User talk:Lord Farin/Backup/Definition:Propositional Calculus/Alphabet

Are $\vdash$ and $\dashv$ letters? --GFauxPas 17:07, 14 June 2012 (EDT)

I would say that they make sense in an arbitrary theory, and are therefore part of the metalanguage of model theory (or something like that). Thus, I think that they are not letters in the sense of formal systems. --Lord_Farin 17:22, 14 June 2012 (EDT)

No. In the specific context of propositional calculus which is being discussed here, they are not defined, in the sense that they "do not even exist". In the more informal context of propositional logic, an older field (dating in its expounded form from De Morgan, Boole and Peirce etc.) it is indeed defined, but "propositional logic" as such is not a formal system like propositional calculus. --prime mover 18:08, 14 June 2012 (EDT)