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 de.wikipedia.org/wiki/Robert_Fran%C3%A7ois_Raymond_Marty <https://de.wikipedia.org/wiki/Robert_Fran%C3%A7ois_Raymond_Marty?fbclid=IwAR0N4S-t_avO38YlBYcj_-a2YYcsNvl6joIhTkajX0lMQhV8CXRQjQeXXxQ> Le lun. 3 août 2020 à 18:18, <[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. > > -----Original Message----- > From: Jon Awbrey <[email protected]> > Sent: 3-Aug-20 11:35 > To: Peirce List <[email protected]> > Subject: [PEIRCE-L] Re: Pragma, Pragmata, Pragmatitude! > > > > Dear Gary, All ... > > > > I was obviously having a lot more fun with words in those days ... > > sigh, good times ... the point of it all being I always see the whole > complex of meanings associated with the Greek root "pragma, pragmata" > through the more threadbare veil of the Latin "object". > > That complex contains all the senses of aims, concerns, ends, goals, > intentional objects, and purposes we tend to express more obliquely through > the use of "object" to mean "objective". Still, the latter use does have > some currency in cybernetics, operations research, and systems theory, so > it's a handy sense to keep in mind. > > > > Cf: Liddell & Scott > > > http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Dpra%3Dgma > > > > Regards, > > > > Jon >
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