner consciousness - might be conceivable. And similarly, how it might seem like Mary, the colour expert who has never seen red, gets a new bit of knowledge when she finally sees red; the knowledge that red looks like <i>this</i>. </span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">What I'd like to do, on this basis, is to put the sophisticated eliminativism in the picture and see what this lets us say about the Zombie Argument. And I have a hunch that there's an interesting and, as far as I know, novel position we could take here.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">The idea is basically that we could regard these phenomenal consciousness reports as <i>inert</i> with respect to metaphysical possibility. If you have some big description which is true of some set of metaphysically possible worlds, or even just one, then adding or removing phenomenal consciousness propositions - the ones which we have in our minds for broadly computational reasons, although (by our sophisticated eliminativism) they don't really describe substantial facts - won't affect the metaphysical modal status of the description.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">This seems to open up a new way of being a physicalist (or, for that matter, being a non-physicalist who believes in God or has other commitments which makes them a non-physicalist, but is suspicious about irreducible phenomenal consciousness). Physicalism (and other metaphysical views which do not posit irreducible consciousness) is often taken to entail that p-zombies are metaphysically impossible. If you need it to be the case that p-zombies are metaphysically impossible, then in the face of the Zombie Argument (see Chalmers (1999), (2009)), it can look like you really only have two broad options:</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">- Deny that p-zombies are conceivable in a strong sense (a sort of conceivability which is robust with respect to getting more non-modal facts and getting more rational). </span><br />
<span style="font-family: "georgia" , "times new roman" , serif;">- Deny that (strong) conceivability entails metaphysical possibility.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">But, if phenomenal consciousness reports are modally inert in the way indicated above, a third option presents itself. One can accept that p-zombies are as conceivable as one likes, and that descriptions involving phenomenal fact statements, and zombie-like descriptions where these are all negative, can both count as describing metaphysically possible worlds. By adding or removing phenomenal propositions, one just doesn't change which world or range of worlds one is talking about.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">This enables one to both avoid setting implausibly high bars on what we should say is conceivable, and to avoid having to reject the idea that conceivability (of the right sort, and perhaps given the right information). One doesn't have to be a pre-Kripke style modal rationalist. One can accept that there are necessary <i>a posteriori</i> truths, but maintain that <i>given</i> certain relevant empirical truths, the modal situation becomes <i>a priori. </i>(I have a <a href="https://philpapers.org/rec/HAZLNT">paper</a> on this, and some ideas in my PhD <a href="https://sites.google.com/site/tristanhaze/TristanHaze-NecessityandPropositions.pdf">thesis</a> and a paper in progress.)</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">One issue here is that there might be more than one set of notions that are being called the metaphysical modal notions in contemporary philosophy. One set is friendly to moderate modal rationalism, but the more metaphysically loaded set may not be, or may not even be in good standing at all. I've found <a href="https://philpapers.org/rec/ROSTLO-2">Rosen's 'The Limits of Contingency'</a> very illuminating on this point. You might want to be a skeptic about the second, more metaphysical set of 'metaphysical modal notions' while being a moderate rationalist about the first set.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">Nevertheless, it looks to me like Schwarz's ideas about the seeming existence of phenomenal facts give us a powerful way to be skeptical about irreducible phenomenal facts (whether this is because of physicalist or otherwise naturalistic predilections or just because of more specific suspicions about ideas about consciousness), while maintaining a (moderate, Kripke-proof) modal rationalism. Could there have been p-zombies? Sure, but that's not actually a <i>different</i> way for things to have been!</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<i><span style="font-family: "georgia" , "times new roman" , serif;">References</span></i><br />
<i><span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></i>
<br />
<div class="export" style="background-color: white; box-sizing: border-box; color: #333333;">
<span style="font-family: "georgia" , "times new roman" , serif;">Chalmers, David J. (1999). Materialism and the metaphysics of modality. <em class="pubName" style="box-sizing: border-box;">Philosophy and Phenomenological Research</em> 59 (2):473-96.</span></div>
