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More on privacy, apriority, and two-dimensionalism

Here are, very quickly, some more thoughts on the matters I talked about here and there, inspired by another discussion with Christian.

You don't have to know much about plutonium to be a competent member of our linguistic community. One thing you have to know is that plutonium is the stuff called 'plutonium' in our community. Maybe that alone suffices. Of course, if noone knew more about plutonium than this, the meaning of 'plutonium' would be quite undetermined. To fix the meaning, it would suffice if a few persons, the 'plutonium experts', knew in addition that this element (where each of the experts points at some heap of plutonium) is plutonium.

New hope for linguistic ersatzism?

Are all truths a priori entailed by the fundamental truths upon which everything else supervenes? If 'entailed' means 'strictly implied', this is trivially true. The more interesting question is: Are all truths deducible from the fundamental truths (deducible, say, in first-order logic) with the help of a priori principles?

If yes, then it seems that Lewis' 'primitive modality' argument against linguistic ersatzism (On the Plurality of Worlds, pp.150-157) fails. Recall: Lewis argues that if you take a very impoverished worldmaking language then even though it will be feasible to specify (syntactically) what it is for a set of sentences to be maximally consistent, it will be infeasible to specify exactly when such a set represents that, e.g., there are talking donkeys. Now if all truths are a priori deducible from fundamental truths, and -- as seems plausible -- fundamental truths are specifiable in a very impoverished language, then we can simply say that a maximal set of such sentences represents that p iff p is a priori deducible from it.

Unfortunately, I find the 'primitive modality' argument quite compelling. So, by modus tollens, I have to conclude that not all truths can be a priori deducible from fundamental truths. Does anyone know whether Lewis himself believes the deducibility claim he attributes to Jackson in 'Tharp's Third Theorem' (Analysis 62/2, 2002)?

Moved

After two weaks of homelessness I've moved into my new flat today.

Everything but the beetles cancels out

This is a continuation of my last post and also partly a reply to concerns raised by my tutor Brian Weatherson.

Imagine a small community consisting of three elm experts A, B, and C.

First case: Each of A, B, and C knows enough to determine the reference of 'elm', but their reference-fixing knowledge differs. However, they belief that their different notions of 'elm' necessarily corefer. This is the case Lewis discusses in 'Naming the Colours'.

Semi-public A-intensions

Some days ago, Christian and I had an interesting discussion about two-dimensionalism. While I don't agree with many of his criticisms (forthcoming in Synthese), I do agree that two-dimensionalism works best if both dimensions belong to an expression's public meaning. I think that Christian thinks that this holds only for context-dependent expressions. I think it holds almost universally. But this may be a matter of terminology: For me it is part of the meaning of 'the liquid that actually flows in rivers' that this would not denote H2O if it would turn out that XYZ flows in rivers, whereas for Christian this is a metasemantic fact. Anyway, problems for two-dimensionalism come when the first dimension doesn't belong to public meaning.

Relative rigidities

Don't miss Brian Weatherson's very insightful answer to my posting on rigidity (from which I've just stripped some irrelevant formalities). I happily agree with everything he says, so I'll just add a footnote here.

Many advantages of the counterpart theory derive from its denial of the equivalence between 'a=b', 'possibly a=b', and 'necessarily a=b'. For example, this allows for a statue to be identical to a lump of gold even though it might not have been. Since, as Weatherson argues, the rejected equivalence is built into the customary ('strong') concept of rigidity, that concept must be weakened to be useful for counterpart-theorists.

Locating the paradox

Brian Weatherson correctly argues that, since premise 2 of argument Z is analytically true, it can be simplified to

Argument Z':
1. If the conclusion of argument Z' is true, then argument Z' isn't sound.
Therefore: Argument Z' isn't sound.

The paradox then arises in two different ways. First, for premise 1 to be false, it must be the case that 'Argument Z isn't sound' is true and argument Z is sound.

Second, and more interestingly, the falseness of premise 1 analytically implies that argument Z is sound, which in turn analytically implies that all premises of argument Z are true, which implies that premise 1 is true.

This second paradox can be further simplified to:

Argument Z'':
1. Argument Z'' isn't sound.
Therefore: Snow is white or snow isn't white.

Rigidity without trans-world-identity?

I wonder how rigidity can be characterized without begging the question against a lot of good semantic theories.

Usually, a rigid expression is defined as an expression which has the same extension in all possible worlds (that is, as an expression with a constant intension, or C-intension).This characterization presupposes literal trans-world-identity between extensions, which is bad, since it carries a commitment to precise essences of individuals on the one hand and (presumably abundant) universals as extensions of predicates on the other, thereby ruling out counterpart theories and accounts on which tropes or classes are the extensions of predicates.

A paradoxical argument

An argument is called sound if it is deductively valid and its premises are true. Now consider the following argument, which I'll dub 'argument Z':

1. If the conclusion of argument Z is true, then argument Z isn't sound.
2. If the conclusion of argument Z is not true, then argument Z isn't sound.
Therefore: Argument Z isn't sound.

Is argument Z sound? (If not, which premise is false?)

What's wrong with canberra-planning causation?

If you're asked to explain how your preferred theory of everything -- that is, your brand of physicalism -- can accomodate some entity X, the first thing to try is the Canberra Plan. It goes as follows: First, collect features that could be said to characterise X. If you're lazy, simply collect everything the folk says about X. Next, say that since these features comprise the essence of X, whatever physical entity has (more or less exactly) those features is X. Finally, explain that of course there is such a physical entity, since otherwise statements about X wouldn't be true.

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