[FOM] Concerning definition of formulas

[Richard Heck]

Saurav wrote:
> This is seemingly convincing. But as ZF is itself made of formulas, we
> can not adopt this definition.
>   
I don't quite understand this. Yes, ZF is a set of formulae. But there's 
nothing circular about using set theoretic language to define the notion 
of a formula of ZF. You aren't /using/ the notion of a formula in the 
definition. The set of formulae is defined in terms of ordinary set 
theoretic notions, ultimately in terms of membership.

It's really quite irrelevant whether the background theory is ZF. If 
you're going to define this notion, or any other, then you have to use 
some background theory. And theories are sets of formulae.

The set theoretic definition is really overkill, though. You can define 
the notion of a formula in a very weak arithmetic, using the techniques 
pioneered by Goedel.

Richard

-- 
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Richard G Heck, Jr
Professor of Philosophy
Brown University
http://frege.brown.edu/heck/
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