<span style="background-color: white; color: #333333;"><span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></span>
<span style="font-family: "georgia" , "times new roman" , serif;"><span style="background-color: white; color: #333333;">Chalmers, David (2009). The Two-Dimensional Argument Against Materialism. In Brian P. McLaughlin & Sven Walter (eds.),</span><span style="background-color: white; color: #333333;"> </span><em style="box-sizing: border-box; color: #333333;">Oxford Handbook to the Philosophy of Mind</em><span style="background-color: white; color: #333333;">. Oxford University Press.</span></span><br />
<span style="background-color: white; color: #333333;"><span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></span>
<span style="font-family: "georgia" , "times new roman" , serif;"><span style="background-color: white; color: #333333;">Haze, Tristan (2019). Linking Necessity to Apriority. </span><em class="pubName" style="background-color: white; box-sizing: border-box; color: #333333;">Acta Analytica</em><span style="background-color: white; color: #333333;"> 34 (1):1-7.</span></span><br />
<span style="background-color: white; color: #333333;"><span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></span>
<span style="font-family: "georgia" , "times new roman" , serif;"><span style="background-color: white; color: #333333;">Rosen, Gideon (2006). The limits of contingency. In Fraser MacBride (ed.), </span><em style="background-color: white; box-sizing: border-box; color: #333333;">Identity and Modality</em><span style="background-color: white; color: #333333;">. Oxford University Press. pp. 13--39.</span></span><br />
<span style="background-color: white; color: #333333;"><span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></span>
<span style="font-family: "georgia" , "times new roman" , serif;"><span style="background-color: white; color: #333333;">Schwarz, Wolfgang (2018). Imaginary Foundations. </span><em class="pubName" style="background-color: white; box-sizing: border-box; color: #333333;">Ergo: An Open Access Journal of Philosophy</em><span style="background-color: white; color: #333333;"> 5.</span></span><br />
<span style="background-color: white; color: #333333;"><span style="font-family: "georgia" , "times new roman" , serif;"><br /></span></span>
<span style="background-color: white; color: #333333;"><span style="font-family: "georgia" , "times new roman" , serif;">Schwarz, Wolfgang (forthcoming). From Sensor Variables to Phenomenal Facts. <i>Journal of Consciousness Studies.</i></span></span>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com2tag:blogger.com,1999:blog-8137988136860941398.post-62691909455531849762019-05-25T20:37:00.001-07:002019-07-05T20:07:32.949-07:00Logical Pluralism<i>In this post I will raise an issue for the logical pluralism of Beall & Restall (hereafter 'B&R') - a much-discussed, topic-revivifying view in the philosophy of logic. My study of their view was prompted by Mark Colyvan, whose course on Philosophy of Logic at Sydney Uni I'm helping to teach this year. Thanks to Mark for encouragement and discussion. </i><br />
<br />
I'll start off in this post by looking at B&R's central thesis, and arguing that it fails to capture an interesting, controversial position in the philosophy of logic. The problem is not that the view is false, but that it's "too easily" true.<br />
<br />
I take their 2000 paper ‘Logical Pluralism’ as the starting point, but where more detail is needed, I draw on their 2005 book <i>Logical Pluralism</i>.<br />
<br />
Their claim concerns the following schema:<br />
<blockquote class="tr_bq">
Generalised Tarski Thesis (GTT): An argument is <i>valid</i><sub>x</sub> if and only if, in every <i>case</i><sub>x</sub> in which the premises are true, so is the conclusion. (2005, p. 29.)</blockquote>
(This is more precise than the corresponding schema, (V) (for 'validity'), from their 2000 as it makes clear what is allowed to vary.)<br />
<br />
They write:<br />
<blockquote class="tr_bq">
Logical pluralism is the claim that at least two different instances of GTT provide admissible precisifications of logical consequence. (2005, p. 29.)</blockquote>
Being an existential, numerical claim (‘There are at least two…’), there are many ways the view could be true. Later in this series of posts I'll look at the ways they imagine it coming out true - B&R hold that 'cases' may be taken to be worlds, Tarski-style models, or situations (in the sense of Barwise & Perry's situation theory, at least in the first instance). But here I want to highlight presumably unintended ways in which it comes out true, or at least appears to me to do so. If I'm right about this, these unintended ways threaten to rob their view of its apparent bite.<br />
<br />
According to B&R, ‘cases’ may be models ‘Tarskian style’ (2000, p. 480) or ‘along Tarskian lines’ (2005, p. 29).<br />
<br />
But this permits differences over exactly what a model is (even for a given language <i>L</i> - to fix ideas, let's consider the language of first-order logic).<br />
<br />
