Dave Chalmers kindly explained his views on deducibility to me. He thinks that anything one could reasonably call non-deferential understanding of the fundamental truths would suffice for being able in principle to deduce macrophysical facts, provided that these fundamental truths, unlike my P, contain phenomenal facts and laws of nature. He also notes that I shouldn't have called these restrictions (to non-deferential understanding and the rich content of fundamental truths) assumptions, since they are really just restrictions. I'm still not sure if any kind of non-deferential understanding would suffice, but with the restrictions in place it's not as easy to come up with counterexamples as I thought.
Back to the question of deducibility.
According to the deducibility thesis, the fundamental truths (plus
indexicals, plus a 'that's all' statement) a priori entail every truth.
More precisely, when P is a complete description of the fundamental
truths and M any other truth, then, according to the deducibility thesis,
the material conditional 'P
M' is a priori.
Dave Chalmers agrees that any concept can be explicitly analyzed by an
infinite conjunction of application-conditionals. But he wants to
restrict 'explicit analysis' to finite analyses. That certainly makes
sense, but I doubt that there are any concepts for which the
application-conditionals cannot be determined by finite means. For
example, I think it will usually suffice to partition the epistemic
possibilities into, say, 50 zillion cases and specify the extension in
each of these cases. Admittedly, I can't prove that, but the fact that concepts can be learned and our cognitive capacities are limited seem suggestive.
Dave Chalmers told me to
read some of his
papers. I have, and I'll probably say more on the
deducibility problem soon. Here is just a little thought on conceptual
analysis.
Chalmers suggests that we don't need explicit necessary and sufficient
conditions to analyse a concept. Rather, we can analyze it just by
considering its extension in hypothetical scenarios. What is it to
consider a hypothetical scenario? The result seems to depends on how the
scenario is presented. For example, 'the actual scenario' denotes the same
scenario as 'the closest scenario to the actual one in which water is H2O'.
But the difference in description could make a difference for judgements
about extensions. Chalmers avoids such problems by explaining
(§3.2, §3.5) that to consider a scenario is to pretend that a
certain canonical description is true. Hence to analyze a concept, we
evaluate material conditionals of the form 'if D then the extension of C is
E', where D is a canonical description. (Are there only denumerably many
epistemic possibilities or can D be infinite?) Now fix on a particular
concept C and let K be the (possibly infinite) conjunction of all those
'application
conditionals' (§3) that get evaluated as true. Replace every
occurrence of 'C' in K by a variable x. Then 'something x is C iff K' is
an explicit analysis giving necessary and sufficient conditions for being
C.
There may not always be a simple, obvious, or finite
explicit analysis, but at least there always is some explicit
analysis. If moreover satisficing is allowed, it is very likely that we
can settle with something much less than infinite.
When I tried to spell out the 'modus tollens' I mentioned on monday, I
came across something that may be interesting.
Frank Jackson argues that facts about water are a priori deducible from facts about H2O:
1. H2O covers most of the earth.
2. H2O is the watery stuff.
3. The watery stuff (if it exists) is water.
C. Therefore, water covers most of the earth.
1 and 2 are a posteriori physical truths, 3 is an a priori conceptual
truth.
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.
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.