display all the ideas for this combination of philosophers
3 ideas
19057 | Classical quantification is an infinite conjunction or disjunction - but you may not know all the instances [Dummett] |
Full Idea: Classical quantification represents an infinite conjunction or disjunction, and the truth-value is determined by the infinite sum or product of the instances ....but this presupposes that all the instances already possess determinate truth-values. | |
From: Michael Dummett (The philosophical basis of intuitionist logic [1973], p.246) | |
A reaction: In the case of the universal quantifier, Dummett is doing no more than citing the classic empiricism objection to induction - that you can't make the universal claim if you don't know all the instances. The claim is still meaningful, though. |
9106 | The word 'every' only signifies when added to a term such as 'man', referring to all men [William of Ockham] |
Full Idea: The syncategorematic word 'every' does not signify any fixed thing, but when added to 'man' it makes the term 'man' stand for all men actually. | |
From: William of Ockham (Summa totius logicae [1323], I.c.iv) | |
A reaction: Although quantifiers may have become a part of formal logic with Frege, their importance is seen from Aristotle onwards, and it is clearly a key part of William's understanding of logic. |
9186 | First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett] |
Full Idea: First-order logic is distinguished by generalizations (quantification) only over objects: second-order logic admits generalizations or quantification over properties or kinds of objects, and over relations between them, and functions defined over them. | |
From: Michael Dummett (The Philosophy of Mathematics [1998], 3.1) | |
A reaction: Second-order logic was introduced by Frege, but is (interestingly) rejected by Quine, because of the ontological commitments involved. I remain unconvinced that quantification entails ontological commitment, so I'm happy. |