Saturday, 11 April 2015

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:

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 '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:

is necessarily F iff '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 'is F' is necessary, there are other propositions ascribing F'ness to a which are not.

This naturally suggests the following:

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:

is necessarily F iff all propositions rigidly designating 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 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:

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:

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: 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:

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

Or equivalently:

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 '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:

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:

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 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:

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 '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 being necessarily F, by ascribing F to 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.

Tuesday, 17 March 2015

On Kripke's Intuitive Anti-Quinean Defence of De Re Modality

This is the second post in a series on de re modality and quantification into modal contexts. The first is here.

Immediately after the passage quoted at the beginning of the last post where Kripke introduces the problem of de re modality, he goes on to argue that de re subjunctive modal ascriptions, and the notion of necessary and contingent properties, have intuitive content. I will quote this influential passage in full, and make a criticism of it. I will then suggest a weaker argument from analogy which could be given in its stead, and finally indicate my own view on the matter.

Here is the passage:

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

I do not want to be dogmatic about this, but I suspect that there may be a bit of a bait-and-switch going on here. Certainly, it seems everyday and intuitive for someone to point at Nixon and say 'That's the guy who might have lost'. But then what this 'first man' says in response to the 'unintuitive man' (the philosopher), is beginning to sound pretty philosophical itself, albeit sounder. It is true that what he says, especially if you're trained in philosophy, seems intuitively compelling. But I think it's quite arguably out of character for the first man.

One way of making good on this suspicion is to reflect that forms like 'could have' and 'might have' do not just signal talk about counterfactual scenarios and counterfactual possibility. They also commonly find a retrospective epistemic modal use. And it seems to me that this is the most natural way to interpret the everyday, non-philosophical remark of the 'first man' above, 'That's the guy who might have lost'. To say that Nixon might have lost, on this suggestion, means something like: at some former stage, things could have gone either way – it would have been unreasonable then to be convinced that he would win.

This seems to me like a fairly everyday thing to say. The meaning Kripke intends – where what is asserted means something like (ignoring the later Finean distinction between essential and necessary properties): its not part of Nixon's essence that he won the election – seems less so.

We can also argue along Gricean lines that the first interpretation yields something which it might actually be good to say in the sort of conversation about contemporary events Kripke has in mind. But saying this thing about – speaking loosely – Nixon's essence seems pragmatically odd; if you know that, then presumably you know something stronger from which it follows (such as that winning some election can't be an essential property of anyone), rather than making it sound as if there's something special about Nixon here. (Consider an obscure bystander around Nixon's age: it seems, from an unabashedly philosophical point of view now, implausible that it is part of this bystander's essence that he didn't go into politics, get to run for Presidential office in the election in question, and lose. So it seems you could say of that guy too that he might have lost the election, in the sense in which Kripke has in mind.)

So, I find Kripke's story about the first man and the unintuitive, philosophical man unconvincing: if the first man were really not a philosopher, I'm inclined to think that his intuitive-sounding utterance of 'That's the guy who might have lost' is far more plausibly interpreted along epistemic lines. This is somewhat ironic, given Kripke's seminal insistence on carefully distinguishing epistemic modality and a priority on the one hand from subjunctive modality on the other.

We can get a better idea of how it might have happened by recalling the grammatical devices Kripke uses to isolate subjunctive modality: what could be the case for all we know a priori is to be distinguished from what could have been the case (given various things we know, and not always a priori). This may lead to an overconfidence in the subjunctive mood (or whatever you want to call it) as a signal of subjunctive modality proper, a signal of the thing Kripke isolated.

Still, this criticism doesn't imply that there is nothing in what Kripke says in this influential passage. Two things can be gleaned from the passage which do militate in favour of his main conclusion, which is that the notion of necessary and contingent properties makes sense.

One is a kind of argument from analogy: even when you interpret the first man's initial, everyday-sounding utterance along more appropriate, epistemic lines, it is clear that what is under discussion is not a statement: that is, de re epistemic modality makes sense. (For a recent study of that topic cf. Seth Yalcin's work.) And so, putting this consideration together with Kripke's compelling isolation of a concept of necessity applying to propositions which is distinct (intensionally and extensionally) from those of a priority and analyticity, we might naturally expect de re modal constructions where the modality is of this broad sort, having to do with alternative ways the world could have been in some non-epistemic sense, to be possible too.

Another is a direct philosophical appeal to our intelligence: forget guys on the street, forget questions about what they may or may not say without thereby becoming philosophers, and just think about it. What the first man is made to say in response to the unintuitive man, even though it just sounds like Kripke doing philosophy, seems awfully compelling. To quote it again: 'the actual winner, had the course of the campaign been different, might have been the loser, and someone else the winner; or there might have been no election at all. So such terms as "the winner" and "the loser" don't designate the same objects in all possible worlds'.

