Thursday 19 December 2013

Sidelle and the Contingency of Conventions: An Objection Regained

This is a draft of a paper.

Alan Sidelle's conventionalism about modality is well-known, and only a bit less of a whipping-boy than the earlier positivistic views of Ayer (1936) and Carnap (1947). Published in his 1989 book Necessity, Essence and Individuation: A Defense of Conventionalism, it focuses on the problem of explaining the existence of the necessary a posteriori from a metaphysical standpoint according to which (in Sidelle's phrase) we, and not the world, are the source of modality. (I think this isn't very clear, but I don't want to press that here.)

I will not give a proper exposition of Sidelle's account here. I will just say that the basic idea is that a modal claim such as 'Necessarily, water is H20' follows from the a posteriori claim 'Water is H20' together with an a priori claim, such as 'If water is H20, then necessarily, water is H20'. The idea is that the a priori claim is somehow a matter of convention.

There are many problems with such a view – see Yablo's incisive (1992) review for a start. For example, can the a priori claim really be said to be a matter of convention? How doesn't this fall prey to the following argument?: it may be that what sentences mean is conventional, but we can't make the propositions they mean true by convention, except for the special case of propositions about conventions. (Yablo calls this the Lewy point, citing Lewy (1976). See also Quine (1936).) And even if this is somehow surmounted, aren't we still in the dark about what necessity is? (While Sidelle's aims, when stated carefully, do not seem to include saying what necessity is, some of his more impressionistic rhetoric does seem to try to say something about that. In any case, his account leaving us in the dark about the nature of necessity, if it does, is something worth taking due note of, since it is commonly taken to be addressing that issue.)

Here I will discuss another central objection (or type of objection) – that from the contingency of conventions. Or rather, Sidelle's recent response to it; in a 2009 paper called 'Conventionalism and the Contingency of Conventions', Sidelle defends his conventionlism about modality from this sort of objection. He carefully distinguishes two objections here, one focusing on truth-making, the other on necessity-making:

  1. Truth-making version. If conventions were different, certain necessary truths would not be true. This seems to follow from conventionalism, catching it in a contradiction – since what it is to be a necessary truth is not failing to be true in any circumstances.
  2. Necessity-making version. If conventions were different, certain necessary truths may have been contingent. This seems to follow from conventionalism, but seems wrong.

Sidelle argues (convincingly, in my view) that (1) is wrong – the conventionalist isn't committed to that. (I refer readers to his paper for this.)

Sidelle acknowledges (2) to be more serious, and devotes his paper to responding to it. Here, I will argue that his response to (2) fails at an early step, for use-mention reasons.

Sidelle considers but rejects one possible avenue of response, a partly bullet-biting response which says: OK, so this shows that, at least sometimes, what is necessarily so may not have been necessarily so (and also that, at least sometimes, what is contingently so may not have been contingently so). Such truths, then, are contingently necessary and contingently contingent, respectively. This is tantamount to rejecting the characteristic axiom of S4 – that what is necessary is necessarily necessary.

Sidelle will not have this. It is simply too implausible that the S4 axiom fails for metaphysical modality. Indeed, there is reason to think that the appropriate system is S5 (since an unrestricted accessibility relation seems appropriate), which is stronger than S4. Furthermore, he says, conventionalists, in his opinion, ought to try to “save the modal phenomena” and not be highly revisionary.

He also has an argument to the effect that even biting this bullet wouldn't suffice, but I do not understand that argument (I think because it involves certain confusions bound up with Sidelle's form of conventionalism, but I won't try to go into that here).

Sidelle's strategy with (2) is to consider an example – that of 'bachelor', and what would be the case if our conventions governing it were different – and try to show that, if we are careful to stick to the proper mode of evaluating counterfactuals, namely where we keep our conventions, and the meanings of our terms, intact, we can see that the relevant (2)-like counterfactuals are not true.

Sidelle supposes for the sake of argument that our conventions make it that 'bachelor' applies to unmarried but eligible men, and not women, and then considers an alternative situation in which the conventions differed so that unmarried, eligible women fell in the extension of 'bachelor':

With such a convention, we would call unmarried Linda ‘a bachelor’, and so, ‘necessarily, bachelors are male’ would be false. However, how should we describe this situation? Is Linda a female bachelor? Of course not—someone counts as a bachelor only if they are male. Our rules for applying ‘bachelor’ tell us that one must be (give or take) ‘a never-been-married, but eligible male’ [footnote 14]—so ipso facto, the rules tell us that what rules the speakers in that world use is quite irrelevant to whether or not someone is a bachelor. They are no more relevant than the rules of Spanish if we are, in English, describing a situation in Mexico. And of course, this is perfectly general. Notice that this has nothing at all to do with Conventionalism—it is what anyone should believe about evaluating counterfactuals, when those counterfactuals contain words governed by certain semantic conventions—and of course, one doesn’t need to be a Conventionalist to believe there are at least some, or even many, such conventions. [footnote 15] And as the conventions in that situation are irrelevant to the truth of ‘Linda is a female bachelor’, so are they to the question of the necessity of bachelors’ being male there, and so, to whether our necessary truth is itself necessarily so (i.e. to whether or not it is necessarily necessary that bachelors are male). Thus, if the conventionalist story is correct, it will not be true that ‘had our conventions been different, what is necessary would (could) have been false’, or not necessary.

The first part of this quote is an unexceptionable rehearsal of how to evaluate counterfactuals dealing with situations where the meanings of words differ: don't get confused into using the words with those different meanings in describing the situation: it isn't the case that, if 'tail' meant 'leg', dogs would have four tails – although 'Dogs have four tails' would be true in such a situation, ceteris paribus. So while 'Dogs have four tails' would, in that situation, say something true, it does not actually say something true of that situation, i.e. about what happens in that situation.

Similarly with the sentence 'Linda is a female bachelor' – it would say something true in the situation in question, but it isn't – given what it actually means – actually true of that situation.