For instances, do models provide assignments to variables, or just to names? That depends on how you like to treat quantification when defining 'true on a model'. (Another option, taken by Tarski, eschews assignments to variables in favour of a trick involving sequences of objects.)<br />
<br />
Some think which option you take here is philosophically significant - see for instance Smith's 'Truth via Satisfaction?'. But few I think would want to say that not all of these options lead to Tarskian style models (in a broad sense).<br />
<br />
But this doesn't actually matter, since there other differences, which seem <i>definitely</i> trivial, over what exactly a model is taken to be in various presentations of first-order logic.<br />
<br />
Is a model a tuple of the form <D, I> (where D is the domain and I contains semantic information about all non-logical terms)? Or is it a tuple of the form <D, P, N>, where predicates’ extensions are given separately from names’ referents? Or do we bundle these ingredients informally, as is often done in introductory texts? (That is, do we think that a model is just: a domain, extensions for predicates etc., without thinking of the model as a mathematical object in its own right?)<br />
<br />
The point is that these differences, while pretty unimportant, <i>do</i> lead to real differences<br />
over <i>which objects</i> are the ‘cases’. And so to different ‘precisifications’ of the notion of logical consequence.<br />
<br />
And so it seems that, if you believe that there is more than one slightly different way of doing broadly Tarksi-style model theory, then you should be a logical pluralist in Beall & Restall's sense. But that seems like the wrong outcome! And in some sense, <i>not what they mean</i>. B&R wanted to carve out and develop a distinctive philosophical view, one which would for instance conflict with the views of someone who thinks that nothing that is not some form of classical logic counts as 'logic'.<br />
<br />
<i>References</i><br />
<i><br /></i>
Beall, Jc & Restall, Greg (2000). Logical pluralism. <i>Australasian Journal of Philosophy</i> 78 (4):475 – 493.<br />
Beall, Jc & Restall, Greg (2005). <i>Logical Pluralism</i>. Oxford University Press.<br />
Smith, Nicholas J. J. (2017). Truth via Satisfaction? In Pavel Arazim & Tomas Lavicka (eds.), <i>The Logica Yearbook 2016</i>. London: College Publications. pp. 273-287.Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com1tag:blogger.com,1999:blog-8137988136860941398.post-23236997094849412462019-04-25T19:14:00.004-07:002019-04-25T19:41:44.930-07:00Williamson's Metaphysical Modal Epistemology and Vacuism about Counterpossibles<span style="font-family: "georgia" , "times new roman" , serif;">Timothy Williamson has argued that our capacity for metaphysical modal judgement comes along with our capacity for counterfactual judgement. This passage gives a flavour of his view:</span><br />
<blockquote class="tr_bq">
<span style="font-family: "georgia" , "times new roman" , serif;">Humans evolved under no pressure to do philosophy. Presumably, survival and reproduction in the Stone Age depended little on philosophical prowess, dialectical skill being no more effective then than now as a seduction technique and in any case dependent on a hearer already equipped to recognize it. Any cognitive capacity we have for philosophy is a more or less accidental byproduct of other developments. Nor are psychological dispositions that are non-cognitive outside philosophy likely suddenly to become cognitive within it. We should expect cognitive capacities used in philosophy to be cases of general cognitive capacities used in ordinary life, perhaps trained, developed, and systematically applied in various special ways, just as the cognitive capacities that we use in mathematics and natural science are rooted in more primitive cognitive capacities to perceive, imagine, correlate, reason, discuss… In particular, a plausible non-skeptical epistemology of metaphysical modality should subsume our capacity to discriminate metaphysical possibilities from metaphysical impossibilities under more general cognitive capacities used in general life. I will argue that the ordinary cognitive capacity to handle counterfactual carries with it the cognitive capacity to handle metaphysical modality. (Williamson, <i>The Philosophy of Philosophy </i>(2007), p. 136. Found in Section 3 of <a href="https://plato.stanford.edu/entries/modality-epistemology/">the SEP article</a> 'The Epistemology of Modality'.)</span></blockquote>
<span style="font-family: "georgia" , "times new roman" , serif;">In order to argue for this, Williamson takes a schematic semantic story about counterfactual conditionals:</span><br />
<blockquote class="tr_bq">
<span style="font-family: "georgia" , "times new roman" , serif;"><span style="color: #1a1a1a;">Where “A>B” express “If it were that A, it would be that B”, (CC) gives the truth conditions for subjunctive conditionals: A subjunctive conditional “A>C” is true at a possible world <i>w</i> just in case either (i) A is true at no possible world or (ii) some possible world at which both A and C are true is <i>more similar</i> to <i>w</i> than any possible world at which both A and ¬C are true.</span><span style="background-color: white; color: #1a1a1a;">(Formulation from Sec 3 of</span> <a href="https://plato.stanford.edu/entries/modality-epistemology/">the SEP article</a><span style="background-color: white; color: #1a1a1a;">.)</span></span></blockquote>
