Dear John, List Your message leads me to multiple questions, which, in my opinion, raise fundamental problems.
1. JS > "*Different people have different ways of thinking and talking."* Yes, but the individuals, as a whole, do not think nor speak independently of each other; diverse common cultural codes connect them learned, inculcated like languages and signs organized in systems; for a significant part of them, they are imposed (symbolic violence). The semiologist Roland Barthes in his speech of reception, remained famous to the College of France (1977), denounced the languages as follows: "*Language, as the performance of all language, is neither reactionary nor progressive; it is quite simply fascist; for fascism is not to prevent saying, it is to oblige to say*." This is obviously a figure of exaggeration. However, it reflects that languages incorporate worldviews common to the people who use them natively (the Hegelian weltanschauung). For my part, I put this quote from Peirce at the beginning of my Ph.D. (1987): *"All speech is but such an algebra, the repeated signs being the words, which have relations by virtue of the meanings associated with them*."(CP 3.418). The fundamental distinction I share with you between thinking in words and thinking in diagrams thus results from the fact that language is a powerful filter in the expression of thought, while diagrams, which depend only on universal (or almost *universal) *graphic conventions, are virtually free of any influence. 2. JS >* "Phenomenology, phaneroscopy, or phenoscopy is the first stage of** analyzing and interpreting the phaneron in diagrams. It depends on the three branches of mathematics (formal logic, discrete math, and continuous math) to derive and classify the elements and patterns of elements." * I agree, but I add that there are two ways to situate these observations: · either in the "*Practical Sciences*"( *i.e.: "scientific inquiry with an ulterior end (1911) "- "for the uses of life",- "e.g. science of morality (ethics in common sense)* "(see The outline of Peirce's classification of sciences <https://www.academia.edu/5148127/The_outline_of_Peirces_classification_of_sciences_1902_1911_> (1902-1911) compiled by Tommi Vehkavaara) · either in the "Sciences of Discovery" in which they depend on mathematics. Then we have to consider a formal mathematized model and look for it in the "mathematical repository." Question: If we find such a model (which is very easy considering only Peirce's definitions and what he says about the interdependence between the universal categories by involvement), don't we have an obligation to take it into account all along its deployment with Phenomenology in the first line, because the dependence of Phaneroscopy to Mathematics becomes quite explicit? Otherwise, won't we remain confined to the Practical Sciences in the company of the eternal conservative-bricoleurs? 3. JS* > "The patterns are possibilities (hypotheses or guesses) whose** probability is evaluated by the normative sciences." *The syntactic mathematical model having been implemented in the universal categories become a semantic model. It appears then constitutive of phaneroscopy as a universal science of discovery; it is neither hypothesis nor enigma, because it does not have to be submitted to an evaluation, being exact by nature in all locations and at all times, unlike the experimental models whose universality must be verified. The above argumentation is clearly in line with the framework below extracted from The Structure of Scientific Theories (Stanford Encyclopedia of Philosophy) <https://plato.stanford.edu/entries/structure-scientific-theories/#toc> : "A table helps summarize general aspects of the three views’ analyses of the structure of scientific theories: *Syntactic View* *Semantic View* *Pragmatic View* Theory Structure Uninterpreted axiomatic system (i) State-space, (ii) Model-/set-theoretic Internal and external pluralism Theory Interpretation Correspondence rules (i) Hierarchy of models, (ii) Similarity, (iii) Isomorphism (i) Structure already inflected by practice, function, and application (ii) Pragmatic virtues Is theory interpretation an aspect of theory structure? Yes No Yes, although the distinction is hard to make. Table 2. General aspects of each view’s analysis of the structure of scientific theories." 4. RM > his leads me finally 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? Honorary Professor; Ph.D. Mathematics; Ph.D. Philosophy fr.wikipedia.org/wiki/Robert_Marty *https://martyrobert.academia.edu/ <https://martyrobert.academia.edu/>* Le sam. 24 juil. 2021 à 04:28, John F. Sowa <s...