Against 'Against Vague Existence'

In 'Against Vague Existence', Ted Sider argues that our quantifiers cannot be vague, because it is impossible to characterize semantic vagueness in our quantifiers in the usual way; that is, in terms of multiple admissible precisifications. Sider considers as a test case whether it could be indeterminate, due to vagueness in the existential quantifier, whether the following was true:

(E): Ex (x is composed of the F and the G).

Sider claims that the ‘familiar model’ for spelling out how such indeterminacy comes about would apply to this case as follows:

(P1): ‘E’ has at least two precisifications, call them E1 and E2. There is an object, x, that is in E1’s domain but not in E2’s domain, and which is composed of the F and the G. Thus, (E) is neither definitely true nor definitely false.

But, as Sider points out, ‘the defender of vague existence thinks that it is not definitely true that there is something composed of the F and the G ... She will therefore not make this speech’ (p. 139).

Sider proceeds to offer three options to the defender of vague existence: rejecting the need to non-vaguely describe the precisifications, using vague quantifiers to non-vaguely describe them, and finding non-quantificational non-vague language to describe them. None of these is my preferred way of resisting Sider’s argument. Nor do I wish to resist (here) his two presuppositions: that the indeterminacy of (E) would have to be semantic (as opposed to ontic), and that this means we need to explain it in terms of multiple admissible precisifications of the existential quantifier.

Instead, I propose we investigate how much can be achieved through paying careful attention to scope in describing the relevant precisifications. Instead of (P1) above, perhaps we can appeal to:

(P2): ‘E’ has at least two precisifications. On the first precisification, there is an object, x, which is composed of the F and the G. But on the second precisification, there is no such object. Thus, (E) is neither definitely true no definitely false.

Note that, now, the existential quantifiers appearing in the account of why (E) is neither definitely true nor definitely false occur within the scope of the operators ‘on the first precisification’ and ‘on the second precisification’. Hence there is no need for any metalanguage commitment to an object which is composed of the F and the G.

(P2) seems to do what Sider requires: it talks about two precifications for ‘E’, and explains what it is about these two precisifications which results in the indeterminacy of (E). So what’s wrong with (P2)?

Field Motivates Concept Grounding

In his paper 'Recent Debates About the A Priori', Hartry Field seems to me to be spot on the following passage (pp. 13-14 of the online paper):

[T]he key issue is ... : why should the fact, if it is one, that certain beliefs or inferences are integral to the meaning of a concept show that those principles are correct? Why should the fact, if it is one, that abandoning those beliefs or inferences would require a change in meaning show that we shouldn't abandon those beliefs or inferences? Maybe the meaning we've attached to these terms is a bad one that is irredemably bound up with error, and truth can only be achieved by abandoning those meanings in favor of different ones ...

However, I don't agree with Field that this point is a step on the way towards his conclusion, namely that to claim we have an entitlement, at least in the case of 'basic' beliefs or logical rules, is merely to express an attitude of approval toward those beliefs or rules.

Rather, what Field's questions rightly raise to notice is the need for some account of why we should trust the meanings we have attached to our words (or, as I would prefer to say, why we should trust the concepts we express by them) to serve as epistemic guides to the way the world is. That is, we need a story about concept grounding to explain why these meanings or concepts are rightly taken as encoding information about the world which we can recover through introspection.

Beall and the Paranormal

This week I've been thinking about JC Beall's fun paper 'True, False and Paranormal'. Essentially, the idea is to model our truth-talk with a disquotational predicate 'T', and have a language which can exhaustively characterize all its sentences as 'true', 'false' or 'other', without thereby admitting true contradictions. Sentences of the model can take any one of five values, 0, .25, .5, .75 and 1, of which .75 and 1 are designated. A new term 'pi' is introduced (sorry I don't have a pi-symbol here!) to mean 'paranormal' (or 'other'), and pi-A takes the value .75 when v(A) = .25, .5 or .75, and takes the value 0 otherwise.

It seems that the view requires that there is no predicate in the model language like D ('D' for 'designated'), where:
v(D[A]) = 1 or .75 when v(A) = 1 or .75
and v(D[A]) = 0 or .25 when v(A) = 0, .25 or .5

Otherwise the sentence
A*: ¬D[A*]
presents a problem. (It is designated iff it isn't.)

But it seems to me that such a predicate is needed in order for the model language to be capable of expressing claims about its own semantic machinery (that is, capable of expressing the designation stuff that we can talk about in the metalanguage). Nothing else will do; in particular, any predicate D' such that the value of D'[A] is .5 when the v(A) = .5 does not express designation; any designation claim must take value .25 or less when v(A) = .5.

