Concept tag
#intuitionism
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Giving up excluded middle would cost school mathematics far too much
I've been reading about intuitionism. Brouwer denied that "P or not-P" holds for every mathematical statement, and so rejected proofs that rely on it. My thesis: whatever the merits for research mathematicians, the cost to the mathematics we actually teach is far…
Started by Vikram Sethi5 replies -
Intuitionists are right to refuse the law of excluded middle for infinite collections
I lean intuitionist, so I declare my bias. Here's the case. For Brouwer, mathematical objects are mental constructions, and to assert that something exists is to be able to construct it. On that view, “P or not-P” is a claim that we…
Started by Ana Clara Ferreira5 replies -
Strong moral intuitions count as evidence, in the same way that perceptions count as evidence
In my ethics seminar we were told that appealing to intuitions is unscientific: they are just gut feelings shaped by upbringing. I want to argue the opposite. W. D. Ross, in The Right and the Good (1930), compared the considered moral convictions…
Started by Aoife Kilbride6 replies -
Reading group: Dummett’s ‘The Philosophical Basis of Intuitionistic Logic’
I keep noticing that people defend intuitionistic logic for two very different reasons. Brouwer's reason was a picture of mathematics as mental construction. Dummett's reason, in his 1973 paper "The Philosophical Basis of Intuitionistic Logic", was a theory of meaning. I'd like…
Started by Ana Clara Ferreira5 replies