The situation, as I see it, is something like this: Kripke has clarified and isolated notions of necessity, contingency etc., which in the first instance apply to propositions and perhaps states of affairs. Now, by analogy with other expressions in our language, we are led to consider forms like 'is necessarily F' and 'There is an which is necessarily F' (or 'There is an x such that it is necessary that x is F'), where we have a vague idea that the terms 'necessarily' and 'necessary' here are, in some way, to express this same notion, which we know in the first instance in application to specific propositions. Consider the syntax of quantified modal logic, where modal operators are combined with first-order logic, in advance of any definite understanding of what these formulas are to mean.

Philosophers often behave like little children who scribble some marks on a piece of paper at random and then ask the grown-up "What's that?" — It happened like this: the grown-up had drawn pictures for the child several times and said "this is a man," "this is a house," etc. And then the child makes some marks too and asks: what's this then? C&V 17e

Our problem is, in a way, similar to that of making a game which is like an existing game, but different in some respects – but where the required similarities and differences are not completely spelt out (and how could they be, without thereby completing the task already?). For example, chess for three players, or with no queens.

In the present case, the task draws us in, since we feel we can already make some dim sense of these constructions. The question of whether this can be spelt out clearly, and the spelling out of it should this be possible, is of logico-philosophical interest. Furthermore, the issue is connected in many people's minds with difficult philosophical topics – with Aristotelian essentialism, with metaphysics, and with confused issues to do with whether modality is 'located' or 'grounded' in language and thought, or in other things.

Accordingly, in the next post in this series I will take up the challenge of de re modality, trying to adapt my account of necessity as an attribute of propositions so that it can be applied to de re modality. My main assumption in taking up this challenge is: there must be a connection here, and a tight one (e.g. not something you would have to describe using worlds like 'sometimes' or 'usually'), and we now have to make this clear. This will also take heat off the idea that de re modality makes no sense, but perhaps in a way which might look strange from the point of view of certain ways of thinking about analysis: the right hand sides of my analyses will in many ways be less simple, more problematic and more difficult than the left hand sides, the things to be analysed. But the problems are not the same ones as affect the left hand sides, and that is important. Roughly, I want to show that de re modal talk is not left hanging by itself, when we have a notion of necessity which applies to propositions. It may in a sense be more intelligible left as it is than when analysed along the lines I propose. But we must distinguish between the first-order intelligibility of a linguistic form on the one hand, and our philosophical conception of how that form works and what it does on the other. Connecting de re modal talk to de dicto can, I think, help a lot with the latter.

(Contrast, for example, Kit Fine's approach of taking essence as something basic – I get the sense of a wall having been erected to keep out trouble, but which also leaves us hapless and isolated. It is similar with his metametaphysical ideas: we must distinguish how things really or metaphysically are from how they are simpliciter, or something like that – and if you don't understand that, too bad: we're up against a wall. The difference, I think, is that in the first case the talk (essence talk) does make some sense, but has been walled off from things which may shed light on it in a way that can make this hard to believe, and hard to grasp, whereas in the second case, you have at most a degenerate, affect-charged sense, and the walls are merely there in a vain attempt to stop this from becoming glaringly apparent.)

Sunday, 15 February 2015

De Re Modality and Quantifying In

This is the first in a series of posts about these issues, the plan for which is given below.

My account of subjunctive necessity treats subjunctive necessity, in the first instance, as an attribute of propositions. That is, it is in the first instance an account of de dicto subjunctive necessity, in the sense that it applies to attributions of necessity and other definable modal properties to propositions (dicta).

As it stands, this account does not apply to propositions which say, of some object, that it necessarily has some property. For example, 'John is necessarily not a number'. That is, the account does not deal with de re subjunctive necessity (assuming such a thing is to be recognized at all).

Now, 'John is necessarily not a number' may look like just another way of saying '“John is not a number” is necessary'. Of course, nothing is stopping us stipulating that it is to be read that way. But furthermore, it might seem to already, naturally, say something equivalent to that. Or it might not. This issue will be seen below to turn on the issue of whether extensionally identical atomic propositions can differ in counterfactual invariance, and in turn modal, status – or more strictly speaking, it will be seen to turn on that given a certain natural approach to the interpretation of de re modal ascriptions.

