The Ways of Reason by LaLumia Joseph;

Author:LaLumia, Joseph; [LaLumia, Joseph]
Language: eng
Format: epub
Publisher: Taylor & Francis Group
Published: 2022-08-15T00:00:00+00:00

Finally, Meyerson warns, none of this must be taken to imply that anyone to whom a mathematical demonstration is being made will also think in terms of extension. On the contrary, he insists, such a person will reproduce in his own mind the type of thinking which in the first place led to the discovery of the theorem in question, that is to say, he will think in intension. "For, as we have shown, it is in this form that theorems, the results of demonstrations, really present themselves to the mind."177

Meyerson is in some serious trouble here, since most scientific literature is surely designed for exposition and communication and since Meyerson, as has been seen, rejects introspection and analysis of behavior as methods of inquiry suited to his purpose. These facts being taken into account, how can Meyerson have found out how the mathematician and the scientist think in the process of making discoveries? As a matter of fact, in regard to mathematical reasoning in particular, we find Meyerson appealing several times to each one's own memory of how he learned mathematical theorems in order to prove some important aspect of his thesis, a recourse that clearly suggests some reliance on introspection.178 But however that may be, it is quite plain that the point-of-view from which Meyerson criticizes mathematical logic and estimates its uses is strictly psychological.

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