Sprachlogik

Structured Modal Operators

2012-01-16T20:48:00.000-08:00

The task

Propositions have modal characters and truth-values. For now, we will distinguish two modal characters and two truth-values: necessary character, contingent character, truth and falsity.

Necessary character is what necessarily true and necessarily false propositions have in common. Contingent character is what contingent truths and mere possibilities have in common.

In effect, the modal operator 'Necessarily' (box), ascribes necessary character and truth to a proposition. 'Contingently' ascribes contingent character and truth. 'Necessarily, it is not the case that' and 'It is impossible that' ascribe necessary character and falsity. 'It is merely possible that' ascribes contingent character and falsity.

But not all modal operators ascribe a particular character/truth-value pair. Some merely rule out certain combinations. For example, 'Possibly' merely rules out the combination of necessary character and falsity.

(NB that I am here talking about what are often called alethic modal operators, rather than modal operators in a more general formal setting in which these claims only hold for certain choices of accessibility relation.)

It is common to see the following list of four modal operators presented, sometimes as though it were exhaustive: possibility, necessity, contingency and impossibility.

But reflect again that, of these four modalities, possibility is an odd one out, since it is non-commital on truth-value. Also, note that systems have been developed where other operators, e.g. one for non-contingency, are taken as primitive.

This can give rise to an uneasy, lost feeling. Are the usual four modal operators just a hodge-podge? What modal operators are there (could there be)? Is there a systematic way of producing them all? And is there then a systematic way of determining logical relations between them?

In this post, I try to begin answering these questions.

The notation

The notation I want to introduce here can be said to stand to the box, the diamond and such symbols roughly as truth-tables stand to truth-functional connectives. (Or instead of truth-tables, Wittgenstein's ab-notation, Venn diagrams, or the shuttle diagrams pioneered by Martin Gardner and extended by Gregory Landini.)

We have said that 'Necessarily', 'Contingently', 'It is impossible that' and 'It is merely possible that' all ascribe a particular character/truth-value pair, or: they all rule out all but one character/truth-value pair.

We can represent operators as matrices containing four cells, one for each character/truth-value combination. We can then mark the fields representing pairs which are ruled out by the operator in question. A blank canvas, not representing any modal operator, looks like this:

(The box and diamond here represent modal characters.)

The four aforementioned operators then look like this:

We can also consider the class of operators which rule out two character/truth-value pairs:

And finally the class of operators which rule out just one character/truth-value pair:

A syntactical test for implication

For any two modal operators A and B, Ap implies Bp iff all boxes crossed in B are crossed in A. (This could license a simple rule of cross-elimination.)

Then, rules could be given allowing detachment of the truth-operator, conversion of the falsity operator to negation, attachment of the truth-operator, possibility operator, etc.

Flipping and inversion

An operator can be negated by inverting its markings. Its operand can be negated in effect by flipping the operator's marking vertically. The dual of an operator can be obtained by inversion and flipping.

Relation to model theory

For now, atoms are treated as, in effect, simply being assigned a truth-value and a modal character in the semantics, but this can be brought into connection with the standard Kripke semantics for modal logic. Given an S5 frame, for example, an atom's having necessary character (at a world, if you like) amounts to its truth-value being invariant across all worlds. Contingent character amounts to its not being so invariant.

To do

Among other things: study iteration of operators. Iteration will raise philosophical issues about the application of the formalism. These will turn, at least in part, on how propositions are individuated. Similarly, a case could be made for distinguishing a third character, impossible character, when propositions are individuated in a fine-grained way such that our proposition 'Hesperus isn't Phosphorus' is not the same as the Babylonian. (Our version has impossible character. Theirs, necessary.)

Against Quine's Argument in Sect. 31 of Word and Object

2011-12-17T02:10:00.000-08:00

NB: This is a draft of a discussion note which is being considered for publication.

Section 31 of Quine's Word and Object contains an arresting fallacious argument. In 1966, R.C. Sleigh Jr. published an objection to it. In 1977, David Widerker published an objection to Sleigh's objection. More recently, in 2007, Charles Sayward has published a paper where Sleigh's objection is further criticized. (References below.)

I will not engage directly with these three papers, but rather aim to give a clearer objection to Quine's argument.

Here is Sayward's apt description of the argument's point:

To a first approximation, the argument purports to show that if Tom has a certain minimal level of logical acuity—a level many of us possess—then if ‘belief’ has a sense in which it is a transparent operator, then Tom, if he in that sense of the word believes anything, he in that sense of the word believes everything. (Sayward 2007, p. 54.)

Quine assumes that Tom believes at least one true sentence and one false one. In fact, he assumes something much stronger: that Tom believes the true sentence 'Cicero denounced Catiline' and the false sentence 'Tully did not denounce Catiline'. (Cicero is Tully.) That these sentences are are (in a sense) contradictories, and that they are about the same object, is not essential for Quine's argument. These features of Tom were needed for earlier, separate arguments in chapter IV of Word and Object.
Here is the argument:

Where ‘p’ represents a sentence, let us write ‘#p’ (following Kronecker) as short for the description:

the number x such that ((x = 1) and p) or ((x = 0) and not p).

[In place of '#', Kronecker and Quine used a different symbol, which I can't easily reproduce here. - TH.]

We may suppose that poor Tom, whatever his limitations regarding Latin literature and local philanthropies, is enough of a logician to believe a sentence of the form ‘#p = 1’ when and only when he believes the sentence represented by ‘p’. But then we can argue from the transparency of belief that he believes everything. For, by the hypothesis already before us,

(3) Tom believes that # (Cicero denounced Catiline) = 1.

But, whenever ‘p’ represents a true sentence,

# p = #(Cicero denounced Catiline).

But then, by (3) and the transparency of belief,

Tom believes that #p = 1,

from which it follows, by the hypothesis about Tom’s logical acumen, that

(4) Tom believes that p.

But ‘p’ represented any true sentence. Repeating the argument using the falsehood ‘Tully did not denounce Catiline’ instead of the truth ‘Cicero denounced Catiline’, we establish (4) also where ‘p’ represents any falsehood. Tom ends up believing everything. (Quine 1960, pp. 148–149).

First, to rehearse Quine's definition of referential transparency. (Familiar readers can skip this paragraph.) Quine defines transparency in terms of 'modes of containment ... of singular terms or sentences in singular terms or sentences'. Definite descriptions count here as singular terms. For Quine, a mode of containment M is referentially transparent iff, 'whenever an occurrence of a singular term t is purely referential in a term or sentence C(t), it is purely referential also in the containing term or sentence M(C(t)). embedded in that context' (p. 144, schematic letters changed). For a singular term t to be purely referential in a term or sentence is for it to occupy a purely referential position there. Quine's 'criterion' for a position's being purely referential is that the position 'must be subject to the substitutivity of identity' (p. 142). That is, to the substitutivity of co-extensive singular terms salva veritate.

Let us begin by simply granting (3) for the sake of argument, ignoring its justification - Quine's 'by the hypothesis already before us'. (After we have identified a later fatal flaw in the argument, we will return to (3)'s justification briefly, since it seems to suffer from essentially the same flaw.)

Now, note that Quine's 'hypothesis about Tom's logical acumen' (hereafter 'the acumen hypothesis') and the steps of his argument are at different semantic levels. The hypothesis is framed in terms of belief in sentences, while in the argument, sentences appear unquoted as the contents of 'that'-clauses. Thus, the acumen hypothesis does not apply directly to 'Tom believes that #p = 1', since that sentence says nothing about Tom's belief in any sentence. Quine is, apparently, suppressing a quotational and a disquotational step here. An expanded version of this part of the argument, in which the acumen hypothesis could be applied directly, would have to run something like:

(i) Tom believes that #p = 1.

(ii) Hence Tom believes the sentence '#p = 1'. (Quotation step.)

(iii) Hence Tom believes the sentence 'p'. (Acumen hypothesis together with (ii).)

(4) Tom believes that p. (Disquotation step.)

Secondly, note that 'believes' in 'Tom believes that #p = 1' is to be taken in a transparent sense, as piece of reasoning preceding it makes clear. (In case of any residual doubt about this: in the very next sentence after the argument as quoted, Quine summarizes it by saying 'Thus in declaring belief invariably transparent ... we would let in too much.')

Putting these things together, we can see the invalidity of Quine's argument: when (i) is taken in a transparent sense, it does not imply (ii).

To see this, consider that Delia Graff Fara believes (in the transparent sense) that Quine wrote Word and Object. We hereby introduce a new name for Quine, 'G6'. Now, since G6 is Quine - since 'G6' and 'Quine' are co-extensive - we may infer that Delia Graff Fara believes (in the transparent sense) that G6 wrote Word and Object. Plainly, we cannot infer from this that Professor Fara, who knows nothing of my convention (at the time of writing), believes the sentence 'G6 wrote Word and Object'.

The problem with Quine's argument as it stands, then, is in the first instance a use-mention confusion. (None of the papers cited makes anything of this point.) We have now seen that the problem cannot be fixed by expanding the argument to contain a quotational and a disquotational step; the quotational step is invalid. Can it be fixed by rephrasing the acumen hypothesis as a schema containing placeholders for unquoted sentences?

It cannot. Such a schema would run: 'John believes that #p = 1 when and only when he believes that p'. The dilemma here is that, if 'believes' is taken transparently, the schema is not a defensible principle of rationality (even for logicians), and if it is taken opaquely, the principle doesn't apply to Quine's argument.

Finally, to return to the first step of the argument, namely (3)'s justification. The 'hypothesis' Quine cites here is, as far as I can tell, the acumen hypothesis. And so this step is just as invalid as Quine's inference to (4). For the case where 'p' is true, however, (3) will be true anyway, so long as Tom believes that 1 = 1.

Tristan Haze
The University of Sydney

References

- Quine, W. V. (1960). Word and Object. The MIT Press.

- Charles Sayward (2007). Quine and his Critics on Truth-Functionality and Extensionality. Logic and Logical Philosophy 16:45-63.

- R. C. Sleigh (1966). A note on an argument of Quine's. Philosophical Studies 17 (6):91 - 93.

- David Widerker (1977). Epistemic opacity again. Philosophical Studies 32 (4):355 - 358.

In with the True - An interview with Peter Boghossian

2011-12-12T17:52:00.000-08:00

Prof. Boghossian writes,

Love your blog. I think your readers may enjoy this highly controversial piece: http://www.philosophynews.com/post/2011/12/05/Interview-with-Peter-Boghossian.aspx

Disclaimer: Sprachlogik is not styling itself here as an atheist blog. Theists and agnostics are most welcome. (My father's a non-churchy theist. I'm all over the place, but basically agnostic.)

Philosophers' Carnival - December 12, 2011

2011-12-11T18:32:00.000-08:00

Welcome to the December 12, 2011 edition of Philosophers' Carnival.

There weren't many good submissions this time around, so I went hunting. If you write substantial philosophical blog posts, please consider making a habit of submitting to the Carnival.

Submitted

Should grad student stipends be tax exempt? - by Matt Hoberg of The Consternation of Philosophy.

Satisficing by Effort - Richard Yetter Chappell of Philosophy et cetera discusses effort-based satisficing consquentialism, a view about ethics.

Is the right to self-defense "unlimited"? - by NChen of Gavagai!.

Found

Reviews of this Blog - a blog, by Brian Rabern, consisting solely of reviews of itself. Inspired by Douglas Hofstadter. (Sorry.)

Ethics and Affectivity - by Levi Bryant of Larval Subjects.

Some Consequences of Perdurantism - by Andrew Brenner of the Florida Student Philosophy Blog.

Comparative Desert and the Bounds of Well-Being - by Antti Kauppinen of PEA Soup.

A Note on Craig's Standard Reply to Mackie on the Kalam Cosmological Argument - by ex-apologist.

Ruling Out the Ruling Out Principle? - by Dan Lopez de Sa of the blogos, the blog of the LOGOS research group.

The insoluble problem of future tense statements - by Edward Ockham of Beyond Necessity.

Philosophy by Humans, 2: Living Metaphorically - by Luke Meuhlhauser A.K.A. lukeprog of Less Wrong. lukeprog is one of the more brilliant and prominent nerds in the Less Wrong community led by Eliezer Yudkowsky. Like it or not, something is happening there.

The truth about infinitesimals - by Denis Des Chene of Philosophical Fortnights.

Extensionalism & Presentism - by Philippe Chuard of BrainPains. The author is discussing extensionalism and presentism about temporal experiences.

Byrne & Hilbert on Color Physicalism - by Justin Fisher of BrainPains. See comments for a response from Hilbert.

Finally, a Wittgensteinian experiment of mine, Twenty Remarks on Necessitarianism and its Negation.

Thanks for visiting. The next Philosophers' Carnival will be at Cognitive Philosophy.

Assessing Epistemic Modals

2011-11-29T23:32:00.000-08:00

Draft paper, here.

After critically examining contextualism and relativism (MacFarlane's view) about epistemic modals, I propose an approach I call 'the dimensions of assessment approach'. Comments welcome.

Twenty Remarks on Necessitarianism and its Negation

2011-11-23T18:36:00.000-08:00

Disclaimer: the following remarks are highly exploratory and are not to be read as expressing anything final.