So far, so good. The trouble is in the last two sentences, when Sidelle tries to conclude from his unexceptionable rehearsal that it's not the case that, if our conventions were different, which propositions are necessary might be different. The last sentence just gives the conclusion. The whole argument, really, is in the second last sentence, so we will concentrate on that. Here it is again, with two words capitalized by me: 

And as the conventions in that situation are irrelevant to the truth of ‘Linda is a female bachelor’, so are they to the question of the necessity of bachelors’ being male there, AND SO, to whether our necessary truth is itself necessarily so (i.e. to whether or not it is necessarily necessary that bachelors are male).

Firstly, there is an ambiguity in Sidelle's phrase 'the truth of “Linda is a female bachelor”'. The conventions in that situation are obviously not irrelevant to the truth, in that situation, of the sentence 'Linda is a female bachelor'. But it is true that they are irrelevant to whether or not that sentence is actually true of the situation: it isn't of course, because there can't be female bachelors in any possible situation. So we can accept this and move on to see what Sidelle is likening it to.

The way Sidelle has put the point, it is not easy to see what the similarity is. The conventions in that situation are irrelevant to the truth of some sentence here, and similarly, to the necessity of bachelors being male there? The points would seem more similar if Sidelle semantically descended for the first bit: just as the conventions in that situation are irrelevant to whether Linda is a female bachelor in that situation, so too are they irrelevant to whether the bachelors are necessarily male there.

In any case, the point can be accepted: bachelors are necessarily male, in all situations. So in a situation where the conventions were different, any bachelors would still need to be male.

But, and this is the crucial point, in saying this, we are using our language, with our conventions, and describing a counterfactual scenario. Our proposition 'Necessarily, all the bachelors are male' is true of that situation. Call the situation S – our more explicit proposition 'Necessarily, all the bachelors are male in S' is true. And you can substitute for 'S' the name of any possible situation.

To ask of that situation, of S, whether the bachelors are necessarily male there, is palpably not to ask whether the proposition that bachelors are male – the proposition now, or whatever thing bears modal statuses, not just the sentence – is necessarily true in that situation. That question just hasn't been raised.

And this is why 'AND SO' is capitalized – it is spurious. It just doesn't follow from all the bachelors in situation S necessarily being male – that's us describing the scenario from here, remember – that the proposition that bachelors are male is necessarily true in that situation – and so you can't conclude from it that some proposition of ours which is necessarily true is necessarily necessarily true. Of course, such a conclusion is itself plausible, but that doesn't mean Sidelle – a conventionalist about the modal statuses of propositions – is entitled to it! And his argument only gets there by means of a subtle, illicit use-mention shift.

Having established to his satisfaction that he is not committed to what is necessary varying with convention, Sidelle then faces the task of explaining why the following plausible constraint on explanation fails in this instance: if A explains B, it can't be that no change in B would ever come about if A changed.

I think there are serious problems with his attempt, and I hope to make this clear in future. My purpose here has just been to show that the previous step, which led Sidelle to having to face this question about explanation, is fallacious. Sidelle has slid from mention to use in the consequents of the counter-conventional, counterfactual conditionals at issue: he can agree with everyone else that, if conventions had been different, any bachelors would still necessarily be male, but this is not the same as being able to agree that, if conventions had been different, the proposition that any bachelors are male would still be necessary. His argument from common knowledge about how to evaluate counterfactuals does not succeed in earning him the right to the latter, only the former. We can conclude from this alone that Sidelle has not adequately responded to the (necessity-making focused) objection from the contingency of conventions. 


Ayer, A.J. (1936). Language, Truth and Logic. London, V. Gollancz, Ltd.

Carnap, Rudolf (1947). Meaning and Necessity. University of Chicago Press.

Lewy, Casimir (1976). Meaning and Modality. Cambridge University Press.

Quine, W.V. (1936). Truth by Convention. In The Ways of Paradox and Other Essays.

Sidelle, Alan (2009). Conventionalism and the contingency of conventions. Noûs 43 (2):224-241.

Sidelle, Alan (1989). Necessity, Essence, and Individuation: A Defense of Conventionalism. Cornell University Press.

 Yablo, Stephen (1992). "Review of Alan Sidelle, Necessity, Essence and Individuation." Philosophical Review 101: 878-81.

Wednesday 13 November 2013

Names: Between Mill and Frege

Followup posts: 

(Added October 2016: my most up-to-date treatment of names can be found in Chapter 6 of my PhD thesis. This is an early, undeveloped attempt.)

Kripke at the beginning of 'Vacuous Names and Fictional Entities':
One of the main concerns of my previous work (Kripke 1980) [Naming and Necessity] is the semantics of proper names and natural kind terms. A classical view which Putnam mentioned, advocated by Mill, states that proper names have as their function simply to refer; they have denotation but not connotation. The alternative view, which until fairly recently has dominated the field, has been that of Frege and Russell. They hold that ordinary names have connotation in a very strong sense: a proper name such as ‘Napoleon’ simply means the man having most of the properties we commonly attribute to Napoleon, such as being Emperor of the French, losing at Waterloo, and the like. Of course, intermediate views might be suggested, and perhaps have been suggested.
My aim here is to propose just such an intermediate view. In future posts I will flesh out the proposal and offer some speculations about why it has not been generally adopted already.

As is well known, the cardinal problem with Millianism about names is Frege's Puzzle, given in his famous article 'On Sense and Reference': Millianism leaves us unable to semantically distinguish, in a systematic compositional way, 'Hesperus is Phosphorus' from 'Hesperus is Hesperus'; since Hesperus is Phosphorus, both names involved in those propositions have the same referent, and thus, on the Millian view, the same meaning. But the two propositions do not seem to have the same meaning - the first is an empirical scientific discovery, and the second is not. Further problems arise with singular negative existentials like 'Santa does not exist' - here, in addition to Frege's-Puzzle-type problems of differentiation ('Santa doesn't exist' and 'Noddy doesn't exist' mean different things, even though both names are the same as regards their referents; neither has one), we have the problem of seeing how any of them could be true, or even mean anything.