<span style="font-family: "georgia" , "times new roman" , serif;">On the basis of this, he proves the following equivalences:</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">(NEC)<span style="white-space: pre;"> </span>□A if and only if (¬A>⊥)</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;">It is necessary that A if and only if were ¬A true, a contradiction would follow.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">(POS)<span style="white-space: pre;"> </span>◊A if and only if ¬(A>⊥)</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;">It is possible that A if and only if it is not the case that were A true, a contradiction would follow.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">(Renderings and spellings out from <a href="https://plato.stanford.edu/entries/modality-epistemology/">the SEP article</a>. The box and diamond are metaphysical modal operators, and the falsum - which looks like an upside-down 'T' - represents a contradiction.)<br /><br />But this only works because the schematic theory of counterfactuals Williamson adopts is understood as working against a background of a notion possible worlds, where Williamson understands this as the notion of <i>metaphysically</i> possible worlds. This theory deems true all counterfactuals with metaphysically impossible antecedents, and this is crucial to his demonstation of the equivalences on the basis of his assumed schematic theory.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">There are lots of reasons not to adopt a theory of counterfactuals which uses the notion of metaphysical possibility in this way. One reason to move away from a theory like this is if you think that there are counterpossibles - counterfactual conditionals with metaphysically impossible antecedents - which have their truth-values non-vacuously. But you might be agnostic about that. For instance, you might be happy with metaphysical modal distinctions but doubt that there are any clear cases where countepossibles have truth-values non-vacuously. In that case you might see no good reason for the backdrop of worlds or scenarios in a theory of counterfactuals to be exactly the metaphysically possible ones. Or, you might be skeptical about the very distinction between metaphysical possibility and impossibility, in which case you won't want to understand the backdrop in a way that involves that distinction. And it seems that you can get most, or even all, of the theoretical benefits of a Stalnaker-Lewis approach to counterfactuals without using that distinction. It doesn't really seem to play a starring role in the theories. </span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">If a semantic theory for counterfactuals which does not draw on any bright line between metaphysically possible and metaphysically impossible scenarios is as good or better than the theory that Williamson uses to prove his equivalences, that seriously undermines the equivalences, and in turn Williamson's story about how we get metaphysical modal knowledge.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">(And note that this turns on Williamson's understanding his chosen theory so that 'possible world' means 'metaphysically possible world' - even accepting an identically worded theory, but where 'possible world' is understood in a way which does not involve the distinction between metaphysical possibility and impossibility, would make Williamson's equivalences unavailable.)</span>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com1tag:blogger.com,1999:blog-8137988136860941398.post-21390268608941519082019-04-07T18:07:00.001-07:002019-04-07T18:13:56.263-07:00Contradictory Premises and the Notion of Validity<span style="font-family: "georgia" , "times new roman" , serif;">When evaluating arguments in philosophy, it can be tempting to call an argument 'invalid' if you determine that it has contradictory premises. For example, in an introductory philosophy course at the University of Sydney, students are taught that a particular argument for the existence of God - called the Argument from Causation - is invalid because two of its premises contradict each other. It is tempting to call such an argument invalid because we can determine <i>a priori</i> that it is not sound, i.e. that it isn't both valid and such that its premises are true. But on a classical conception of validity, any argument with contradictory premises counts as valid, since it is impossible for all the premises of an argument with contradictory premises to be true, and so <i>a fortiori</i> impossible for the argument to have true premises and false conclusion.