Unlike '”John is not a number” is necessary', which refers to a proposition and predicates necessity of it, 'John is necessarily not a number' refers to John, and seems to be open to quantification in a way that the de dicto attribution is not: we can seemingly infer from it that something is necessarily not a number, whereas existential generalization on the de dicto attribution yields only 'Something is necessary'. This suggests that de re modal attributions like 'John is necessarily not a number', at least on one natural reading, do not have corresponding de dicto attributions which say exactly the same thing (even if they are equivalent in some sense). It also raises the issue of the interpretation of quantification into modal contexts.

I will begin in this post with some further consideration of what the problems of de re modality and quantifying in amount to. 

In the next post in the series, I will discuss Kripke's criticism in Naming and Necessity of Quine's attempts to make genuine de re modal attributions look bizarre or unintelligible, including the discussion of Nixon, where Kripke argues that de re modal attributions make good intuitive sense.

In the next post after that, I will go in search of an account of de re modal attribution given in terms of de dicto modality, eventually lighting on one, but leaving certain complications undiscussed for the time being.

In the next post after that, I will address the problem of quantification into modal contexts by giving an interpretation of the formulae of quantified modal logic (in the form of a method of translation into natural language).

The Nature of the Problem of De Re Modality

Here is Kripke introducing the problem of de re modality in Naming and Necessity (first lecture):
There is one more question I want to go into in a preliminary way. Some philosophers have distinguished between essentialism, the belief in modality de re, and a mere advocacy of necessity, the belief in modality de dicto. Now, some people say: Let's give you the concept of necessity. A much worse thing, something creating great additional problems, is whether we can say of any particular that it has necessary or contingent properties, even make the distinction between necessary and contingent properties. Look, it's only a statement or a state of affairs that can be either necessary or contingent! Whether a particular necessarily or contingently has a certain property depends on the way it's described. This is perhaps closely related to the view that the way we refer to particular things is by a description.

It is important to separate three parts of what Kripke says 'some people say' here:
  1. Given an understanding of de dicto necessity, the issue of de re modal attribution remains, and creates additional problems.
  2. It's only a statement or state of affairs that can be necessary or contingent.
  3. Whether a particular necessarily or contingently has a certain property depends on the way it is described.
I fully endorse (1), as the existence of this section would suggest. But that does not mean I endorse (2) or (3), both of which are curious and not altogether clear. I do not want to be overly pedantic about something which was said, in a fairly preliminary way, in a lecture delivered without notes, but separating these things and considering what (2) and (3) might mean will help us get clearer about the issue of de re modality. It will also help when we consider, in the next post, Kripke's intuitive defence of de re modality (which he gives right after the above quoted passage).

(2) needs finessing if it is not to be a trivial point of language. Someone – say, an Aristotelian essentialist, or Kit Fine – can hold that de re modal attribution makes perfect sense, and fully reject any (3)-like suggestions that the truth of these attributions is somehow description-dependent, and still agree with (2) as stated. They are not saying that an object (one which isn't a statement) can 'be necessary or contingent', but that it can have properties and stand in relations necessarily or contingently.

The real suggestion behind (2), I suggest, is that the notions of necessity and contingency – the notions of subjunctive or metaphysical modality clearly isolated by Kripke – only apply to statements (propositions) or states of affairs. And 'apply' here is understood in such a way that these notions are not automatically precluded from appearing in some other way than in predications of the form 'x is necessary', for example adverbially ('x is necessarily F').

(2), so understood, is not something I want to endorse. While I accept that de re modal attribution poses difficulties over and above de dicto, I think it may be possible to meet these difficulties. However, the meeting of these difficulties will be attempted here by accounting for de re modal attributions (and quantification into modal contexts) in terms of de dicto attributions. (But that doesn't mean there is no other way – I am giving an account, not the account.)

There is something potentially misleading about this talk of difficulties which may perhaps be met (rather than just cleared away, for instance) – as though there is some reason for us to hope that they may be. But that is not how I see the matter. This has to do with my doubts about whether there is any pre-existing intuitive understanding of de re modal attribution and quantifying-in, which I will elaborate in the next post.

So much for (2). What about (3): 'Whether a particular necessarily or contingently has a certain property depends on the way it's described'? This is very curious in a way. Far from being part and parcel of some attitude one might have on these questions consonant with (1) and (2), (3) seems incompatible with what we understood (2) to be getting at; if the relevant modal notions only apply to propositions or states of affairs, then, it would seem, we cannot speak of particulars necessarily or contingently having a certain property, and so we cannot say that their doing so depends on anything.

There is perhaps a way of interpreting what some skeptic about de re modality might mean by this, but there are also good reasons for them not to say it (not least of all that it is highly ambiguous and confusing).

