Robert, List: I do not recall ever *denying *the value of the poset (3→2→1) as a mathematical hypothesis with application to phaneroscopy, or that there is indeed a sense in which it is isomorphic to Peirce's universal categories (3ns→2ns→1ns). In fact, last week I explicitly *acknowledged *that it "is a a mathematical (i.e., iconic/diagrammatic) *representation *of Peirce's categories and (especially) their relations," denying only that it is "properly identified with the categories *themselves*" ( https://list.iupui.edu/sympa/arc/peirce-l/2021-08/msg00039.html).
Moreover, as discussed on the List last month ( https://list.iupui.edu/sympa/arc/peirce-l/2021-07/msg00091.html), Francesco Bellucci similarly proposes that the formal logic of relations/relatives is what enables Peirce to "establish that the elements of the Phaneron have valence" ( https://www.academia.edu/11664897/Peirce_on_Phaneroscopical_Analysis, p. 3). I suggested that this is likewise an example of *applied *mathematics, "using principles adapted from mathematics within phaneroscopy" ( https://list.iupui.edu/sympa/arc/peirce-l/2021-07/msg00082.html). Regards, Jon S. On Wed, Aug 11, 2021 at 11:30 AM robert marty <robert.mart...@gmail.com> wrote: > Jon Alan, List, > > JAS > " ... what is allegedly still not being recognized?" > > But I will tell you! What now stands in the way of your recognizing the > value of the mathematical object (Poset) "3→2→1" (C) (the arrow > representing abstracts morphisms)? Because I have shown very simply ( see > Podium, section 6, p.18) that this object is isomorphic to the > phaneroscopic object "Thirdness →Secondness →Firstness" (D) ( with the > arrow representing involvements). I have been proposing it for a very long > time as a provider of the mathematical principles of phaneroscopy. If you > can present me a better one I am ready to redirect my research ... > > Regards, > > Robert Marty > Honorary Professor ; PhD Mathematics ; PhD Philosophy > fr.wikipedia.org/wiki/Robert_Marty > *https://martyrobert.academia.edu/ <https://martyrobert.academia.edu/>* > > Le mer. 11 août 2021 à 16:56, Jon Alan Schmidt <jonalanschm...@gmail.com> > a écrit : > >> Robert, List: >> >> Where has anyone disputed anything stated in the quotation below from >> Peirce or implied by the subsequent question? Having acknowledged >> repeatedly that formulating ideal hypotheses from which necessary >> conclusions are subsequently drawn indeed falls within the scope of pure >> mathematics, what is allegedly still not being recognized? >> >> Regards, >> >> Jon Alan Schmidt - Olathe, Kansas, USA >> Structural Engineer, Synechist Philosopher, Lutheran Christian >> www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt >> >> On Wed, Aug 11, 2021 at 8:01 AM Robert Marty <robertmarty...@gmail.com> >> wrote: >> >>> 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. >>>> >>>>
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