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">I have heard this anomaly explained away by appeal to the fact that, while an argument with contradictory premises may count as <i>formally </i>valid, we are looking at <i>informal </i>validity, and in an informal sense perhaps any argument with contradictory premises should count as invalid. But I don't think that's right. If 'formal' is meant to signal that we are not interested in the meanings of non-logical terms and are only interested in what can be shown on the basis of the form of the argument, then that is clearly a different issue: premises could be determined to be contradictory on the basis of form alone, or in part on the basis of the meanings of the non-logical terms. The issue of contradictory premises is similarly orthogonal to the issue of 'formality' if 'formal' is instead meant to signify something like 'in an artificial language' or 'in a precise mathematical sense'. </span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">In fact, it's arguable that the standard treatment of validity of arguments in classical formal logic should be supplemented, so that an argument counts as valid iff it has no countermodel <i>and</i> its premises are jointly satisfiable.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">If we defined 'valid' that way in classical logic, then to test an argument for validity using the tree method, you might have to do two trees. First, one to see if the premises can all be true together. If the tree says No, the argument is invalid and we can stop, but if the tree says Yes, then we do another tree to see if the premises together with the negation of the conclusion can all be true together, and if the tree says No, the argument is valid.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">Whether or not it's worth adopting in practise, it is worth noting that this augmented definition of 'valid' in classical logic seems to correspond more closely to the ordinary, informal notion of deductive validity than the usual definition. This even delivers at least one of the desiderata which motivate relevance logic.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">However, note that while we seem pretty disposed to call an argument invalid if it has contradictory premises, there is no equally strong tendency to say corresponding things using 'follows from', 'is a consequence of', or 'implies'. This is interesting in itself. It looks like, when we're talking about implication, our focus is on the putative implier or impliers and what can be got out of them, whether or not they're true. By contrast, when we talk about arguments, we're often more focused on the conclusion and whether it is shown to be true by the argument in question, so that validity is treated as one of the things we need to verify along the way. If validity is playing that role, it makes sense to declare an argument invalid if we work out that its premises can't all be true.</span>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com4tag:blogger.com,1999:blog-8137988136860941398.post-84945727899616909102019-02-05T23:57:00.003-08:002019-02-06T16:23:25.974-08:00Two Sources of Interest in Metaphysical Modality (and Kripke in Light of Them)<span style="font-family: "georgia" , "times new roman" , serif;">Source 1: We want to know the vocabulary and syntax of being, or as Rosen puts it in 'The Limits of Contingency', 'the combinatorial essence of the world'. What are the basic elements and how may they be combined?<br /><br />Source 2: We want to know, as it were in advance, whether various kinds of statements that are not put in terms of the basic elements count as high-level descriptions of any possible world. </span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">Many of Kripke's arguments that certain kinds of statements are necessary furnish considerations which purport to show that <i>whatever</i> the possibilities are exactly, none of them is correctly described as one in which '...'. </span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">This mode of argumentation on Kripke's part can make it look like his modal notions can ultimately be explicated along conceptual or semantic lines. But, as Putnam came to appreciate in between 'The Meaning of "Meaning"' and 'Is Water Necessarily H2O?', this is not so.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">In this connection it is notable that all of Kripke's distinctive modal theses are negative as regards possibility. (His claims, in the course of arguing against descriptivism about names, that well-known facts about Aristotle etc. could have been different, are an exception, admittedly - but for <i>those</i> arguments, I don't see that he needs these alternative possibilities to be real, metaphysical possibilities. The modality used in <i>those </i>arguments could be deflated to conceptual or semantic without affecting the arguments, which are after all for a semantic conclusion - that names aren't synonymous with descriptions.) As f</span><span style="font-family: georgia, "times new roman", serif;">ar as I know, Kripke never seriously argues that such and such </span><i style="font-family: georgia, "times new roman", serif;">really is possible</i><span style="font-family: georgia, "times new roman", serif;">, </span><i style="font-family: georgia, "times new roman", serif;">really is a way the world could have been</i><span style="font-family: georgia, "times new roman", serif;">. Rather, he just works on the assumption that there are many quite various ways things could have been, but then seeks to draw some limits in high-level vocabulary.