Gary F., List
It's not a response and my post was not an attack but a counterattack to your exploitation of the quote from John's post, in conjunction with your insistence on the term "imaginary" :* "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"*. Who can disagree with that? But what about the ability of mathematics to grasp "real relations" by means of "relations of reason"? Not a word ... You seem to ignore the important word *"if*" ... *By editorializing a truism you undermine by omission the role of mathematics in the construction of theories*. And then you triumph by trumpeting that mathematics is not a positive science, which nobody supports. If you want to go beyond CP 1.240 to 1.245 you will read this: *Beginning with Class I, mathematics meddles with every other science without exception. There is no science whatever to which is not attached an application of mathematics. This is not true of any other science, since pure mathematics has not, as a part of it, any application of any other science, inasmuch as every other science is limited to finding out what is positively true, either as an individual fact, as a class, or as a law; while pure mathematics has no interest in whether a proposition is existentially true or not. In particular, mathematics has such a close intimacy with one of the classes of philosophy, that is, with logic, that no small acumen is required to find the joint between them."* (CP 1.245) *Some additional remarks*: " Diagrammatic signs are not so good at that" ... another truism: they are *Iconic Sinsigns* so they are not indexical signs, but they play a capital role in the abductive phase of formal constructions because they bring the first information about the dynamic object. On the other hand, "genuine indexes" are *Dicent Sinsigns* (they point to the dynamic object and provide information about it) and "degenerate indexes" are *Rhematic Indexical Sinsigns* which also point to the dynamic object without providing information. There is a relation of presupposition between them. See : "Second: An *Iconic Sinsign* [*e.g., *an individual diagram] is any object of experience in so far as some quality of it makes it determine the idea of an object. Being an Icon, and thus a sign by likeness purely, of whatever it may be like, it can only be interpreted as a sign of essence, or Rheme. It will embody a Qualisign."(CP 2.255) "Third: A *Rhematic Indexical* Sinsign [*e.g., *a spontaneous cry] is any object of direct experience so far as it directs attention to an Object by which its presence is caused. It necessarily involves an Iconic Sinsign of a peculiar kind, yet is quite different since it brings the attention of the interpreter to the very Object denoted." (CP 2.256) "Fourth: A *Dicent Sinsign* [*e.g., *a weathercock] is any object of direct experience, in so far as it is a sign, and, as such, affords information concerning its Object. This it can only do by being really affected by its Object; so that it is necessarily an Index. The only information it can afford is of actual fact.* Such a Sign must involve* an *Iconic Sinsign* to embody the information and a *Rhematic Indexical Sinsign* to indicate the Object to which the information refers. But the mode of combination, or *Syntax, *of these two must also be significant." These relations can of course be read in Peirce as above but also and at a glance in the lattice of the 10 classes of signs (a mathematical object that encapsulates the 10 classes). 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 mer. 5 août 2020 à 13:52, <[email protected]> a écrit : > 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 > > 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. > >
_ _ _ _ _ _ _ _ _ _ ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to [email protected] with no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