1. What is the status of the claim with which Lewis begins On the Plurality of Worlds? (That there are other ways the world could have been other than the way things are.) We have a tendency to hear it in the wrong key. Imagine someone who had lost a loved one saying 'Things really could have been different'. (There seems something self-deluding in this, although it is no ordinary self-delusion. You don't fix it with negation.)

2. Ayer, Carnap and others wanted to say: the necessities fall out of our linguistic/conceptual scheme. Codify 'the rules of correct English' (cf. Language, Truth and Logic) and you've codified the necessities (or a base from which they may be logically derived). But the Kripkean necessary a posteriori, semantic externalism etc. make it clear that one needs a lot more fine structure than 'rules of correct English', and that some structures are in some sense not correct, in a way which has nothing to do with internal incoherence, but rather to do with inadequacy to an external referent.

* * *

3. 'I went to X, but could have gone to Y instead.'

How might such a proposition be used? A retrospective epistemic use. Or to point to various facts - e.g. that Y wasn't too far away, or that I was under no compulsion to go to X, or that I was seriously considering going to Y, etc. But what if I say that none of that is quite to the point? 'Sure, those things might be true, but over and above that, I'm saying that I really could have gone to Y. The world could have gone differently here, and my going to X was just how it happened to turn out.' What could this mean? (We can imagine someone being bothered, preoccupied, by the thought that things really could have gone differently.)

4. Consider these propositions:

(1) There are things which could have gone otherwise.

(2) There are contingencies.

When a philosopher asserts (1) or words to that effect, typically the reaction they want is 'of course!'. Now, this would happen sometimes, but more common among non-philosophers might be perplexity - 'what do you mean?' - and skepticism - 'but how do you know?'. (I have some experience of this.)

5. Both in and out of serious philosophy, there is a tendency to take (1) and (2) in what I would call the wrong way. Roughly: as though they described something extremely fundamental and general about reality. And yet that is not an entirely wrong-headed thought, for it is immensely important that we talk and think about non-actual scenarios.

6. It is as though, when someone pushes a statement of counterfactual possibility in a certain way, we take them to be making a very strong claim, quite beyond our ken.

7. When one hears (1) and (2) in an "inflated" way - whatever that comes to - necessitarianism can seem like the antidote: something wrong has been said, and so it should be denied. But then the denial turns out to be just as troublesome, if not more! (Now it is trivially false, instead of trivially true - like Idealism in relation to Realism.)

8. The disease is not fully containable in any one proposition.

* * *

9. It can be very important to realize that some propositions are necessary - 'One cannot feel another's pain', 'The opium worked (if it worked at all) by means of a dormitative power'. Likewise, contingent - 'There are two sexes', 'We have one body each', 'We use the decimal system to count'. It can be very instructive to get clear about the "modal status" of these things. And of course this does not mean leaving the view that they are contingent (or necessary) and coming over to the other side, but rather: noticing something, which one might have been quite blind to. Think of the conceptual development of children - one cannot truly say that they go through a phase of believing that everyone knows the same as them, but we can see what this is getting at. In the place where we have a fundamental distinction or concept of great importance in adult life, they do not have anything to speak of.

10. So: it can be important to realize the modal status of certain propositions. But - and this is crucial - it does not at all follow from this that it is important, desirable or possible to draw a line which clearly divides all propositions according to modal status.

11. What is the modal status of 'Our conceptual scheme has moving parts'? I.e. how could anything else be a conceptual scheme? (Mind of God.) And yet the proposition easily acquires the flavour of a general fact of nature. Why? Well, lots of important facts lie immediately underneath.

* * *

12. The notion of the mind of God. It can look as though everything is an approach to this ideal, and yet we have absolutely no grip on the ideal. We (i.e. myself and most active philosophers) do not have any positive belief in the mind of God in the old sense, and all the minds we do believe in are completely un-Godly.

13. Our conceptual scheme has moving parts. But if God knows all, he doesn't need any moving parts. (Spinozistic necessitarianism, Liebniz's difficulties.)

14. So now it looks like, in a sense, the ideal conceptual scheme has no moving parts - no need to dance further with experience or reason. And yet we will always need a conceptual scheme with moving parts, and can really make no sense of anything else. Thus how could the mind of God be our ideal?!

15. From this perspective, one could imagine pantheism as a kind of scholastic solution to our present problem. (For it would block the assimilation of our mind with God's.) ('A full, non-redundant model of an object must be a duplicate of the object, or the object itself.')

16. We say things could have been otherwise - I could have walked somewhere else today. But then someone says 'but could that really have happened?' and it's like the stakes are raised somehow. But isn't this a shift to a more specialized modality?

17. "What makes you think things could have really been different, and that this isn't just a function of our ignorance?" - The first thing to say is there's no simple answer here: one can't just point to evidence. The question is symptomatic of something.

18. One pernicious kind of confusion when talking about metaphysical necessity - the modality identified, and separated from other concepts, by Kripke - is to think of it in a manner which would be appropriate for some kind of deep and remote form of retrospective epistemic possibility. This is illustrated by the notion of the Creation as an event. God did something, and it may have been reasonable to expect this to go various ways. It is important for our concerns here that such an idea is natural to some degree.

19. It is possible to feel that any kind of conceptual view of necessity, even if we grant everything to the concepts including external adequacy, somehow makes modality flimsy, shadowy - somehow still overlooks reality in some way. "The way things really could have been, concepts aside." (The notion of an inconceivable object. If such a thing is impossible, how is that not just a piece of luck? Thus it can seem that the conceptualist must rely on some kind of pre-established harmony between possible concepts and possible realities, which would of course be highly suspicious.)

20. There is a strong philosophical tendency to think of knowledge of how things must be as penetrating deeper into the world than mere contingent knowledge. As though we saw how a machine behaved, but then looked into its workings and saw that it had to behave that way. Or, we form a hypothesis about the workings based on, and in order to make sense of, the behaviour. (This gets us into difficulties, but it would be stupid to call it incorrect - or correct for that matter.)

Tristan Haze

For more on modality see here, here and here.

Toward an Understanding of De Dicto Subjunctive Necessity (draft paper)

2011-11-01T01:10:00.000-07:00

Here.

Please share this with any people you know who may be interested.

Email comments or questions of any kind to tristanhaze (at) gmail (dot com), or post them here.

I would appreciate any feedback, no matter how minimal or unlikely to be helpful you think it is. (For example, let me know if something didn't make sense to you, or just seemed wrong.) I'm very keen to improve the presentation of these ideas, as well as the ideas themselves.

This is an early draft, and many of my current formulations are probably inadequate.

The paper is written for a fairly specialized audience. I intend to give a more thorough and accessible treatment of these ideas in a projected book. Its working title is Necessity and Conceptual Systems.

The overall aim is to draw connections between modal concepts and broadly semantic concepts (the latter including the notion of a conceptual system). The basic idea is that necessarily true propositions are in some sense invariant through all configurations of the systems they belong to. (This is squared with the view that not all necessary truths can be known a priori by means of the notion of an empirically defeasible concept-formation.)

A Plea for Conceptual Schemes

2011-10-25T00:05:00.000-07:00

Introduction

In 1974, Donalad Davidson published a now famous paper entitled 'On the Very Idea of a Conceptual Scheme', in which he attacked that idea and exhorted the reader to give it up. One reason Davidson set upon this idea was his evident hunch that it lay behind the pernicious, nebulous doctrine of the relativity of truth. Another, perhaps more fundamental, reason, was his desire to see the world and our understanding of it in terms of a metaphysics of sentences and objects, without employing things like concepts and propositions.

I think the idea of a conceptual scheme a highly serviceable one, and that Davidson's attack is confused. I believe that the idea of a conceptual scheme has a good deal of unrealized potential in the philosophy of modality and many other areas. My object here is simply to vouchsafe the idea from Davidson's attack.

The Problem of Comparison and Neutrality

Early in his paper, Davidson makes this remark, which goes to the essence of his attack:

[T]here is no chance that someone can take up a vantage point for comparing conceptual schemes by temporarily shedding his own.
(Davidson 1979/1984, p. 185. Page references are to the 1984 version.)

This is true, but misleading. True, because we cannot do anything by temporarily shedding our conceptual scheme - the immediate reason being is that there is no such thing as 'temporarily shedding our conceptual schemes' in the required sense (i.e. while retaining some kind of rationality or sentience). Misleading, because it seems to carry the implication that scheme-shedding would be the way we ought to proceed with a comparison, if only this were possible.

Against this, I want to insist that the only conceivable way we could compare two conceptual schemes is from within our own. We have a conception of the world (surely!). Part of that conception is the idea that there are conceptions - of the world, in the world. We are self-conscious. We think about our thinking and that of others, and when we do this we employ our conception of our own conceptions, and our conception of others' conceptions.

Of course, if we compare our conceptual scheme with another, our ideas of these two schemes will not be on a par epistemologically. This difference cannot be factored out. However, we should try to be as objective as we can, and this means trying to improve our conception of our conceptions, and those of others, and the relations between them.

Davidson, on the other hand, apparently has some idea to the effect that, as long as we are 'stuck' in our own conceptual schemes, comparison will be impossible or at the very least greatly hampered. Indeed, some notion of being stuck seems to lie at the root of this part of the confusion.

'The Dualism of Scheme and Content'

According to Davidson

[the] dualism of scheme and content, of organizing system and something waiting to be organized, cannot be made intelligible and defensible. It is itself a dogma of empiricism, the third dogma. (p. 189.)

Now, I do not want to argue with the claim that no dualism between scheme and content could be made good sense of. Rather, the point is that no notion of a dualism is called for to support the idea of a conceptual scheme.

In our ordinary ideas of 'scheme and content', I should think, it is understood that the scheme itself is potentially part of the content, and parts of this potential content - such as concepts - inhere in the scheme.

Simply put: There is no dualism of scheme and content. A distinction is not a dualism.

The idea of a dualism of scheme and content is bound up with a fundamental misunderstanding of the 'content' part of that idea, arising from a certain picture we possess of the situation, and an attitude toward this picture which most of us, in certain circumstances, are strongly inclined to take. (Cf. the notion of the thing-in-itself.) While this phenomenon is of fundamental importance in parts of philosophy, I maintain that it is not an essential part of our practical understanding of the idea of a conceptual scheme. On the contrary, and as the existence of Davidson's paper shows, it can be an obstacle.

The Problem of 'Uninterpreted Reality'

Davidson wants us to give up 'dependence on the concept of an uninterpreted reality, something outside all schemes and science'. The great unclarity here is: what do the phrases 'uninterpreted reality' and 'something outside all schemes and science' mean in this context?

As suggested in the previous section, the 'content' or 'world' term of the conceptual representation relation need not be thought of as some amorphous fundament, some uninterpreted thing-in-itself. We live in the world - in reality - and we interpret it. Reality, since we are real and interpret it, just is interpreted; there is no reality which, as a whole, is completely uninterpreted.

What about parts of reality? The particular objects, events and processes which intelligent beings talk and think about are parts of interpreted reality - parts of reality which get interpreted. Thus my desk is part of interpreted reality, as are Denmark, Donald Davidson, Beethoven's Ninth, Saturn and many other things besides.

It is quite commonly believed, in our culture, that other parts of reality are uninterpreted; if some small pebble somewhere has never been apprehended or encountered in any way by an intelligence, then this individual is, in some sense, part of uninterpreted reality. Quite obviously, this is not the sort of thing Davidson means by 'uninterpreted reality'.

We might instead take the phrase 'uninterpreted reality' to mean 'reality considered separately from any interpretational or conceptual apparatus'. Then surely this can include chairs, tables, and the rest of it. ('Considered separately from interpretational or conceptual apparatus' obviously doesn't mean 'considered without recourse to any interpretational or conceptual apparatus'.) So this doesn't seem to be what Davidson means, either.

Regarding the phrase 'something outside all schemes and science': isn't the desk I am working at now outside all schemes and science? Surely my desk is not inside a conceptual scheme, or inside science (whatever that means).

The following passage from Rorty, who enthusiastically embraced Davidson's critique of the idea of conceptual schemes, gives us more to work with:

The notion of 'the world' as used in a phrase like 'different conceptual schemes carve up the world differently' must be the notion of something completely unspecified and unspecifiable - the thing in itself, in fact. A soon as we start thinking of 'the world' as atoms and the void, or sense data and awareness of them, or 'stimuli' of a certain sort brought to bear upon organs of a certain sort, we have changed the name of the game. For we are now well within some particular theory about how the world is.

(Rorty 1982, p. 14.)

I deny the first assertion. The notion works like this: we use our conceptual schemes and understand there to be chairs, tables, numbers, quarks, experiences, concepts and schemes thereof. Then we form an idea of different schemes carving up the world differently. Here, our idea of the world is still our idea of the world, i.e. an idea of something which contains chairs, tables, numbers, quarks, experiences, concepts and schemes (among who knows what else).

In a strange way, Davidson and Rorty seem to make the very mistake they appear to be warning against. In saying queer things about 'uninterpreted reality', they try to identify a thing we can't say anything about. Or: they try to give the content of a notion they want to criticize, but in so doing they only embroil themselves in the confusion which bothers them. It is this confusion, I believe, which leads Davidson and Rorty to loudly and violently reject the idea of a conceptual scheme. They reached for the saw; I suggest we consider a scalpel.

Tristan Haze

References

Davidson, D. 1974. 'On the Very Idea of a Conceptual Scheme', Proceedings and Addresses of the American Philosophical Association, Vol. 47, pp. 5-20.

