Williamson's Metaphysical Modal Epistemology and Vacuism about Counterpossibles

Timothy Williamson has argued that our capacity for metaphysical modal judgement comes along with our capacity for counterfactual judgement. This passage gives a flavour of his view:

Humans evolved under no pressure to do philosophy. Presumably, survival and reproduction in the Stone Age depended little on philosophical prowess, dialectical skill being no more effective then than now as a seduction technique and in any case dependent on a hearer already equipped to recognize it. Any cognitive capacity we have for philosophy is a more or less accidental byproduct of other developments. Nor are psychological dispositions that are non-cognitive outside philosophy likely suddenly to become cognitive within it. We should expect cognitive capacities used in philosophy to be cases of general cognitive capacities used in ordinary life, perhaps trained, developed, and systematically applied in various special ways, just as the cognitive capacities that we use in mathematics and natural science are rooted in more primitive cognitive capacities to perceive, imagine, correlate, reason, discuss… In particular, a plausible non-skeptical epistemology of metaphysical modality should subsume our capacity to discriminate metaphysical possibilities from metaphysical impossibilities under more general cognitive capacities used in general life. I will argue that the ordinary cognitive capacity to handle counterfactual carries with it the cognitive capacity to handle metaphysical modality. (Williamson, The Philosophy of Philosophy (2007), p. 136. Found in Section 3 of the SEP article 'The Epistemology of Modality'.)

In order to argue for this, Williamson takes a schematic semantic story about counterfactual conditionals:

Where “A>B” express “If it were that A, it would be that B”, (CC) gives the truth conditions for subjunctive conditionals: A subjunctive conditional “A>C” is true at a possible world w just in case either (i) A is true at no possible world or (ii) some possible world at which both A and C are true is more similar to w than any possible world at which both A and ¬C are true.(Formulation from Sec 3 of the SEP article.)

On the basis of this, he proves the following equivalences:

(NEC) □A if and only if (¬A>⊥)
It is necessary that A if and only if were ¬A true, a contradiction would follow.

(POS) ◊A if and only if ¬(A>⊥)
It is possible that A if and only if it is not the case that were A true, a contradiction would follow.

(Renderings and spellings out from the SEP article. The box and diamond are metaphysical modal operators, and the falsum - which looks like an upside-down 'T' - represents a contradiction.)

But this only works because the schematic theory of counterfactuals Williamson adopts is understood as working against a background of a notion possible worlds, where Williamson understands this as the notion of metaphysically possible worlds. This theory deems true all counterfactuals with metaphysically impossible antecedents, and this is crucial to his demonstation of the equivalences on the basis of his assumed schematic theory.

There are lots of reasons not to adopt a theory of counterfactuals which uses the notion of metaphysical possibility in this way. One reason to move away from a theory like this is if you think that there are counterpossibles - counterfactual conditionals with metaphysically impossible antecedents - which have their truth-values non-vacuously. But you might be agnostic about that. For instance, you might be happy with metaphysical modal distinctions but doubt that there are any clear cases where countepossibles have truth-values non-vacuously. In that case you might see no good reason for the backdrop of worlds or scenarios in a theory of counterfactuals to be exactly the metaphysically possible ones. Or, you might be skeptical about the very distinction between metaphysical possibility and impossibility, in which case you won't want to understand the backdrop in a way that involves that distinction. And it seems that you can get most, or even all, of the theoretical benefits of a Stalnaker-Lewis approach to counterfactuals without using that distinction. It doesn't really seem to play a starring role in the theories. 

If a semantic theory for counterfactuals which does not draw on any bright line between metaphysically possible and metaphysically impossible scenarios is as good or better than the theory that Williamson uses to prove his equivalences, that seriously undermines the equivalences, and in turn Williamson's story about how we get metaphysical modal knowledge.

(And note that this turns on Williamson's understanding his chosen theory so that 'possible world' means 'metaphysically possible world' - even accepting an identically worded theory, but where 'possible world' is understood in a way which does not involve the distinction between metaphysical possibility and impossibility, would make Williamson's equivalences unavailable.)