As is also well known, the cardinal problems for descriptivism - what Kripke above calls the view of Frege and Russell - are given by Kripke in Naming and Necessity. I will not try to summarize Kripke's whole case properly, but it is often divided into three prongs: the semantic objection, the epistemological objection, and the modal objection. Very roughly, the semantic objection is 'Which description or descriptions constitute the meaning of some given name? Isn't any answer bound to be arbitrary? And since different people might associate different descriptions with the same name and the same object, how aren't they just talking past each other when they use the name?'. The epistemological objection is 'Take any plausible meaning-giving description or cluster thereof. I can surely use the name in question correctly without knowing all this - I don't have to know much of anything about someone in order to pick them out with a name'. And the modal objection is 'Suppose "Aristotle" means "the teacher of Alexander". How does it come about, then, that "Had things gone differently, Aristotle might not have been the teacher of Alexander" seems true, while "Had things gone differently, Aristotle might not have been Aristotle" seems false?'.

I am not concerned here to argue that no versions of Millianism or descriptivism have legs. I will not, for example, argue against Millianisms which try to fill the apparent semantic gap in their accounts by means of linguistic pragmatics, nor will I argue against "wide-scope" or "actualizing" versions of descriptivism. I want to propose what I think is an elegant and natural view in between Millianism and descriptivism which avoids the problems of both.

I have two ways of expressing what I take to be essentially the same view, but others may prefer to think of me as offering a disjunction of two structurally similar views. The first is in terms of the use of a name, or the role it plays in the system of language to which it belongs. The second is in terms of individual concepts - the ideas of particular objects which we (sometimes) tie names to. I more-or-less identify these things in my own thinking, but since the concepts 'use' and 'role' on the one hand, and 'concept' and 'idea' on the other are quite different (as are the uses or roles of these terms!), it is worth giving both formulations, in case someone prefers one over the other. The use-conception is inspired, at least in part, by Wittgenstein (particularly the middle period, for example Philosophical Grammar). The concept/idea-conception is more traditional.

The view, then, is that names have uses, or are tied to individual concepts, and that these are partly constitutive of their semantics. (We may say that uses, or individual conepts, constitute the internal meanings of names.)

Individual concepts or name-uses do some of the work Frege wanted to do with his senses, but there are important differences. One important difference is that Frege held, of his senses, that they determine reference, whereas individual concepts or name-uses avowedly do not do this in general; someone on Twin Earth can use a name in the same pattern (i.e. with the same concept or use), but with a different referent - in a word, semantic externalism is true of individual concepts or name-uses. (We can of course have a notion which adds an extensional component to the individuation of these things, so that two concepts or uses are distinct if they have different objects, or different projective relations to reality, but we can also isolate the internal component.)

Another important difference is that, while Frege indicates that the sense of a name is that of, or can be given by means of, a definite description, I hold no such thing with respect to individual concepts or name-uses. Names are in an important sense indefinable, as Wittgenstein held in the Tractatus. But that does not mean their referents are all there is to (what you might, though possibly misleadingly, call) their meanings, i.e. Millianism doesn't follow. (Wittgenstein expresses Millianism too in the Tractatus, when speaking of 'names', although there is an exegetical question whether this term is meant to cover ordinary proper names, which is what I am talking about, or names in some philosophically idealized sense, e.g. names in an "ideal logical language".)

Individual concepts or name-uses combine, in a very simple way, the difference-making power of Frege's senses with invulnerability to Kripke's arguments against descriptivism. 

Frege's Puzzle is solved, much in the same way as Frege did with his senses: 'Hesperus is Phosphorus' and 'Hesperus is Hesperus' are different propositions with different meanings, since 'Hesperus' and 'Phosphorus' are tied to different individual concepts and have different uses. (Likewise with 'Clark Kent' and 'Superman'.)

But unlike with Frege's senses, this conception of names is not only compatible with Kripke's rigid designation thesis, but predicts it, at least when formulated in terms of individual concepts: 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 meaning of the proper name - the associated individual concept.

Individual concepts or name-uses also allow for an important kind of flexibility, which we must recognize in order to solve Kripke's puzzle about belief. We can individuate name-uses and individual concepts - as well as the uses or meanings of other terms, and other concepts, and larger units such as propositions - at different granularities, so that what at one granularity might count as instances of different uses/concepts may count on another (coarser) granularity as instances of the same. This is an important ingredient of my view, and will be discussed in a future post.

I have now at least mentioned all the main ingredients of the view of names I want to propose. Further posts - on semantic granularity, on internal and external meaning, and on why the view I propose hasn't already been generally adopted - will fill out the picture. I will conclude this post by trying to avert a couple of possible misunderstandings:

(1) The term 'individual concept' is sometimes used in philosophical logic and technical philosophy of language to refer to functions from possible worlds or state-descriptions to individuals (or similar constructions). I am not using it that way. For one thing, that way of going would make the problem of empty names harder - i.e., it would reduce the utility of my approach with respect to the problem of empty names - since one needs individuals for the functions to map to. For me the notion of an individual concept is more basic - it is just a refined version of the ordinary idea of an idea of an object.

(2) I am not saying that any sort of theory which associates names not with name-uses or individual concepts (in my sense), but with something else, and calls the associates 'the semantic values' of the names, is wrong. My attitude here is that expressed by Chalmers in this passage from 'The Foundations of Two-Dimensional Semantics':
A methodological note: in this paper I will adopt the approach of semantic pluralism, according to which expressions can be associated with semantic values in many different ways. Expression types and expression tokens can be associated (via different semantic relations) with extensions, various different sorts of intensions, and with many other entities (structured propositions, conventionally implied contents, and so on). On this approach, there is no claim that any given semantic value exhausts the meaning of an expression, and I will not claim that the semantic values that I focus on are exhaustive. (I think that such claims are almost always implausible.)

