Nam Nguyen wrote: > On 29/05/2013 3:25 AM, Peter Percival wrote: >> Nam Nguyen wrote: >> >>> >>> Well, then, why don't you express infinity with purely logical >>> symbols, for us all in the 2 fora to see? Seriously, that would >>> be a great achievement! >> >> It is easy enough to find formulae whose only models are infinite. > > Go ahead and write down one such formula that would express infinity > but has only logical symbols.
As remarked elsewhere, FOL with no extra-logical symbols is the theory of identity. Most formulations of FOL have at least some constants/function symbols/predicates. Just one binary predicate (for example) suffices to write down a suitable formula.
-- I think I am an Elephant, Behind another Elephant Behind /another/ Elephant who isn't really there.... A.A. Milne