CS Peirce : 1897 [c.] | On Multitude | MS [R] 26:1 Mathematics is a study of exact hypotheses, in so far as consequences can be deduced from them. *To limit mathematics to the deduction* of those consequences would be to separate from it some of the greatest of the achievements of modern mathematicians – achievements which nobody but mathematicians could have performed – such as the formation of the idea of the system of imaginaries, and of the idea of Riemann surfaces*. It must be allowed, therefore, that the formation of the hypotheses is a part of the business of mathematics*." [emphasize mine]
Of course, since recognizing mathematical forms in experiments (his own or those submitted to him by phaneroscopists) requires having the right forms in his mind... why not recognize it? 🤷 Le mer. 11 août 2021 à 13:18, <g...@gnusystems.ca> a écrit : > Continuing our slow read on phaneroscopy, here is the next slide of André > De Tienne’s slideshow posted on the Peirce Edition Project (iupui.edu) > <https://peirce.iupui.edu/publications.html#presentations> site. > > Gary f. > > > > > > Text: > > - What mathematicians observe (and construct and manipulate) are *pure > hypotheses, possibilia* that get represented in diagrams. > - The significance and truth-value of such constructs depends only on > their *internal* inferential coherence, *not on the world of > experience*. > - Mathematics seeks to *derive consequences* that are true in *every > possible configuration*, and not merely what is true of the actual > world. > - In that regard, *pure mathematics plays freely with forms*, > unconcerned with whether they play any part in experience. > > _ _ _ _ _ _ _ _ _ _ > ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to > peirce-L@list.iupui.edu . > ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to > l...@list.iupui.edu with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the > message and nothing in the body. More at > https://list.iupui.edu/sympa/help/user-signoff.html . > ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and > co-managed by him and Ben Udell. >
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