The above reprinted 1984 in Donald Davidson (ed.), Inquiries Into Truth and Interpretation. Oxford: Oxford University Press.

Rorty, R. 1982. 'The World Well Lost', Consequences of Pragmatism, Minneapolis: University of Minnesota Press.

Deduction and the Necessary A Posteriori

2011-10-10T19:27:00.000-07:00

Consider: There is a cat here, therefore there is an animal here.

Assuming we want to say that this inference is valid in some sense, here are three things we might say about it:

1) It is an elliptical argument, involving an unarticulated premise, namely that cats are animals.

2) It is an enthymematic or gappy argument, involving unarticulated reasoning.

3) It is a complete argument in itself - neither (1) nor (2) is the case.

On the first approach, the deduction is clearly a priori. But this is not the only possible attitude. While the belief that cats are animals could conceivably be overturned by experience, it is arguably not a contingent fact that all the cats around are animals (cf. Kripke 1980). So rather than regarding this as part of the matter being reasoned from, we might regard it as part of the deductive apparatus.

Thus, on the second interpretation, we might regard the move from 'cat' to 'animal' as being licensed by an unarticulated principle of reasoning (which may be expressed in the form of an inference rule, or an axiom such as 'All cats are animals'). Or we might resist even this, and say that nothing is unarticulated - perhaps still allowing that the argument can be justified by the principles of reasoning which are held to be unarticulated on the second interpretation.

Note how natural these latter two approaches are; there does seem to be some sense in which the conclusion follows from the single articulated premise. Note also that the argument by itself satisfies the natural (admittedly problematic) modal characterization of validity, if we take the relevant modality to be subjunctive or metaphysical modality ("what could have been the case") rather than a priori possibility or epistemic modality ("what could be the case"): it could not have been the case that there was a cat here yesterday but no animal here yesterday.

This may suggest that, according to some intuitive and central concept of deduction, some facts about what can be deduced from what are empirical (i.e. not knowable a priori).

However, this flies rather completely in the face of previous philosophical thinking about deduction. It also raises the following puzzle: on one way of thinking about necessity, our holding it to be necessary that all cats are animals means that we have made a certain kind of connection between our cat-concept and our animal-concept (an empirically defeasible connection, held constant when describing counterfactual scenarios). But it is natural to think of this conceptual connection as partly constitutive of the content of thoughts involving these concepts - thoughts such as 'There is a cat here' and 'There is an animal here'. Thus, someone who doesn't have such a connection arguably isn't in a position to have those two thoughts at all: there would appear to be little room for them to have those exact thoughts and yet not be able to work out a priori that one implies the other.

My suggestion is that, when faced with this sort of puzzle, one should try to distinguish different ways of individuating content, some more fine-grained than others. When talking about thoughts in, e.g., the context of communication, a relatively course-grained individuation scheme is often most appropriate. When talking about the epistemology of deduction - and not just the epistemology - a more fine-grained approach is called for. (That is, an approach where what are for many purposes two instances of the same thought get treated as distinct structures.)

Insofar as this is right, the more general moral is perhaps something like: when doing philosophy, be willing to put multiple modes of content-individuation on the table - don't let one obsess you to the exclusion of all others.

Tristan Haze

Reference

Saul A. Kripke (1980). Naming and Necessity. Harvard University Press.

An Analysis of Davidson's Slingshot Argument

2011-09-21T21:29:00.000-07:00

There is a peculiar kind of logical fallacy which, ironically, is only committed by people who have an acquaintance with formal logical theory. Fallacies of this kind arise when principles of inference from formal logic are applied inappropriately to arguments carried out in a natural language.

Here I make a case-study of Donald Davidson's famous version of the Slingshot argument against facts. The argument, in its dialectical context, is meant to show that if true statements correspond to facts, then every true statement corresponds to every fact. Davidson tries to demonstrate this conditional in order to motivate us to give up its antecedent (that true statements correspond to facts). Here is the argument:

The confirming argument is this. Let ‘p’ abbreviate some true sentence. Then surely the statement that p corresponds to the fact that p. But we may substitute for the second ‘p’ the logically equivalent “(the x such that x is identical with Diogenes and p) is identical with (the x such that x is identical with Diogenes)”. Applying the principle that we may substitute coextensive singular terms, we can substitute ‘q’ for ‘p’ in the last quoted sentence, provided ‘q’ is true. Finally, reversing the first step we conclude that the statement that p corresponds to the fact that q, where ‘p’ and ‘q’ are any true sentences. (Davidson 1969, p. 753.)

Let us go through it bit by bit.

The first apparent inference in the argument is curious. 'Then surely' suggests that reasoning is taking place here, but from what? Apparently:

Let ‘p’ abbreviate some true sentence.

But that is an instruction, not something we can infer from at all. This shows that what Davidson has supplied is not an argument, so much as a recipe for making one. And since this first step is not an inference, it can't be a fallacious inference. Still, in its slightly confusing use of a technique from logic (in this case, schematization) it gives us a small taste of things to come.

Now, following Davidson's recipe, we shall let 'p' abbreviate 'snow is white'. For perspicuity, we shall not use these abbreviations in our writings-out of the steps of the argument. (Surely this could not affect validity.) Thus our first real premise is:

The statement that snow is white corresponds to the fact that snow is white.

Now we are told we may make a substitution, yielding:

The statement that snow is white corresponds to the fact that (the x such that x is identical with Diogenes and snow is white) is identical with (the x such that x is identical with Diogenes).

The first thing to note about the above is that it doesn't obviously mean anything. This should make us suspicious. After all, we are not supposed to be merely calculating with signs here. This is supposed to be an argument - a reasoned chain of statements leading to a conclusion. How did we get to the above sentence, then? There are two things Davidson needs us to accept if we are to go along with this inference:

(1) That it is valid when arguing in English to substitute, for a sentence, a logically equivalent sentence - even when this sentence is embedded in a larger one.

(2) That 'snow is white' is logically equivalent to '(the x such that x is identical with Diogenes and snow is white) is identical with (the x such that x is identical with Diogenes)'.

In trying to assess these claims, we face a stumbling block: the lack of a clear, agreed upon notion of logical equivalence as a relation between sentences of natural languages. Some would say that 'snow is white' is logically equivalent to 'snow is white and Socrates is either mortal or not mortal'. Others would deny this, on the grounds that Socrates' existence is not implied by the original sentence. Some would say that 'John is a bachelor' is logically equivalent to 'John is an unmarried man', by the logics of bachelorhood, gender and marriage. Others would say these are perhaps analytically, but not logically, equivalent, because the equivalence does not turn on the use of "logical vocabulary".

Having made due note of this difficulty, let us observe that Davidson has no problem bringing in, out of the blue, mention of Diogenes. This gives us some handle on Davidson's intended notion of logical equivalence - enough, I think, to justify us in sweeping the difficulty under the carpet so that we may proceed to ask if (1) might be true.

That the answer is 'no' can be seen from these invalid instances:

(i) It is obvious that snow is white. Therefore, it is obvious that snow is white and [some elaborate and opaque tautology].

(ii) If you assume that the square root of two is rational, it is easy to derive a contradiction. Therefore, if you assume that [some elaborate and opaque logical equivalent to 'the square root of two is rational'], it is easy to derive a contradiction.

(iii) The statement that snow is white involves no semantic concepts. Therefore, the statement that snow is white and "grass" either refers to grass or does not refer to grass, involves no semantic concepts.

(In classical formal logic, the range of possibilities for sentential embedding is far narrower than in natural languages, and therefore no analogous counterexamples arise.)

How about (2)? For a start, can we even understand '(the x such that x is identical with Diogenes and snow is white) is identical with (the x such that x is identical with Diogenes)'? The use of the variables and brackets is, in itself, not a deal-breaker, since we can understand '(the x such that x is identical with grass) is green'. But now: on this understanding, what is the role of that which comes after 'such that' in the bracketed construction? Intuitively, the construction as a whole is a referring term, and after the 'such that' ought to go conditions relating to the variable which are met by exactly one of its possible values, thus determining a unique referent.

But then what happens if, as well as conditions involving 'x', we insert closed sentences like 'snow is white'? Well, on the intuitive idea behind the bracketed construction, this just doesn't make sense. Nevertheless, "appropriate" reference-conditions come to mind: a bracketed 'the' construction refers iff the conditions relating to the variable are met by exactly one object and all constituent closed sentences are true. To complete the semantics, we can stipulate that if such a construction refers, it refers (of course) to the condition-meeting value of the variable.

Thus we can define a new kind of referring construction, albeit a strange one. Also, it does appear that our complicated identity sentence, in light of this definition, is logically equivalent (in some sense) to 'snow is white'. Of course, this is of no use to us, since the principle whose application we wanted the equivalence for is invalid.

Before we move on: the addition of this new referring construction to our language may render previously valid principles invalid, so we must now be extra careful. (If, earlier, we had decided that (1) was true - that the unrestricted substitution of logical equivalents was valid - we would now have to go back and reconsider.)

Now, despite the fact that things aren't going very well for our argument, let us press on. We have gotten as far as:

The statement that snow is white corresponds to the fact that (the x such that x is identical with Diogenes and snow is white) is identical with (the x such that x is identical with Diogenes).

And now, citing the principle that we may substitute coextensive singular terms, Davidson has us substitute some true sentence - let us pick 'grass is green' - for 'snow is white'. (This then yields a new 'singular term', '(the x such that x is identical with Diogenes and grass is green)'.) Thus we get:

The statement that snow is white corresponds to the fact that (the x such that x is identical with Diogenes and grass is green) is identical with (the x such that x is identical with Diogenes).

And now we must ask: does the principle of substitution of coextensive singular terms hold in natural language? Notoriously, and as anyone familiar with twentieth-century philosophy of language will know, it (very arguably) does not; there are numerous contexts where such substitutions (strongly seem to) fail. (Witness the existence of intensional logics.) Here is an example of one kind of invalid instance:

Lois Lane knows that Clark Kent is Clark Kent. Therefore, Lois Lane knows that Clark Kent is Superman.

There are also well-known problems with substitution into modal contexts. Furthermore, and closer to our current context: 'the fact that Clark Kent is Clark Kent' does not obviously have the same reference as 'the fact that Clark Kent is Superman', even though the differing embedded singular terms are coextensive. And certainly the statement that Clark Kent is Clark Kent is not identical to the statement that Clark Kent is Superman. For all these reasons, we can not accept an unrestricted principle of substitution of co-extensive singular terms. Thus our last inference was invalid.

Since the final inference is a reversal of the first substitution, that concludes our step-by-step evaluation.

If there be any residual doubt about the invalidity of Davidson's argument (recipe): note that no special properties of the sentence 'The statement that snow is white corresponds to the fact that snow is white', beyond its embedding 'snow is white', are drawn upon in the derivation of 'The statement that snow is white corresponds to the fact that grass is green'. If this were really a valid way of arguing, we would also have to accept the following:

Suppose there is a chameleon, Euclid, who lives in a field of grass. Suppose further that Euclid is green because grass is green. Using Davidson's form of argument. we can infer from this supposition first:

Euclid is green because (the x such that x is identical with Diogenes and grass is green) is identical with (the x such that x is identical with Diogenes).

Then:

Euclid is green because (the x such that x is identical with Diogenes and Davidson is the author of 'True to the facts') is identical with (the x such that x is identical with Diogenes).

And finally:

Euclid is green because Davidson is the author of 'True to the facts'.

Tristan Haze

Reference

Donald Davidson. True to the facts. The Journal of Philosophy, 66(21):748–64, November 1969.

Vote Sprachlogik at 3quarksdaily

2011-09-08T21:10:00.000-07:00

Please consider voting for the Sprachlogik post 'Sketch of a Way of Thinking about Modality, pt. 1' at the 3quarksdaily philosophy blog prize.

Vote here.

UPDATE: Voting is now closed. The post got through the voting round and has been selected by the editors for the finals.

Essence, Belief and Epistemic Modality (Part 2 of Sketch)

2011-08-13T23:55:00.000-07:00

This is part 2 of a Sketch of a Way of Thinking about Modality. In this part we shall consider:

- Essences and the de re/de dicto distinction,
- The indefiniteness of necessity,
- Intentional contexts ("propositional attitudes"), and
- Epistemic modality.

The first topic is really the main one. What I say about the remaining topics will be very scant - a rough indication of how these issues are to be approached according to the way of thinking being sketched out here, rather than an attempt to really deal with them. (I hope to really deal with them in my book.) They fit quite naturally here, since intentional contexts come into the more substantial discussion of the first topic. If nothing else, the brief discussion here should prevent readers from thinking that I have given no consideration to such issues, or that my account of modality is straightforwardly unable to deal with them.

Three Interpretations of Modal Claims about Individuals

As a preliminary, it should be noted that epistemic modal claims are not counted in this taxonomy. Consider, to begin with, sentences of the form 'a is necessarily F'. I distinguish the following three interpretations of such statements:

(1) The contextual interpretation. The locus classicus for this interpretation is Lewis in On the Plurality of Worlds, who expresses it better than I can:

I suggest that those philosophers who preach that origins are essential are absolutely right - in the context of their own preaching. They make themselves right: their preaching constitutes a context in which de re modality is governed by a way of representing (as I think, by a counterpart relation) that requires match of origins. But if I ask how things would be if Saul Kripke had come from no sperm and egg but had been brought by a stork, that makes equally good sense. I create a context that makes my question make sense, and to do so it has to be a context that makes origins not be essential.' (p. 252)

There is one ruffle here: Lewis (who is notorious for playing fast and loose with ordinary modal language) talks of 'how things would be if Saul Kripke had...', rather than how things would have been. This might suggest a kind of epistemic reading, concerning what it would be like if it turned out that Saul Kripke actually had such-and-such an origin. But the range of possibilities in this sense - the things which could turn out to be true of an individual, for all we know (or all we know a priori) - is something quite different from what we are discussing here. In two-dimensional semantics, this corresponds roughly to the difference between A- and C-intensions.