Chalmers, David J. (2006). The foundations of two-dimensional semantics. In Manuel Garcia-Carpintero & Josep Macia (eds.), Two-Dimensional Semantics: Foundations and Applications. Oxford University Press.

Frege, Gottlob. (1952). first pub. 1893. ‘On Sense and Reference’, in P. Geach and M. Black (eds.) Translations from the Philosophical Writings of Gottlob Frege, Oxford: Blackwell.

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

Kripke, Saul A. (2011). Vacuous Names and Fictional Entities. In Saul A. Kripke (ed.), Philosophical Troubles. Collected Papers Vol I. Oxford University Press.

Wittgenstein, Ludwig. (1922). Tractatus Logico-Philosophicus. Dover Publications.

Wittgenstein, Ludwig. (1974). Philosophical Grammar. Blackwell.

Monday 21 October 2013

Formal Logic Isn't a General Science of Validity

'Tell me how you are searching, and I will tell you what you are searching for.' - Wittgenstein.


A curious feature of the philosophical landscape is that the most fundamental and influential discussions of several key issues in the philosophy of formal logic occur, in large part, in introductory logic textbooks. There's something Wild-West-ish and exciting about this, even if it stems partly from regrettable neglect of these issues. While proficient philosophically-trained logic teachers all impart a certain core of technical understanding, they differ greatly on what they tell their students formal logic is all about.

Here I want to give an argument for a thesis in the philosophy of formal logic:

(NGV) Formal logic is not aptly regarded as having, among its aims, that of giving a general account of validity.

This argument, if any good, should be of considerable interest, since the view which (NGV) denies – call it (GV) – is widely held, and plays a large role in our collective understanding of the nature of formal logic. I will use as a foil N.J.J. Smith's 2012 textbook Logic: The Laws of Truth, which endorses (GV).

My argument in compressed form is as follows: there are glaring lacunae in formal logic construed as a general account of validity; if that were one of its aims, it would be blatantly neglecting certain basic phenomena which it is meant to account for. But no one with any close relationship to formal logic cares, and we cannot put this down to laziness or stupidity. Therefore, it is inappropriate to construe formal logic as having a general account of validity among its aims. 

What I Mean by 'Formal Logic' and 'Validity' 

Before explaining the argument further with an example, a brief word about what I mean by 'formal logic' and 'validity'. 'Formal logic' means the formal, mathematized discipline of logic – syntax, formal semantics, proof-theory. Observations about the validity of natural language arguments, even if validity can be aptly conceived as turning on the form of propositions, are not themselves bits of formal logic, on this usage. By 'validity' I mean the thing which gets explicated sometimes as 'necessary truth preservation in virtue of form', or 'necessary truth-preservation in virtue of the meanings of logical (or subject-matter neutral) vocabulary', but also in other ways. A key point is that the valid inferences are a subset of the deductive (in a common sense of 'deductive'). We may deduce 'There is a vehicle' from 'There is a car', but this is not a valid inference in the relevant sense, since it turns on 'vehicle' and 'car'. 'There is a car, therefore there is a car or a vehicle', on the other hand, is valid. We say that the conclusion of a valid argument is a logical consequence of the premises. (Often what I am calling 'validity' here gets called 'logical validity', or even 'narrowly logical validity'. This may not be a bad practise, but here I follow the logicians who use 'validity' in this already-narrow way.)

There are different ways of spelling out what validity consists in. 'Valid' may also be a vague or indeterminate predicate (if, for example, the form/content distinction or the distinction between logical and non-logical vocabulary is vague or indeterminate), but that doesn't matter.

This should suffice to identify the relevant basic intuitive idea of validity, an idea which plays a major role in thinking about logic. It is not our purpose here to investigate the notion of validity, or the nature of validity, any further. We just needed to get it clear enough for the purpose of giving the argument for (NGV).


Here is a clear expression of a conception involving (GV) - the view that formal logic is aptly regarded as having, among its aims, that of giving a general account of validity - in The Laws of Truth (pp.20-21, Chapter 1: Propositions and Arguments):

When it comes to validity, then, we now have two goals on the table. One is to find a precise analysis of validity. (Thus far we have given only a rough, guiding idea of what validity is: NTP [necessary truth-preservation - TH] guaranteed by form. As we noted, this does not amount to a precise analysis.) The other is to find a method of assessing arguments for validity that is both
1. foolproof: it can be followed in a straightforward, routine way, without recourse to intuition or imagination—and it always gives the right answer;
2. general: it can be applied to any argument.
Note that there will be an intimate connection between the role of form in the definition of validity (an argument is valid if it is NTP by virtue of its form) and the goal of finding a method of assessing arguments for validity that can be applied to any argument, no matter what its subject matter. It is the fact that validity can be assessed on the basis of form, in abstraction from the specific content of the propositions involved in an argument (i.e., the specific claims made about the world—what ways, exactly, the propositions that make up the argument are representing the world to be), that will bring this goal within reach.

One of the philosophically most important sections of the book is 14.4, 'Expressive Power', where four kinds of propositions are discussed which may seem to create difficulties for first-order logic with identity (FOL=) construed as a general account of validity (what follows is summary and paraphrase, not quotation):

(1) 2 + 2 = 4. (Translatable into FOL=, but the result is considerably more complex, and this may make us hope for something more elegant.)

(2) She will see the doctor but she hasn't yet. (Quantification over times is required to translate this adequately into FOL=, and, like with (1), we might hope for something else. And there is something else: tense logic.)

(3) Propositions involving vague predicates. (FOL= requires predicates to have definite extensions. But there is fuzzy set theory and other formal tools which could deal with these.)