Why? Because .5 is not a designated value. Of course, that only means its true-in-real-life that .5 is not designated, which you might want to say does not imply that the value of D[A] should be an undesignated value. Truth-in-real-life (as JC has helpfully stressed to me in conversation) is not supposed to be modelled by designation but by truth-in-the-model (i.e. the behaviour of 'true' in the model).

But I think in order for our D to express designation we need D[A] to be false-in-the-model when v(A) = .5, which (unless I'm missing something) means we want F[D[A]] to be designated when v(A) = .5, i.e. we want T[¬D[A]] to be designated, which can only happen if ¬D[A] is designated, which in turn requires that v(D[A]) be at most .25 (because in this model negation toggles designated values with values of at most .25).

If Beall is saying that no model is capable of expressing these things he seems to be forced to say either that no model is adequate as a model of English, which can talk about its own semantic machinery, or that, like the models, English cannot express claims about its own semantic machinery.

If one says the first thing, then one has to admit that these models can't help us understand the Liar - after all, the Liar arises because English can express claims about its own semantic machinery, and if the models don't model this feature of English, they are irrelevant to the Liar. (This point relates to Beall's claim to have preserved exahustive characterization: the exhaustive characterization we wanted was an exhaustive characterization of all the sentence in the model in terms of their semantic values, but we didn't get that.)

And familiarly, if one says the second thing, one places an implausible limitation on the expressive powers of English.

UConn

I’ve just got back from the University of Connecticut, where I gave my paper on Modal Knowledge at the Philosophy Department Colloquium and got lots of helpful feedback. The UConn grad students have just started a blog, What Is It Like To Be a Blog?.

I also attended a conference on Conditionals. On Saturday, Dorothy Edgington told us what she thinks about subjunctive conditionals, namely that they do not have truth values but rather express the speaker’s belief that the conditional probability of the consequent on the antecedent is high (i.e., basically, they function pretty much the way she thinks indicatives do, but in a different tense).

I was worried that there seem to be cases where the consequent is unlikely to be true given that the antecedent is, yet still would be true if the antecedent was. The existence of such cases suggests that subjunctives and conditional probabilities are not correlated in the way Edgington claims. We discussed the following example (one suggested by Edgington when I raised my worry in discussion time). Suppose you decide at the last minute not to get on a plane which is very unlikely to crash, and the plane in fact crashes, killing all its passengers. It’s tempting to think that the probability of your dying conditional on having got on the plane is low, because the plane’s chances of crashing were low, yet clearly if you had got on the plane you would have died.

Edgington replied that we simply have to find the right conditional probability, in much the same way that (say) someone who likes closest-world semantics for these conditionals has to find the right similarity relation. In the above case, she said, the right conditional probability is that of your dying given that you got on the plane and it crashed. To save the proposal, you just need to find the right pieces of further information about the world to take into account, besides what is mentioned in the antecedent. This information will makes the conditional probability of the consequent high.

This might be thought to be a bit ad hoc, given that the crashing is not mentioned in the antecedent of the conditional we’re actually interested in. But regardless of that, I think it is a problem that the response won’t always work if there is indeterminacy in the world. For in that case, there will – or at least, could – be some unlikely events that just happen, and are not rendered any more likely however much further information about the world we take into account.

Suppose C is an event that would have happened, without being determined, if A had happened, although it was very unlikely to do so. Then the subjunctive:
If A had happened then C would have happened
looks true, although the conditional probability of C on A is low. And in this case there is no further information about the world that we can take into account which will make the conditional probability of C high – that is, there is nothing which can play the role played by the fact that the plane crashed in Edgington’s response to the first example.

So Edgington’s account of counterfactuals seems at risk of giving the wrong results unless we assume there is no indeterminacy. And this seems to be a distinctive problem for the account, not analogous to an problem faced by closest-world approaches.

Time Travel and Backwards Causation

It seems to be quite widely assumed (I am informed, by sources who read more about this sort of thing than I do) that backwards time travel requires backwards causation. It wouldn't suffice for time travel if in 2015 I climbed into a time machine and someone looking and acting exactly like how I look in 2015 came into existence for no apparent reason in 1926. Rather, that person's turning up in 1926 would have to be caused by my actions in 2015.

I agree with the insufficiency claim. But I'm not sure whether the causal requirement is motivated by it. (I'm also hung up on whether it might be a conceptual truth that causation happens forwards, not backwards, but let's not worry about that.) Wouldn't it be enough if there were the right kind of non-casual explanation of this person's turning up in 1926, in terms of my actions in 2015? If not, why not?