Modal Realism and Counterpossibles: A Tension in Lewis

David Lewis held that possible worlds are worlds as concrete as our own (cf. Lewis (1986)). He also held, in his work on counterfactuals (cf. Lewis (1973)), that all counterfactuals with impossible antecedents - 'counterpossibles' - are vacuously true. These two views do not fit together well. Embracing modal realism leads to especially compelling counterexamples - counterexamples given modal realism, that is - to the thesis that counterpossibles are all true. These take the form of conditionals whose antecedents are not intuitively impossible, but which are impossible given modal realism.

These arise because, according to modal realism, reality as a whole – that is, the totality of the posited worlds – is necessarily the way it is. Lewis is very upfront about this. Witness:

There is but one totality of worlds; it is not a world; it could not have been different. (Lewis 1986: 80.)

So, for example:

'If there had been two fewer men in reality as a whole than there actually are, there would have been fewer women.'

There is no reason to think this is true. And yet Lewis's thesis about counterpossibles, together with modal realism, implies that it is vacuously true.

Perhaps worse:

'If there had been fewer men in reality as a whole than there actually are, there would have been just as many men in reality as a whole as there actually are.'

This seems positively false.

Postscript

Thanks to Quentin Ruyant for pointing out that the last counterfactual, given modal realism and the thesis that there are infinitely many worlds with men in them, actually seems to come out true in a funny way: if there had been two fewer men, there still would have been infinitely many. So this was a bad example. Consider instead:

'If there had been no Model-T Fords in reality as a whole, there still would have been some Model-T Fords in reality as a whole'.

References

Lewis, David K. (1973). Counterfactuals. Blackwell Publishers.

Lewis, David K. (1986). On the Plurality of Worlds. Blackwell Publishers.

Toward an Account of De Re Modal Ascriptions

This is the third post in a series on de re modality and quantification into modal contexts. This one is quite exploratory and anything but final. The first two posts are here and here.

Let us begin by considering a simple proposal and two problems with it:

a is necessarily F iff 'a is F' is necessary.

The first problem may best be called a potential problem. It affects this approach if the question 'Can propositions which ascribe the same property (or relation) to the same object (or n-tuple of objects) differ in modal status?' is correctly answered in the affirmative.

If propositions can be ascriptionally identical and yet differ in modal status, then while my proposition 'a is F' may be necessary, someone else may have a proposition in another system, let us say using the sign 'b is G' (but of course it may also be the same sign as I use), which is ascriptionally identical but contingent. In such a case, we might not want to say that a, that object, is necessarily F, since some propositions which ascribe the property F'ness to the object a are not necessary – we might want to say, generally that an object fails to be necessarily F if there is any proposition which ascribes F to it and isn't necessary.

This gives rise to various terminological opportunities and options – e.g. we might want to distinguish 'weak' and 'strong' necessity, and may go different ways on questions like 'If something is F, but is not strongly necessarily F, is it contingently F?'. We will come back to this. For now, we will go along with saying that a thing fails to be necessarily F if some proposition says of it that it is F, and that proposition fails to be necessary.

Furthermore, we will go along with the idea, while actually remaining agnostic, that ascriptionally identical propositions can differ in (ICI, and in turn) modal status – that is, we will try to solve this potential problem, without actually deciding for sure that it is a problem.

The second problem, unlike the first (potential) problem, does not threaten the truth or validity of the account, but rather its power. Recall the simple proposal we began with:

a is necessarily F iff 'a is F' is necessary.

The second problem lies with generalizing this: the above, if it is not read as being about some specific proposition, is a schema. And getting a general statement, a universal quantification, about when an object x, say, is necessarily F (or necessarily has some property y), is still a non-trivial task given the above, since the schematic letters occur on the right hand side in a quotational context.

I will now pursue the first problem for a long and tortuous stretch (this will hopefully be instructive). In the end, it will emerge that by solving the second problem in a certain way, we can modify the result so that it solves the first problem (using, for this modification, what we will have learned by that point about the first problem). This solution is, in essentials, the solution we will offer in the next post to the problem of quantifying into modal contexts, although the success conditions there may be a bit different. Therefore in this section, at the end of the long and tortuous stretch, I will just briefly state the solution, and explain how it solves the second problem as well.

