[FOM] Concerning definition of formulas
Alex Blum
blumal at mail.biu.ac.il
Tue Oct 2 06:01:31 EDT 2007
Arnon Avron wrote:
>
>
> So the real answer to the question (in the spirit of Poincare)
>is that there are basic concepts which cannot
>really be defined, and can only be explained in terms of themselves
>(or some equivalent notions). There is no way to explain the quantifiers
>"forall" and "exists" without using at least one of these quantifiers,
>and the same applies to other logical notions (I believe that
>anybody who has taught a basic course in logic, and explained
>Tarski's semantics, has faced some student claiming: "but
>you use "forall" to define the meaning of "forall"!").
>
I wonder if givinvg the truth conditions of say the universal quantifier
is intended to do more than make precise the use of the formal
counterpart of ''for all ', rather than define it. And thus at least
in this case circularity does not enter.
Alex Blum
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