There suggests that there is a danger that (3) is playing a straw man role, or a more subtle bait-and-switch role, in Kripke's influential arguments for the intuitive intelligibility of de re subjunctive modal attributions: trading on a charitable interpretation to make it a plausible attribution to philosophers (the bait), and then switching to an interpretation on which it couldn't possibly be right or even coherent (the straw man).

In light of this, I will now go into (3) at some length. I will do my best to make it easy to keep track of the argument, and its place in the bigger picture.

Something someone could say while maintaining (2) (as we have understood it) is this: the only clear, philosophically hygienic thing it could mean to say 'Nine is necessarily odd' is '”Nine is odd” is necessary', and all it could mean to say that 'The number of planets is necessarily odd' is '”The number of planets is odd” is necessary'. (Note however that I will not be advancing this view.)

Now, such a person would then face the issue: where does that leave the question of whether the referent of 'nine' and 'the number of planets', that particular number, possesses the property of oddness necessarily or contingently? What, if anything, does that mean?

It seems to me that the most consistent course for this person would be to say: this question just amounts to whether the proposition:

'The referent of “nine” and “the number of planets”, that particular number, possesses the property of oddness'

is necessary or contingent. Either that, or it has no clear meaning.

But Kripke has this person say that this question somehow depends on how we describe that particular number. But note carefully that this question, interpreted in the way I suggested was most consistent for the hypothetical person we are imagining, concerns a particular proposition. If someone asks something, and what their question really asks is whether some particular proposition is necessary or contingent, you can't respond by saying 'Well, that depends on how you describe …'. The describing has already taken place, in the proposition in question, and it is now time to proceed to actually answering the question.

Another thing this person could say which is similar to (3), but clearer, is this: that the truth of propositions which, superficially, designate an object somehow and say that it has some property necessarily or contingently, depends on how that object gets designated. But in this case, if we say that, surely we should say that these propositions have a misleading form. We should not go along with this form and say, as a kind of explanation of it, that whether some object has a property necessarily or contingently depends on how it is described. (The most deserving meaning for this expression here may still not be deserving enough.)

This can perhaps be seen better by comparing our case with one in which we might genuinely say something like this – i.e. that whether an object is some way or other depends on how you describe it. Consider these propositions: 'The number of planets is, in the subject-term of this proposition, being described as the number of planets', 'Nine is, in the subject-term of this proposition, being described as the number of planets'. The truth of these propositions patently does depend on how the referent of the subject-term is described (or, we might say more neutrally, designated). And we can say that whether that referent, that particular number, has the property of being described in some given proposition as the number of planets depends on how it is described by that proposition. Indeed this seems like a tautology. Or consider an object which naturally, whenever it is described as red, turns red if it is not already red (i.e., irrespective of whether the description was true, it becomes true), but turns another colour if it is described as non-red. Of such an object, we could say: whether it is red or not depends on how it is described.

The modal case is plainly not like this at all. Saying that whether a particular has a property necessarily or contingently depends on how it is described is, at best, a clumsy way of saying that the truth of (what superficially look like) de re modal attributions depends on how the object in question is designated. At worst, it is a tortuously confused piece of nonsense.

Another, perhaps more Quinean, thing someone might say which is along the lines of (3) is: de re modal discourse is confused, incoherent – in part because the truth of its claims of necessary or contingent property possession for an object would have to depend on how that object is described. This isn't really clearer than saying that the truth of such claims actually does depend on how the object is described, but the unclarity is less objectionable, since it is being asserted that de re modal discourse is incoherent, and so the thing about description-dependence can be regarded as an incoherent, absurd consequence – where the whole point of bringing it in is to argue that we are not able to make real sense of it.

So, (3) itself seems in danger of being a bit of a straw man for Kripke – it has little to recommend it, and doesn't obviously belong to anyone.

So, we have separated and examined three things involved in the position of the skeptic of de re modality as characterized by Kripke. The first, that given an understanding of de dicto necessity, the issue of de re modal attribution remains, and creates additional problems, is important and endorsed by me. The second, the idea that it is only a statement of a state of affairs that can be necessary or contingent, is something which I hope to undermine in subsequent posts. The third, the idea that whether something has a property necessarily or contingently depends on how you describe it, I have tentatively suggested to be a straw man.

Stay tuned for the next post, on Kripke's intuitive anti-Quinean defence of de re modality.

Tuesday, 20 January 2015

On 'If you're a brain in a vat then you don't have hands'

Much ink has been spilled on skeptical arguments like the following:
  1. If you're a brain in a vat then you don't have hands
  2. You don't know that you're not a brain in a vat
  3. Therefore you don't know that you have hands
There are many variations on this sort of argument, and many issues have been raised about it, for example the issues of the closure of knowledge under implication, and the closure of knowledge under known implication.

