Moved
After two weaks of homelessness I've moved into my new flat today.
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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'.
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.
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.
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.
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.
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?)
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.
Within the last 24 hours, this page has been literally flooded by tens of people, most of them following a friendly link at Brian Weatherson's weblog. What's more, I'm now the world's leading authority on higher-order mereological contradictions! Seid umschlungen, Millionen.
There are many ways to update a belief system. For example, 1) believe every proposition that comes to your mind; 2) believe everything that makes you feel good; 3) believe everything Reverend Moon says. In "A Priority as an Evaluative Notion", Hartry Field argues that there is no fact of the matter as to which way is best.
In one sense, this is trivial. Of course the normative question which way you should choose does not have a purely factual answer. Which way you should choose depends on what you want from your belief system.
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