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">But these Kripkean results, if that's what they are, only satisfy interest in metaphysical modality that derives from the second source. How we might satisfy our interest that derives from the second source is largely left untackled, and this is one reason why many have found Kripke's work frustrating. He elicits epistemic hopes, someone might complain, without giving us even so much as a roadmap for how so satisfy them.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">His suggestion that metaphysical possibility may coincide more closely with physical possibility than has often been supposed may however be suggestive. On the other hand, he is against physicalism, so this couldn't be the whole story from his point of view.</span>Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com2tag:blogger.com,1999:blog-8137988136860941398.post-82871610123410509072019-01-10T19:04:00.002-08:002019-01-10T19:14:56.139-08:00Rigidity and General Terms: Two Different Analogues of the Singular Case<i><span style="font-family: "georgia" , "times new roman" , serif;">This post wrestles with and begins to settle on a view about the confusing issue of how Kripke's notion of <a href="https://plato.stanford.edu/entries/rigid-designators/">rigidity</a> may apply to general terms. </span></i><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">One analogue of rigidity for general terms: how about we think of it as a rigid connection between properties (or alternatively, an additional connection between the "rigid" term and a further property).</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">So for example, 'water' in the first instance picks out the property of being water, which is tied rigidly to the property of being (mainly composed of) H20.</span><br />
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<span style="font-family: "georgia" , "times new roman" , serif;">Or 'cat' is tied in the first instance to the property of being a cat, and that is tied rigidly to the property of being an animal.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">But now there is another kind of thing which seems different, and comes up with sentences like 'John has the property we talked about yesterday'.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">Suppose the property we talked about yesterday was the property of having the property that is discussed in Book A. And suppose Book A contains a discussion of the property of redness. </span><span style="font-family: "georgia" , "times new roman" , serif;">Now 'has the property we talked about yesterday' rigidly designates the property of being a property we talked about yesterday, but it also non-rigidly designates the property of having the property that is discussed in Book A, as well as the property of redness.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">This motivates the picture of, behind a predicate, a stack of properties, where the top one is designated rigidly, and the ones below not.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">Problem: we might want to say that 'cat' rigidly designates a certain kind of animal. And I may then want to rephrase that as: 'cat' rigidly ascribes animality. </span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">But doesn't the 'rigid' bit here fall away? Take the phenomenological, underlying-nature-neutral counterpart of 'cat' - 'catty thing'. Now even if in our world all the catty things are cats, it doesn't sound right to say that 'catty thing' ascribes the property of being a cat at all - it's not that it ascribes that property, only non-rigidly. </span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">So now it is beginning to look like the distinction we are after here is between a term merely covering things with property P, vs. ascribing to them property P.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">But then that seems wrong when we go back to 'John has the property we discussed yesterday', since if what we talked about yesterday was the property of redness, there is a sense in which that sentence ascribes redness to John. </span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">This is hell!</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">But this whole problem, occupying the last few paragraphs, perhaps only arises from mixing together two <i>different</i> analogues of rigidity that we get when we look at predicates.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">It may be protested that 'John has the property ...' is not a property ascription syntactically at all, but rather a 2-place relational statement with a non rigid second term.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">Be that as it may, we can still classify 'has the ...' as a predicate and can still talk about a rigid/non-rigid distinction. And so I think we need to recognise that there are at least two quite different things going on here - two different things which are a bit similar to rigidity/non-rigidity as applied to names.