(4) 'There are finitely many Fs'. (Can't be expressed in FOL=, but there are extensions in which it can be.)


Note carefully that Smith is not claiming that classical first-order logic is enough for a general account of validity. He admits, for example, that it cannot adequately represent propositions of type (4). But none of this casts any real doubt on (GV).

I want to bring a different kind of example into the mix. It will perhaps seem a bit boring or basic, but that's actually what makes it philosophically important.

Example: From 'Only' to 'All' 

Consider this argument:

Only horses gallop, therefore all gallopers are horses.

This is at least as non-trivial as 'A and B, therefore A', which formal logic deigns to capture.


I think this is, in a way, a more philosophically instructive sort of "problem for classical logic", in that it doesn't seem like much of a problem, and this gives us a way of seeing that (NGV). The argument isn't "fancy", it doesn't seem to make us want new systems, and the problem-propositions involved are translatable in a loose sense with no worries at all. But there is no way of capturing the inference in first-order logic. You either wind up with the premise the same as the conclusion, or a premise which differs from the conclusion (e.g. by using existential quantification), but no more similar to the natural language premise than the formal conclusion is, and so not capturing the original inference at all. 

This translatability in a loose sense is important. Since we can quite easily see that only Xs Y if and only if all Y'ers are X's, we just translate 'only' propositions using ordinary first-order quantifiers. But the logical insight we needed for that was at least as real and non-trivial as that which we need to see that 'A and B' implies 'A'.

We must ask the logician: if you're bothering to codify things like 'A and B, therefore A', and you're quite generally interested in the validity of arguments in natural and other languages, why are you so content to leave 'Only horses gallop, therefore all gallopers are horses' unaccounted for by your science?

The fact that we are so content shows (GV) to be misleading, indeed false. In doing formal logic, we are actually doing something quite different from: trying to construct a general account of validity.

It seems like what we are really doing is something more like: developing artificial languages fulfilling certain desiderata, arguments in which can be easily inspected for validity. (Quine, regimentation.) Or perhaps, getting a sense of what validity turns on, without trying to give a general account. (Realistically, it's probably both of these plus many others, right down to aesthetic or even social motivations.) At least, if we were doing either of those things, our formal neglect of the Only-to-All argument would be quite intelligible.

Again: if we're so keen on a general accoubt of validity, how can we be so ready to not care about having no formal account of 'Only Xs Y, therefore all Y'ers are Xs'? Because it is so trivial? That can't be right, since things we do try to capture are no less trivial. No, there is no way out - the fact that we don't care shows that we really aren't so keen on a general formal theory of validity. That idea doesn't capture the real life of formal logic.

We might tell ourselves we want a general account of validity, but then when we're underway, we think 'Why bother formalizing "only", when we've already formalized "all" and can use that?' - the fact that we take that attitude gives the lie to the idea that we're really after a general account of validity.

We sense that it would be fairly uninstructive to formalize 'only' once we've got 'all' etc. - we should let that help guide our thinking about what we're really doing when we do formal logic (hence the Wittgenstein quote at the beginning).

That is my argument for (NGV) and against (GV).

Other Kinds of Examples
The above example may be resisted on the grounds that 'only' has been studied from within Montague semantics, and perhaps from other perspectives. My reply to that, in the first instance, is that these contributions were not generally thought of as part of formal logic, nor have they come to be incorporated into it. I think that's the right reply, but it isn't entirely satisfying - it might seem overly legalistic and trusting in the status quo. Fortunately, other examples are to hand.

What other kinds of examples are there, besides the Only-to-All argument, which show the same thing? A couple more I have thought of are:

- 'All men are mortal, therefore everything is such that its being a man materially implies its being mortal', or 'There are men, therefore there is something which is a man'. That is, arguments which take us from basic natural quantifier-constructions to something of the quantifier-variable form. These arguments embody logical insights due to the inventors of quantification theory (such as Frege and Peirce), and yet it seems we don't care about giving formal accounts of the arguments themselves.

- Arguments involving truth-functional compounds where the premise is written in some non-standard notation (such as: Venn diagrams, Gardner-Landini shuttle diagrams, Wittgensteinian ab-notation, truth-tables construed as propositional signs), and the conclusion is written with regular connectives (or vice versa).

These two kinds of examples differ from the Only-to-All argument in involving technically-formed propositions, whereas 'All gallopers are horses' and 'Only horses gallop' are forms that come naturally to us.

Wednesday 9 October 2013

Philosophers' Carnival #156

Welcome to the 156th edition of the Philosophers' Carnival! It's exactly one year since I took over organizing duties from Richard Chappell, so I have chosen to host this month.

Below the Carnival proper you will find a Metacarnival covering the last twelve months' editions (procrastinators beware: a large amount of absorbing content lies only 1 to 2 clicks away).

- Are basic moral principles empirically falsifiable? - by David Sobel at PEA Soup

- The Nature of Desire: A Liberal, Dispositional Approach - by Eric Schwitzgebel at The Splintered Mind.

- The Space of Languages - by Jeffrey Ketland at M-Phi

- A Problem for Hume's Problem of Induction - by Jason Zarri at Philosophical Pontifications.

- Respect for Truth in Science and the Humanities - by David Maier at 3QuarksDaily.

- Pretend Numbers - by Richard Brown at One More Brown.

- Alief and Knowledge from Fiction - by Allan Hazlett guesting at Aesthetics for Birds

- Seven Puzzles of Pictorial Content - by Gabriel Greenberg guesting at Aesthetics for Birds.

- Theistic frequentism and evolution - by Alexander Pruss at Prosblogion.

- Testimony and Moral Understanding - by Richard Chappell at Philosophy et cetera.

- Pets, Livestock, and Narrative Value - by David Killoren guesting at Philosophy et cetera

- Against countable additivity - by Wolfgang Schwarz at wo's weblog.