(2) The "unrestricted" interpretation. In contrast to the above, we are now beginning to enter the realm of what could more legitimately be called 'essence'¹, and are looking at proper metaphysical (or subjunctive) modality. On this interpretation, something like the following holds: 'a is necessarily F' is true iff 'a is F' is satisfied by all configurations of the host system of these propositions, and the concepts involved are adequate to their objects with respect to 'a is F'. (This form of account is introduced more generally in part 1.)

Thus, in this case, we might say that the necessity, as opposed to contingent truth, of 'a is F' stems from the nature of the individual concept of a, rather than any contextual restrictions placed on our representations. Why, then, are there scare-quotes around 'unrestricted'? This is because the present way of looking at things may over-dramatize the difference between the contextual restrictions of Lewis's account, and the constitution of concepts in the relevant fine-grained sense. We might think of the nature of these concepts as being at least partly determined by more-or-less invariant restrictions of some more general apparatus. This more general apparatus can be used to understand epistemic modality (and epistemic space).

On this interpretation, to say that a is necessarily F is to say something like: according to the way I think of a - and this way is adequate - it could not have failed to be F. (This isn't meant to be a proper analysis.) But we will probably want to recognize the possibility of slightly different concepts in other systems which have a as their object, and are adequate. Thus while we might think of John in such a way that we may say, intending the present "unrestricted" interpretation, that he is necessarily F, we might recognize that other people might legitimately think of John in such a way that they may say that he is contingently F. (This could be called 'adequacy pluralism about concepts'.)

(3) The generalized "unrestricted" interpretation. Clearly, we will want an interpretation of modal claims about individuals which does not tie their truth to one particular conceptualization (namely, that embodied in the host system of the modal claim). This interpretation gives us that. On this interpretation, something like the following holds: 'a is necessarily F' is true iff all configurations of all systems containing an adequate concept of a represent a as being F. (Another, less natural interpretation would be to substitute 'at least one system' for 'all systems'. This interpretation would be natural for 'a is possibly F'.)

A Simplification

I have simplified the above by concentrating on subject terms and ignoring different construals of the role of the predicate. One might distinguish interpretations analogous to (2) and (3) above, i.e. an evaluation involving a particular F-concept in a system, versus one involving all systems with some concept of the property F. An analogous simplification will be made below in the discussion of ascriptions of intentional content.

The Indefiniteness of Necessity

The account of necessity given here, based on the notion of all configurations of a conceptual system, may give the impression that I think a sharp boundary can be drawn between necessary and contingent truths. It is important to realize that this is not the case. (I probably should have emphasized this already in part 1.)

One way of responding to this would be to try to modify our picture of modality - instead of picturing a conceptual system as being like a mechanical apparatus which can be put into a definite set of configurations, one might imagine a device with an indefinite set of configurations; one might, for example, imagine growing resistance as one manipulates the apparatus into further out configurations (i.e. further from what we think is actually the case).

This sort of response has its place, but we needn't respond like that. We can also hold on to our simpler, more definite picture, but with due regard to the indefiniteness of its application.

Either way, it is important to note that there are clear cases. Some propositions are clearly necessary, and some are clearly contingent, and the distinction between them is of fundamental importance.

The following analogies from Wittgenstein are very helpful in connection with this theme:

The use of the words 'proposition', 'language', etc. has the haziness of the normal use of concept-words in our language. To think this makes them unusable, or ill-adapted to their purpose, would be like wanting to say 'the warmth this stove gives is no use, because you can't feel where it begins and where it ends'.

from Philosophical Grammar, Part 1. p. 120.

It is essential to logic to draw boundaries, but no such boundaries are drawn in the language we speak. But this doesn’t mean that logic represents language incorrectly, or that it represents an ideal language. Its task is to portray a colourful, blurred reality as a pen-and-ink drawing.

from The Big Typescript, p. 144.

The De Re/De Dicto Distinction(s)

This is widely acknowledged to be a confusing topic. The pair of terms 'de re' and 'de dicto' appear to get employed in philosophy to mark several important distinctions (or sorts of distinction). Complete clarification of this will have to wait for another time, but for now I want to characterize two basic sorts of distinction for which these terms can be used:

(1) De re: Generalization (universal or existential) over dicta involving a particular object vs. De dicto: specification of a particular dictum. (Dicta here are contents, propositions - something like that.) The distinction above between the "unrestricted" and generalized "unrestricted" interpretations of modal claims about individuals is an instance of this. It echoes, at least in part, Quine's distinction between believes-notional and believes relational.

In intentional contexts (for example, belief-reports), the distinction appears in the following way. The name 'Hesperus' in a belief report like:

(A) Ralph believes that Hesperus is F.

can be read as doing two things at once. (1) specifying the object of Ralph's belief, and (2) specifying the concept (or mode of presentation) via which he has it. On such a reading, (1) could be expanded to:

(B) Ralph believes, of Hesperus, via his Hesperus-concept, that it is F.

(A similar thing could be done for the 'F'.) Some belief reports, on the other hand - purely de re belief-reports - may be read as only specifying the object. (A) read this way could be expanded to:

(C) Ralph believes, of Hesperus, via some concept(s), that it is F.

(Cases such as 'John believes that Santa Claus exists' suggest that there are also readings where the name just functions to indicate an individual concept or intension involved in the propositional attitude, i.e. does not specify any real extension.)

Substitution of co-referring terms salva veritate (i.e. without change in truth-value) will fail in modal and intentional contexts which are de dicto in this sense.

(2) De re: Involvement of a dictum featuring a rigid (or rigidified) designator vs. De dicto: Involvement of a dictum featuring a non-rigid, unrigidified designator. This distinction most clearly makes its appearance with definite descriptions.

To illustrate: as a result of these two distinctions together, a sentence like 'The winner could have been shot' - once we rule out salient epistemic readings and Lewis-style contextually restricted readings - still has three readings left:

De dicto in both senses (1) and (2): true iff the non-rigid dictum 'The winner was shot' is satisfied by at least one configuration of the host system. (In this configuration (so to speak), the winner might be someone else.)

De dicto in sense (1) and de re in sense (2): using 'The winner' to indicate an individual concept - the concept of the actual winner, that very person - i.e. as a rigidified description, and true iff that dictum is satisfied by at least one configuration of its host system.

De re in sense (1) and therefore neither de re nor de dicto in sense (2): using 'The winner' purely to indicate a particular object, and then making a claim about all dicta which are rigidly about that object and which fulfil certain conditions (in this case: saying that the object was shot, or saying that the object was shot using some particular concept of being shot). It is only on this sort of reading, I submit, that substitution of co-referring terms salva veritate will be valid.

Clarifying and separating these distinctions helps to clarify Quine's skepticism about de re modality, and Kripke's famous arguments against Quine's attitude, as well as making it clearer why this debate is so confusing. Below is a lengthy quote of an important passage of Naming and Necessity. The above discussion can help us disambiguate the ensuing talk of particulars having modal properties independently of how they are described: this may be indicating de re-ness of the second kind (involvement of an individual concept rather than a non-rigid, unrigidified designator), or the first (generalizing over concepts of a particular object, rather than fixing on a particular concept).

Some philosophers have distinguished between essentialism, the belief in modality de re, and a mere advocacy of necessity, the belief in modality de dicto. Now, some people say: Let's give you the concept of necessity. A much worse thing, something creating great additional problems, is whether we can say of any particular that it has necessary or contingent properties, even make the distinction between necessary and contingent properties. Look, it's only a statement or a state of affairs that can be either necessary or contingent! Whether a particular necessarily or contingently has a certain property depends on the way it's described. This is perhaps closely related to the view that the way we refer to particular things is by a description. What is Quine's famous example? If we consider the number 9, does it have the property of necessary oddness? Has that number got to be odd in all possible worlds? Certainly it's true in all possible worlds, let's say, it couldn't have been otherwise, that nine is odd. Of course, 9 could also be equally well picked out as the number of planets. It is not necessary, not true in all possible worlds, that the number of planets is odd. For example if there had been eight planets, the number of planets would not have been odd. And so it's thought: Was it necessary or contingent that Nixon won the election? (It might seem contingent, unless one has some view of some inexorable processes....) But this is a contingent property of Nixon only relative to our referring to him as 'Nixon' (assuming 'Nixon' doesn't mean 'the man who won the election at such and such a time'). But if we designate Nixon as 'the man who won the election in 1968', then it will be a necessary truth, of course, that the man who won the election in 1968, won the election in 1968. Similarly, whether an object has the same property in all possible worlds depends not just on the object itself, but on how it is described. So it's argued.

It is even suggested in the literature, that though a notion of necessity may have some sort of intuition behind it (we do think some things could have been otherwise; other things we don't think could have been otherwise), this notion [of a distinction between necessary and contingent properties] is just a doctrine made up by some bad philosopher, who (I guess) didn't realize that there are several ways of referring to the same thing. I don't know if some philosophers have not realized this; but at any rate it is very far from being true that this idea [that a property can meaningfully be held to be essential or accidental to an object independently of its description] is a notion which has no intuitive content, which means nothing to the ordinary man. Suppose that someone said, pointing to Nixon, 'That's the guy who might have lost'. Someone else says 'Oh no, if you describe him as "Nixon", then he might have lost; but, of course, describing him as the winner, then it is not true that he might have lost'. Now which one is being the philosopher, here, the unintuitive man? It seems to me obviously to be the second. The second man has a philosophical theory. The first man would say, and with great conviction 'Well, of course, the winner of the election might have been someone else. The actual winner, had the course of the campaigner been different, might have been the loser, and someone else the winner; or there might have been no election at all. So such terms as "the winner" and "the loser" don't designate the same objects in all possible worlds. On the other hand, the term "Nixon" is just a name of this man. When you ask whether it is necessary or contingent that Nixon won the election, you are asking the intuitive question whether in some counterfactual situation, this man would in fact have lost the election. (Kripke, Naming and Necessity, first lecture.)

Epistemic Modality and Ascriptions of Intentional Content

For the purposes of understanding metaphysical or subjunctive modality, I have been talking about conceptual systems in a fine-grained sense such that changing one's mind about an empirical identity statement involving individual concepts, for example, constitutes a change in the system itself. Since we believe that Hesperus is Phosphorus, there is no configuration of our fine-grained system which satisfies 'Hesperus is not Phosphorus'. And yet we can truly say things like 'It could turn out that Hesperus is not Phosphorus after all', and even (despite worries of Kripke's) 'It could have turned out that Hesperus was not Phosphorus'.

This is connected with the idea of 'two spaces of possible worlds' in other approaches. (Cf. Chalmers' 'The Nature of Epistemic Space'.) When we say that it could be that Hesperus isn't Phosphorus, we are not considering a configuration of our existing system in the sense we have been talking about, but are rather considering a change in our system. But in another sense, of course, making this change would constitute a reconfiguration of some "wider" system - the system relevant to epistemic modality. Making various abstractions and idealizations, we can imagine a space of possible ways things could be for all we know a priori - epistemic space. Moving from that to the space of ways things could have been involves getting rid of epistemic possibilities which are not metaphysically possible (the lesson of the necessary a posteriori), but also adding epistemic impossibilities which are metaphysically possible (the lesson of the contingent a priori), i.e. things which couldn't be the case, but could have been, such as this room being bigger than it is. (This latter thing will occupy us in part 3.)

So, we can configure our systems in the wide sense to represent ways things might be, and the way we think things are. But, speaking roughly, such a configuration of the wide system yields a system in the fine-grained sense, of ways things could have been. Sometimes, when we change our beliefs, this can be understood as simply moving to another configuration in the fine-grained system (and thus not directly changing any of our metaphysical modal judgements), whereas other times this must be regarded as involving change of the fine-grained system itself (e.g. going from believing that Hesperus is not Phosphorus to believing that it is).

(Note that I am not saying that the ways things really could be all have corresponding configurations in some system of ours, nor that the ways things really could have been all have corresponding configurations in our fine-grained system - not only may we be wrong, there will be possibilities we haven't dreamt of. Clearly much more needs saying here about these notions of 'the ways'. Some speculations can be found here.)

The Metaphysical Possibility of Metaphysically Impossible Thoughts

Hesperus could be distinct from Phosphorus after all, if we're radically deceived, but given that it is Phosphorus, it could not have been distinct from Phosphorus. So 'Hesperus is not Phosphorus' is not satisfied by any configurations of our fine-grained system. And yet 'John believes that Hesperus is not Phosphorus' is metaphysically possible, is satisfied by configurations of our fine-grained system.