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">One is the difference between 'has the property discussed earlier' and 'is red'. Another is the difference between 'is water' and 'is watery' (one brings <i>being composed of H20</i> along with it in counterfactual scenario descriptions, and the other doesn't), or 'is a cat' and 'is a catty thing'. </span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">One reason the second analogue may be counterintuitive if presented <i>as a kind of rigidity</i> is that in the case of singular terms, rigidity is associated with simplicity (both syntactic and semantic), but in the case of predicates (let's look at 'is gold', 'is water', 'is a cat' and put aside 'has the property...') it's the opposite. The "non-rigid" predicates just don't take any further property along with them, but the rigid ones do. I.e. 'is a catty thing' or 'is catlike' just picks out one property, but 'is a cat' is tied to the further property of being an animal.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">Actually, the 'any' in 'any further property' is probably wrong! Maybe all predicates rigidly take some further properties along with them. So this second sort of "rigidity" we can talk about in connection with general terms should be thought of as relative to whatever further property is in question. (For instance, 'is a pencil' is arguably counterfactually locked to 'is a physical object'. So 'is a pencil' rigidly picks out physical objects - we might want to say something like that.)</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">One thing that is emerging here is that the 'has the property discussed earlier' vs. 'is red' thing is one distinction which pattern-matches with Kripke's discussion of rigidity as applied to names, but there is also another thing going on - predicates dragging further properties along with them in counterfactual scenario descriptions - which actually corresponds better with Kripke's informal applications of the notion of rigidity to general terms.</span><br />
<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<span style="font-family: "georgia" , "times new roman" , serif;">Now it looks like the general-term-"rigidity" considerations in <i>Naming and Necessity</i> are actually closer to the "necessity of constitution" and similar considerations than they are to the "necessity of identity" considerations.</span><br />
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<span style="font-family: "georgia" , "times new roman" , serif;"><br /></span>
<i><b><span style="font-family: "georgia" , "times new roman" , serif;">Background Reading:</span></b></i><br />
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Online:<br />
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- Section 4.2. of the SEP entry for Rigidity: <a href="https://plato.stanford.edu/entries/rigid-designators/#ObjAppRigTerForKinPro">https://plato.stanford.edu/entries/rigid-designators/#ObjAppRigTerForKinPro</a></div>
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Also:<br />
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- Kripke, Saul (1980). Naming and Necessity. Harvard University Press.<br />
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- Soames, Scott (2002). Beyond Rigidity: The Unfinished Semantic Agenda of Naming and Necessity. Oxford University Press<br />
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- Salmon, Nathan (2004). Are general terms rigid? Linguistics and Philosophy 28 (1):117 - 134.<br />
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- Linsky, Bernard (2006). General Terms as Rigid Designators. Philosophical Studies 128 (3):655-667.<br />
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- Martí, Genoveva & Martínez-Fernández, José (2011). General terms, rigidity and the trivialization problem. Synthese 181 (2):277 - 293.<br />
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- Schwartz, Stephen P. (2002). Kinds, general terms, and rigidity: A reply to LaPorte. Philosophical Studies 109 (3):265 - 277.<br />
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- de Sa, Dan López (2007). Rigidity, General Terms, and Trivialization. Proceedings of the Aristotelian Society 107 (1pt1):117 - 123.<br />
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- Marti, Genoveva (2004). Rigidity and General Terms. Proceedings of the Aristotelian Society 104:131-148.<br />
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- Zouhar, Marián (2009). On the Notion of Rigidity for General Terms. Grazer Philosophische Studien 78 (1):207-229.<br />
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- Orlando, Eleonora (2014). General terms and rigidity: another solution to the trivialization problem. Manuscrito 37 (1):49-80.<br />
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- Gómez-Torrente, Mario (2004). Beyond Rigidity? Essentialist Predication and the Rigidity of General Terms. Critica 36 (108):37-54.<br />
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- Kosterec, Miloš (2018). Criteria for Nontrivial General Term Rigidity. Acta Analytica 33 (2):255-270.</div>
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Tristan Hazehttp://www.blogger.com/profile/18008340011384137776noreply@blogger.com2