Dear Jon, List,
> I know what book you are talking about; today it can be downloaded for > free... > I looked at your diagram... it rejuvenated me... indeed, I was always the > terror of my students because, whenever they presented me with a diagram I > demanded that every single point, every single line be documented... so I > look at your diagram and I see first of all ovals,5 , with words inside... > I wonder if they delimit sets of points of the plane which would represent > each one an object of the extension of each of the labels inscribed in the > oval... the answer is obvious, it's not. So the ovals are just decorative > elements that direct attention to the 5 terms of the language they surround. > I come to the lines ... the graphic conventions in use (signs of law) > strongly suggest to me that they are relationships between concepts ... > perhaps of dependence given the context of communication ... the same > conventions and context suggest that they should be considered top-down > relationships ... I can't go beyond that as I have no information about > these lines and the modes of correspondence they cover ... in advance of > the upcoming debate, I say that if all the lines represent top-down > dependency relationships then this diagram comes into open conflict with > Peirce's classification ... conflict involving debate in the Sciences of > Discovery ...I am ready... > > On Thu. Jul 29, 2021 at 2:30 PM, Jon Awbrey <jawb...@att.net> wrote: > Dear Robert, John, Edwina, ... > This discussion reminds me a lot of the time I spent the big bucks > buying a book on "Diagrammatology" which ran to over 500 pages with > many sections in very small print and had just over 50 diagrams in > the whole thing. > > So I think the real "versus" here is more like the difference > between people who "think in words about thinking in diagrams" > and people who "think in words about thinking in words". > > Those of us, the very few, who have actually been > working on "moving pictures" from the very get-go, > have learned to see things somewhat differently. > > https://inquiryintoinquiry.files.wordpress.com/2014/08/peirce-syllabus.jpg > > Regardez, > > Jon > > On 7/29/2021 5:27 AM, robert marty wrote: > > Dear John, Edwina, List > > > > Let me clarify my question: > > > > The references in parentheses refer to the classification > > < > https://www.academia.edu/5148127/The_outline_of_Peirces_classification_of_sciences_1902_1911_ > > > > compiled by Tommi Vehkavaara. > > > > The classification of the Sciences of Discovery places Mathematics (AI) > > ex-ante the Phaneroscopy; the whole mathematical activity is per se, > > independent of any implementation and does not depend on anything, since > it > > incorporates its own mathematics (of Logic) (AIa) as a constituent part > of > > itself. > > > > The discrete mathematics (so the algebra) (AIb) depend on it, and then > the > > Mathematics of Continuum (AIc) depends on them. > > > > The discrete mathematics (so the algebra) (AIb) depend on it, and then > the > > Mathematics of Continuum (AIc) depends on these last ones. > > > > In the ladder of dependencies that penetrate inside the "well of truth" > > (Peirce's metaphor is a way of expressing his agreement with Auguste > Comte) > > comes the (AII) Cenoscopy - Philosophia prima, which is only a generic > > label covering all the positive sciences "which rests upon familiar, > > general experience." At the first rank of them, the Phenomenology (AIIa), > > the study of Universal Categories "all present in any phenomenon: > > Firstness, Secondness, Thirdness." Indeed, any particular science of > nature > > is the study of a phenomenology. We can see that it is at this level that > > Peirce situates the elaboration of his universal categories. > > > > I will stop here for a moment before addressing the question of the > > Normative Sciences (AIIb) because you have referred three Universes of > > Discourse. > > > > JS >. " *In his three universes of** discourse -- possibilities, > > actualities, and necessities – mathematics is first because it includes > > every possible pattern of any kind.*" > > > > In Universe of Discourse | Dictionary | Commens > > <http://www.commens.org/dictionary/term/universe-of-discourse> there is > a > > set of texts in which Peirce expresses himself on his conception of the > > Universe of Discourse. I take one of them, which seems to me to be > > representative (if this were not the case, you could indicate to me > whether > > I am introducing any bias by this choice: > > > > *"1903 | Graphs, Little Account [R] | MS [R] S27:9-10* > > > > *…if one person is to convey any information to another, it must be upon > > the basis of a common experience. They must not only have this common > > experience, but each must know the other has it; and not only that but > each > > must know the other knows that he knows the other has it; so that when > one > > says ‘It is cold’ the other may know that he does not mean that it is > cold > > in Iceland or in Laputa, but right here. In short it must be thoroughly > > understood between them that they are talking about objects of a > collection > > with which both have some familiarity. **The collection of objects to > which > > it is mutually understood that the propositions refer is called by exact > > logicians the universe of discourse." *[emphasize mine] > > > > Then you consider the three universes of discourse which are > possibilities, > > actualities, and necessities. In other words, the universe of discourse > > discussed above is now divided into 3 collections of objects. It remains > to > > know how this division occurs. > > > > Peirce gives us a well-known (but not exclusive) answer, as one could do > in > > any observational science: > > > > * "** Phaneroscopy is the description of the phaneron; and by the > phaneron > > I mean the collective total of all that is in any way or in any sense > > present to the mind, quite regardless of whether it corresponds to any > real > > thing or not. If you ask present when, and to whose mind, I reply that I > > leave these questions unanswered, never having entertained a doubt that > > those features of the phaneron that I have found in my mind are present > at > > all times and to all minds. So far as I have developed this science of > > phaneroscopy, it is occupied with the formal elements of the > phaneron*"(CP > > 1.284) [emphasize mine] > > > > It is well