[FOM] Frege and logic

Dean Buckner Dean.Buckner at btopenworld.com
Sat Oct 18 04:29:29 EDT 2003

> It is not the ... question as to whether
> [Frege] created quantification theory ex nihilo.
> It's a question of who he influenced, not
> about who (if anybody) influenced him.

Exactly, this is the first time this point hs been mentioned.  It's not
enough to create something, even to publish it.  Someone has to read it,
there has to grow a critical mass of people who accept the ideas, develop
them so they are accepted into the canon.  Mere invention is not enough.

Peirce i think was simply rediscovered in 1950's, if he was ever discovered
at all (although Christine Ladd-Franklin was a disciple).  The same perhaps
applies to Frege.  It's very difficult to understand where Frege's ideas
come from, as he rarely acknowledges his sources.  As to where they went,
I've suggested in another posting they may have influenced Zermelo.  They
certainly influenced Russell.  But then the question is how far did Russell
influence the actual development of anything, aside from being a (very good)
populariser of it?

I have another question about what "quantification theory" actually is.
I've been reading Russell again, who credits to Peano the idea that

    if x is a man then x is mortal
    x is a man

are completely different propositions (since the first is always true
whatever we substitute for x, whereas the second is not).  Surely this idea
is fundemental to "modern" quantification.  Otherwise we would credit
Aristotle with the idea - after all the words "some" and "all" define the
"quantity" of a proposition, the word "quantity" being a scholastic term
which was borrowed.


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