Two Conceptions of Truth? Comment

[...]we constantly and unashamedly employ classical logic and classical mathematics in reasoning with concepts with imprecise boundaries. Because of the vagaries of immigration status, the set of people who live in Canada isnt a sharply dened set and the population of Canada isnt a sharply dened number, and in spite of that demographers studying Canadian social trends make unabashed use of classical statistics. There is no fact of the matter there to be known, so that even God doesnt know. [...]a sharper version of the doctrine is availableIf the Pope says that u ex cathedra, then u is determinately true.In other words, the thesis, Everything the Pope says ex cathedra is true, holds even if truth is understood in the correspondence sense.There is nothing special about the Pope in this. For this purpose, the correspondence notion will work as well as the disquotational.Without a doubt, one can contrive examples knights and knaves puzzles, things like that21 that rely on its being disquotational truth, rather than correspondence truth that is being employed. [...]disquotational truth is valuable because its the bird in the hand. [...]we prove the Godel sentence for PA by introducing a truth predicate for the language of arithmetic, then allowing the truth predicate to appear within instances of the induction axiom schema.If we understand arithmetical language and we are willing to allow that there are such things as natural numbers, then we shall accept the principle of mathematical induction.