[hist-analytic] Proving

jlsperanza at aol.com jlsperanza at aol.com
Fri Jan 8 11:01:35 EST 2010


R. B. Jones in post of Fri, Jan 8, 2010 12:55 pm:


"A crucial difference here being that the requirement that the premises 
be necessarily true is weaker than the requirement that they be 
self-evident, and one may be satisfied of this is one s willing to 
accept the axioms of ZFC..."

Very good, and thanks for the other comments which I will elaborate on 
time. I was impressed by this little (well, this is innuendo) book on 
¨Proof and Disproof in formal logic": the subtitle reads, "An 
introduction for programmers", which I didn´t know I _was_, for I found 
it to be "my cup of tea" and much more readable than books I only 
narrowed myself to read, e.g. Strawson (Intro Logical Theory) or 
Sainsbury (Logical Form) in what they self-label, like Grice, 
¨philosophical logic".

I will try and find out what the other term other than ´demonstrative 
proof´ for Aristotle was. Yes, problematic or dialectical sound just 
right.

Your mention of ´necessary true´ is an interesting claim as it being 
weaker than ´self-evident´. Indeed, I never understood ´self-evident´. 
Self-evidently true, I presume. But how can an axiom have a _self_? I 
assume "self" there translates "auto-", which is a very confusing 
prefix anyway (cfr. "if driving fast automobiles you like, if old hymns 
you like...").

I think it is pretty plausible to accept ZFC.

Incidentally, when I said, trying to take up D. Frederick´s new usage:

   Christopher Columbus derived that the Earth was round.

or

   Copernican derived that the Earth gyrates around the sun,
       thus underiving Ptolemy.

I have to concentrate on the ´psychological´ reading of ´prove´. For it 
may well be that Columbus landing in Santo Domingo did prove that the 
earth is round, which would not entail that he himself proved that.

Grice thinks that "to reason" works like "to prove", although perhaps 
"to prove" is more general. He attempts a nec/suff analysis of "reason" 
which is always FROM premise TO conclusion:

    1. Agent thinks P
    2. Agent thinks C
    3. Agent thinks that there is a proof from P to C, or derivation.
    4. 1 is cause of 2.

Of course Grice was no Phyrronean, and would allow for ´proof´ to be of 
various types, not unlike Toulmin and his field- or 
territorial-dependent validities (with _equi_-vocation, though, in 
Grice´s parlance)

Phyrroneans, as I believe, just were, like Danny, and me on Tuesdays, 
so demanding with terms that they would not allow people to use things 
like "proof" or "know" gratuitously at all.

Etc.

J. L. Speranza
   for the Grice Club
          -- this sobriquet to note that I´m not trying to refute or 
disprove Grice.



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