(I am concerned that I will be trussed up in a sack and sent back to Cambridge for posting on this, but I'm going to do it anyway ...)

Basic Knowledge Workshop: Call For Graduate Papers

I'm organizing an Arché workshop on Basic Knowledge, which will take place on 24-25 November 2006. Speakers will include Jason Stanley, Duncan Pritchard, Jessica Brown and Timothy Williamson. There will be a slot for a graduate student paper. Graduate students, and those who obtained their PhDs within the last twelve months, are invited to submit papers of not more than 5000 words. Please send me submissions as email attachments in Word or similar format (no pdf files please). Suitable topics include: Sceptical Paradox, Transmission and/or Closure, Non-Evidential Warrant, Internalism and Externalism, and A Priori Knowledge. Particularly welcome are papers which open up new areas of enquiry within these fields, and/or highlight directions in which further research is needed. Travel and subsistence will be covered by Arche for the author of the selected paper. The deadline for submissions is 31 August 2006.

ADDENDUM: Submissions should be prepared for blind review.

Counterfactuals and Ontic Vagueness

Following on from the idea I floated in this post, I'm posting a draft of a note on why you shouldn't use counterfactuals to characterize commitment to ontic vagueness (which won't surprise those who know that I tend to think you probably shouldn't use counterfactuals to characterize anything metaphysically interesting ...). Comments very welcome, as always.

Lewis/Blackburn Again

A slightly improved draft of the Lewis/Blackburn note is here.

Weighing Implausibilities

Here's something I was wondering about during Tim Williamson's talk at the Arché Vagueness Workshop yesterday.

Suppose you want to keep bivalence, and you also think that the only way for something to be an aspect of a predicate's meaning is for our use of the predicate to determine that it is (both Williamsonian thoughts, I gather). But you also think it is at least prima facie implausible that usage determines an exact cut-off point for all the vague predicates (a thought pressed against Williamson by McGee and McLaughlin).

We seem to have at least two options.
1: Accept the implausible-sounding claim (with Williamson), or
2: Argue that many of the things we think are vague predicates ('red', 'bald' etc.) are in fact not predicates at all. By bivalence, in order for them to be predicates we would need there to be cut-off points for their application. But it is implausible that our use of these terms determines such cut-off points. And there is nothing else which can do this sort of meaning-constituting work.

It's initially implausible, sure, that words like 'red', 'bald' and so on are not predicates. But my question is: by what sorts of methodological considerations do we weigh this implausibility against that of the claim that usage determines cut-off points for all such terms?

(Incidentally, Williamson mentioned that he talks about Option 2 in his book on vagueness, which I haven't had a chance to look at yet. He obviously has reasons for preferring Option 1, which I will be interested to read.)

Lewis/Blackburn Note

I wrote up some thoughts relating to my previous post as a short note. Comments welcome!

Quasi-Realism No Fictionalism (But Not Quite For Blackburn's Reasons)

I've just been leading the MRG on the Lewis/Blackburn exchange in this collection concerning whether quasi-realism is fictionalism (Blackburn's half of which is online here).

It seems to me that Lewis's claim that quasi-realism is a version of fictionalism is mistaken, but not for a reason that comes through in Blackburn's response.

Lewis's argument, in essentials, is that the quasi-realist wants to say everything the realist does, so must either be a realist or be making believe that realism is true. But he is not a realist, therefore he is making believe that realism is true, i.e. he's a fictionalist.

I think we can show what's wrong with that argument in a few lines. The sense in which the quasi-realist 'says everything the realist does' is not the one which enforces either being or pretending to be a realist. This would be enforced if the quasi-realist was making the same assertions as the realist, but he isn't (indeed, the paradigm quasi-realist isn't making assertions at all). The quasi-realist says things which sound like what the realist says, but they are to be interpreted differently - in the moral case, as expressions of attitudes, rather than as committing to moral properties. Expressing an attitude requires neither belief in moral properties (realism) or pretense that moral properties exist (making believe that realism is true).

So here's why quasi-realism is not fictionalism:
The fictionalist differs from the realist in adopting the realist account of the meaning of the target sentences but dissenting from those sentences (same content, different attitude) whereas the quasi-realist differs from the realist in adopting a different account of the meaning while continuing to accept those sentences (different content, same - or at least similar - attitude).

Entitlement and Rationality

My paper on Crispin Wright's notion of Entitlement is now also up - though NB still in draft form - on my home page. Comments welcome on this too!

Knowability Again

I've just posted the final draft of my knowability paper on my home page. Comments are still welcome!