specified further on: > > > > *" What I term phaneroscopy is that study which, supported by the direct > > observation of **phanerons and generalizing its observations, signalizes > > several very broad classes of **phanerons; describes the features of > each**; > > shows that although they are so **inextricably mixed together that no one > > can be isolated, yet it is manifest that their **characters are quite > > disparate; then proves, beyond question, that a certain very short **list > > comprises all of these broadest categories of phanerons there are; and > > finally **proceeds to the laborious and difficult task of enumerating the > > principal subdivisions **of those categories. *(CP 1.286, 1902) > [emphasize > > mine] > > > > That this answer is not exclusive, he showed it himself by having > recourse > > to justify it, on many occasions, to the triadic reduction of polyadic > > relations that he did not really establish himself. It was established > > later, notably by Herzberger, Burch and more recently by Dau F., Correia > > J.H. (2006 <https://link.springer.com/chapter/10.1007%2F11671404_7>) > > > > *" A thorough study of the logic of relatives confirms the conclusions > > which I had reached before going far in that study. It shows that logical > > terms are either monads, dyads, or polyads, and that these last do not > > introduce any radically different elements from those that are found in > > triads. I therefore divide all objects into monads, dyads, and triads; > and > > the first step in the present inquiry is to ascertain what are the > > conceptions of the pure monad, free from all dyadic and triadic > admixtures; > > of the dyad (which involves that of the monad) free from all triadic > > contamination, and what it is that is peculiar which the dyad adds to the > > monad; and of the triad (which involves those of the monad and dyad) and > > what it is that is characteristic of the triad". *(CP 1.293 1894) > > > > I note, moreover, that this text also contains the reasons that allow us > to > > conclude that the categories are interdependent by involvements. > > > > In any case, this answer is provided by Mathematics, which brings us > closer > > to what is meant today by scientific theory and reassures us about the > > possibility of really founding phaneroscopy as a normative science. > Indeed, > > the difference with the observational posture is important when we think > > about the claim to universality of the categories. Indeed, it isn't easy > to > > grant universality to the former, which is rather an act of faith that > many > > consider as an axiom. They can thus free themselves from any mathematical > > reference and send them back to an unimportant level, rather cumbersome. > (but > > this is another story). > > > > As far as you are concerned, you place mathematics in the possibilities > > (1ns); I conclude (you will tell me if I am wrong) that it is from 1ns > that > > the two other categories 2ns and 3ns would be constituted as > complementary > > sub-universes. We would then have an answer to the question of dependence > > which would arise from the possibility contained in an original category > to > > produce the two others, and it would perhaps also be necessary to grant > it > > the possibility to produce itself in a self-referential way, as a > category > > of possibility. > > > > Indeed, there would be no conflict of views as you think: the poset 3 →2 > > -1, a syntactic mathematical structure of the external world would be > > natively present as a possibility of semantic structure (model) in the > > internal world, with the capacity to divide it into three encapsulated > > sub-universes in the following way Thidness→Secondness →Firstness where > the > > arrows represent relations of involvement (or presupposition) and the > > isomorphism between the two posets would also be native. > > > > This approach is very convenient for me because it certainly improves on > > mine by explicitly capturing the implementation of the isomorphism > between > > the two structures. > > > > So my question is, "What about your own side? " ... > > Honorary Professor; Ph.D. Mathematics; Ph.D. Philosophy > > fr.wikipedia.org/wiki/Robert_Marty > > *https://martyrobert.academia.edu/ <https://martyrobert.academia.edu/>* > > > > Le mar. 27 juil. 2021 à 21:55, John F. Sowa <s...@bestweb.net> a écrit : > > > >> Robert> This leads me to a final question to be discussed: should the > >> classification of sciences according to Peirce be considered as a kind > >> of imperative to be respected or can phenomenology be approached from > >> the logic that depends on it according to this classification? > >> > >> There is no conflict among any of those views. Peirce's classification > >> subsumes, relates, and clarifies all of them. In his three universes of > >> discourse -- possibilities, actualities, and necessities -- mathematics > >> is first because it includes every possible pattern of any kind. That > >> includes everything that any human or any living thing of any kind could > >> imagine -- plus all the possible patterns that no finite being could > >> imagine. > >> > >> It's not possible for anybody to imagine any pattern that cannot be be > >> described and analyzed by mathematics (Alice in Wonderland, for example, > >> was imagined by a mathematician/logician). > >> > >> Actuality consists of everything that exists in space and time. It's > >> what nominalists claim is everything. But they have no answer to the > >> mathematicians about the reality of mathematics. And they have no > >> answer to the nominalists about the reality of the laws of nature. > >> > >> Peirce's three universes include Aristotle's answer to Plato: > >> mathematical forms are pure possibilities, which exist in actuality only > >> when embodied. But those forms are really real in the sense that they > >> exist independently of what anybody may think of them. > >> > >> As for the scientific methodology in the Stanford article, that is an > >> example of Peirce's methodeutic for evaluating any proposed theory. > >> That is an example of normative logic, as distinguished from formal > >> logic, which is a branch of pure mathematics. > >> > >> John > >> > > -- Honorary Professor ; PhD Mathematics ; PhD Philosophy fr.wikipedia.org/wiki/Robert_Marty *https://martyrobert.academia.edu/ <https://martyrobert.academia.edu/>*
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