- The Libet experiment as a refutation of dualism - by Bill Skaggs, a neuroscientist guesting at Brains

- Relativism about Epistemic Modals: Some Experimental Data - by Joshua Knobe and Seth Yalcin at Certain Doubts.

- A voting puzzle, some political science, and a nerd failure mode - by Chris Hallquist at Lesswrong.

- On the Limitations of Philosophical Writing, or What is Wisdom? - by Eric Schliesser at NewAPPS

- Why is it easier to get crap published? The Stanley Hypothesis - by Jon Cogburn at NewAPPS.

- Skolemizing Laws - by Robbie at Metaphysical Values.

- The Truth-Tracking Account of Knowledge: Two New Counterexamples - by Tristan Haze (me) here.

The next edition will be hosted next month at FsOpHo, a blog about logic and epistemology. Submit here.


#155: Blogging the End - Septermber 10, 2013.
#154: Nick Byrd's Blog - August 10, 2013
#153: Philosophy on Philosophy - July 10, 2013
#152: Siris - June 10, 2013
#151: Camels With Hammers - May 10, 2013             
#150: The Splintered Mind - April 10, 2013
#149: - March 10, 2013
#148: In Search of Logic - February 10, 2013
#147: Philosophy and Polity - January 10, 2013
#146: Talking Philosophy - December 10, 2012
#145: Philosophical Pontifications - November 10, 2012
#144: Sprachlogik - October 10, 2012

Thursday 26 September 2013

The Truth-Tracking Account of Knowledge: Two New Counterexamples

In recent years Nozick's notion of knowledge as tracking truth has witnessed a revival. - Horacio Arló-Costa, 2006.

[This is a draft of a paper.] [Added 3/9/15: The paper is forthcoming in Logos & Episteme.]

Here I present two counterexamples to the truth-tracking account of knowledge. As far as I have been able to tell, they are new.

The simple version of Nozick's famous (1981) truth-tracking account runs as follows:
S knows that p iff
1. p is true
2. S believes that p
3. If p weren’t true, S wouldn’t believe that p

4. If p were true, S would believe that p
Counterexample 1: I have a deep-seated, counterfactually robust delusional belief that my neighbour is a divine oracle. He is actually a very reliable and truthful tax-lawyer. There is a point about tax law he has always wanted to tell me, p. One day, he tells me that p, and I believe him, because I believe he is a divine oracle. I would never believe him if I knew he was a lawyer, being very distrustful of lawyers.

In this case, it seems to me, I do not know that p: my belief rests on a delusion, albeit a counterfactually robust one. But it is true, I believe it, and my belief tracks the truth: if it were true, I would have believed it, and if it were false, I would not have believed it. (The lawyer, being reliable and truthful about tax law, would not have told me that p if p were not the case.)

Counterexample 2: My neighbour is a tax lawyer. Here, unlike in the previous counterexample, I have no delusional belief. It is my neighbour who is the strange one: for years, he has intently nurtured an eccentric plan to get me to believe the truth about whether p, where p is a true proposition of tax law, along with five false propositions about tax law. His intention to do this is very counterfactually robust. He moves in next door and slowly wins my trust. One day, he begins to regale me with points of tax law. He asserts six propositions: p and five false ones. I believe them all.

It seems to me that I do not know that p in this case either. But I believe it, it is true, and my belief tracks the truth: if p were the case, I would have believed it, and if p were not the case, I would not have believed it (remember, the tax lawyer has long been anxious that I believe the truth about whether p).

These counterexamples carry over to Nozick's more complicated method-relativized version of the account (since there is only one method in question in each case). That version runs as follows:

S knows, via method (or way of knowing) M, that p iff
1. p is true
2. S believes, via method M, that p
3. If p weren’t true, and S were to use M to arrive at a belief whether (or not) p, then S wouldn’t believe, via M, that p
4. If p were true, and S were to use M to arrive at a belief whether (or not) p, S
would believe, via M, that p.

The final account of knowing is then: 
S knows that p iff there is a method M such that (a) she knows that p via M, her belief via M that p satisfies conditions 1 – 4, and (b) all other methods via which she believes that p which do not satisfy 1 – 4 are outweighed by M.
(Formulation taken from Matthew Nudds, 'Truth Tracking' (handout).)
They also carry over to the recent account of Briggs and Nolan (2012), which replaces counterfactuals with dispositions. (Their account was designed to deal with cases where the truth-tracking account undergenerates. Here, it overgenerates.)

Furthermore, they are unaffected by a recent defence of the truth-tracking account, due to Adams and Clarke (2005), against already-known putative counterexamples; these ones seem importantly different, and nothing Adams and Clarke say carries over to them, at least in any way I have been able to discern.

Thanks to John Turri, Fred Adams and Murray Clarke for helpful correspondence.


Adams, F. & Clarke, M. (2005). Resurrecting the tracking theories. Australasian Journal of Philosophy. 83 (2):207 – 221.

Briggs, R. & Nolan, D. (2012). Mad, bad and dangerous to know. Analysis. 72 (2):314-316.
Nozick, R. (1981). Philosophical Explanations. Harvard University Press.

Monday 19 August 2013

A Fallacy in Hofweber's Arguments in Ontology

[This is a draft of a paper.]

Hofweber's ontological project crucially involves inferring negative existential statements from statements of non-reference, i.e. statements that say that some term or terms do not refer. Here, after explaining the context of this move, I want to show that it is fallacious, and that this vitiates Hofweber's ontological project.

Thomas Hofweber has for several years been developing a distinctive approach to ontological and metaontological questions.

One of his starting points is the way some ontological questions in philosophy can apparently be settled with trivial arguments - for example, since mathematics has established that there are infinitely many prime numbers, it follows that there are numbers, and so there is no room for a special philosophical discipline of ontology (if it is to respect mathematics) to deal with this as a substantial question, the way ontologists of mathematics seem to try to do. Call this the puzzle about ontology.