New Arche Blog

Arche now has a blog on which all Arche members can create posts. The aim is to encourage philosophical interaction between Archeans and friends around the world. We also welcome participation from other philosophers - comments are publicly open.

Cook on Unknowability

Roy Cook has just argued that there are some unknowable propositions provided it is possible for the following situation to obtain. Ava, Brigitte and Dorothy are all inhabitants of Smullyan’s (1978) island occupied solely by knights and knaves. Knights are people who always speak truly, knaves are people who always speak falsely. Simultaneously, they utter the following:
Ava: What Brigitte is now saying cannot be known to be true
Brigitte: What Dorothy is now saying cannot be known to be true
Dorothy: What Ava is now saying cannot be known to be true

Cook shows that if this happens then at least two of Ava, Brigitte and Dorothy must be knights (see his p. 12), and goes on to show as a consequence of this that at least one of them – we do not know which one – has uttered a true but unknowable proposition. He assumes classical logic and certain facts about the behaviour of the knowability operator in order to get this result, all of which we can grant here for the sake of argument.

Cook stresses that his argument relies on the thought that the scenario he describes is free from ‘any paradox, failure of reference, or other pathology’ (p. 14). It seems to me, however, that the anti-realist who accepts the principle p --> Kp will think Cook’s scenario is paradoxical, because it presents a version of the paradox raised by what Cook would call the semantic open triple (sorry, no corner quotes):
p: ¬Tq
q: ¬Tr
r: ¬Tp
(where T is the truth predicate). No assignment of (classical) truth values to these three propositions is consistent.

Anti-realists for Cook’s purposes are those who accept that if p then p is knowable, which Cook represents as p --> Kp, the contrapositive of which is ¬Kp --> ¬p. By this and the contrapositive of disquotation for the truth predicate, ¬p --> ¬Tp, these anti-realists will also accept that ¬Kp implies ¬Tp. Hence the three characters in Cook’s story are uttering claims which are either stronger than or identical in strength to the paradox-creating claims of the semantic open triple. In fact, anti-realists will presumably think the claims are identical in strength; for they are happy to accept ¬Kp --> ¬Tp, and ¬Tp --> ¬Kp is trivial.

One might respond that this is to beg the question; the only reason that is being offered for thinking that Cook’s situation is paradoxical is adherence to p --> Kp, which, of course, one does not accept unless one is an anti-realist.

But we need to be clear about where the burden of proof lies. Cook is (tentatively) offering an argument that should be capable of persuading anti-realists that there could be an unknown truth. To do this, as he acknowledges, the situation he describes should not be paradoxical. But the anti-realist will think it generates a Liar-like paradox, namely the semantic open triple. Therefore Cook’s argument will not be persuasive to an anti-realist.

I Wanna Have Control

Here's a point that came up recently following a talk by Arché visitor Dean Zimmerman on Molinism.

It can't be sufficient, to count as having control over someone else's actions, that their actions vary counterfactually with yours - that were you to F they would F, and were you to G they would G, etc.. For if this were the case we could have symmetric control. It might also be that were they to F you would F too, and so on. (Suppose that, necessarily, you F iff they do.) But you can't each be controlling the actions of the other - control is an asymmetric relation.

So what do we need in order to explicate the notion of control? It doesn't help to specify that exactly one of them is aware of the counterfactual relationship between his actions and the other guy's, and say the controller is the one who's aware. For one can perfectly well be aware that one's actions are being controlled by someone else (who is not aware of the fact).

Unsurprisingly, I think what we need to appeal to here is probably explanation. What matters is whose actions explain those of the other. You are in control just in case your actions explain the other guy's. Explanation brings with it the right kind of asymmetry, as well as making sense of the feeling that the controllee's actions depend upon the controller's.

Knowability

I'm just about to start work on the final draft of my new paper on Fitch's Knowability argument, so I'm posting the current draft here to invite comments. The earlier Fitch paper of mine which I refer to can be found here and the forthcoming Kvanvig paper I talk about is online here.

What I'm Doing On My Holidays

I'm writing a paper on modal knowledge over this Christmas/New Year break. In it I'm trying to argue that we can answer two questions simultaneously:

1. How can experience be a guide to modal truth?
2. How can conceivability be a guide to modal truth?

by proposing that experience grounds our concepts (that is, makes them knowledge-conducive guides to the structure of the world), and that what we can conceive of is constrained by what our concepts are like in such a way that the information about the world's structure which is in encoded in the structure of our concepts is recoverable through the activity we call 'attempting to conceive'.