I have long felt that there is something very dubious about the first premise in the above formulation (and the analogous premises in the variations). I suspect that coming to terms with this would involve throwing a spanner in the works of some of our ways of thinking about how language functions (we being analytic philosophers, broadly speaking). Not necessarily at the level of explicit commitments, either. And perhaps that is part of the reason why this premise has not been questioned, in anything like the way I want to question it, much in the literature1; it seems very difficult.

In this essay I want to begin to explore this issue. It is a pretty large and confusing issue, and this is only meant to be a beginning, so I will try to be fairly non-technical and to avoid bringing in any very particular overarching theoretical framework, out of fear that if I did so the issue or important aspects of it would get lost.

I will suggest that (1) is not true – or at least, that it isn't true on its most natural readings. If I am right, then we may have a way of avoiding the repugnant conclusions of skeptical arguments like the above, without having to show that we do somehow know that we are not brains in vats. This seems attractive to me – it does intuitively seem to me that I do know that I have hands and that I do not know that I'm not a BIV. Or perhaps better, and from a broadly Lewisian contextualist perspective on knowledge-ascriptions (a perspective I find independently attractive)2, it seems to me that there are levels of strictness – or sets of relevant alternatives – on which 'I know I have hands' comes out true while 'I know I'm not a BIV' comes out false.

So, one thing which may come out of this discussion is a way of diffusing a large class of skeptical arguments. But my motivation isn't primarily epistemological – isn't to vouchsafe certain bits of presumed knowledge. For my part, I don't think that sort of philosophical anxiety about whether we really know such-and-such should always be indulged and attempts made to alleviate it by the straightforward course of trying to come up with reasons to be reassured. It seems largely pathological to me – something which ought to be scrutinized and dissolved, as I think Wittgenstein tried to do.3

No, I'm more interested in (1) for its own sake, and for the sake of the issues which come up once we begin to question it. As we will see, these are fundamental issues in the philosophy of language – for example, the issue of what propositions are, and the issue of whether we ought to think of propositions as sorting all possibilities into two categories (one of which may be empty): those in which the proposition holds, and those in which it does not. (We will not have space to go deeply into these issues in a general way, but we will end up seeing that we have here found one good path into them.)

So much for scene-setting. To kick off the investigation, let us note that (1) is generally supposed to be accepted readily, as though it were obvious. It just appears in skeptical arguments as a premise, which we're meant (by the skeptic) to accept without argument. Once you start scrutinizing it as I have done, this quickly begins to seem very odd and confusing. So, to try to avoid being hampered by such confusion when we do scrutinize it, let us first ask the question: why might (1) seem true?

Silly as it sounds – silly as it is – the answer appears to be something like: when (1) strikes us as true, we are as it were picturing a brain sitting in a vat, and observing that there are no hands in that picture. Or we are picturing a brain sitting in a vat, and a mad scientist tending it, and noticing a striking contrast between the two figures – the scientist-figure has a body and hands, whereas the other figure is just an organ (in a vat). Something along those lines.

And here is a good place to consider and put aside one particular line of attack on (1). It is a comically literal-minded objection. I did not think of it myself, but found it when I was searching the literature for previous attempts at calling propositions like (1) into question. (And this is all I found.) Roush (2010) argues that it is not true that if you're a brain in a vat then you don't have hands, on the grounds that you might be a brain in a vat with hands just stuck on (!) – that is, where there are attached hands in the environment which contains the brain and the vat, not the environment simulated for the brain. Maybe the hands are just stuck on with glue and dangle there, or maybe they are delicately connected up neurologically with the brain, making for a queer straddling of two “worlds” (or environments, or levels of reality) on the part of the BIV.

There is something very frustrating about this objection. It is frustrating, I think, because if you just accepted this objection, deciding on its basis that (1) is false, and then walked away, you would have bypassed all the deep issues in the philosophy of language which we can dig up by scrutinizing (1), thus losing a valuable opportunity.

Calling the objection into question – scrutinizing it – may lead somewhere, however. For instance, we may ask whether a BIV with the envisaged appendages really counts as 'having hands', or whether this is really the best candidate meaning for 'having hands' in connection with a BIV. And here we begin to get the sense of an abyss, this sense of unforeseen ambiguity or indeterminacy, and the sense that this sort of thing, since it's not very clear how we should think about it, has ominous implications for how we think philosophically about language.

These spectres raised just now are at the heart of what I am concerned with here, but they come up with (1) itself anyway, quite apart from the literal-minded objection we have just looked at. So, what I propose is that we put this objection to one side, go back to what we said about why (1) might seem plausible, and proceed from there.

