[hist-analytic] Proving

Roger Bishop Jones rbj at rbjones.com
Fri Jan 8 16:48:52 EST 2010

On Friday 08 January 2010 16:01:35 jlsperanza at aol.com wrote:

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

It is definitely dialectical.  I don't know where he introduces the term, but 
he uses it in the sense we are considering right at the beginning of the prior 


> 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.


> 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.

I might add on this topic that in modern logic the distinction which Danny 
attempts to draw between proof and derivation is not sustainable.
It rests too heavily on the distinction between an axiom and a rule, and 
exactly the same deductive system (i.e. having the same theorems) can be 
presented entirely without rules, or entirely without axioms or with a mixture 
of the two.  For example, it is not unusual for axioms to be treated as 
inference rules which require no premises.
Furthermore, from a sceptical point of view, there is no better reason in 
general to trust an inference rule than an axiom, and so no basis for 
accepting derivations but denying that there can be proofs.

Roger Jones

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