[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


More information about the FOM mailing list