Again: the first problem is, roughly, that instances of the simple schema might come out false if, while my proposition 'a is F' is necessary, there are other propositions ascribing F'ness to a which are not.

This naturally suggests the following:

a is necessarily F iff all propositions ascribing F'ness to a are necessary.

One problem with this which is, I think, not hard to surmount, lies with the possibility of non-rigidly designating an object and ascribing a property to it, in the sense of: ascribing that property to whatever falls under the description. I mean, for example, propositions such as:

The number I have written on this piece of paper is odd.

This can certainly be read as a contingently true proposition. Suppose I have '3' written on a piece of paper. Now, we will want to say that the number three, that very object, is necessarily odd. But since I might have written a different number, the above proposition, on the reading I have in mind, is contingent. And yet we might say that this proposition, so construed, satisfies the condition 'is a proposition ascribing F'ness to a'. The solution is to add the condition that the proposition rigidly designates a.

So really, what we want to consider is:

a is necessarily F iff all propositions rigidly designating a and ascribing F'ness to it are necessary.

Another problem is that a proposition may rigidly designate a and ascribe F'ness to it, but also do a bunch of other things, such as designating b and ascribing G'ness to it. And this extra stuff may make them contingent. For example: '3 is odd and this piece of paper has a 3 on it'.

The solution to that problem is to add a “that's all” clause – e.g. to talk about propositions which just rigidly designate a and ascribe F'ness to it, and do nothing else.

These problems, then, are easily solved. In the discussion of more serious difficulties which follows, I will not incorporate these solutions in order to keep things simple.

So, what (besides the two problems we saw how to fix) is wrong with:

a is necessarily F iff all propositions ascribing F'ness to a are necessary?

The problem is: what if there just aren't enough relevant propositions around in the actual world? (Whether this is a problem depends on the view of propositions one takes.)

And that leads to the thought:

a is necessarily F iff all possible propositions ascribing F'ness to a are necessary.

Disambiguation of 'Possible Propositions'

There is an unfortunate ambiguity here in talking about 'possible propositions'. I will not try to fix the terminology, but only explain the ambiguity: this means 'a proposition which can exist'. By contrast, when I speak of a proposition being necessary, I mean being subjunctively necessary, necessarily true in the Kripkean sense. I don't mean a proposition which must exist. A subjunctively possible proposition, then, is one which is true and not necessary – but the talk here of 'possible propositions' does not mean this. Fortunately this ambiguity is, for me, largely confined to these modes of construction, rather than particular constructions, since I hardly ever speak of the property of being subjunctively possible, and I never – except in this note – speak of propositions which must exist: so 'possible proposition' always means 'proposition which can exist', and 'necessary proposition' means 'proposition which is necessarily true'.

The 'All Possible Propositions' Strategy

We were considering the thought: a is necessarily F iff all possible propositions ascribing F'ness to a are necessary

This raises two worries: (i) is there a circularity problem here?, and (ii) what about impossible propositions, or perhaps better: what about objects and properties such that no possible proposition can say of the object that it has the property?

Regarding the first worry, it is not obvious that there is a circularity. Recall that we are not trying to analyze all modal notions in terms of other notions (indeed, the very idea of doing that may, for all that is said in this book, be chimerical) – inherent counterfactual invariance, for instance, is characterized in terms of all counterfactual scenarios a system can produce. Furthermore, the use of 'possible' here doesn't on the face of it seem to be the sort of de re modal attribution we are concerned to analyze. It's not about properties or relations possibly holding of actual things, but about possible things (in this case propositions), things which might exist, and that is very different. Secondly, the modal space in question may best be regarded as broader and more inclusive in certain respects than subjunctive modal space.

Furthermore, even if there is a circularity here (which may be quite indirect and subtle – i.e. may be present even if the 'possible' here is not itself to be regarded as directly invoking subjunctive modality), perhaps it's not a vicious circularity – for instance, we could say that we have still reduced the mysteries of necessary property possession (de re modality) to the mysteries of logical space.