This may be quite puzzling given a certain way of visualizing the fine-grained system and its relation to the wider epistemic system which gives rise to it. For a while it seemed like a real problem to me, and I called it 'the containment problem'. The bothersome thing is the way in which epistemic modal space seems to be contained in metaphysical modal space via our machinery for ascribing intentional states and propositional attitudes - our machinery for representing the thoughts and representations of others - despite epistemic modal space outrunning the metaphysical in the well-known Kripkean way.

It is very tempting to try to "fix" this "problem" by going metalinguistic. I.e. saying something like: 'When we say that John believes that Hesperus is not Phosphorus, we aren't really simulating, constructing, or dealing directly with a thought that Hesperus is not Phosphorus. Rather, we are simply employing our concepts of Hesperus, the Hesperus-concept and the Phosphorus-concept, and forming an idea of a proposition in another system which has the relevant properties.' That may be a good view of what we do sometimes (especially with very foreign thoughts), but it seems wrong - gratuitous, even - to suppose that this is always how we do it. After all, we naturally and frequently envisage epistemic possibilities which fall outside our current fine-grained system. We step outside it all the time. So, when we think something like 'John believes that Hesperus is not Phosphorus', we can think of this as employing - in tandem - our fine-grained system together with a configuration of our wider system which falls outside it, but which is "pointed to": to give ourselves the thing John believes, we step outside our fine-grained system and construct the thought directly, so to speak - and all of this in a sense just constitutes a configuration of our fine-grained system, but of a special kind.

Compare Russell's treatment in the Logical Atomism lectures of 'propositions with more than one verb', and his remark about Wittgenstein's 'discovery' that propositions like 'A believes that p' are 'a new beast for our zoo' (p. 226, Logic and Knowledge).

A Desultory Postscript about Water

Contrary to plan, I haven't included a proper section on 'Water is H20' and related examples (or apparent examples) of the necessary a posteriori. I don't have much to say about such examples for now, except that it is very difficult to avoid dogmatism when treating them; specifically, in the move from the fact that water is H20 - something we've all learned - to a particular interpretation and logical explication of 'Water is H20'.

One might regard this sentence as expressing a 'theoretical identity' as in Kripke. Scott Soames critically examines this way of going in detail in his book Beyond Rigidity. Alternatively, one might regard the 'is' here as being "the 'is' of constitution", and this in turn might be construed as a (non-symmetric) relation. Or one might simply interpret 'is H20' as a predicate. On the 'water' side, one may construe this as being tied to a concept of water in the Kripke-Putnam way (i.e. such that 'Water is H20' is necessary), or it may be construed functionally or phenomenologically, such that 'Water is H20' is contingent.

All these contents seem to exist, so to speak, and all seem like natural ways of interpreting 'Water is H20'. So we must be wary not to fall into holding views which might implicitly suggest otherwise; we can and should develop simplified, systematic, abstract views of logic and language, but we hinder and discredit this very development if we neglect the underlying variety of language use. Among other things, this may give the false appearance that the whole logico-philosophical enterprise depends on there not being this variety.

(Part 1, recently edited, is here.)

(See this paper for a newer presentation of the basic ideas of part 1.)

1. For present purposes, I pass over Kit Fine's contention that not all necessary properties are essential in an intuitive sense (roughly because they are not all intrinsic to the thing in question). The classic example of a necessary property which is arguably not an essential property is Socrates' membership in his singleton set {Socrates}. There may be something important which distinguishes the essential properties from the merely necessary ones, but they will still be necessary properties, and hence will be amenable to my view.

Wild Thoughts on Modality, Propositions and Concepts

2011-08-07T23:41:00.000-07:00

Here. (Readers who like Sprachlogik for its clear-headedness are duly warned that this title is no joke.)

Individual concepts and modality at Philosophy etc.

2011-08-05T20:33:00.000-07:00

I've got a guest post at Philosophy etc., 'An advertisement for individual concepts'. The comments are more substantial than the original post.

The proposal made there is closely connected with the ideas featured in my Sketch of a Way of Thinking about Modaliy, part 2 of which will be posted in the next few days.

Mind-Independence and Propositions

2011-07-27T01:52:00.000-07:00

I will try to say something about a profound confusion or blindness which occurs in connection with the notion of mind-independence. What I will say will be reminiscent of some of Wittgenstein's ideas from his mid-late period, especially the ones which influenced Waismann's work on 'language strata' (see references).

This post was prompted by a recent lecture of David Macarthur's, wherein he emphasized that propositions were not linguistic items for Moore and Russell. (Nor, I would add, were they linguistic items (signs) in a projective relation to the world, as in the early Wittgenstein.) Instead, they were supposed to be abstract objects1 which do not in general depend on minds or on language for their existence. This aspect of Moore and Russell's early post-Hegelian thought is often labelled 'Platonism' or 'Platonic realism'. Macarthur wanted to emphasize that this is quite a difficult idea - i.e. to think of propositions as being 'so completely language-independent' (I think he used some such expression).

I want to say: no, not necessarily - this last statement has to be qualified, although it is appropriate enough in connection with the philosophical views of Moore and Russell. I will try to explain what I mean.

We talk of concepts, meanings, propositions, statements and the like. Our talk about these things has a certain logic and grammar; it makes sense to say that a concept is used by somebody, but it makes no sense to say that a concept is three metres away from somebody. It makes sense to call a proposition true, but not red.

I think it is plausible to think of the notion of a proposition, or statement - in something like the sense of 'that which is asserted by a meaningful declarative sentence' - as ordinarily not coming into direct contact with the notion of dependence as it applies to minds and spatiotemporal things. In Wittgensteinian-Waismannian terms, the relevant notion of dependence is part of one stratum of language, and the notion of a proposition is part of another. We don't talk of a proposition depending for its existence on this or that mind, thing, process, etc., any more than we talk of a house being tautological.

At least, this is how it is in the ordinary, or primary language-game. (I think the term 'primary' is perhaps better, since I don't mean to imply that there is anything especially folky about the primary language-games we play with the word 'proposition'.) And this, I believe, is what - in the first instance - makes it correct to say 'Propositions do not depend for their existence on minds', just as it is correct to say 'Houses do not themselves possess arithmetical properties'.

But there is something which makes the statement about propositions significant to us, in a way which the statement about houses is not likely to be. As a piece of grammar, this statement can be said to warn us against a mixing up of language strata which – for reasons which I will not inquire into here – we are especially prone to when philosophizing.

However, 'Propositions do not depend for their existence on minds' is not a reliable guard against this confusion, due to its superficial similarity to non-grammatical statements such as 'The nobility in fourteenth century England did not depend for their existence on the King'. This leads to what might be called a Platonic interpretation of this statement. Rather than being taken as a grammatical warning or prohibition against bringing the mind-(in)dependence concept into direct contact with the proposition concept, these concepts are brought together, and propositions are thought of as, so to speak, being positively independent.

This supports, and is supported by, strange uses of “pictures” of propositions which resemble our pictures of physical objects, ideas of durability and hardness being applied to propositions, Plato's Heaven, and the like. (This is of course very loose talk.) Also, consider the expressions used in this remarkable statement of Russell's in the Logical Atomism lectures: 'To suppose that in the actual world of nature there is a whole set of false propositions going about is to my mind monstrous.'

We should be careful not to confuse the grammatical sense of 'Propositions do not depend for their existence on our minds' with an apparently material sense which arises from a confused mixing of levels (or from a language-game which goes beyond the primary ones we play with 'proposition' and related words).

In the primary game, we simply don't talk about existential dependence on minds in relation to propositions, and this is perfectly in order. That is what is hard to see.

The idea that we simply don't, or can't, talk about propositions (in the ordinary or primary sense) depending on this or that mind, may have an air of quietism and renunciation about it. 'Whereof we cannot speak, thereof we must remain silent' etc. Even worse, it might seem depressingly parochial and conservative. To a great extent, this would be a mistaken reaction. We are not prevented at all from talking about 'propositions' 'depending' on minds - however, if we do so, and if this is anything more than a mere grammatical confusion, then we are simply not playing the primary game.

Despite the anti-metaphysical political stance of the historical antecedents for this sort of view (particularly in the Vienna Circle), I don't see these points as being hostile to philosophical speculation, or the development of new ways of thinking. And perhaps a lot of what is called 'metaphysics' can be thought of as an attempt to develop such new ways of thinking (and talking) about the world. (None of this, by the way, should be taken to imply any sort of Rortian antirealism, excluding considerations of objectivity and correspondence to reality, or anything like that.)

Consider in this connection the growing attention paid by metaphysicians to the way they are using language, especially quantifiers and terms like 'real' and 'exists' (e.g. Hofweber) and also - more relevantly - terms like 'depends on' and 'grounds' (e.g. Schaffer). Investigations into such matters are increasingly common, and often go under the headings 'metametaphysics' and 'metaontology'.

The remarks above are not very well-made, nor are they particularly original. I make them anyway because they seem to embody an important sort of consideration which seems somewhat neglected in contemporary post-linguistic-turn philosophy (although hopefully this is changing).

The relative obscurity of this sort of consideration today has, of course, to do with the fact that it involves something like an analytic-synthetic distinction, or perhaps more like Wittgenstein's arguably non-exhaustive distinction between grammatical and empirical propositions. Such distinctions sit under a dark cloud today. This in turn has to do with the ideas of Quine in 'Two Dogmas' and 'Truth by Convention', and a shift in emphasis toward certain modal notions, arising from Kripke's clear isolation of them.

Tristan Haze

Cf. this freely available copy of Waismann's article, 'Verifiability', which has some material on language strata. (Note however that one can use the notion of language strata without accepting a verificationist view of meaning.)

References:

Thomas Hofweber (2005). A puzzle about ontology. Noûs 39 (2):256-283.

Thomas Hofweber (2007). Innocent statements and their metaphysically loaded counterparts. Philosophers' Imprint 7 (1):1-33.

Saul A. Kripke (1980). Naming and Necessity. Harvard University Press.

Willard Van Orman Quine (2010). Two dogmas of empiricism. In Darragh Byrne & Max Kölbel (eds.), Arguing About Language. Routledge.

Willard Van Orman Quine (1951). Two dogmas of empiricism. Philosophical Review 60 (1):20-43.

Jonathan Schaffer (2009). On what grounds what. In David Manley, David J. Chalmers & Ryan Wasserman (eds.), Metametaphysics: New Essays on the Foundations of Ontology. Oxford University Press.

Friedrich Waismann (1946). The many-level-structure of language. Synthese 5 (5-6):221 - 229.

Ludwig Wittgenstein (1975). Philosophical Remarks. University of Chicago Press.

Ludwig Wittgenstein (1974). Philosophical Grammar. Blackwell.

1 Or at least partly abstract objects; Russell thought propositions about concrete objects had those concrete objects as constituents.

Quine and Lewis on Semantic Relativity

2011-07-19T21:50:00.000-07:00

This post is by guest author Timothy Scriven.

In 'Ontological relativity' Quine suggests that the linguist's translation of a term into another language is radically indeterminate. Neither the intension nor the extension of terms can be deduced from behavior alone. In his famous example “Gavagai” might refer to a rabbit, an undetached rabbit part, a time slice of a rabbit or any number of other entities. This under-determination is not merely an epistemological problem (perhaps one we could solve via inference to the best explanation), for if anything is meaning constitutive, it is behaviour.

Quine does concede that the linguist is likely to make certain sorts of translations and not others. Quine says that “Enduring and relatively homogenous object[s]” which “[move] as a whole against a contrasting background” are likely to be selected as the translations for short expressions. We might call this “the rule of moving blocks” (RMB). Surely though there will be other rules that linguists tend to use to resolve indeterminacy, let’s call these rules R collectively.

Imagine a linguist considering lexicons from a variety of languages, and noticing a pattern of R-preserving meanings. For example, languages tend to have words for “Horse” but not “The undetached lower half of a horse”. A linguist might think that they have uncovered a human universal in RMB, and in whatever other rules they may extract. Quine, however, thinks this is purely an artifact of our interests, and the way we do linguistics. Roughly speaking, translations consistent with R rules tend to be more natural.

Quine thinks that if we are being purely philosophical and bracketing our values and interests, we cannot make a choice between the alternative translations, one of which preserves R as much as possible, and one of which disregards R. Only facts about our interests determine which translation it is best to adopt. Quine says that he would recommend adopting the semanticist’s practice of sticking with R-friendly or natural translations to anyone. But this is only for practical reasons, from what we might think of as a purely theoretical perspective, we’re stuck with massive indeterminacy.

There’s a ruffle in the carpet for Quine’s view that isn’t urged by commentators often enough. Quine sets up a dialectic in which he is being philosophical, refusing to attend to pragmatic interests at least for a while, and considering alternative translations schemas without referring to human interests. The semanticist on the other hand attends to the mucky practical requirements of her field. What she should say is relative to her interests. Not her pecuniary, ethical or emotional interests, but certain cognitive interests- simplicity, tractability etc. No blame falls on the semanticist for this, but the projects of the philosopher and the semanticist are clearly divergent.

How does Quine come to the view that semanticists typically make assignments on the basis of adjoining words to natural things or types? Why, by parsing the semanticist’s language of course. Presumably he reaches his understanding of the semanticist’s language through an interpretive theory, but either this theory is incomplete and does not uniquely select an interpretation, or it is laden with interests. Thus Quine “shows” that linguists interpret relative to a set of pragmatic concerns, but he can only show this by smuggling in pragmatic concerns of his own, inferences about meaning beyond what his cherished behavioral data would permit. There is no strict self-refutation here, but it is surely compromising nonetheless.

