Robert, answering your attack on a straw man would hardly be worthwhile, as it is apparently based on a misquotation of my post and your own hostile reaction to the word “imaginary.” Rather than unleash a barrage of quotes, i will just give one example where Peirce uses that word as i did in my paraphrase. This is from his classification of the “theoretical sciences,” CP 1.240 (1902):
[[ The first is mathematics, which does not undertake to ascertain any matter of fact whatever, but merely posits hypotheses, and traces out their consequences. It is observational, in so far as it makes constructions in the imagination according to abstract precepts, and then observes these imaginary objects, finding in them relations of parts not specified in the precept of construction. This is truly observation, yet certainly in a very peculiar sense; and no other kind of observation would at all answer the purpose of mathematics. ]] Gary f. From: robert marty <[email protected]> Sent: 5-Aug-20 04:49 Gary F., Edwina, John, Auke, List So you're sending mathematics back into the field of the imaginary. Peirce isn't as radical as you. He begins a simple and clear classification of science with: - the mathematical sciences: "the study of ideal constructions without reference to their real existence", If we stopped reading it here, we wouldn't be so preoccupied with mathematics, as you seem to want us to be. But as he goes on he writes: -Empirical sciences: "the study of phenomena with the purpose of identifying their forms with those mathematics has studied" which puts them back at the center of scientific thought and creates an obligation of scientific morality. In other words, what will you do with your "genuine indexes" if you do not have universal forms to support them. Will you prefer doctrines that have remained in an unformed state rather than having formalized theories that can be applied in the real world? By the way, Peirce ends his classification with : - the pragmatic sciences, "the study of how we ought to behave in the ligth of the truths of empirics." (C.S. Peirce, 1976: NEM , vol III.2 1122, MS 1345) which shows without question that pragmatism cannot do without even "imaginary" mathematics and even that they are the cornerstone of its pragmatism. To claim as you do that "theoretical reasoning is only a mathematical procedure, it leaves aside the experiential element of Peirce's methodology and his pragmatism" is an insult to Peirce himself and is in fact a certain negationism. I am not going to go into a recollection of the innumerable texts in which Peirce asserts the role he attributes to mathematics. I believe that the one I am quoting above is more than sufficient. On the other hand, if you were not blinded by this kind of a priori rejection of mathematics you could have benefited from the lattice of the classes of signs, as noted by Edwina, which would have shown you that the dicent and rhematic indexical legisigns encapsulate the corresponding dicent and rhematic indexical sinsigns and furthermore that the legisigns themselves are encapsulated in dicent and rhematic symbols which combined using deductive or inductive arguments produce theories. But as they say in French "il n'est pire sourd qui ne veut entendre"! (he's the worst deaf person who doesn't want to hear!) Best regards Robert Marty Semiotics is a fighting sport Honorary Professor ; PhD Mathematics ; PhD Philosophy fr.wikipedia.org/wiki/Robert_Marty <https://fr.wikipedia.org/wiki/Robert_Marty> <https://de.wikipedia.org/wiki/Robert_Fran%C3%A7ois_Raymond_Marty?fbclid=IwAR0N4S-t_avO38YlBYcj_-a2YYcsNvl6joIhTkajX0lMQhV8CXRQjQeXXxQ> de.wikipedia.org/wiki/Robert_Fran%C3%A7ois_Raymond_Marty Le lun. 3 août 2020 à 18:18, <[email protected] <mailto:[email protected]> > a écrit : Jon et al., The basic point of my post was that the interpreter of a sign can keep its dynamic object “in view” only by means of the indexical function of the sign, which connects it to actual experience. Diagrammatic signs are not so good at that. The relevance to John's original post, as i see it, is this: if theorematic reasoning is only a mathematical procedure, it leaves out the experiential element of Peirce's methodology and his pragmatism. Mathematics is not a positive science, meaning that it involves no actual experience (other than the experience of doing mathematics, in which the universe of discourse is entirely imaginary). All positive sciences (including phaneroscopy, logic and semiotic) deal with what Peirce calls real relations as opposed to relations of reason (CP 1.365, for instance). A proposition in a positive science thus must employ a genuine Index <http://gnusystems.ca/TS/snm.htm#gndx> , as opposed to a degenerate index such as ‘the letters attached to a geometrical or other diagram’ (EP2:172). Gary f.
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