Regarding the second worry, about the possibility of things and states of affairs which no possible proposition can refer to or represent: perhaps this can be overcome by taking 'possible' in a very wide sense.

Accordingly, I think this analysis may not be without value, but these worries create difficulty enough that a somewhat different approach seems desirable.

I think something like the following: intuitively, part of what the truth of a proposition of the form 'a is necessarily F' reflects is an internal connection between a proposition's ascribing F'ness to a and its modal status. One strategy we might try for capturing this is two-pronged: semantically ascend and invoke a priority. As a first pass:

a is necessarily F iff 'All propositions ascribing F'ness to a are necessary' is a priori.

Or equivalently:

a is necessarily F iff 'If a proposition ascribes F'ness to a, it is necessary' is a priori.

But this cannot be quite right, for necessity implies truth, and some necessary propositions are a posteriori. If 'a is F', for example, is just such a necessary a posteriori proposition, then it can't be a priori that if a proposition ascribes F'ness to a, it is necessary. Just like with our main analysis of necessity, i.e. as a category of propositions, we have to separate truthmaking from necessity-making.

This suggests employing, as we did in the main analysis of necessity, the notion of inherent counterfactual invariance:

a is necessarily F iff (a is F and 'All propositions ascribing F'ness to a are inherently counterfactually invariant' is a priori).

This is a definite improvement, but now out analysis falls victim to the same type problem which motivated our holding that necessity is closed under implication. Recall that we can't say:

A proposition is necessary iff it is inherently counterfactually invariant and true.

Since a disjunction of a necessary a posteriori proposition and a contingent proposition, where the necessary disjunct makes it true, is not inherently counterfactually invariant (since if it is held true on the basis of the second disjunct only, it will be allowed to vary across counterfactual scenario descriptions), but this disjunction will be necessary in the case that its necessary disjunct makes it true, so that the above analysis undergenerates: it says that, e.g., 'All cats are animals or I had lunch today' is not necessary, when it is. And recall that this problem is avoided by the account advocated:

A proposition is necessary iff it is, or is implied by, a proposition which is both inherently counterfactually invariant and true.

We get a similar problem with the above analysis of de re modal attribution, but involving disjunctive properties rather than truth-functional, propositional-level disjunction. Consider for example:

'Hesperus is either identical to Phosphorus or a common object of philosophical examples'

Or, to remove any possibility of a truth-functional construal:

'Hesperus has the property of either being identical to Phosphorus or being a common object of philosophical examples'.

(Instead of 'being identical to' I will just say 'being'. I will also abbreviate 'being a common object of philosophical examples' as 'being a comex'.)

Now, according to the rough, dimly seen intuitive meaning of de re modal attributions which we are trying to analyse, it would seem we should say, since Hesperus is Phosphorus and in view of Kripkean considerations:

'Hesperus necessarily has the property of either being Phosphorus or being a comex'.

But this doesn't come out true on the analysis we are now considering. Plugging it in, we get:

Hesperus necessarily has the property of either being Phosphorus or being a comex iff:

- Hesperus has the property of either being Phosphorus of being a comex, and

- 'All propositions ascribing being either Phosphorus or being a comex [or, more strictly uniformly, having the property of being either etc.] to Hesperus are inherently counterfactually invariant' is a priori.

And the second clause fails to be true – far from being true a priori, the proposition mentioned is not true at all, since it is possible to hold it true while disbelieving that Hesperus is Phosphorus but believing that Hesperus is a comex, in which case it would be allowed to vary across counterfactual scenario descriptions (since things could have been such that quite other objects were comexes). Indeed, the mentioned proposition is false a priori.

But if we close under implication, as in our main analysis of necessity:

- 'For all propositions ascribing either being Phosphorus or being a comex to Hesperus, there is some inherently counterfactually invariant proposition which implies that proposition' is a priori.

we get something true, as required. We are making progress, but while both clauses come out true in this case, the analysis will still not give intuitively right results. Now it will overgenerate in some cases. Consider, for example:

Hesperus necessarily has the property of either being Saturn or being a comex.

This is intuitively false, since Hesperus is, intuitively, necessarily not Saturn, and only contingently a comex.