(If you think the objection does show (1) to be simply false, you may be more comfortable with the ensuing discussion if you exchange (1) for something like 'If you're a brain in a vat without appendages as envisaged in Roush (2010), then you don't have hands'. But really, it hardly matters, since the point of this discussion is not really to determine the truth-value of (1). Indeed, the idea that (1) as used in skeptical arguments has a definite meaning, and a definite truth-value, may not survive scrutiny. And our idea of what a 'definite meaning' is, and of what role the notion of definiteness should play in thinking about meaning, may have to be altered too.)

So, we picture a BIV and there are no hands in the picture. And we picture a scientist tending the BIV and see a contrast between the figure of the scientist and the BIV-figure. And with this in mind, we might be tempted to say 'The BIV doesn't have hands and the scientist does'.

But consider a different situation, in which we have two BIVs. It doesn't matter whether or not they are plugged into the same simulation. What does matter is that, in their lives in their simulation(s), one of them is an anatomically normal human, while the other has been in an accident and lost their hands. Mightn't we, if this was the first case we had considered, be tempted to say 'One BIV has hands, the other does not'? And if we would be right in so saying, then we would be wrong to say (without shifting the meanings of relevant terms) that if you're a brain in a vat you don't have hands; the first BIV would then be a counterexample to (1).

Here it might be objected that it would not be correct to say, unqualifiedly, 'One BIV has hands, the other does not' – rather, one would, to be both right and completely explicit, have to say something like 'One BIV has hands in its simulated environment, the other does not'.

Suppose we go along with the objection. We can still ask about things the BIVs may say, in their simulations. And we could reason as follows: Surely, if the first BIV says, in the simulation, 'I have hands', they are, in the simulation, saying something true. And surely if they say, in the simulation, 'I am a BIV', they are, in the simulation, saying something true (even if they could never know it to be true). And thus, if they said 'If you're a brain in a vat then you don't have hands', they would be saying something false – something to which their very case is a counterexample. And if that's right, how could (1) fail to be false? How could our situation differ from the BIV in question's situation in such a way that (1) is true, whereas their utterance – in the simulation – of 'If you're a brain in a vat then you don't have hands' – is not? I can see no way. And furthermore, if there was a way, surely it would turn on us not being BIVs, not living in a simulation – and in that case, we wouldn't be able to know (1) without first knowing that we are not BIVs, and so the skeptical argument could no longer be run.

Now, the above reasoning seems natural, but of course it could be challenged. The most salient way it could be challenged would be to follow Putnam's notorious paper (1981) in saying that, when the BIV says, in their simulation, 'I am a BIV', they are saying, in their simulation, something false, contra the above reasoning.

I do not have space here to lay out Putnam's arguments in full, and to discredit them in detail, but I think it is important to realize that Putnam is completely wrong on this point, and to see why. I will now briefly try to defend this, and to say something about what was going on with Putnam for him to be led so far astray.

Putnam begins with a causal theory of reference, according to which what you're talking about when you say something is what stands in an appropriate causal relation with your utterance. He argues, from the causal theory, that since a BIV could have no causal contact with the brain they are, and the vat they are in, they could not be talking about that when they say 'I am a brain in a vat' – rather, their utterance is, according to Putnam, about 'vats-in-the-image', 'or something related (electronic impulses or program features)'. And since they, the utterers, are not vats-in-the-image, i.e. not vats belonging to their simulation, nor the relevant 'related' things, what they thus say comes out false.

There are lots of things about this we could argue with – the idea that the BIV's talk might literally refer to electronic impulses or program features seems to me very crude and objectionable, for instance – but I will confine myself to three points, the first two of which are closely related to each other.

Firstly, note that singular reference – reference to particular objects – isn't what is in question here. Putnam isn't saying that to say something which is made true by the state of some particular object O requires that we have causal connections to O itself. That, after all, would yield absurd consequences (not that that tends to stop Putnam, but ignore that; these absurd consequences aren't as cool or interesting). For example, I may say, let us suppose on a whim, 'A man will walk into the room now', and if a man immediately walks in, what I said is true, in virtue of that particular man's walking in. But of course the man need not have any causal connection with what I said. All Putnam would insist on is that, in order to be about men at all, my talk needed to have an appropriate causal connection with some man or men. Likewise, in order for a BIV to think or say they are a BIV, their thought or talk doesn't have to be causally connected with the brain they are or the vat they are in. It just has to be connected with some brain(s) and vat(s).