Lewis is famous for expounding the view that natural properties play a vital role in fixing meaning (c.f. 'New work for a theory of universals'). For Lewis, it’s not that, as a contingent psychological matter, people tend to refer to natural properties instead of unnatural properties. Instead it’s part of the meaning of “meaning” that translation schemes which are “higher scoring” with respect to certain virtues, like mapping onto natural properties, win out over lower scoring schemas.

At heart, these views have very little separating them. Perhaps this is unsurprising. In my view, Lewis can be read as Quine, with greater respect for Moorean facts.¹ Both Quine and Lewis acknowledge the role of something like naturalness in deciding our theories of meaning. Quine just insists that naturalness gets a role for “pragmatic reasons”. When the difference is put so, I think it becomes difficult indeed to give a reason to be a Quinean rather than a Lewisian. One might insist that Quine has one less ontological commitment than Lewis, he doesn’t need to hold there is anything actually like natural properties. But if Quine can do without these properties in his semantics and metaphysics, I think we can reconfigure the Lewisian thesis as simply stating that the correct meaning theory is the competitor that preserves naturalness the best². as captured by R, without a commitment to any particular ontology.

It is not even clear that there is a material difference between the views. One could talk about the set of meaningsQ and the set of meaningsL. The meaningsQ of a word W are those that are compatible with all available data on F that Quine would consider acceptable. The meaningsL of a word W are those that are compatible with all available data on W that Lewis would consider acceptable. The set of MeaningsL for W will hopefully consist in just one meaning, since, unless there are ties, there will only be one top ranked meaning for each term, accounting for all of Lewis’s ranking criteria. MeaningQ is underdetermined, meaningL is not, so we are inclined to use meaningL.

Timothy Scriven

The University of Sydney

References

David Lewis (1983). New work for a theory of universals. Australasian Journal of Philosophy 61 (December):343-377.

Quine, W. V. (1968). Ontological relativity. Journal of Philosophy 65 (7):185-212.

1 Compare for example Quine’s reasons for accepting Platonism, and Lewis’s reasons for accepting modal realism. Of course Lewis is a modal realist, but even this position was reached by trying to respect deep principles of commonsense.

2 Of course there may be other criteria.

Philosophers' Carnival - July 18, 2011

2011-07-18T01:36:00.000-07:00

Welcome to the July 18, 2011 edition of Philosophers' Carnival. Marvel at the range of different topics discussed! No analytic-continental divide here!

Crazyism - Eric Schwitzgebel of The Splintered Mind introduces the concept of crazyism about some given area of inquiry - the view that something crazy (in a certain sense) must be true about that area. (I think the 'must' here is just epistemic, but I may be wrong.)

Logical Positivism and the Copenhagen Interpretation of Quantum Mechanics - by Aaron Kenna of the Florida Student Philosophy Blog.

Constitution - Kevin Somerville of dthat discusses the relation 'x constitutes y' in connection with the philosophy of mind.

Atheism, agnosticism and theism 2: What it is to have a belief - by John Wilkins of Evolving Thoughts.

Where I am at with Hume's is-ought distinction - by Maryann Spikes of Ichtus77.

The Open Question Argument - Richard Yetter Chappell of Philosophy, et cetera issues a call for objections to a defence of the Open Question Argument. Please try to refute him as soon as possible.

Kevorkian's Legacy And The Right To Die - by David Fryman of The Bennett Commentary.

Paradoxes for "expresses the proposition" - Wolfgang Shwarz of wo's weblog discusses a Liar-related paradox which arises when propositions are treated as sets of possible worlds. Dustin Tucker has made some detailed and learned comments.

Public sector pension reform: my advice to the Prime Minister - thanks to Thom Brooks of The Brooks Blog for giving me the unexpected pleasure of posting a link, on this blog, to an article in which a philosopher gives advice to a head of state. I mean this in the best possible way.

And now for two special sections, exclusive to this edition of the carnival:

Criticisms of Readings of Great Philosophers

Why Kant Was Not A Cognitive Scientist - Matt Whitlock of A Rigid Designator presents a criticism of Andrew Brook's reading of Kant's Critique of Pure Reason.

Nietzsche on Agency and the Will - the mysterious Carlos AKA Narziss criticizes an aspect of Brian Leiter's reading of Nietzsche.

Arguably Inappropriate Submissions

Deconstructing Godel (sic) - I include this post because it's about Goedel. It's essentially a short and maybe slightly dubious biographical sketch. (I don't think Goedel was ever actually part of the Vienna Circle, but someone please correct me if I'm wrong.) I feel bound by duty to inform the prospective reader that the title is a bit misleading; whatever it may mean to deconstruct Goedel, I'm pretty sure it doesn't occur here. Some may say this is for the best.

7 Reasons To Never Lie Again - by Kyle Warren of Follow the FLOW (indeed). I'm pretty sure this isn't meant to be a serious piece of philosophy, but it was submitted, and I include it because it made me laugh several times. It was posted over a year ago, which adds to the arguable inappropriateness.

That's all for this edition of the carnival. The next one is at the Blog of Noah Greenstein on August 8.

Sketch of a Way of Thinking about Modality - Part 1

2011-06-23T02:13:00.000-07:00

[UPDATE: This sketch, except for parts of part 2, will soon be made mostly redundant by a paper I am working on. I expect to make a draft of this paper available in early November. A link will appear here. - TH 13/10/2011]

[UPDATE 2: The paper mentioned above is here.]

This is the first installment of a two-part series of posts where I aim to sketch some ideas about modality which will feature in a book I am working on, Necessity and Conceptual Systems. The material is still very much under development, and I apologize for the obscurities which the reader will inevitably find in it. Comments and criticisms are very welcome.

In this first part, I will introduce the approach, and indicate how it handles the necessary a posteriori, using 'Hesperus is Phosphorus' as a case-study. In part 2 I will discuss the notion of de re modality, of essence, and natural-kind examples such as 'Water is H20', as well as some more general issues which arise on my approach (especially to do with epistemic modality and ascriptions of intentional content).

In the Golden Age of analytic philosophy, necessarily true propositions were widely taken to be those which are satisfied by (or 'come out true' on) all configurations of some conceptual or linguistic system. Possibility was understood in terms of satisfaction by at least one configuration. Our conceptual system, our means of understanding the world, is here thought of as something like a model, or a machine, which has moving parts, and which can be put into various positions or configurations. Each configuration can be thought of as corresponding to, or satisfying, or even being, a set of propositions. (I have taken many liberties in the formulation of this description.)

Conceptual or linguistic systems of the kind in question were thought to be describable with "semantical rules" for a language, and necessary propositions were thus commonly taken to be a priori and true "in virtue of the meaning" of the terms involved (cf. Carnap's Meaning and Necessity, Ayer's Language, Truth and Logic). This yields a notion of necessity reminiscent of the notion of truth-functional tautologousness. (Earlier, in the Tractatus - which was a major inspiration to both Ayer and Carnap - this relationship is much closer than mere reminiscence.)

This sort of view was attacked by Quine in at least two ways (cf. his 'Truth by Convention', 'Two Dogmas of Empiricism'). Quine's undifferentiated picture of language had a sobering or worrying effect, but it did not stop people carrying on with some version of the view in question. This is connected with the fact that it amounted to a kind of quietism or abstinence with respect to the relevant sorts of notions (semantic, modal), rather than a sustained attempt to attain positive insight about them.

The really decisive blow to the Golden Age view of modality came from Kripke. His fundamental contribution was to persuasively argue that the a priori does not coincide with the (metaphysically) necessary, and relatedly, that epistemic modality ("what could be the case") is to be distinguished from metaphysical modality ("what could have been the case" in a certain unrestricted sense). This contribution was closely bound up with Kripke's ideas concerning naming and reference, more on which in a moment. The recognition of the necessary a posteriori in particular, and the associated idea that conceivability doesn't entail possibility, has led to a reaction against views of modality of the Golden Age sort.

(About 'metaphysical modality': one sometimes hears it said of a philosopher that they countenance metaphysical modality, as though this indicates that the person holds some sort of doctrine, which may be quite esoteric. But 'metaphysical modality' is just a label for me - synonymous with 'subjunctive modality' - for a notion "detected" in the logic of language. That said, someone who felt this notion was, e.g., a trivial artifact of the way we happen to talk, rather than a deep artifact of the way we think, would probably not want to use this label.)

My approach to modality retains the view that necessity - metaphysical necessity - can be fruitfully understood in terms of invariance through all configurations of a conceptual system. But it also takes Kripke's separation of the a priori and the metaphysically necessary fully to heart. This latter point is one respect in which my approach differs from that of the two-dimensional semanticists. Another key contrast is that the possible worlds framework is not fundamental to my view.

Broadly speaking, I handle the necessary a posteriori by doing two things. Firstly, I work with a much more fine-grained notion of 'conceptual system' than did the logical empiricists. (The sense of 'fine-grained' here should become clearer in a moment.) Secondly, I embrace a certain kind of semantic externalism - roughly, the view that sense doesn't determine reference (other ways to put this which for me are roughly equivalent: intension doesn't determine extension, concept doesn't determine object).

I will illustrate how this works with respect to a classic example of the necessary a posteriori: 'Hesperus is Phosphorus'.¹

I follow Kripke in holding that proper names do not have reference-determining senses (which hangs together with semantic externalism via Putnam's idea of Twin Earth), and also that proper names do not have a semantics which can be given in the form of general conceptual content such as definite descriptions, or clusters thereof (irrespective of whether this content can be said to determine reference).

I do not, however, accept the (to my mind very strange and confused) idea that proper names are 'mere tags' (Ruth Barcan Marcus's phrase), that all there is to the meaning of a name is its referent, etc. This idea is sometimes associated with Mill's claim that names have no 'connotation', only 'denotation', and also with the phrase 'direct reference'.²

We have individual concepts - concepts of individuals, of particular objects - and we often associate these with proper names. This sheds light on Kripke's rigid designation thesis (the thesis that a referring proper name designates the same object in all possible worlds at which that object exists). If names are associated with individual concepts - concepts of particular objects - then it is immediate that they will designate the same object in all possible worlds where that object exists; designating another object is out of the question, since we are holding fixed the associated individual concept. We may thus distinguish rigid designators such as ordinary proper names, which designate rigidly because they are directly associated with individual concepts, from other rigid designators such as definite descriptions in mathematics.

Once we recognize individual concepts in this way, we can say that when someone accepts that Hesperus is Phosphorus (having previously taken them to be distinct), there is a change in their conceptual system - in the relevant fine-grained sense. Of course, in a more coarse-grained (and more ordinary) sense, we can say that they have before and after the same conceptual system. The fine-grained change consists in the unification of two individual concepts. The original concepts, we might say, are not blended irrevocably but remain as aspect-concepts united under a common master. From now on, it should be kept in mind that conceptual systems will usually be individuated here in this fine-grained sense.

In the former conceptual system (call this 'the Babylonian system'), where the Hesperus-concept is separated from the Phosphorus-concept, the distinctness of Hesperus and Phosphorus is invariant through all configurations of the system; if one positively believes that Hesperus and Phosphorus are distinct, one will say that, although it might conceivably turn out that Hesperus is Phosphorus after all, given that it isn't, Hesperus could not have been Phosphorus. (And one will of course be wrong.) In the latter conceptual system (call this 'our system'), where the Hesperus- and Phosphorus-concepts are unified, the identity of Hesperus and Phosphorus is invariant through all configurations of the system; when one knows that Hesperus is Phosphorus, one will say that, although it might conceivably turn out that Hesperus is distinct from Phosphorus after all, given that it isn't, Hesperus could not have been other than Phosphorus.

Now, with our fine-grained understanding of conceptual systems in place, I maintain that we can still say that all (metaphysically) necessarily true propositions are satisfied by all configurations of their host conceptual systems. We can even say that a truth is metaphysically necessary iff it is satisfied by all configurations of its host system. We just can't say that all propositions which are satisfied by all configuration of their host systems are necessary truths. So far, then, we can say what distinguishes necessary from contingent truths, but we can't say what distinguishes necessary truths from other proposition which are satisfied by all configurations of their host systems - we might call these 'false propositions of necessary character'. What can we say that will do this?

I think we can say something like: a proposition P is necessarily true iff it is satisfied by all configurations of its host system and the concepts involved in P are jointly adequate to their objects with respect to P.

First I want to say that I am not concerned to provide a reductive analysis of modal concepts. Relatedly, I am happy for the relevant modal notions and my ternary relation of 'adequacy' to be explanatory of each other; I do not suppose it is a one-way street, where my notion does all the explaining, nor do I take my notion to be more "fundamental" in any metaphysical sense. I am interested in showing (and making) connections.

I will make a start at explicating the above proposal by indicating how it applies to the 'Hesperus is Phosphorus' case. In the Babylonian system, the Hesperus-concept and the Phosphorus-concept are not unified (are taken to represent distinct objects), but they both have the same object, the same extension, and so together (jointly) they are inadequate to their objects with respect to 'Hesperus is not Phosphorus'. So their proposition 'Hesperus is not Phosphorus' fulfills the first condition given above, before the 'and' - it is satisfied by all configurations of their system - but it does not fulfill the second. Our Hesperus- and Phosphorus-concepts, which also have the same extension, are in contrast united, as aspect-concepts, under a common master concept (the concept of Venus). Hence they are adequate to their objects - or object - with respect to our proposition 'Hesperus is Phosphorus'.

