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.
A sentence is context-dependent if different utterances of it in different contexts have different truth values. A common kind of context-dependence is contingency. For instance, 'there are unicorns' is true when uttered in a world that contains unicorns, and false otherwise. Now look at Convention T:
'p' is true iff p.
When 'p' is context-dependent, it doesn't really make sense just to call it true. However, Convention T certainly isn't meant to apply only to non-contingent (and otherwise non-context-dependent) sentences. So what shall we make of it? Two possibilites come to mind:
1) 'p', uttered in the present context, is true iff p.
Let S be the sentence "S contains a quantifier that does not range over everything".
S (and every utterance of S) is contradictory. Interestingly, it is so even if the quantifier in S really does not range over everything. From which it follows that either there are true contradictions, or "S contains a quantifier that does not range over everything" is not true iff S contains a quantifier that does not range over everything.
First: Are fundamental particles mereological atoms?
Fundamental particles are 'the ultimate constituents of the world',
those upon whose properties and relations everything else supervenes. Many
of us believe that the instrinsic properties of complex things supervene
upon the properties and relations of their consituents. Then maybe the
fundamental particles can be identified with the ultimate constituents of
the world, if there are any. In fact, when we find that some things are
composed out of smaller things, we will usually not call the complex things
'fundamental particles'. I think it is in this sense that fundamental particles are supposed to be
indivisible -- not because we lack the means to break them into parts, nor
because it is impossible 'in principle' to break them, but simply because
they lack (proper) parts.