[FOM] FOM Formation Rules

[Neil Tennant]

On Mon, 16 Oct 2006, John Corcoran wrote:

> No matter what is meant by rigorous this is an interesting question. I
> would like to know when logicians started thinking of formal languages
> as subsets of the set of finite strings over a finite alphabet, which of
> course is what they are. My guess would include reference to Emil Post's
> dissertation in the 1920's.
>  
> In order to make the original question precise one should specify more
> fully what is mean by rigorous. If by rigorous you mean stated in a
> formalized metalanguage having axioms characterizing the class of string
> over the alphabet of the formal language in question, then the answer is
> probably the Alfred Tarski 1933 truth-definition paper known as
> "Wahrheitsbegriff" (references below). Unfortunately, it must be
> admitted that Tarski seems to show no awareness of the essential
> finiteness conditions.

John,

I think you may be too hard on Tarski here. Or, if I'm being too easy on
him, please let me know why! See my earlier posting

http://www.cs.nyu.edu/pipermail/fom/2006-October/010966.html

for how it is that Tarski secures finiteness.

Best,
Neil