Why do I not simply say that a proposition is necessarily true iff it is satisfied by all configurations of its host system and its concepts are jointly adequate to their objects? Why do I add 'with respect to that proposition'? I will explain this with an example. Assume for the sake of argument that Hesperus (Venus) is necessarily not intelligent - i.e. that Hesperus could not have been intelligent. Now, suppose someone believes that Hesperus is intelligent, and necessarily so - loosely speaking, that it is part of their concept of Hesperus that it is intelligent. In that case, their concept of Hesperus would not be adequate to its object with respect to 'Hesperus is intelligent'. But they may know, for all that, that Hesperus is Phosphorus, and so their concepts of Hesperus and Phosphorus might be jointly adequate to their object with respect to 'Hesperus is Phosphorus'.

Conversely, someone may know that Hesperus is necessarily not intelligent, while mistakenly believing that Hesperus is not Phosphorus, thus having an adequate conceptual situation with respect to propositions about the intelligence of Hesperus, but not with respect to propositions about the identity of Hesperus and Phosphorus.

Speaking broadly, necessity is, on this understanding, not simply a matter of a proposition having a certain status in a conceptual system. It is, as well as that, a matter of the system being adequate to its objects with respect to that proposition. The adequacy of some set of concepts to their objects obviously depends on the identity (and nature) of those objects - and this is not in general determined by the system. (This is how semantic externalism fits in.) Hence you cannot, in general, tell simply by looking at a proposition in a system whether or not it is necessarily true - there are a posteriori necessities.

The compatibility of externalism with rigid designation
(Postscript added 14 August, 2011.)

It may look as though there is a tension between my externalist claim that the extension of an individual concept is not in general determined by the concept itself, and the claim that names rigidly designate: if names are tied to individual concepts, and individual concepts do not in general determine their extension, it looks like a given individual concept can have different extensions in different environments. This is so (at least, when we individuate concepts internally) but there is no real tension here: the rigidity applies to names in use - names tied to token individual concepts embedded in an environment. Individual concepts are not like general concepts: the whole point of them is to apply to one particular object. And so the contrast between names and definite descriptions remains: when we consider counterfactual scenarios and hold the meaning of our terms fixed, our names which are tied to individual concepts always refer to 'the same object'.

This is all perfectly compatible with the fact that the same concept, in a different environment, might be connected up to a different object. The extension of our individual concepts may in some cases even change over time: if an object we know is replaced with a substitute, and we don't notice, after a while it will become true to say that our individual concept has changed its extension. But we don't let the extension change "across possible worlds" when representing counterfactual scenarios using a particular individual concept in a particular environment.

Part 2.

Individual concepts are under-discussed in contemporary philosophy. For further online reading on what they can do, see:

- My post at Philosophy, et cetera, 'An advertisement for individual concepts'

- A recent article by linguist Barbara Abbott, 'Support for Individual Concepts'.

- John McCarthy's article, 'First Order Theories of Individual Concepts and Propositions'. (Warning: arguably contains some use-mention confusion.)

Interestingly, neither of these authors are (primarily) philosophers.

1 I pass over one well-known issue here, to do with the fact that Hesperus/Phosphorus might not have existed. There is a discussion of this on Greg Frost-Arnold's blog. If one is really worried about this, consider instead the example 'If Hesperus exists, then Hesperus is Phosphorus'.

2 It should be noted, however, that Mill's claim is appropriate if 'connotation' is interpreted to mean 'reference-determining sense' or 'general conceptual content', and likewise that the phrase 'direct reference' is appropriate if 'direct' is interpreted to mean 'not via general conceptual content' or 'not via reference-determining sense'.

Three True Semantic Externalisms

2011-05-22T23:11:00.000-07:00

Putnam's catchphrase 'Meanings ain't in the head', and the associated label 'semantic externalism', are not without ambiguity, as many authors have pointed out. My aim here is not to separate and discuss everything which 'semantic externalism' could reasonably mean, or even everything it has meant to philosophers, but rather to identify three different true and insightful things it can mean. I believe that having all three insights, and having them separate, can pay big dividends in the philosophies of language and modality, but I won't try to make a case for that here.

We can look at language and thought on three levels:

1. Local marks and noises, local neural and sensory events.
2. Sense; game and moves; conceptual system and configuration; intension; internal content.
3. Reference; extension; external content in abstraction from internal.

We can individuate thoughts and propositions according to 2 alone, 3 alone, or 2 and 3 together. For example, on 2 alone, 'I am here' is the same proposition when you an I utter it, or when I utter it in different locations - we are making the same sort of move in the same sort of language-game. On 3 alone, 'I am here' expresses the same proposition as 'John is at location X' when the former is uttered by John at location X - extension (reference) is the same. On 2 and 3 together, 'I am here' is distinct when uttered by different people and at different locations, due to difference in extension, and also distinct from 'John is at location X' when both are uttered by John at X, due to conceptual difference (difference in sense, intension, language-game).

To take another kind of example, on 2 alone, 'Hesperus is Phosphorus' is distinct from 'Hesperus is Phosphorus', but identical to the Twin Earthian thought or proposition 'Hesperus is Phosphorus' - call this thought or proposition 'Twin-"Hesperus is Phosphorus"'. On 3 alone, 'Hesperus is Phosphorus' expresses the same proposition as 'Hesperus is Hesperus', but not the same proposition as any thought about Twin Venus. On 2 and 3 together, 'Hesperus is Phosphorus' is distinct from 'Hesperus is Hesperus' (due to difference with respect to 2), as well as from Twin-'Hesperus is Phosphorus' (due to difference with respect to 3) and from Twin-'Hesperus is Hesperus' (due to difference with respect to both 2 and 3).

The three semantic externalisms which I want to identify and separate can all be seen as underdetermination theses. They are:

Wittgenstein externalism: 1 doesn't determine 2 (i.e. local happenings don't determine intension).
Intension-based Putnam externalism: 2 doesn't determine 3 (i.e. intension doesn't determine extension).
Happenings-based Putnam externalism: 1 doesn't determine 3 (i.e. local happenings don't determine extension).

Note that the first two externalisms don't imply the third - while the relation of determining is arguably transitive, the relation of not determining isn't. Note also that 'determine' here means 'always determine' or 'generally determine' - determination in some cases is not being ruled out. I should also say that I attach no great importance to the labels used here for the three externalisms.

Finally, note that the expression 'internal content' above is not supposed to express the problematic notion of narrow content. Narrow content is often thought of as a kind of minimal intension, sense or internal content which is determined by happenings inside an agent's brain or body. That problematic notion isn't being discussed here.

I am currently working on a book on modality, in which this separation plays a key role.

Tristan Haze

Suggested reading

For Wittgenstein externalism: Wittgenstein's Philosophical Investigations. Also his Zettel, and other later work.

For the Putnam externalisms: Putnam's classic 1975 paper 'The meaning of 'meaning', published in Minnesota Studies in the Philosophy of Science 7:131-193, reprinted in The Twin Earth Chronicles: Twenty Years of Reflection on Hilary Putnam's ``the Meaning of `Meaning' '' edited by Andrew Pessin & Sanford Goldberg, 1996, published by M. E. Sharpe.

Breckenridge and Magidor on Arbitrary Reference: An apparent counterexample

2011-04-29T01:35:00.000-07:00

NB: This is a draft of a discussion note which is being considered for publication.

In an interesting paper forthcoming in Phil. Studies, Breckenridge and Magidor argue for this thesis:

Arbitrary Reference (AR): It is possible to fix the reference of an expression arbitrarily. When we do so, the expression receives its ordinary kind of semantic-value, though we do not and cannot know which value in particular it receives.

Their primary argument in favour of AR is that it can be used to give an attractive account of 'instantial reasoning' such as this (their 'Argument 1'):

(1) There is someone x such that for every person y, x loves y [Premise]
(2) Let John be such a person
(3) For every person y, John loves y [Existential Instantiation on 1]
(4) Let Jane be an arbitrary person
(5) John loves Jane [Universal Instantiation on 3]
(6) There is some person x such that x loves Jane [Existential Generalisation on 5]
(7) But since Jane was an arbitrary person, for every person y there is some person x such that x loves y [Universal Generalisation on 6]

I will not attempt to rehearse, or even summarize, their arguments, since they state them well and their paper is freely available on Magidor's website. My purpose here is to give an apparent counterexample to the claim that AR can be used to give an attractive account of instantial reasoning.

The following appears to be a logical truth:

(Unref) If (all unreferred-to objects are white and there is an unreferred-to object), then there is a white object.

(By 'unreferred-to object', I mean an object which is never referred to by anyone or anything.) Here is a quasi-formal argument for (Unref):

(1) All unreferred-to objects are white and there is some unreferred-to object. [Assumption]
(2) All unreferred-to objects are white. [Conjunction Elimination on 1]
(3) There is some unreferred-to object. [Conjunction Elimination on 1]
(4) Let O be such an object.
(5) O is white. [Universal Instantiation on 2]
(6) There is some white object [Existential Generalization on 5]

(Unref) now follows from (1) - (6) by conditional proof.

This seems to be a valid argument. But the theory of instantial reasoning advanced by Breckenridge and Magidor seems to imply that the expression 'O' above refers to an unreferred-to object, which is absurd.

Tristan Haze
The University of Sydney

Reference
Breckenridge, Wylie & Magidor, Ofra (forthcoming). 'Arbitrary reference'. Philosophical Studies.

There is a post about this paper on Ross Cameron's blog here.

On the Interpretation of the Propositional Calculus

2011-04-19T21:54:00.000-07:00

I've just posted another (more recent) longer article on my homepage, On the Interpretation of the Propositional Calculus. The next post will be a short article, I promise.

Comments are welcome. Here is the abstract:

The question considered is 'How can formulae of the propositional calculus be brought into a representational relation with the world?'. Four approaches are discussed: (1) the denotational approach, on which formulae are taken to denote objects, (2) the abbreviational approach, on which formulae and connectives are taken to abbreviate natural-language expressions, (3) the truth-conditional approach, on which truth-conditions are stipulated for formulae, and (4) the modelling approach, on which formulae, together with either valuation- or proof-theory, are regarded as an abstract structure capable of bearing (via stipulation) a representational relation to the world.

The modelling approach is developed here for the first time. The simple technical apparatus used for this is then applied to two issues in the philosophy of logic. (1) I demonstrate a corollary or converse to Carnap's result that certain 'non-normal' valuation-functions can be added to the set of admissible valuations of formulae without destroying the soundness and completeness of standard proof-theories. This sheds considerable light on a recent thread of the inferentialism debate which involves dialectical use of Carnap's result. (2) I show how the approach can be extended to quantification theory, by defining a model-theoretic notion of validity equivalent to the usual one, but making use of a proof-theoretic apparatus in place of the device of assigning values to formulae. This sheds light on the close relationship between proof- and valuation-theory.

On Identity Statements

2011-04-17T06:17:00.000-07:00

I've just posted a longer article on my homepage, On Identity Statements: Against the ascriptional views.

Apart from minor revisions, it is about 18 months old now. I would not write it in the same way now, but I still hold the views expressed there. Comments welcome, here or by email (my email address is on my homepage and on the 'About/contribute' page here).

Comment on Brogaard and Salerno's 'Counterfactuals and Context'

2011-04-07T21:54:00.000-07:00

NB: This is a draft of a discussion note which is being considered for publication.

It is quite commonly believed by contemporary logicians that contraposition, strengthening the antecedent and hypothetical syllogism fail for counterfactuals. In their (2008), Brogaard and Salerno argue that the putative counterexamples to these principles are actually no threat, on the grounds that they involve a certain kind of illicit contextual shift.

Here I suggest that this particular kind of contextual shift, if it is properly so called, is not generally illicit, and therefore the counterexamples cannot be blocked with the kind of blanket restriction Brogaard and Salerno appear to advocate. This sort of restriction, I suggest, ought to be made at the level of particular inference rules.

Brogaard and Salerno conduct their discussion within the framework of the standard Lewisian account of counterfactuals, which says that

a subjunctive of the form ‘if A had been the case, B would have been

the case’ is true at a world w iff B is true at all the A-worlds closest (or

most relevantly similar) to w.¹

They introduce the term 'background facts', by which they mean to designate 'the respects in which A-worlds are relevantly similar to w'. Thus every counterfactual, once understood on the standard theory, is attached to a set of background facts. Now, the central claim of their article is that 'the set of contextually determined background facts must remain fixed when evaluating an argument involving subjunctives for validity'. One set of background facts per argument. Let us call this the Brogaard-Salerno Stricture. Brogaard and Salerno say that to break this stricture is to commit an illicit contextual shift, and since the putative counterexamples to contraposition etc. break the stricture, they should not be accepted.

For an argument to comply with Brogaard-Salerno Stricture, all counterfactuals occurring within it have to be alike in background facts. What I wish to point out is that this condition is plainly unsatisfied by a great many arguments, including the following:

If Mary hadn't had breakfast, she would have lunched sooner.

If John had worn black shoes, he would have worn black socks.

Therefore, if Mary hadn't had breakfast, she would have lunched sooner, and if John had worn black shoes, he would have worn black socks.