Secondly, why can't there be a general category marked with the word 'vat' which includes as members both “vats-in-the-image” - vats in simulations – and vats outside simulations? (Likewise for 'brain'.) I think there can. Consider things like happiness and intelligence: a BIV with a rich life is surely acquainted with these things, and causally connected with exemplars of them – and so they can have a category, for example marked 'expressions of happiness', and this category would include both things in their simulated environment and any appropriate things outside the simulation. And so Putnam's argument falls down here, by implicitly holding that the relevant reference classes – the 'brain' class and the 'vat' class – can only include things in the utterer's “world”. Once we see this is not so, we can go along with Putnam's basic causal-theoretic starting point, but maintain that there is nothing stopping them thinking they are BIVs, because they can form categories – by means of causal connections to brains and vats in their environment – which manage to include the brain they are and the vat they are in, despite those particular instances not being in their environment.

Thirdly, and stepping back a bit, note how implausible and crude Putnam's interpretation of the BIV's utterance 'I am a BIV' is; it's supposed by Putnam to assert something which to the BIV would be obviously wrong – namely, that they are brains in their environment in vats in their environment. And yet a reflective BIV might not find their utterance of it obviously wrong at all. This suggests that something has gone badly wrong. At a very general level, we may say that Putnam's problem is that he has inappropriately treated the language-game of talking about being a BIV as being just like an ordinary one about things in our environment. But it is plainly not that. Language, we might say, is here playing an entirely new trick. We may not be able to come up with a theoretical understanding of it which would satisfy Putnam, but that does not mean he gets to falsify it.

So, if I'm right about Putnam here, then the reasoning we went through just before considering him seems hard to argue with. And thus, it seems that (1) isn't true, at least on the most natural ways of understanding it. At the very least, it should certainly seem by now that (1) is not the straightforward truth it may have looked to be at first. There are serious challenges to be raised against the naïve, unreflective procedure of just (doing something like) picturing a brain in a vat, observing that there are no hands in the picture, and drawing (1) as a conclusion.

But we are in a bit of a muddle now, only halfway through the essay. A lot of arguments and worries have piled up. I want now to try to restore our energies by clearing the table and approaching the issue from the other side: why might we think (1) is false?

I have an intuitive case to make for thinking that (1) is false. It involves considering statements made in ordinary, everyday conversation, statements which intuitively seem to imply that the utterer has hands, but which intuitively seem not to imply that the utterer is not living in a simulation. For example, suppose someone asks me to help them with something and I say 'OK, one second - I'm just washing my hands'.

This statement – that I'm washing my hands – surely implies that I have hands. Furthermore, I find it very intuitive that it does not imply that I'm not living in a simulation, or that I'm not a BIV; that simply isn't at issue at all. It is completely independent of the truth of what I said.

Having hands is compatible with it not being the case that I'm not a BIV. And so, having hands is compatible with my being a BIV. And so it can't be true that if you're a BIV then you don't have hands.

The key intuition there – that my ordinary statement does not imply that I'm not living in a simulation – can perhaps be bolstered by thinking a bit about the space of scenarios in which I am living in a simulation, and seeing that it is possible to take an attitude to many of these scenarios which is quite unlike regarding them as epistemic nightmares, i.e. situations in which we're in really bad shape epistemically – where much of what we ordinarily think we know fails to even be true.

Certainly we can imagine simulation-scenarios which are epistemic nightmares. We may be BIVs whose tending scientists are engaging in all kinds of foul play, planting false memories and moving things around on us. Also diabolical would be if some or all of the apparent agents we are interacting with are not sentient, or not as fully sentient as we think. I don't so much mean that they may not be constituted the way we are, or the way we think they are – after all, multiple realizability might be the case – but rather that maybe all there is to these agents is what's required to generate our interactions with them. And in lots of cases, corners may be cut, so to speak – when we think they're off by themselves having a rich mental life, perhaps often nothing of the sort is true. But nightmarish scenarios like this are clearly a special subset of all simulation scenarios; in many of the latter, we may not be wrong about much of anything. It just might be the case that, unbeknownst to us, there is a higher level of reality “hosting” the one we inhabit, and this level may involve brains in vats.

From this point of view, we can see that there is no need to respond to the news that you're a brain in a vat by revising your belief that you have hands. Why not treat the news instead as telling you, among other things, something new about your hands (and everything else in your environment), namely that they are “hosted” at a higher level of reality, or speaking crudely, are constituted by electrical impulses or program features. (I say 'crudely' because the relation is obviously not the normal one of constitution from normal physical inquiry. Physics can be done in a simulation, too, and facts about the simulation being a simulation need not be regarded as belonging to it.)

I contend, then, that once we reflect a bit, we can see that (1) is false, at least on the most natural ways of construing it.

