Supp-supplement: Sorry, in my previous two posts I had gotten confused. I try again (everybody may try three times, isnt it?)
Quotation marks indicate a concept, minusses indicate a quotation. About his own universe, a propositioner cannot justifiedly, nonparadoxically, say: -There is no "no A"-, because by having uttered this, the concept "no A" does exist in his universe.
But, if he talks about another universe he does not live in, in which neither horses, nor the concept of them exist, he may truly say: -There is no "no horses"-.
If there, in that remote universe, the concept "B" does not exist, neither B can exist, because if B would exist, the concept "B" too would exist, at least for this universe (universes have minds, and thus concepts about all that they consist of). So from -There is no "no horses"- (with "no horses" being "B") follows -There is no no horses-. In classical logic this would mean, that there are horses. But there are not. So, in this case, with the propositioner speaking of a universe he does not live in, the double negation is something else than affirmation.
I wonder, is this an example of intuitive versus classical logic, or have I only blended in something like the difference between passive and active negation?
Please forget the rest, from here on
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Supplement: My deduction in the middle of the second paragraph is false. It is only true, if we assume, that a concept is constructed by existence- or by making up: It might be, that in the universe in which no horses exist, people have made up the concept of them nayway, as it might be, that another universe exists, in which unicorns exist. So the claim is, that in the universe in talk neither horses, nor a made-up concept of them exist. But the basic claim is, that a concept, an idea, merely exists, if it is constructed. But another view is thinkable, a quasi-Platonian one: It would say, that all ideas exist, as think-possibilities. This is becoming quite complicated, and I am losing the oveall view.
Jon, Gary, List,
I didnt get a feeling so far about intuistic logic, the not excluded middle and the double negation being something else than the non-existent negation. All I can do, is reconstruct these ideas with my own thoughts, otherwise I cannot understand them. I am very interested in your opinions whether my thoughts are in accordance with yours or Peirce´s:
If the proposer exists in a universe, in which the concept of A exists, the middle is excluded, and the double negation is the same as no negation. But if the proposer talks about a universe he does not live in, but knows, that in that universe a concept "A" of A, let´s say "horses" does not exists, if he says "There is no horses", that is true, but if he says "There is no "no horses"", that is false, because, as there is no concept of horses, there cannot be a concept of no horses. Something, of which no concept exists, can itself not exist, because existence is self-conceptualizing: At least the universe itself has a concept of something that exists in it. So from "There is no "no horses"" follows "there is not not horses", but this second proposition cannot mean that there are horses, because there aren´t. So, to talk about a universe the proposer does not live in requires intuistic logic, and classical logic does not apply.
So, a complete logic would require quotation marks. Only in classical logic, which applies to the universe the proposer lives in, these can be left out. But the consequence is, that classical logic is a subset of intuistic logic, and not the other way round, as I have understood it from Wikipedia.
Best, Helmut
21. Dezember 2020 um 06:35 Uhr
"John F. Sowa" <s...@bestweb.net>
wrote:
Gary F, List,
Peirce's immense volume of writings is a mixture of systematic developments in the sciences (which include philosophy) and many
"occasional" remarks that can be as puzzling as Zen koans.
GF> Consequence comes before negation.
That is a technical point from one stage in the development of Peirce's systems of logic.
GF> I hadn’t really considered that a relation of negation can be either symmetrical or asymmetrical. . I wonder which
case applies to this early (18) remark
of Peirce’s: “The individual man, since his separate existence is
manifested only by ignorance and error, so far as he is anything apart
from his fellows, and from what he and they are to be, is only a
negation” (EP1:55, CP 5.317). Either? Both? Neither?
A dyadic logical operator (And, Or, If) can be symmetric or asymmetric. But the criteria for symmetry are not meaningful for a monadic operator such as Not.
But when a logical operator is applied to people, as in the quotation from EP 1:55, it is a metaphor whose interpretation depends entirely on the context of the text and Peirce's thoughts at the moment.
But context is also important for interpreting Peirce's scientific writings. The idea that consequence comes before negation happened to be the original insight for the scroll in the initial development of entitative and existential graphs (1896-1897).
He toyed with that idea for a few years. But in June 1911, he switched his choice of logical primitives to And, Not, and Existence. The symmetric operator And can be combined with Not to define the asymmetric If-Then: "If p then q" is identical to "Not(p And (Not q))".
There was a long thread about these issues a few months ago. For a summary, see the attached file eg1911x.pdf. That is a screen shot from an article I'm writing.
John
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