Gary F., List: Returning after a few days of vacation ...
GF: Consequence comes before negation. Indeed, I have been pointing this out for a while now. The fundamental asymmetry of logic is why in existential graphs, besides the symmetrical relations of coexistence (blank sheet) and individual identity (heavy line), the unsymmetrical relation of consequence (scroll) is a logical *primitive* as Peirce himself affirms. CSP: We have seen that there are three relations which subsist between the parts of graphs. The first is the relation expressed by the scroll. This is the most important of all, since this is the relation of premiss and conclusion; that is, if it be true that if A is true B is true, then should A occur as a premiss we have a right to conclude B. The second relation is that expressed by writing two graphs side by side AB, that is to say, the relation of coexistence, and the third is the relation of individual identity expressed by the heavy line. (R 466:18-19, 1903) In fact, he implies on multiple occasions that there *must* be at least one unsymmetrical relation that is a logical primitive, because although a symmetrical relation can be derived from unsymmetrical relations, it is impossible to derive an unsymmetrical relation from symmetrical relations. CSP: But we are bound to carry our logical analysis to the furthest point, when the analysis of thought is the very business we have in hand. Hence, if one sign can be expressed as a complication or special determination of another, we are bound so to express it in logical analysis. Now an unsymmetrical relation can never be expressed as a complex or special case of a symmetrical relation; but a symmetrical relation may be expressible by means of an unsymmetrical relation. (R 482:12, 1896-7) CSP: It is, however, important to state that the relations of identity and of coexistence ... are the only *simple* dyadic relations which are symmetrical, that is, which imply each its own converse. All other symmetrical relations are compounded and involve asymmetric elements. (R 284:88[83], 1905) CSP: In my own system of existential graphs, the only formal signs are the sheet, the cut or enclosing line, and the line of identity, each of which expresses a dyadic symmetrical relation. But that does not amount to developing the principles of logic from symmetrical relations alone. The first relation of logic that of antecedent and consequent is unsymmetrical. Now an unsymmetrical relation cannot result from any combination of symmetrical relations alone ... (NEM 3:821, 1905) Peirce even explains elsewhere that reasoning of any kind *requires* the unsymmetrical relation of consequence but is possible *without* the "notion of falsity." CSP: [T]here must have been a time when men used language with some syntax, and yet were not fully conscious of it; and as long as they were in that condition, they could hardly have had much notion of falsity, although they might very well have drawn simple inferences, such as the Scroll of Fig. 5 represents; but these would have furnished them no notion of falsity or even of contradiction. (RS 30:20-21[Copy T:14-15], c. 1906) CSP: It was forced upon the logician’s attention that a certain development of reasoning was possible before, or as if before, the concept of falsity had ever been framed, or any recognition of such a thing as a false assertion had ever taken place. Probably every human being passes through such a grade of intellectual life, which may be called the state of paradisaical logic, when reasoning takes place but when the idea of falsity, whether in assertion or in inference, has never been recognized. (R 669:18-19[16-17], 1911) CSP: [T]he denial implies recognition of the affirmation, while the affirmation is so far from implying recognition of the denial, that one might imagine a paradisaic state of innocence in which men never had the idea of falsity, and yet might reason ... (RL 376, R 500:12, 1911) As I have suggested before, presumably a child (or even a pet) first learns the meaning of the word "no" by drawing simple inferences from experience. For example, *if* an adult human says "no" and I do it anyway, *then* something unpleasant happens to me. GF: ... the concept of negation is in a sense derived from the principle of excluded middle. Not negation in general, but negation as a *symmetrical *relation. CSP: Such a relation as “not” is symmetrical only because for every element A:B it contains another B:A. It is thus what you will call symmetrical by composition but not *thoroughly* symmetrical. (NEM 3:821, 1905) With excluded middle, as in classical logic, the relation of negation is "symmetrical by composition" such that the negation of the negation of A is equivalent to A itself as represented by the double cut rule in existential graphs. Without excluded middle, as in intuitionistic logic, the relation of negation is unsymmetrical such that the negation of the negation of A is *not* equivalent to A itself. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Mon, Dec 14, 2020 at 8:46 AM <[email protected]> wrote: > Jon Alan, list, > > Three years ago when I posted my transcription of Lowell Lecture 2 on my > website (https://gnusystems.ca/Lowell2.htm) I was quite baffled by > Peirce’s derivation of the negating signification of the cut from the > signification of the scroll with a blackened inner close or “pseudograph”. > I even posted to the Peirce list expressing my bafflement. I wish I could > have read (and understood) this post of yours back then, because it would > have cleared things up for me. But then I probably couldn’t have understood > it because I was still a beginner in the study of Existential Graphs. Your > post explains succinctly much of what I’ve learned about them since. > > In logical terms, the key is that excluded middle is a principle only of > *deductive* reasoning, not of *ampliative* reasoning, which always comes > first in any *inquiry*; and the concept of negation is in a sense derived > from the principle of excluded middle. Consequence comes before negation. > At least that’s my understanding now, thanks to your explanation. > > Gary f. > > > > } Seeking enlightenment apart from the world is like looking for horns on > a hare. [Hui-neng] { > > https://gnusystems.ca/wp/ }{ living the time >
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