Hofweber attempts to solve the puzzle about ontology by independently motivating a distinction between two different readings of quantifiers, or two sorts of quantification: internal and external. Internal quantificational statements, unlike external ones, do not work by placing conditions on a domain of objects. (To see that we might need something like this, consider the quantifier in 'Santa Claus doesn't exist, therefore there is something that doesn't exist'.) He then argues that the trivial arguments go through, but only when the quantifiers are given an internal reading. Give the quantifiers an external reading, and it is not clear that their premises have been established - in the case of 'There are infinitely many prime numbers', for instance, it might be that mathematics has established this on its internal reading, but not on its external reading.

Hofweber doesn't just want to solve the puzzle about ontology with his internal/external distinction, however. He also wants to use it to establish answers to certain (external) ontological questions - negative answers. This is what I call 'Hofweber's ontological project'.

Taking the number case, the project goes roughly like this. Hofweber argues that, if we can establish internalism about number-talk, including arithmetic (i.e. if we can establish that the quantifiers involved in number-talk, including arithmetic, are internal ones which do not place conditions on a domain of objects), we can show that the external question of whether numbers exist is left open by this talk, and is thus free for the taking by ontology.

Next, Hofweber argues that numerals, number words like 'four', and terms like 'the number 2' are not referring terms. I.e., that they are not in the business of referring to things. They sometimes assume the superficial grammatical position of referring terms for sophisticated linguistic reasons involving the notion of a 'focus construction' (and other considerations, depending on the kind of occurrence).

Then, on the basis that number terms don't refer, Hofweber concludes (via a principle designed to enable one to infer non-existence of things from statements of non-reference) that numbers don't exist, i.e. that there are no numbers (the quantifier here being intended externally), thus answering one of ontology's fundamental questions. I will good-naturedly call this last step 'the Howler'.

A couple of years ago, I inconclusively argued that Hofweber's distinction between internal and external quantification is ill-motivated. Here, I want to grant that distinction, and even grant that it enables Hofweber to explain the validity of the trivial arguments.

I want to make it clear that the Howler is a fallacious move, and that this vitiates Hofweber's project for answering certain ontological questions (e.g. about numbers, properties and propositions) in the negative. I will not be concerned here with whether Hofweber succeeds in establishing internalism about number-talk - my point is only that his argument from internalism to negative answers in ontology contains a fallacy.

The Howler appears in Hofweber's contribution to the influential 2009 anthology, Metametaphysics: New Essays on the Foundations of Ontology. The contribution is called 'Ambitious, Yet Modest, Metaphysics'. (I include other relevant papers in the bibliography, to help readers piece together a more detailed view of Hofweber's overall project, but he gives a good sense of it in the paper just mentioned.)

I think my criticism will be most effective if I quote the Howler along with the argument in which it appears, rather than reconstructing it and insisting that that is what Hofweber was doing. Here is the argument:

Let’s briefly reflect on what seems to be a central thesis about reference or denotation: 
(REF) If Fred exists then ‘Fred’ refers to Fred. 
Of course, I am assuming that ‘Fred’ is unambiguous, or at least used in the same way throughout. (REF) is uncontroversial, I take it, and probably a conceptual truth. Note that it implies the following: 
(REF∗) If ‘Fred’ doesn’t refer to Fred then Fred doesn’t exist. 
There are two ways for an expression not to refer. One is to aim to refer, but not to succeed. A classic case of this are empty names. Although the details of any example one might try to give of this are controversial, let’s nonetheless take ‘Sherlock’ to be an empty name of this kind. That is, suppose Sherlock is a name and thus has the semantic function of picking out an object. But it fails in carrying out that function. It thus doesn’t succeed in referring, and thus doesn’t refer. Thus Sherlock does not exist. Nothing in the world is Sherlock, no matter what in general the world contains. There could be all kinds of people, with all kinds of professions, but no matter how general properties are instantiated in the world, nothing in it is Sherlock. And nothing could be. If ‘Sherlock’ does not refer then Sherlock does not exist. This is all fairly trivial, but I go over it to make it vivid for our next case. 
Names aim to refer, but they can fail to succeed in what they aim for. The second way in which an expression might not refer is when it does not even aim to refer. Non-referential expressions, like ‘very’, don’t refer since they don’t even aim to refer. If internalism is correct about talk about numbers, properties, and propositions, then the relevant singular terms are non-referential. They do not aim to refer, and thus they do not refer. According to the above version of internalism ‘two’ is just like ‘most’. But since it doesn’t refer we know that there is no such thing as the number two. Since ‘two’ and ‘the number two’ are non-referring expressions nothing out there is (or can be) the number two. There can be all kinds of objects, abstract or concrete, they can have all kinds of properties and relations to each other. Nonetheless, none of them is (or can be) the number two. Or any of the other numbers. Internalism thus answers the ontological question.

Note first that Hofweber says that '[a]ccording to the above version of internalism "two" is just like "most"'. But what do we get if we substitute 'most' for 'Fred' in Hofweber's (REF*) principle?:

(REF*-Most) If 'most' doesn't refer to most then most doesn't exist.

But this seems like ungrammatical nonsense. Furthermore, it doesn't seem that 'Does most exist?' or 'Is there such a thing as most?' are substantial, sensible questions. It may be argued that 'Does most exist? No.' is not complete gibberish, if it is construed as a kind of metalinguistic point - it's not true to say 'Most exists'. This question-and-answer does not appear to be about whether the domain of our external quantifiers meets certain genuine conditions (and not simply metalinguistic conditions such as 'being referred to by the word "most"').

So if 'two' really is just like 'most' in all relevant respects, Hofweber has a problem. There is, of course, an important difference. Consider:

(REF*-Two) If 'the number two' doesn't refer to the number two then the number two doesn't exist.

