Logique du second ordre et d'ordre supérieur
20 décembre 2007
There are two approaches to the semantics of second-order logic. They differ on the interpretation of the phrase “for every set of objects.” Does this have some fixed meaning to which we can refer, or do we need to consider the variety of meanings the phrase might have? In the first case (which will be called standard semantics), we are taking for granted certain mathematical concepts. In the second case (which will be called general semantics), much less is being taken for granted. In this case, to be considered valid, a sentence will need to be true under all the allowable meanings of the phrase “for every set of objects.”