For the first premise, one of the background facts might be that Mary has a normal appetite. Another might be that she does not like to go hungry. These are plainly irrelevant to the second premise, i.e. these are plainly not background facts for the second premise. Conversely, John's sense of style has nothing to do with the first. We cannot stipulate that these premises are attached to the same set of background facts without doing obvious violence to their meaning. These two premises, if they are to be understood the way they are meant to be understood, cannot figure in the same argument without breaking the Brogaard-Salerno Stricture. But the above argument is obviously valid. Therefore the stricture is not generally appropriate. I suggest that a better course would be to restrict particular rules - starting with contraposition, strengthening the antecedent and hypothetical syllogism - in respect of background facts pertaining to counterfactual evaluation, rather than deductive argumentation in general. Other rules may be fair game too. In this connection, consider this passage:

But suppose we are wrong about this. Suppose shifting context mid-inference is no fallacy at all. Then a rather surprising consequence follows. Modus ponens - which many possible world accountants love and cherish - fails too. (2008, p. 44).

On my suggestion, the evidence for the claim of the last sentence might motivate the view that modus ponens needs to be restricted too - but still, not all deductive argumentation. Conjunction introduction, for example, is prima facie OK without such a strong restriction.

Tristan Haze

The University of Sydney

References

Brogaard, B. and Salerno, J. 2008. Counterfactuals and context. Analysis 68.1: 39–46.

Lewis, D. 1973. Counterfactuals. Oxford: Blackwell.

1 This is the formulation used by Brogaard and Salerno. It is adapted from Lewis (1973).

A Note on Hofweber's Distinction between Internal and External Quantification

2011-03-16T17:07:00.000-07:00

ABSTRACT: Thomas Hofweber's distinction between internal and external quantification is crucial to the solution he offers to his now well-known puzzle about ontology. Here I argue that this distinction is not well motivated by the considerations he employs.

In a series of interesting papers (2000, 2005b, 2007), Thomas Hofweber has identified a puzzle about ontology and developed a novel solution. Briefly, the puzzle is that questions such as 'Do numbers exist?' seem trivial from one point of view, but highly contentious from another. On the one hand, it is obvious that, e.g., there are even numbers smaller than 6. It follows trivially from this obvious statement that there are numbers. On the other hand, it is hotly disputed among philosophers whether or not there are numbers. Hofweber himself denies their existence. Nonetheless, he agrees that, e.g., there are even numbers smaller than 6.

Hofweber's solution to this puzzle crucially involves a distinction between two kinds of quantification which he calls 'internal' and 'external'. External quantification is familiar; externally quantified statements impose conditions on a domain of objects. Hofweber plausibly argues (2000, 2005b) that we must also recognize a kind of quantification which does not impose such conditions. His strategy is to highlight a certain 'inferential role' which quantifiers play in natural language, which enables them to function as place-holders for incomplete information; suppose we knew that Fred admires Thomas Edison, but then forgot this, remembering only that there is someone Fred admires. Hofweber argues that 'this situation is completely general', and that 'the only instances of the quantifier might be things that don't exist'.¹

With this distinction between internal and external quantification on board, Hofweber's solution to the puzzle about ontology is that the "trivial arguments" to the existence of contentious entities are indeed trivially valid, on the proviso that the quantifiers in their conclusions are given an internal reading. Questions about what there is, where 'what there is' is construed externally, thus remain as a non-trivial subject matter for ontology.

My object here is to show that the distinction Hofweber intends to make is not what it may appear to be at first glance, and furthermore that it cannot in fact be motivated solely by means of the considerations (indicated above) which he employs.

Let us begin with the question: why can't external quantification play the role of facilitating the expression of incomplete information? From the considerations offered, it seems that the only reason is that, as Hofweber says, the only instances of the quantifier might be things that don't exist. Thus we might think of internal quantifiers as characterised by the fact of ranging over both merely intentional objects and not-merely-intentional objects, in contrast to external quantifiers, which range over not-merely-intentional objects only. (I will call this 'the simple intentional-permissive understanding' of internal quantification.) This, however, is not how Hofweber conceives the distinction.

This becomes clear once we look at his views about arithmetical discourse with the distinction between the merely intentional and the not-merely-intentional in mind.² You can look for a prime between 24 and 28, and thus be looking for something. However, you will not find one: in this sense, there is no such thing. Hofweber fully recognizes this distinction, while nonetheless believing all quantification in arithmetic to be internal. Thus Hofweber's distinction between internal and external quantification cannot be understood in terms of the pre-existing distinction between the intentional and the not-merely-intentional. And yet this pre-existing distinction seems a natural and sufficient basis for a notion of quantification fit to play the inferential role Hofweber identifies. Therefore his consideration of this role is not by itself a good motivation for his internal-external distinction.

Note carefully that this argument does not require that the simple intentional-permissive understanding of internal quantification be a suitable basis for a solution to the puzzle about ontology. Furthermore, it does not rule out Hofweber's using the puzzle itself as a motivation for a special reading of quantification. The point is that he has not succeeded in establishing an independent motivation for such a reading.

It might be objected that I have not made an adequate case for the possibility of the simple intentional-permissive understanding of internal quantification. But I am not seeking to establish this conclusively; only, given that Hofweber has identified an inferential role which calls for a non-external reading of the quantifiers, the simple intentional-permissive conception is prima facie a better candidate than one based on Hofweber's internal-external distinction (considered apart from any puzzle about ontology). It may seem as though I'm not being quite fair, since I haven't really made his distinction clear in its own right. But I have no idea how to do this. Hofweber wants a reading of quantification such that the following comes out true:

There is an x such that x is not a merely intentional object, and x does not exist (in the external sense).

It has not been made sufficiently clear that such a reading is available.

Finally, one might wonder how Hofweber's internalism about arithmetical discourse avoids trivializing arithmetic. For on this conception, so-called "existence statements" about merely intentional objects (e.g. the largest prime) can easily come out true. Hofweber handles this with a supplementary doctrine to the effect that quantification in arithmetic is generally restricted to statements which have instances containing number words or numerals ('one', '46', etc.). However, and as Hofweber himself acknowledges, this sort of account cannot be extended to the reals, since we do not have number words for all of them.³ This gives rise to the worry that whatever the truth is about our quantification over the reals, it may also account for our quantification over natural numbers in arithmetic, rendering internalism about arithmetic theoretically superfluous.

Tristan Haze

The University of Sydney

References

Hofweber, T. 2000. 'Quantification and Non-Existent Objects', in Empty Names, Fiction and the Puzzles of Non-Existence, eds. Everett, A. and Hofweber, T. CSLI Publications.

Hofweber, T. 2005a. 'Number Determiners, Numbers, and Arithmetic', The Philosophical Review 114:2.

Hofweber, T. 2005b. 'A Puzzle about Ontology', Nôus 39:2.

Hofweber, T. 2007. 'Innocent Statements and their Metaphysically Loaded Counterparts', Philosophers' Imprint 7:1, <www.philosophersimprint.org/007001/>.

These papers are available on Hofweber's homepage: http://web.mac.com/hofweber/Thomas_Hofwebers_homepage/Papers.html

1 (2000), p 16.

2 These views are indicated in his (2005a).

3 Thanks to Thomas Hofweber for helpful correspondence on this and related points.

A Liar Paradox of Material Implication

2011-02-24T01:38:00.000-08:00

Here I present a new objection to the material or "hook" analysis of indicative conditionals - the thesis that an indicative conditional 'If A then C' has the truth-conditions of the so-called material conditional - based on Liar-like reasoning. This objection seems invulnerable to any Grice-Lewis-Jackson-inspired pragmatic rejoinder.

(1) If (1) is true, (1) is false.

Let us call (1)'s antecedent 'A', and its consequent 'C'. I propose that the following sentence is intuitively true, or true based on intuitive and unproblematic reasoning:

(S) On the assumption that (1) is neither true nor false, A and C are false.

The reasoning is: Assume that (1) is neither true nor false. Then A is false, since it says that (1) is true, and C is false since it says that (1) is false.

If we accept the hook analysis, however, this reasoning is not secure. For if A and C are false, and the hook analysis is right, then (1) must be true. But if (1) is true, then A must be true (since it says that (1) is true), and C must be false (since it says that (1) is false). But then, by the hook analysis, (1) must be false, since it has true antecedent and false consequent. But if (1) is false, then A must be false since it says that (1) is true, but then by the hook analysis (1) must be true. But then...

The point is, the hook analysis treats (1) as a truth-functional compound, and this places it squarely in the Liar family, making our straightforward argument to (S) veer into paradox. Yet (S), and our argument for it, seem clearly correct. Therefore we should reject the hook analysis.

There are already plenty of intuitions around which seem to cast doubt on the hook analysis. This one has more bite, I submit, since it cannot be explained away with the customary sorts of pragmatic story. Take a case like 'If I die tonight, I will be alive tomorrow'. The typical proponent of the hook analysis will maintain that, given that I will not die tonight, this sentence is true but not assertable, since I should assert something stronger,¹ or something robust with respect to the antecedent,² etc. But (S) is an example of an intuitively true sentence which comes out as paradoxical (i.e. leads to paradox) if we apply the hook analysis to (1). It is hard to see how any Grice-Lewis-Jackson-inspired pragmatic story could account for our asserting, or treating as true, sentences which are "really" paradoxical.

That's the objection. While not exceedingly complicated, it is quite easy to misunderstand, so I shall conclude with a few clarifications. Firstly, the argument is not: when we apply the hook analysis to (1) we get Liar-like paradox, and since Liar-like paradox is undesirable, we should reject the hook analysis for (1). It is irrelevant to my objection whether Liar-like paradox is good, bad or indifferent. It is also irrelevant whether there is (or could be) a solution to these paradoxes. The point is simply that, intuitively, we do not get into Liar-like paradox with (1) and (S), and so the hook analysis seems to deliver the wrong answer on this point. For a truth-functional analysis of English conjunctions, on the other hand, generation of Liar-like paradox would be the intuitively right answer for certain sentences (e.g. 'This sentence is false and this sentence is false').

Secondly, I put (S) in the form 'On the assumption that X, Y', because if I had used the conditional form, the objection would have become messy through having to avoid begging the question against the hook analysis.

Finally, I am not maintaining that (1) is in no way paradoxical. It is paradoxical. To illustrate:

Suppose (1) is true. Then by (1) and modus ponens, it is false. Therefore, by conditional proof, if (1) is true then it is false. But that is just what (1) says, so it is true, but then by modus ponens (this time not within the scope of any assumption), it is false. Paradox.

What should be said about this and similar arguments, I regard as an open problem. Some thoughts: rejecting unrestricted conditional proof seems like a promising avenue, since several authors have done this for independent reasons.³ However, it is hard to shake the feeling that if (1) is true, it is false. Perhaps the object of this feeling could be accounted for as a 'Mackie conditional' or 'telescoped argument',⁴ and thus kept semantically distinguished from (1) read as an ordinary conditional. But if these telescoped arguments turn out to be truth-apt in some sense, and to sustain modus ponens, we would seem to be back where we started.

In sum, (1) does not appear to be a (full) member of the Liar family. An important difference can be expressed thus: while there are arguments involving the assumption that (1) is true which lead to paradox (and not just within the scope of the assumption), the bare assumptions that (1) false, or that it is neither true nor false, do not intuitively yield any such arguments (as they do with Liar-like sentences). Hence, we can and should accept (S) as straightforwardly true. And this means rejecting the hook analysis.

Tristan Haze

The University of Sydney

References

Beall and Murzi. draft. 'Two flavours of curry paradox'.

[draft available on the authors' websites, where it is listed as under review]

Bennett, Jonathan. 2003. A Philosophical Guide to Conditionals. Clarendon Press, Oxford.

Grice, Herbert Paul. 1975. ‘Logic and Conversation’, in The Logic of Grammar, D. Davidson and G. Harman (eds.), Encino, California, Dickenson, pp. 64-75. Reprinted in Grice (1989).

Jackson, Frank. 1979. 'On assertion and indicative conditionals.' in The Philosophical Review 88, 565-589.

King, Peter. 2004. "Peter Abelard" in The Stanford Encyclopedia of Philosophy (Fall 2008 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/fall2008/entries/abelard/>.

Lewis, David. 1976. 'Probabilities of conditionals and conditional probabilities.' in Philosophical Review, 85(3):297–315. Reprinted with Postscript in Philosophical

Papers, Volume II, pp. 133-152.

Mackie, J.L. 1962. ‘Counterfactuals and causal laws’, in R.J. Butler, (ed.), Analytical Philosophy, 1st series, Blackwell.

Thomason, Richmond H. 1970. 'A Fitch-style formulation of conditional logic' in Logique et Analyse, 52:397–412.

1 cf. Grice (1975), Lewis (1976).

2 cf. Jackson (1979).

3 According to King (2004), Abelard rejected something like conditional proof. More recently, cf. Thomason (1970), Bennett (2003), and Beall and Murzi (draft).

4 cf. Mackie (1962).

Welcome!

2011-02-24T00:54:00.000-08:00

Here, until further notice, I will occasionally post short and often critical articles on various topics in philosophy, mainly the philosophies of logic and language. For now (at least) these will be written by me, but anyone who wishes to contribute can email an article to tristanhaze at <the domain-name of Google's email service> dot com, and I will consider it. (Needless to say, this is not a peer-reviewed journal.)

My name is Tristan Grøtvedt Haze, and I am a PhD student at The University of Sydney.