But the following both hold:

- Hesperus has the property of either being Saturn or being a comex, and

- 'For all propositions ascribing the property etc., there is some inherently counterfactually invariant proposition which implies that proposition' is a priori.

The second clause comes out true, because 'Hesperus is Saturn', while false, is inherently counterfactually invariant and does imply 'Hesperus has the property of either being Saturn or a comex'. And presumably, for any other proposition which might also ascribe the property in question to Hesperus, there would be some proposition identifying it with Saturn which implies it.

This would be solved by somehow requiring the (possibly hypothetical) implying propositions to be true as well as ICI, without jeapoardizing a priority. But it is not clear to me how this could be done.

For if we just tack on 'and true' to 'some inherently counterfactually invariant' above, yielding this as a second clause:

- 'For all propositions ascribing the property etc., there is some inherently counterfactually invariant and true proposition which implies that proposition' is a priori.

We are back to our problem of the second clause failing to be true as required for the case of Hesperus necessarily either being Phosphorus or a comex: its not a priori that the implying proposition, 'Hesperus is Phosphorus', is true, even though it is true.

We want our second clause, in general, to say something like: for all propositions P ascribing F'ness to a, there is some true proposition Q such that it is a priori that Q implies P.

But if we say that we have forgone the semantic ascent part of our two-pronged strategy, taking us back to our problems of non-existent and impossible propositions (or things for which there are no possible propositions of the relevant kind).

I find it surprising that it is apparently impossible to solve all these problems at once. I am far from sure that I haven't overlooked a possibility (i.e. an analysis quite close to the last few above, involving the strategy of semantic ascent together with the invocation of a priority, or a similar strategy, but which doesn't face such blatant material adequacy problems).

Be that as it may, there is still a further issue with any account along these lines. And it happens that, by considering this further issue which would still arise and describing that issue in a natural way, a quite different strategy comes into view.

Would Semantically Ascending Achieve Anything, or Just Mask Something?

It may seem that our move from talking about, say, 'all possible propositions' (with all its attendant difficulties) to talking about whether a priority is possessed by a proposition which says that all propositions of a certain kind are a certain way (namely a priori) – even if it could surmount the difficulties found above – would be a silly move, merely complicating things and getting us nowhere.

It might seem that this is so, because the right hand side of the analysis involves mentioning a proposition about the object in question, and so we can only state it when dealing with an object which we can talk about. But note that this doesn't stop it from being the case that all instances of:

a is necessarily F iff <one of our last analyses' RHSs>

are true (although other things were seen to). What this does get us is a way of dealing with any 'a is necessarily F'-form proposition, as it comes a long. We cannot apply it to an object which we cannot speak about – or rather, 'applying it to an object which we cannot speak about' makes no sense here. But given that we have such a proposition, what the analyses were designed to do was avoid any problems pertaining to nonexistent (and perhaps in a sense impossible) propositions: if some of those ascribe (or would ascribe if they existed) F'ness to a and aren't (wouldn't be) necessary, we do not want to say that a is necessarily F.

This shows that the strategy was not totally idiotic. Better than that, the last sentence (especially the clauses in brackets) suggests another approach to the first problem: solve it by first solving the second problem along conditional lines, where the antecedent condition (which very arguably doesn't have to be possible) covers all the cases which might have caused the first problem. (This should become clearer along with the proposal.)

So, we will go back to our original simple schema, and propose a conditional approach to our second problem – the problem of generalizing it. The simple schema was:

a is F iff 'a is F' is necessary.

Now as we saw, if we go along with the first problem, not all instances of this will be true. Let us ignore this for the moment, and consider how we might generalize it along conditional lines. We might say the underlying point of this (faulty) schema is something like:

An object x possesses a property y necessarily iff: if you were to say of x that it possesses the property y, you would say something necessary.

Now, if we interpret this conditional on the right hand side in one way, we get the first problem again, just as we did with the simple, faulty schema. (And that is fitting, for a generalization of the schema.) But if we interpret it in another way (in broadly Lewisian terms, by widening the class of relevant A-worlds), it is no longer a generalization of the schema, and is no longer vulnerable to the first (potential) problem.

