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4 ideas
13979 | Logic studies consequence, compatibility, contradiction, corroboration, necessitation, grounding.... [Ryle] |
Full Idea: Logic studies the way in which one thing follows from another, in which one thing is compatible with another, contradicts, corroborates or necessitates another, is a special case of another or the nerve of another. And so on. | |
From: Gilbert Ryle (Are there propositions? [1930], IV) | |
A reaction: I presume that 'and so on' would include how one thing proves another. This is quite a nice list, which makes me think a little more widely about the nature of logic (rather than just about inference). Incompatibility isn't a process. |
16867 | Logic not only proves things, but also reveals logical relations between them [Frege] |
Full Idea: A proof does not only serve to convince us of the truth of what is proved: it also serves to reveal logical relations between truths. Hence we find in Euclid proofs of truths that appear to stand in no need of proof because they are obvious without one. | |
From: Gottlob Frege (Logic in Mathematics [1914], p.204) | |
A reaction: This is a key idea in Frege's philosophy, and a reason why he is the founder of modern analytic philosophy, with logic placed at the centre of the subject. I take the value of proofs to be raising questions, more than giving answers. |
16863 | Does some mathematical reasoning (such as mathematical induction) not belong to logic? [Frege] |
Full Idea: Are there perhaps modes of inference peculiar to mathematics which …do not belong to logic? Here one may point to inference by mathematical induction from n to n+1. | |
From: Gottlob Frege (Logic in Mathematics [1914], p.203) | |
A reaction: He replies that it looks as if induction can be reduced to general laws, and those can be reduced to logic. |
16862 | The closest subject to logic is mathematics, which does little apart from drawing inferences [Frege] |
Full Idea: Mathematics has closer ties with logic than does almost any other discipline; for almost the entire activity of the mathematician consists in drawing inferences. | |
From: Gottlob Frege (Logic in Mathematics [1914], p.203) | |
A reaction: The interesting question is who is in charge - the mathematician or the logician? |