In part II of Meaning and Necessity Carnap defines 'L-determinate designators' for rather specific languages (coordinate languages). I think that a more general definition is possible that pretty much meets Carnaps ideas. This more general definition simply identifies L-determinacy with what we nowadays call rigidity.
Does anyone know a good resource on probability theory with infinite
probabilty spaces (if there is such a thing)? For example, I would
like to know if the probability that an arbitrary real number lies
between 0 and 1 is defined, and if so, how the obvious awkwardness of
any answer can be explained away.
If you recently received an email from somebody called 'Wolfgang Schwarz'
mentioning wolfgang@umsu.de and containing a strange attachment, please
don't open it. It is the worm W32.Bugbear@mm. If you have opened the
attachment, this page tells you how to remove it. Also
please don't reply to the sender who is not me and completely innocent,
since the mess really spread from my old windows machine. I'm very sorry
about this.
It is often said, correctly I think, that there are contingent but a priori
sentences, e.g. "water is the dominant liquid on earth". Are these
sentences analytic or synthetic? That is, what puts you in a position to
know these sentences? Does understanding suffice, or do you have to invoke
some other a priori means, like Gödelian insight? To me this seems
wildly and unnecessarily mysterious. Of course understanding suffices, at
least in ordinary cases. So there are contingent but analytic sentences. I
wonder why this is hardly ever said. Does anyone really believe that those
statements are synthetic a priori?
Since narrow content is not determined by external factors, it depends
much more on other propositional states than wide content. For example, if
you believe that Aristotle was human whereas I believe he was a poached
egg, the narrow content of all our beliefs about Aristotle will differ.
When I believe that Aristotle was Alexander's teacher, you can't have a
belief with exactly the same narrow content unless you also come to believe
that Aristotle was a poached egg. Likewise for imaginings: When we both
imagine Aristotle teaching Alexander, our imaginings cannot have the same
narrow content.
Similarly, I think, if Ted believes that for any atoms there is a
fusion, whereas Cian disbelieves this, they cannot share any imagining
about atoms.
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.