I will briefly explain this here, but leave discussion of certain further difficulties of interpretation to the discussion of quantification into modal contexts in the next post, where the approach taken to quantification is very much along the lines of this approach to de re modal attributions. I will first state two basic assumptions about counterfactual conditionals. (Not that they're absolutely required – see below.)

Two Basic Assumptions About Counterfactual Conditionals

I will take as a basic assumption about how counterfactuals work that they can be understood as requiring a set of A-scenarios (scenarios at which the antecedent is true) to all be C-scenarios (scenarios at which the consequent is true). This is not to commit to any particular story (for example, David Lewis's) about how the relevant A-scenarios are determined. It also doesn't commit us to only dealing with possible scenarios, as for example Lewis does. It also doesn't commit us to any particular story about the nature of scenarios.

The second basic assumption is that (and here I agree with Lewis) the relevant set of A-scenarios will not always be the same. And it isn't just that different forms of words induce different relevant sets – the counterfactual conditional in the analysis above, for example, can be intended and interpreted different ways, making different A-scenarios relevant. And in the present philosophical context, we need to explicitly specify and discuss different interpretations (that is, I know of no other way of inducing contexts in which they get the readings I am interested in, and have no reason to think there should be a way).

These assumptions can in principle be jettisoned, by trading in the counterfactual conditional form in the proposed analysis above (and in our special treatment of quantification below) for explicit talk about what 'all relevant scenarios' are like, and then specifying which they are (but this time not as a way of fixing a reading of some conditional). But making the assumptions serves a heuristic purpose, since they are very plausible and the counterfactual conditional form is highly familiar to us.

Two Interpretations of the Words of the Account

Now, recall that the account I propose, in its simplest (but in a sense ambiguous) form, runs:

An object x possesses a property y necessarily iff: if you were to say of x that it possesses the property y, you would say something necessary.

Now, we must ask, about the counterfactual on the right hand side: which A-scenarios (scenarios in which you say of x that it is y) are required to be C-scenarios (scenarios in which you say something necessary) here? Which facts about the actual world are to be held fixed, and which allowed to vary? Or briefly, what is the relevant set of A-scenarios?

The thing to see is that, if we take a “closest worlds” approach, or at least if we take such an approach in a natural and simple way, we will run into the (potential) problem which would stem from ascriptionally identical propositions being able to differ in modal status. If, on the other hand, we take an approach on which a wider set of A-scenarios must be C-scenarios, we may avoid it. (The propriety of doing this without departing from the natural meaning of counterfactuals can I think be defended, but again this is not absolutely essential, since regarding it as a technically modified sort of counterfactual, or going straight for talk about a relevant set of A-scenarios and abandoning the counterfactual form, are both options.)

Suppose, for example, that your proposition 'a is F' is necessary, but that some other proposition, in some other system, which ascribes the same property to the same object, is contingent. In that case, we will (according to the kind of usage I want to go with here) not want to say that a is necessarily F.

Nevertheless, the relevant counterfactual comes out true, if the relevant A-scenarios are to be kept close to the actual world: on this approach, we can say that, indeed, if you were to say of a that it possesses the property F, you would say something necessary – because if you were to do that, you would do it using your proposition 'a is F'!

This is a perfectly legitimate interpretation of that counterfactual, but it is not the one we want. We want to hold less things fixed, and allow more things to vary (which sounds like it amounts to the same thing, but it may not, since we may have to explicitly widen the overall space of scenarios in question, i.e. explicitly allowing impossible scenarios). In this way, for any (actual, possible, or maybe even impossible) proposition which might make trouble for a being necessarily F, by ascribing F to a and not being necessary, will be covered – it will be what you said in some relevant A-scenario – so that the conditional will be falsified as required.

We will return to the question of how to get a better grip on what our relevant sets of A-scenarios for instances of our proposed analysis must be like in the next post in this series, once we have our special interpretation of quantification on the table, since that will raise a similar question.

For now, our account may be regarded as partially but not wholly specified.

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. 

References 

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.

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.

References

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.

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:

THE SIMPLE THEORY
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.