display all the ideas for this combination of philosophers
2 ideas
15926 | Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine] |
Full Idea: The distinctive feature of second-order logic is that it presupposes that, given a domain, there is a fact of the matter about what the relations on it are, so that the range of the second-order quantifiers is fixed as soon as the domain is fixed. | |
From: Shaughan Lavine (Understanding the Infinite [1994], V.3) | |
A reaction: This sounds like a rather large assumption, which is open to challenge. I am not sure whether it was the basis of Quine's challenge to second-order logic. He seems to have disliked its vagueness, because it didn't stick with 'objects'. |
15934 | Mathematical proof by contradiction needs the law of excluded middle [Lavine] |
Full Idea: The Law of Excluded Middle is (part of) the foundation of the mathematical practice of employing proofs by contradiction. | |
From: Shaughan Lavine (Understanding the Infinite [1994], VI.1) | |
A reaction: This applies in a lot of logic, as well as in mathematics. Come to think of it, it applies in Sudoku. |