Why the hedge about 'most natural ways'? Well, there is one way of construing 'hands' I can think of which is not totally discontinuous with what 'hands' really means and which would make (1) come out true. Namely, a way on which hands are taken as a matter of definition to be things which exist only at the highest level of reality. (Note, in case it seems woolly or unclear, that this notion of levels of reality I've been throwing around does not precede, or exist apart from, considerations of simulations. It is a special notion for talking about these very special matters. Despite possible appearances, there's no more general story about it which could be missing or unsatisfactorily hand-waved to here.)

So there is this construal. But when we adopt it, the conclusion of the skeptical argument, that we don't know that we have hands, isn't particularly repugnant any more. And this, by the way, shows that the construal in question isn't very natural, since we do feel the conclusion as ordinarily understood to be highly repugnant. That conclusion can't be put at the end of the skeptical argument without either rendering (1) false, or keeping it true but equivocating on 'hands'.

So much for (1) and its role in the skeptical argument. I will now begin to conclude, with some more general remarks about meaning and propositions.

It seems like there's something artificial about pinning a particular resolution of these issues of 'What exactly does it take to be a hand, anyway?' on ordinary talk about hands, no matter which one we pick. Rather, something along the lines of there being no fact of the matter seems to be the case. Consider in this connection Wittgenstein's case of the disappearing chair:

§80. I say "There is a chair". What if I go up to it, meaning to fetch it, and it suddenly disappears from sight?—"So it wasn't a chair, but some kind of illusion".—But in a few moments we see it again and are able to touch it and so on.—"So the chair was there after all and its disappearance was some kind of illusion".—But suppose that after a time it disappears again—or seems to disappear. What are we to say now? Have you rules ready for such cases—rules saying whether one may use the word "chair" to include this kind of thing? But do we miss them when we use the word "chair"; and are we to say that we do not really attach any meaning to this word, because we are not equipped with rules for every possible application of it?

So, what of propositions? What of meaning? Should we say that hand-talk is somehow incomplete, failing to express determinate propositions? Well, we could say that, but this is taking the notions of a proposition and of meaning pretty far from home. And what for? Perhaps the only answer is: to preserve certain ways of thinking about how propositions work, and what they do (for example, the idea we mentioned at the outset that propositions sort all possibilities into two categories). But is that wise? Were these ways of thinking the results of investigation, or a priori requirements? (Cf. entry 107 of the Investigations.)

In any case, does the breakdown of these ways of thinking here mean they have to be chucked out entirely? No – we could think of them as offering an idealized perspective. A perspective which is robust in some areas of thinking, useless perhaps in others, and worse than useless in others again.

Now to stop and take stock. Firstly, (1) is no straightforward truth. Secondly, there's a lot more to it than there might seem to be at first glance. Thirdly, it is very arguably false on the most natural ways of understanding it. There's one somewhat natural way on which it's true, but on that one the conclusion isn't very repugnant. Finally, we have looked fleetingly at what all this might mean for the fundamentals of philosophy of language, and suggested that certain ways of thinking about language which run into trouble here are either just bad, or at best are idealizations which have some value but can easily break down and become inappropriate. And they do break down and become inappropriate very quickly once we scrutinize (1).


Lewis, D.K. (1996). Elusive knowledge. Australasian Journal of Philosophy 74 (4):549 – 567.

Putnam, H. (1981). 'Brains in a Vat', Chapter 1 of Reason, Truth, and History. Cambridge University Press.

Roush, S. (2010). Closure On Skepticism. Journal of Philosophy 107 (5):243-256.

Wittgenstein, L. (1953/2003). Philosophical Investigations: The German Text, with a Revised English Translation. Blackwell.

1. I say 'much in the literature' in case there are documents I am unaware of which question it in something like the way I have in mind; I haven't been able to find any. On the other hand, this does seem to me to be the sort of thing that a philosopher might register in passing in a document mainly about something else. I wouldn't be at all surprised therefore to find myself anticipated to some extent in that way.

2. Cf. Lewis (1996).

3. I am uneasy about this though, since running with such epistemological worries and trying to meet them straightforwardly and on their own ground has borne spectacular philosophical fruit, as it were along the way, even if the worries are ultimately never thus met. Russell's quest for certainty and his work, in service of this quest, in mathematical logic and philosophy of language, seems a spectacular example. The quest seems a sad vestige of a screwed up childhood, while the result of the quest includes spectacular advances in logic, the theory of descriptions, and long-overdue attention to Frege. This kind of alchemy seems unsettlingly rife in philosophy – at least, it's a bit unsettling if you hope to do fundamental work in the subject yourself. Another example would be Nietzsche's writing Zarathustra in the wake of his humiliating falling out with Paul Rée and Lou Salomé.