Here at Humboldt University, there's a reading group about analytic
philosophy (Sam already mentioned it). The flyer
advertising this group describes analytic philosophy as a sort of new and
fascinating kind of philosophy characterised by its perspicuity and
ignorance of philosophical tradition. The funny thing is that the
organisers of the reading group decided that we'll be discussing David
Wiggins' Sameness and Substance Renewed. I don't want to know
how much Hegel one has to read to find Wiggins perspicuous (and
ignorant of philosophical tradition).
Some expression can't be properly understood unless one believes certain
things: In some sense you don't understand "irrational number" unless you
believe that no natural number is irrational; You don't understand "grandmother"
unless you believe that grandmothers are female; Maybe you don't understand
"cat" unless you believe that cats are animals.
This is all quite vague because "understanding" and "believing" are vague.
I now want to suggest that a sentence is analytic iff you can't understand
it unless you believe it. Analyticity is also vague, so the vagueness of
the explicans is fine for this purpose.
I've made some slides about logic programming (PS) for my presentation next week in the logic seminar.
The following restriction might be a way out of the problems I mentioned in
my last posting:
The gamma rule must not be applied if the result of its
previous application has not yet been replaced by the Closure rule.
(The gamma rule deals with 
and 
formulae; the Closure rule is the rule that allows to replace dummy
constants by real constants iff that leads to the closure of at least one
branch.)
I just noticed that my tree prover fails on this simple formula! This is a good opportunity to rewrite the part of the script that does the proving and implement some shortcuts, and maybe some "loop detection".
I've added keyboard commands to Postbote: If the focus is on the frame with the mail listing, press "R" to refresh, "A" to select all mails, and "G" to quickly change the listing offset (this is for Hermann, who has 1600 mails in his mailbox...).
Suppose some theory T(F) implicitly defines the predicate F. If we want to
apply the Ramsey-Carnap-Lewis account of theoretical expressions, we first
of all have to replace F by an individual constant f, and accordingly
change every occurrance of "Fx" in T by "x has f" etc. The empirical
content of the resulting theory T'(f) can then be captured by something
like its Ramsey sentence f T'(f), and the definition of f
by the stipulation that 'f' denote the only x such that T'(x), or nothing
if there is no such (unique) x.
In the previous three entries, I've tried to argue that there are no
genuinely implicit definitions: Whenever a new expression is introduced via
an alleged implicit definition, either there is no question of definition
at all, as in the case of new expressions used as bound variables in
mathematics, or there is an explicit definition nearby.
This latter fact, that sometimes explicit definitions are only
nearby, provides a partial vindication of implicit definitions. For
example, let's assume that folk psychology implicitly defines "pain". But
folk psychology itself is not equivalent to the nearby explicit definition.
To get an explicit definition, we have to turn folk psychology into
something like its Carnap sentence. So the theory itself could be called a
genuinely implicit definition.
I've said that an explicit definition introduces a new expression by
stipulating that it be semantically equivalent to an old expression. If
there are no non-explicit definitions, this means that you can only define
expressions that are in principle redundant. Aren't there counterexamples
to this claim?
Consider the definition of the propositional connectives. We can
explicitly define some of them with the help of others, but what if we want
to define all of them from scratch? The common strategy here is to
recursively provide necessary and sufficient conditions for the truth of a
sentence governed by the connective: A 
B is true iff
A is true and B is true.
