|2nd order Logic: Predicate logic of the 2nd order goes beyond predicate logic of the 1st level allowing quantification over properties and relations, and not just objects. Thus comparisons of the powerfulness of sets become possible. Problems which are expressed in everyday terms with terms such as "greater", "between", etc., and e.g. the specification of all the properties of an object require predicate logic of the 2nd order. Since the 2nd level logic is not complete (because there are, for example, an infinite number of properties of properties), one often tries to get on with the logic of the 1st order._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments.|
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Imbroglio / Geach / Cresswell: e.g. Each of two Turks fought against each of two Greeks. - Problem: the following does not work: each of two Greeks was F and each of two Turks was F.
E.g. most fundamentalists are creationists. - Problem:it is not easy with two predicates F and C - it is not possible in 1st order logic to bring it in an order.
Solution: 2nd order Logic: here we can say that there is a 1:1 function of F-creationists to fundamentalists, but not vice versa. - (> Everyday language)._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.
M. J. Cresswell
Semantical Essays (Possible worlds and their rivals) Dordrecht Boston 1988
M. J. Cresswell
Structured Meanings Cambridge Mass. 1984