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