Definition talk:Language of Propositional Logic/Alphabet/Letter

It's probably worth mentioning the infinite nature of the alphabet. The point is that the alphabet needs to be non-finite to be valid. If you define an alphabet with $N$ symbols, then this invalidates a statement of the form $p_1 \land p_2 \land \cdots \land p_N \land p_{N+1}$. However big $N$ may be it *has* to be big enough to allow *all possible* valid statements and hence the specification that it necessarily has to be infinite.

If you like we can write a page mentioning this: Alphabet of Propositional Logic is Infinite or some such. --prime mover (talk) 00:11, 5 December 2013 (UTC)


 * Well, in some contexts, only finitely many propositions are of interest. Think of truth tables. That's why I removed the mention of "infinite".


 * Of course, this can also be dealt with by partial boolean interpretations. I concede that this is the clearer of the two approaches. &mdash; Lord_Farin (talk) 07:50, 5 December 2013 (UTC)