Battleground God says that there are three contradictions in my views about God. Of course I don't believe my views are contradictory. Here are the alleged contradictions:
First, I accepted both of the following as true:
4. Any being which it is right to call God must want there to be as little suffering in the word as is possible.
12. If God exists she could make it so that everything now considered sinful becomes morally acceptable and everything that is now considered morally good becomes sinful.
Is this a contradiction? I'm not quite sure whether (12) is an indicative or a subjunctive conditional, but I think if it was subjunctive it would have to go "If God existed ..." or "If God would exist ...". So I think it's meant to be indicative (in the sense of "If God exists, then it is the case that: She could ..."). Like most people, I find it difficult to evaluate indicative conditionals with false antecedents, but at least for today I felt like embracing the Grice-Jackson-Lewis view that they are true. The website complained that I "say that God could make it so that everything now considered sinful becomes morally acceptable". But that's not what I said!
I've fixed a couple of (five, to be precise) problems in Postbote.
On Friday, I wrote:
Conclusion 2: If we want to avoid Bradley's regress, there is
no reasonable way to defend the principle that every meaningful expression
of our language has a semantic value. (Russell's paradox is an independent
argument for the same conclusion.)
Today, I was trying to prove the statement in brackets. This is more
difficult than I had thought.
Semantic paradoxes usually (always?) arise out of an unrestricted
application of schemas like
Friends who know English better than I often tell me that when I write English, my sentences get too long and complicated. So I noticed with considerable relief this resolution from the University at Buffalo on open source software.
Frege believes that predicate expressions have semantic values (Sinne and
Bedeutungen) which can't be denoted by singular terms. Hence "the
Bedeutung of 'is a horse'" does not denote the Bedeutung of 'is a horse'.
Before the discovery of Russell's paradox, the only reason he ever gave for
this view -- apart from claiming that it is a fundamental logical fact that
just has to be accepted -- is that otherwise the semantic values of a
sentence's constituents wouldn't "stick together". The more I think about
this reason, the less convincing I find it.
That new Whitespace programming language looks fun. It uses only three different whitespace characters. So I've been thinking about a possible language with just a single character. The only information contained in the source code of such a program would be the code's string length. The compiler would have to read all instructions from the properties of this number, e.g. its digits, its prime factors, etc. I couldn't come up with anything that looks even remotely feasible though. (The cheap trick of course is to interpret the string length as the Gödel number of some C code.)
The war and the Spring, that broke out almost simultaneously, both
distract me from philosophy. I also have to think about where to go
when I move out of my flat in about two weeks time. Should I stay in
Berlin and enjoy another cheap and relaxed summer, or should I rather go to
Bielefeld and enjoy some reasonable philosophy? Unfortunately, in Germany
the quality of philosophy departments is inversely proportional
to the attractiveness of the cities where they are located.
Frege uses second-order quantification in both his formal and informal
works. So far, I have always assumed that his second-order logic is
standard second-order logic. But couldn't it also be second-order logic
with Henkin semantics, which would in fact be a kind of first-order logic
(compact, complete and skolem-löwenheimish)? Unfortunately, I know far too
little about second-order logic to answer this question.
Are there any second-order statements that are satisfiable in standard
semantics, but not in Henkin semantics? (I guess there must be: Wouldn't
second-order logic with standard semantics have to be complete otherwise?
Not sure.) If so, do any of Frege's theorems belong to these?
I've finished the exercises. I still have to put together some of the
solutions, but since Word always crashes when I draw complicated tables and
trees, I've decided to take a break in order to save my mental health. (In
fact, Word not only crashes frequently in these cirumstances, it also
deletes the currently open file while crashing.) So now I'm working
on the Frege paper again, which I really want to finish soon.
Brian Weatherson has
posted a
couple of interesting
entries on imaginative resistance.
I've finally managed to introduce the provability predicate and its properties without mentioning representability and recursiveness. The exercise is then to derive Löb's theorem and Gödel's incompleteness theorems. Unfortunately these deductions are not as simple as I thought they were. Probably too difficult for an introductory book.
I've also just made up this puzzle, which is not very difficult I think. ("Not very difficult" even in the ordinary sense of "not very difficult", not only in the David Chalmers sense.)