List, My aim is not to differ from André's approach to discovering categories. I do not want to engage in an endless philosophical debate about the reality of mathematical objects and their complex relationship with experience. The disagreements will come later because I assume a Categorical Theoretic Structuralism position in mathematics. I extend it to phaneroscopy using an isomorphism between an abstract mathematical object (Poset or Functor) and the set of relations between Peirce's universal categories as he defines them. It seems to me that this consolidates the scientific status of phaneroscopy. Then - note that this is my conclusion - I point out all the interest in considering these structures because they agree with Peirce's objective idealism if we need a philosophical reference.
Your quotation from Peirce introducing the question of truth is enlightening in this respect: *"And this truth like every truth must come to us by the way of experience. No apriorist ever denied that*.". Indeed, whether you consider me as an apriorist or not, it will not destroy this isomorphism. All means are good to reach the truth; let us not waste time in vain quarrels. Sincerely, Robert Marty Honorary Professor; Ph.D. Mathematics; Ph.D. Philosophy fr.wikipedia.org/wiki/Robert_Marty *https://martyrobert.academia.edu/ <https://martyrobert.academia.edu/>* Le sam. 26 juin 2021 à 15:07, <[email protected]> a écrit : > List, > > Robert, except for a few inaccuracies (like the misspelling of > *prescission*), your account of the discovery of the categories is very > much in line with André’s, although the terminology is different. If I may > focus on one sentence of your summary, I have a question about your usage > of the term *a priori* here: “the act of precession is a simple > observation that we can discover an organization a priori in the phaneron.” > In most philosophical discourse (since Kant anyway), *a priori* means > “prior to experience” (usually meaning *sense* experience). If you mean > that we can discover this “organization” without relying on any > *particular* sense experience, this is certainly true of phaneroscopic > observation, because the phaneron includes that “organization” *as well > as* sense experience. But obviously the discovery cannot be prior to > observation of the phaneron. Once it has been formulated, mathematically or > otherwise, the organization has been generalized *from the observation*, > not the other way round. If you agree with that, your account is in > agreement with André’s, as far as I can see. > > As for Peirce, one relevant comment on the issue is this one: > > CSP (CP 1.417,): [[ The questions which are here to be examined are, what > are the different systems of hypotheses from which mathematical deduction > can set out, what are their general characters, why are not other > hypotheses possible, and the like. These are not problems which, like those > of mathematics, repose upon clear and definite assumptions recognized at > the outset; and yet, like mathematical problems, they are questions of > possibility and necessity. What the nature of this necessity can be is one > of the very matters to be discovered. This much, however, is indisputable: > if there are really any such necessary characteristics of mathematical > hypotheses as I have just declared in advance that we shall find that there > [are], this necessity must spring from some truth so broad as to hold not > only for the universe we know but for every world that poet could create. > And this truth like every truth must come to us by the way of experience. > No apriorist ever denied that. The first matters which it is pertinent to > examine are the most universal categories of elements of all experience, > natural or poetical. ]] > > Gary f. > > *From:* [email protected] <[email protected]> *On > Behalf Of *robert marty > *Sent:* 26-Jun-21 04:08 > > List, > > Since it is a slow read, we have the convenience of dealing with the > questions one after the other. > > I observe that it is admitted in the previous slide that the reader is > familiar with the categories. They have a logical role, form a small set > gradually ordered, participate in a step-by-step process that incorporates > them. Each category is found inductively (in the phaneron, I suppose); > finally, they are tested by precession. > > I notice that no formal definition of the categories have been presented > (like CP 8.328), nor any justification of their reduction to three > (Reduction Thesis), and that the terms "mode of being" have not been > mentioned so far. > > > > Slide 7 provides more details on testing. > > - it is an act of abstractive analysis (it is thus an operation of the > mind on what is in front of it, i.e., a phaneron). > > - This operation seeks to identify (used as an intransitive verb) in this > phaneron logically (sic) distinct components. The latter has the > particularity of having non-reciprocal* dependency relations between them. > This is how sets of three components connected by these relations are > formed, that an act of analysis has abstracted from the phaneron. > > The next two points introduce "active determinations" and particular rules > (to be discussed later). > > > > At this point, I summarize: the act of precession is a simple observation > that we can discover an organization a priori in the phaneron. An > organization that is already there. Now, in the mathematical repository, we > find a very simple axiomatized structure (Partially Ordered Set, Poset) > devoid of any empirical contamination which gathers in a single diagram (3 > à2à1) the totality of the information brought by De Tienne. Why not > extract this structure from the "cloudy manifold"? Everything would become > so much simpler! Especially considering that Peirce advocates it in his > Classification of Sciences (MS 1345, CP 2.119): > > > > "[ … ]- *mathematics,* the study of ideal constructions without > reference to their real existence, > > - *empirics*, the study of phenomena *with the purpose of identifying > their forms with those mathematics has studied,* > > - *pragmatics*, the study of how we ought to behave in the light of the > truths of empirics." > > (Peirce, MS 1345, undated, transcription 1976: NEM, III.2, 1122) [bold > emphasis is mine] > > > > *(i.e. whenever there is a relation of dependence between two components A > and B, there is no relation of dependence between B and A) > > > > Sincerely, > > Robert Marty > > > > Honorary Professor; Ph.D. Mathematics; Ph.D. Philosophy > > fr.wikipedia.org/wiki/Robert_Marty > > *https://martyrobert.academia.edu/ <https://martyrobert.academia.edu/>* > > > _ _ _ _ _ _ _ _ _ _ > ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. 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