Unlike (REF*-Most), (REF*-Two) is superficially grammatical. It even appears not to be nonsense (if we consider it independently of Hofweber's views). Do either of these two differences help?

Superficial grammaticality doesn't help; consider the nonsensical but superficially grammatical question 'Is there a rock of eggs?'. This doesn't seem to turn on whether a domain of objects meets some genuine condition, and 'Is there a rock of eggs? No.', like the 'most' case, seems to be a metalinguistic point at best.

The appearance of sense doesn't help either, for Hofweber has no way of explaining it except in terms of internalism; he explains occurrences of number-expressions always in terms of their being non-referring terms that appear in the syntactic guise of referring terms (for sophisticated linguistic reasons). And it is not at all clear what these could possibly be doing in an external quantificational context.

In general, the point might be captured by the following principle: non-existence of something only follows by semantic descent from non-reference when the non-referring term plays the semantic role of referring. Otherwise you can't semantically descend to a well-formed, sensical proposition.

(This is a necessary condition for the non-existence of something following by semantic descent from non-reference, but it may not be sufficient. I say 'follows by semantic descent' rather than simply 'follows' because '"X" does not refer' may be argued to always imply 'The referent of "X" does not exist' - but there is no semantic descent there, as there is in Hofweber's arguments.)

This seems like the natural view, in lieu of some special story, and Hofweber hasn't given any such story.

In a forthcoming post, I will argue that Hofweber's ontological project is impossible, for a different (though related) reason: internalism at the strength he requires it is inconsistent with the thesis that there is a substantial ontological question about numbers left open by arithmetic and other non-metaphysical number-talk, since such a question would constitute a counterexample to internalism. This mistake is, I think, more profound than the one exposed here - making it involves a kind of sawing-off of the branch one is sitting on.


Main reference: 

Hofweber, T. 2009. 'Ambitious, yet modest, metaphysics', in David John Chalmers, David Manley & Ryan Wasserman (eds.), Metametaphysics: New Essays on the Foundations of Ontology. Oxford University Press.

Background reading for Hofweber's project:

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, <>.

These papers are available on Hofweber's homepage:

Wednesday 31 July 2013

A Problem for the Simple Theory of Counterfactuals

In a recent blog post called 'The Simple Theory of Counterfactuals', Terrance Tomkow argues extensively for a theory of counterfactual conditionals along broadly Lewisian lines, explicitly restricted to counterfactuals with nomologically possible antecedents. The theory, Tomkow says, was first proposed by Jonathan Bennett in 1984, but later abandoned. Lewis held a more complicated theory.

Tomkow argues successfully, in my opinion, against Bennett's reasons (given in his Philosophical Guide to Conditionals) for rejecting his own theory. (Tomkow tells me, in a private communication, that Bennett has agreed with these arguments of Tomkow's, also in a private communication.) There is much else of value in the post as well. However, I cannot agree with Tomkow that the theory as he states it, even with its restriction, is correct.

The Simple Theory, or the Bennett-Tomkow Theory, is this:

A > C iff  C is true at the legal A-worlds that most resemble @ at TA.

('A > C' is a shematization of 'counterfactual statements of the form: If ANTECEDENT had been the case then CONSEQUENT would have been the case.'

'@' denotes the actual world. 'Tp' denotes the time that the proposition 'p' is about. 'Legal' worlds are nomologically possible worlds.

The restriction of the this theory is then given as follows: 'To keep things simple, we will only deal with cases where A is false at @ but nomologically possible.')

Now, before giving the objection which is the main point of the present post, I want to note a simpler but less powerful objection. Some counterfactuals with nomologically possible antecedents are categorical - that is, require that all A-worlds are C-worlds. For example 'If I had met a bachelor this morning, I would have met an unmarried man this morning', in the context of a language-lesson. I argue for this here. The Simple Theory seems to assign the wrong meaning here, since it says that such a counterfactual is true iff C is true at the legal A-worlds that most resemble @ at TA, and these won't be all A-worlds, as intuitively required by the counterfactual. This objection is less powerful than the one I am about to give, because it can be easily avoided by simply restricting the theory to non-categorical counterfactuals.

Now the more powerful objection. This is inspired by my cartoon understanding of the confirmation of relativity, but let's just treat it as a fiction. Einstein asserted a law in paper N which actually holds, and which, together with the facts of some experimental setup E, predicts that some light will bend.

Now, it seems to me we can evaluate counterfactuals where the relevant closest A-worlds are worlds where the law doesn't hold, for example ones with the antecedent '~L' (where L is the law in question). Tomkow seems to agree, saying in a comment that 'we do need an account of counterfactuals with contra-legal anteced[e]nts'. So far, no problem for the Simple Theory.

My idea is that there are counterfactuals whose antecedents are legal, but where the similarity relation is contextually understood in such a way that the closest relevant A-worlds are counter-legal. So, with the following counterfactual:

(H) If Einstein had been wrong in paper N, this light would not have bent.

both what Einstein wrote and the experimental setup may be held fixed during evaluation (i.e. match in these respects required for close similarity), while the actual laws of nature are not held fixed. The antecedent itself is legal, however, since there are legal worlds where Einstein is wrong in paper N, but where he writes something else.

I will now try to make this more precise, and spell the objection out.

For a given counterfactual and contextual understanding of it, call the 'focus set' the set of A-worlds at which C is required, by the counterfactual, to be true. (This of course assumes that a theory with broadly Lewisian/strict-implication outlines is basically right.)

The special property (H) was designed to have is thus: having a legal antecedent, yet being legitimately and naturally understandable such that its focus set contains counter-legal worlds.

If there are counterfactuals with that property, that's a problem for the Simple Theory as stated, since it says that 'A > C iff C is true at the legal [my emphasis] A-worlds that most resemble @ at TA'.

Their having legal antecedents puts them in the scope of the Simple Theory as stated, but the presence of counter-legal worlds in their focus sets (on the relevant understandings of them) conflicts with it.