@bestweb.net> a écrit : > Different people have different ways of thinking and talking. That is > important, because the world is so complex, so diverse, and so dynamic > that no single method could comprehend and describe it all. Peirce's > method of diagrammatic thinking, which is the foundation for his logic > and philosophy, is more fundamental than thinking in words. > > For Peirce, words are necessary, but imperfect methods of communication. > For example, his 76 definitions of the word 'sign' do not imply 76 > different meanings. The multiplicity of definitions and "outlandish" > terminology in the Commens dictionary shows his lifelong struggle to map > his diagrammatic insights to words. > > Phenomenology, phaneroscopy, or phenoscopy is the first stage of > analyzing and interpreting the phaneron in diagrams. It depends on > the three branches of mathematics (formal logic, discrete math, and > continuous math) to derive and classify the elements and patterns of > elements. The patterns are possibilities (hypotheses or guesses) whose > probability is evaluated by the normative sciences. > > For background, see the three appendices below: (1) quotations by > Peirce about diagrammatic reasoning; (2) quotations by other > mathematicians; and (3) quotations by Peirce about formal, mathematical > methods. > > For details, see Frederik Stjernfelt's "Diagrammatology: An > Investigation on the Borderlines of Phenomenology, Ontology, and > Semiotics". Stjernfelt goes into great detail about the mathematical > foundations. He shows that Peirce and Husserl, despite completely > different terminology, had developed closely related theories. > http://frederikstjernfelt.dk/Peirce/Diagrammatology.%202007.pdf > > Husserl, by the way, had a PhD in mathematics and a strong background in > logic. Both Peirce and Husserl were influenced by Hegel, and both of > them used mathematics to develop a better foundation for phenomenology. > > As Peirce wrote, "the arbitrariness of Hegel's procedure... is in great > measure avoided by my taking care never to miss the solid support of > mathematically exact formal logic beneath my feet." (R318, 1907) > > John > > --------------------------------- > > Appendix 1: Quotations about diagrammatic reasoning > > These quotations by Peirce are discussed in "Natural logic is > diagrammatic reasoning about mental models" and related to current > research in cognitive science. See http://jfsowa.com/pubs/natlog.pdf > > All necessary reasoning without exception is diagrammatic. That is, we > construct an icon of our hypothetical state of things and proceed to > observe it. This observation leads us to suspect that something is > true, which we may or may not be able to formulate with precision, and > we proceed to inquire whether it is true or not. For this purpose it is > necessary to form a plan of investigation, and this is the most > difficult part of the whole operation. We not only have to select the > features of the diagram which it will be pertinent to pay attention to, > but it is also of great importance to return again and again to certain > features. (EP 2:212) > > The word diagram is here used in the peculiar sense of a concrete, but > possibly changing, mental image of such a thing as it represents. A > drawing or model may be employed to aid the imagination; but the > essential thing to be performed is the act of imagining. Mathematical > diagrams are of two kinds; 1st, the geometrical, which are composed of > lines (for even the image of a body having a curved surface without > edges, what is mainly seen by the mind’s eye as it is turned about, is > its generating lines, such as its varying outline); and 2nd, the > algebraical, which are arrays of letters and other characters whose > interrelations are represented partly by their arrangement and partly by > repetitions. If these change, it is by instantaneous metamorphosis. > (NEM 4:219) > > We form in the imagination some sort of diagrammatic, that is, iconic, > representation of the facts, as skeletonized as possible. The > impression of the present writer is that with ordinary persons this is > always a visual image, or mixed visual and muscular... This diagram, > which has been constructed to represent intuitively or semi-intuitively > the same relations which are abstractly expressed in the premisses, is > then observed, and a hypothesis suggests itself that there is a certain > relation between some of its parts -- or perhaps this hypothesis had > already been suggested. In order to test this, various experiments are > made upon the diagram, which is changed in various ways. (CP 2.778) > > Diagrammatic reasoning is the only really fertile reasoning. If > logicians would only embrace this method, we should no longer see > attempts to base their science on the fragile foundations of metaphysics > or a psychology not based on logical theory. (CP 4.571) > > --------------------------------- > > Appendix 2: Related quotations by other mathematicians > > The following quotations are discussed in "Peirce, Polya, and Euclid: > Integrating Logic, Heuristics, and Geometry" and compared to closely > related comments by Peirce. http://jfsowa.com/talks/ppe.pdf > > Archimedes: "Eureka!" Shouted as he jumped out of his bathtub. > > Leonhard Euler: "The properties of the numbers known today have been > mostly discovered by observations... long before their truth has been > confirmed by rigid demonstrations." > > Paul Halmos: "Mathematics -- this may surprise or shock some -- is > never deductive in its creation. The mathematician at work makes vague > guesses, visualizes broad generalizations, and jumps to unwarranted > conclusions. He arranges and rearranges his ideas, and becomes > convinced of their truth long before he can write down a logical > proof... the deductive stage, writing the results down, and writing its > rigorous proof are relatively trivial once the real insight arrives; it > is more the draftsman’s work not the architect’s." > > Albert Einstein: "The words or the language, as they are written or > spoken, do not seem to play any role in my mechanism of thought. The > psychical entities which seem to serve as elements in thought are > certain signs and more or less clear images which can be voluntarily > reproduced and combined... The abovementioned elements are, in my case, > of visual and some of muscular type. Conventional words or other signs > have to be sought for laboriously only in a secondary stage, when the > mentioned associative play is sufficiently established and can be > reproduced at will." > > --------------------------------- > > Appendix 3: Quotations by Peirce about formal, mathematical methods > > 1898; We pretend that the [existential] graph is a general description > of a certain recognized state of things. We only pretend that it is so; > for our purpose is merely to study formal logic, and the graph is a mere > specimen of an assertion for whose matter we care nothing. In the > contents of consciousness we recognize three sorts of elements, > Firstness, Secondness, Thirdness. (R339, 11 June 1898) > > 1902: Accordingly by regarding logic as a science of signs or formal > semeiotic, and in the main as a science of symbols, or formal symbolic, > we accurately cover its subject matter, and at the same time insure > ourselves against all risk of being led astray into psychology. (R > 425:117-118, 1902) > > 1903: For every symbol is a living thing, in a very strict sense that > is no mere figure of speech. The body of the symbol changes slowly, but > the meaning inevitably grows, incorporates new elements and throws off > old ones. (CP 2.222). > > 1903: Phenomenology ascertains and studies the kinds of elements > universally present in the phenomenon. (CP 1.186, 1903) > > 1905: The other doctrine of mine which Royce attacks, as remarkably > shows how unscientific his training has been. He attacks my > one-two-three doctrine in the very field where it is most obviously > defensible, that of formal logic. (Letter to William James, August > 1905) > > c 1906: Phaneroscopy... is the science of the different elementary > constituents of all ideas. Its material is, of course, universal > experience, -- experience I mean of the fanciful and the abstract, as > well as of the concrete and real. Yet to suppose that in such > experience the elements were to be found already separate would be to > suppose the unimaginable and self-contradictory. They must be separated > by a process of thought that cannot be summoned up Hegel-wise on demand. > They must be picked out of the fragments that necessary reasonings > scatter; and therefore it is that phaneroscopic research requires a > previous study of mathematics. (R602, after 1903 but before 1908) > > 1907: My trichotomy is plainly of the family stock of Hegel’s three > stages of thought, -- an idea that goes back to Kant, and I know not how > much further. But the arbitrariness of Hegel's procedure, utterly > unavoidable at the time he lived, -- and presumably, in less degree, > unavoidable now, or at any future date, -- is in great measure avoided > by my taking care never to miss the solid support of mathematically > exact formal logic beneath my feet.... (R318, 1907, p. 37) > > CSP: The little that I have contributed to pragmatism (or, for that > matter, to any other department of philosophy), has been entirely the > fruit of this outgrowth from formal logic, and is worth much more than > the small sum total of the rest of my work, as time will show. > (CP 5.469, R318, 1907) > > In a footnote to CP 4.240, Peirce added "'Formal logic' is also used, by > Germans chiefly, to mean that sect of Logic, which makes Formal Logic > pretty much the whole of Logic." Since Whitehead and Russell also > adhered to that "sect", the term 'formal logic' means any version of > logic that uses some precisely defined notation, linear or graphic. > _ _ _ _ _ _ _ _ _ _ > ► 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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