Francesco, List: I still reject the first premiss of your summary syllogism.
FB: Now Peirce says in 1904–1906 that signs are according to their IO are either p, s, or u. Technically he said that Signs are vague (not particular), singular, or general (not universal). In any case, I am not ultimately seeking to explicate Peirce's 1904-1906 efforts at classifying Signs; I am trying to develop a viable framework for understanding Signs and their relations based on Peirce's *entire *corpus, especially his late writings. He eventually generalized the division of Signs according to the IO as Descriptive/Designative/Copulative, which is *not *inherently limited to propositions. All Symbols (including propositions) are Copulative overall, Designative with respect to Rhemes that serve as subjects, and Descriptive with respect to Rhemes that serve as predicates. FB: This means that only that which is either p, s, or u is divisible according to the IO (for otherwise Peirce should have said: some signs are divisible according to the IO into p, s, g and some other signs are divisible according to the IO into x, y, z). Or it means that Peirce *primarily *had propositions in mind when he wrote the word "signs" *in that context*. Again, my interpretation is that quantification is an *aspect* (not "part") of the IO *of a proposition*, but is not intrinsic to the concept of the IO *in general*. Specifically, I continue to maintain that quantification is what converts the *general *Object of the subject Rheme into the *individual *Object of its Replica for a particular *Instance *of the proposition. Otherwise, why did Peirce explicitly say elsewhere that *every *Sign has an IO? By contrast, as far as I know, he *never *said that *any *class of Sign *does not* have an IO. FB: That which allows the division of propositions into p, s, and g is what Peirce calls the "subject" of a proposition: in "All men are mortal", the Peircean subject is "For any x..." while the predicate is "x is either not a man or is mortal"; in "Some men are wise" the Peircean subject is "For some x..." and the predicate is "x is both a man and mortal"; in "Socrates is mortal" the subject is "Socrates" and the predicate "x is mortal". That is *one *way to analyze a proposition--throwing everything into the predicate except the quantification. Another is to "throw into the subject everything that can be removed from the predicate," which Peirce evidently came to prefer because it carries the analysis "to its ultimate elements" (SS 71-72; 1908). In "Any/Some/This man is mortal," the subjects are "Any/Some/This man" (Designative) and "mortality" (Descriptive), while the (continuous) predicate is "_____ possesses the character of _____" (Copulative). FB: The predicates in these sentences are rhemes. Rhemes do not have "subjects", they are not quantified. Rhemes do not *have *subjects, but they *serve *as the subjects of propositions, as I just outlined. That being the case, here is what I sincerely would like to understand from a *systematic *standpoint. If Rhemes (including terms) did not have *Immediate *Objects, how could they have *Dynamic *Objects? How could they have Logical *Breadth*, as Peirce explicitly affirmed, if there were nothing in the Sign-Replica itself that somehow "hints" at its Object? More narrowly, how could they have *Essential *Breadth corresponding to the *minimal *state of knowledge that *only *encompasses the meanings of words? Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Wed, Sep 12, 2018 at 12:31 AM, Francesco Bellucci < [email protected]> wrote: > Jon, List > > Thanks for the summary. > > To say that particular/singular/universal is a division of propositions is > to say that that which is either p, s, or u is only a proposition, i.e. > that only propositions are either p, s, or g. Now Peirce says in 1904–1906 > that signs are according to their IO are either p, s, or u. This means that > only that which is either p, s, or u is divisible according to the IO (for > otherwise Peirce should have said: some signs are divisible according to > the IO into p, s, g and some other signs are divisible according to the IO > into x, y, z). Now, since only propositions are either p, s, or g and > since that which is either p, s, or u is divisible according to the IO, it > follows that only propositions are divisible according to the IO. > > Now, that only propositions are divisible according to the IO ceratinly > means that propositions have an IO, but does not exclude that > non-propositional signs also have an IO. This I concede. But if one wonders > *what > on earth *the IO of a proposition is, that non-propositional signs have > no IO becomes evident. > > For since propositions are divisible according to the IO into p, s, and g, > that which constitutes the IO in them is that which allows such division. I > see no warrant for claiming that the p-s-g aspect in a proposition is > "part" of the IO, as Jon suggests. For in that case Peirce should have made > it clear that propositions are *divisible according to a part *(= the > quantificational part) of the IO into p, s, and g. He should have made it > clear that the IO does not exhaust the quantificational dimension of > propositions, and, I surmise, he should have made it clear that > propositions are divisible according to one part of the IO into p, s, and > g, and according to another part of the IO into, say, x, y, and z. As far > as I know, Peirce never speak of "parts" of the IO, one of which would be > the quantificational dimension. I think it is safe to conclude that that > which constitutes the IO in a proposition is that which allows the division > into p, s, and g. > > That which allows the division of propositions into p, s, and g is what > Peirce calls the "subject" of a proposition: in "All men are mortal", the > Peircean subject is "For any x..." while the predicate is "x is either not > a man or is mortal"; in "Some men are wise" the Peircean subject is "For > some x..." and the predicate is "x is both a man and mortal"; in "Socrates > is mortal" the subject is "Socrates" and the predicate "x is mortal". The > predicates in these sentences are rhemes. Rhemes do not have "subjects", > they are not quantified. Since that which allows the division into p, s, > and g is the IO, and since the IO is – in the case of those signs for which > it is *comprehensible* what on earth the IO is – the subject, it follows > that lack of a subject involves lack of an IO. > > In sum: > > In order for a sign to have an IO, it should be divisible into p, s, and g > (this I think is evident from Peirce's claim taht "signs are divisible > according to the IO into p, s, and g.) > Rhemes are not divisible into p, s, and g > Therefore, rhemes do not have an IO > > Francesco >
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