[peirce-l] Re: on continuity and amazing mazes

[Bernard Morand]

Joseph Ransdell a écrit : Arnold says:    I would venture to suggest (subject to the better sense of those on the list who have greater experince with the MSS than I have) that the notion of a Sign contains the concept of a transitive function, making a very strong case for what Thomas has said on this subject.  Other transitive functions in Peirce can be found in Vols III and IV of the CP (see especially 3.562)RE   RESPONSE:   You won't get any objections from me on that, Arnold.  Let me quote myself (from my dissertation many year ago (1966) on CSP's conception of representation):  "Peirce indicates in several places that he regards the nota notae as the generic inference principle (see esp. 5.320 and 3.183).  [Nota notae est nota rei ipsius: the mark of the mark is the mark of the thing itself.]  Further, he identifies this with the dictum de omni (4.77) [which is in Aristotle], and with what De Morgan called the principle of the transitiveness of the copula.  (2.591-92).  The latter is in turn identified with the illative relation (3.175), and this, again, is explicitly said to be the "primary and paramount semiotic relation." (2.444n1). I suggest, therefore, that all of Peirce's statements of the representation relation may thus be taken as so many variant expressions of what he understands to be expressed by the nota notae, the dictum de omni, the notion of the transitivity of the copula, or the principle of illation." (Charles Peirce: The Idea of Representation, 63)   Joe Ransdell Thanks Joe for these very promising associations of logical ideas about representation. I returned to the sources and fell short with the following: ------------------------------CP 3.175---------------------------- 175. The forms A -< B, or A implies B, and A ~-< B, or A does not imply B †3, embrace both hypothetical and categorical propositions. Thus, to say that all men are mortal is the same as to say that if any man possesses any character whatever then a mortal possesses that character. To say, 'if A, then B ' is obviously the same as to say that from A, B follows, logically or extralogically. By thus identifying the relation expressed by the copula with that of illation, we identify the proposition with the inference, and the term with the proposition. This identification, by means of which all that is found true of term, proposition, or inference is at once known to be true of all three, is a most important engine of reasoning, which we have gained by beginning with a consideration of the genesis of logic --------------------------------------------------------------------- The assertion I have underlined in bold strikes me: I would say exactly the converse. Am I wrong? or did the editors make a mistake or did Peirce makes it? (there seems to be a conflict here between extension and comprehension) [The remainder works well for me] Bernard --- Message from peirce-l forum to subscriber archive@mail-archive.com