What's all that got to do with knowledge of what's possible and necessary? Well, things are easy if you think that modal facts are , or metaphysically depend upon, structural facts about the actual world. Because the latter are the kinds of facts that 'attempts to conceive' put us in touch with.

What I'm looking at now are ways in which people who don't like that metaphysical idea might also get in on my epistemological act. Ways, that is, in which you might think that information about actual-world structure can be an epistemic guide to modal facts even though these facts do not depend metaphysically on facts about actual-world structure.

One option is to believe in metaphysical dependence in the other direction: that is, to think that actual-world structural facts depend on modal facts. But that option doesn't have much prima facie plausibility (at least, not to me).

Alternatively you might think both actual-world structural facts and modal facts depend on some other class of facts in a way which explains the correlation between the two. (But what sort of facts would they be?)

There's always the option of brute correlation, but we'll need a damn good story about why we should take the correlation to be brute, to tell to those who think that it's actually evidence of metaphysical dependence in one direction or the other.

Finally, I thought, perhaps you might think there is some satisfying explanation of the correlation which does not appeal to metaphysical dependence at all. (But what would it look like?)

As always, any comments/suggestions/further possibilities are very welcome here.

Happy New Year!

Chalmers, Carnap and Lightweight Existential Quantification

I clicked through to David Chalmers's powerpoint slides on Ontological Indeterminacy yesterday, wondering if I might get a discussion of ontic vagueness. In fact I found something else equally interesting: a discussion of 'deflationary' (=, roughly, Carnapian) views about certain existential questions.

I have a few comments (though NB I have not heard the full talk, so maybe some of these points are addressed there):

1. I'm not sure whether the kind of 'relativism' Chalmers describes should count as deflationary. To say that there are many equally good answers to a question (which I think is the core of the proposed 'relativism') is prima facie different from saying that there is *no* substantial answer to the question (deflationism). To get the latter from the former we seem to need to assume that relativism about answers to a question is incompatible with the thought that the question and its answers are metaphysically substantial.

2. I think substantial ontological existence claims can be what Chalmers calls 'lightweight', i.e. a priori knowable or analytic or something in that area. Which is to say, in effect, that I don't think 'lightweight' (a priori knowable) existential claims need be genuinely lightweight. The envisaged connection between 'lightweightness' and real , metaphysical, lightweightness is, I guess, supposed to be effected by the thought that a priori reflection can only address what Carnap would call 'internal' questions, while genuinely heavyweight ontological questions must be 'external'. But personally (for what it's worth), I think concept-led a priori reflection might well lead to knowledge of substantial conclusions, including existential conclusions. Once we acknowledge that concepts can be grounded - i.e. sensitive to the way the world is in such a way as to make them good epistemic guides to reality - we can think (in Carnapian terms) of frameworks as being selected on more-than-pragmatic grounds, that is, selected for their fit with the world. And then there is no reason to doubt that a priori reflection on concepts within a framework can give us epistemically respectable answers to (what Carnap would have called) external questions.

Non-trivial Counterpossibles

A reflection that was triggered by hearing Timothy Williamson give a paper here last weekend at the last ever Arché Modality Workshop.

Some people (classically, Lewis) think any counterfactual with an impossible antecedent is trivially true, and I'm prima facie inclined to agree. But we should be able to distinguish between ones where there appears to be something non-trivial going on, such as:
1. If the square root of 2 were rational, it could be represented as n/m with n, m integers
and ones which don't seem to have this feature, such as:
2. If the square root of 2 were rational, there would be lemonade rivers.

Two options are:
A: to say that the difference between trivial and non-trivial counterpossibles is one of assertability (1 is assertable in many contexts where 2 is not),
B: to say that this difference is a matter of epistemic accessibility (you can know 1 is true without knowing it has an impossible antecedent, whereas this looks doubtful for 2).

But I'm currently wondering whether, in some cases at least, neither assertability nor epistemic access gives the deepest or most insightful characterization of the difference - they may rather be symptoms. For instance, you might think that in some cases it is the existence of some metaphysically interesting connection between states of affairs described in 'A' and 'B' that really explains why a counterpossible conditional 'A []--> B' is non-trivially true. You would then expect this conditional to exhibit the pattern of assertability and epistemic accessibility usually associated with non-trivial counterpossibles, although that behaviour is not what its non-triviality amounts to but rather a sign of it.

(PS For the record, I don't assume there will be the same story to tell in every case about what sort of factor underlies the assertability and accessibility symptoms.)

(PPS I will - hopefully - get round to replying to the interesting comments on my previous post soon ...)