display all the ideas for this combination of texts
4 ideas
| 23248 | Early empiricists said reason was just a useless concept introduced by philosophers [Galen, by Frede,M] |
| Full Idea: The so-called Empiricists in Hellenistic times [as cited by Galen] denied the existence of reason, treating it as a useless theoretical postulate introduced by some philosophers | |
| From: report of Galen (An Outline of Empiricism [c.170], 87.4-9.28ff) by Michael Frede - Intro to 'Rationality in Greek Thought' p.3 | |
| A reaction: I think 'be sensible' is understood by everyone, but 'use your reason' is far from obvious. The main role of reason seems to be as an identifier for human exceptionalism. Animals obviously make good judgements. Frede thinks the empiricists were right. |
| 16877 | A 'constructive' (as opposed to 'analytic') definition creates a new sign [Frege] |
| Full Idea: We construct a sense out of its constituents and introduce an entirely new sign to express this sense. This may be called a 'constructive definition', but we prefer to call it a 'definition' tout court. It contrasts with an 'analytic' definition. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.210) | |
| A reaction: An analytic definition is evidently a deconstruction of a past constructive definition. Fregean definition is a creative activity. |
| 11219 | Frege suggested that mathematics should only accept stipulative definitions [Frege, by Gupta] |
| Full Idea: Frege has defended the austere view that, in mathematics at least, only stipulative definitions should be countenanced. | |
| From: report of Gottlob Frege (Logic in Mathematics [1914]) by Anil Gupta - Definitions 1.3 | |
| A reaction: This sounds intriguingly at odds with Frege's well-known platonism about numbers (as sets of equinumerous sets). It makes sense for other mathematical concepts. |
| 16878 | We must be clear about every premise and every law used in a proof [Frege] |
| Full Idea: It is so important, if we are to have a clear insight into what is going on, for us to be able to recognise the premises of every inference which occurs in a proof and the law of inference in accordance with which it takes place. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.212) | |
| A reaction: Teachers of logic like natural deduction, because it reduces everything to a few clear laws, which can be stated at each step. |