Dear Helmut, See what I have discover today: a->b = (a) a->b->c->d = (a,b,c) a->b and a->c =(a) The implication depends only by the falsity of the premise so is the conjunction of the premise. If only one is false the proposition is false. Not need negation. I think you have drive me to the solution. Regards Mauro
Il ven 9 apr 2021, 18:41 Helmut Raulien <[email protected]> ha scritto: > Mauro, Jon, List, > > The extension of A is included in B, but the intension of B is included in > A. Extension is due to composition, intension is due to classification. > > Now I think it my be, that all is more difficult than I thought: > > Reflection, like that in a mirror turning around left and right sides, > turns around time: What happens first, and what happens then. But in both > cases, the reflected is not the reality, it is just a picture of the > reality. > > So, in the case of the tennis ball and the ball, both in reality, and in > reflection, a tennis ball has more distinction marks than a ball. Both > intensionally and extensionally, because the million different traits of > extensionally different balls are not distinction marks between tennis ball > and ball, as they are not topics of the concept "ball". > > But with inference and double negation there is a difference: One may say, > that the concept of negation does not have an extension. It is only a > matter of reflection. Reality and extension contain only things that exist, > but not the nonexistence of things. So the concept of negation is a concept > of nothing. > > So, if negation does not exist in reality, you are right, that > implication/inference is the primitive. But not, because negation is less > primitive than it, but because negation does not exist at all. Only the > concept of negation exists. > > The question now is: What about the reflection? Is, in reflection, the > concept of negation, a concept without extension, less primitive in this > special case, than the concept of inference? or is, like I think, that > primitivity is only a matter of reality? In this case, negation neither is > primitive nor not primitive, and therefore either implication is the only > primitive, or primitivity does not apply here either. I dont know anything > anymore for sure. > > Best, > Helmut > > > 09. April 2021 um 16:33 Uhr > "Mauro Bertani" <[email protected]> > *wrote:* > Dear Helmut, > I'm not sure to have understood what you have said. > Let's: > A={n: n=4*i con i (1..infinity)} > B={n: n=2*i con i (1..infinity)} > > I see that all a are also b. But at one moment I will see that there are > some b, like for example 6,that are not a. So the not existence of a that > are not b and the existence of b that are not a, drive me to conclude that > A is included in B and A implies B. So if..then come after negation. > It's right? > regards > Mauro > > On Fri, 9 Apr 2021 at 10:27, Helmut Raulien <[email protected]> wrote: > >> >> Mauro, Jon, List, >> >> again, reflection goes in the opposite direction than real action and >> evolution do, but "primitive" is a concept about evolution, not about >> reflection, isn´t it? >> >> In logical reflection, inference comes before double negation, but >> anyway, first there were no As without being Bs, then somebody experienced, >> that if A, then B, then this somebody reflected "why is that so? Ah, >> because there are no As without being Bs!" So the situation of the >> nonexistence of As being not Bs was first, is more primitive, than the >> if-then-experience. >> >> Best, Helmut >> >> 09. April 2021 um 09:43 Uhr >> "Mauro Bertani" <[email protected]> >> wrote: >> >> Dear list, >> Last year I read part of the book of Peano [1]. In this book Peano >> explains the state of art of logic in 1888. He explains in this way the >> rudimental concept of implication: >> [link to pag 9 of book >> <https://books.google.it/books?hl=en&lr=&id=5LJi3dxLzuwC&oi=fnd&pg=PA9&dq=peano+calcolo+geometrico&ots=4xikZ7toBC&sig=yvGzsGadG6UgBZ7pBHp9SA6wvLs&redir_esc=y#v=onepage&q=peano%20calcolo%20geometrico&f=false> >> ] >> a < b or b > a the class [proposition] defined by the condition a is >> part of by those defined by b, or in another way a has as a consequence >> b >> a = b if a is true and also b, and viceversa >> a ^ b the condition assuming that both a and b are true >> a U b the condition assuming that or a or b are true >> (a) the condition that we obtain negating a >> F the absurd condition >> T the identical condition >> >> Than the book explains the calculus of proposition and terminates with >> this 4 type of proposition: >> [link to pag 14 of book >> <https://books.google.it/books?hl=en&lr=&id=5LJi3dxLzuwC&oi=fnd&pg=PA14&dq=peano+calcolo+geometrico&ots=4xikZ7toBC&sig=yvGzsGadG6UgBZ7pBHp9SA6wvLs&redir_esc=y#v=onepage&q=peano%20calcolo%20geometrico&f=false> >> ] >> I) All a are b >> II) No a is b >> III) Some a is b >> IV) Some a is not b >> And he transforms the first proposition in >> a ^ (b) = F >> that is more similar at >> (a(b)) the cactus formula for implication >> Peano named these propositions in this way: >> The I) and II) are Universal. The III) and IV) that are negations of >> universal preposition, he named them particular. The I) and the III) that >> contain an even number of negations, he named them proposition >> affirmative. The II) and IV) that contains an odd number of negations, he >> named them negative. >> >> SoI think that implication, being an universal affirmative proposition, >> came before negation. >> >> In another book [2] Peano describe the continetur and the deducibur ( >> inclusion and implication) as the same operator >> >> >> maybe >> regards >> Mauro >> >> Ref: >> [1] Peano, Giuseppe. *Calcolo geometrico secondo l'Ausdehnungslehre di >> H. Grassmann: preceduto dalla operazioni della logica deduttiva*. Vol. >> 3. Fratelli Bocca, 1888. >> [2] Peano, Giuseppe. Arithmetices principia, nova methodo exposita. >> Roma, Fratres Bocca, 1889. >> >> On Fri, 9 Apr 2021 at 08:40, Helmut Raulien <[email protected]> wrote: >> >>> >>> >>> >>> Supplement: Now I am wondering, how "primitive" is defined. I said, that >>> the consequent in >>> *IF* "IF-THEN", *THEN* "NOT WITHOUT" >>> like in >>> *IF* "tennis ball" *THEN* "ball" >>> must be more primitive than the antedecent, because it has fewer traits >>> (distinction marks), is more general than it, is its superclass. On the >>> other hand, it provides more possibilities for variations: A ball may have >>> the size of a planet, may be of gold covered with diamonds...., while a >>> tennis ball has a certain size and material. >>> But possibilities are not implications, but the opposite of them, like a >>> distinction mark is the opposite of a possibility. In my understanding, >>> "primitive" means to have less distinction marks and so more possibilities. >>> >>> Jon, List, >>> >>> I was not talking about the implication/inference, from which can be >>> inferred a double negation, but about the inference, which infers a double >>> negation from an inference. The underlined one, not the other: >>> >>> *IF* "IF-THEN", *THEN* "NOT WITHOUT" >>> >>> Best, Helmut >>> >>> >>> 09. April 2021 um 02:22 Uhr >>> "Jon Alan Schmidt" <[email protected]> >>> *wrote:* >>> Helmut, List: >>> >>> No one is disputing that the antecedent of an implication is logically >>> prior to its consequent. Rather, at issue is whether the logical relation >>> of implication is more primitive than the logical relation of negation. >>> That is Peirce's consistent position, and it is central to his entire >>> philosophy of logic because implication mirrors inference. We can judge one >>> proposition (the consequent B) to be true *because *another proposition >>> (the antecedent A) is true, *without *necessarily taking the additional >>> step of recognizing it to be false that A is true and B is false. >>> >>> >>> CSP: For in reasoning, at least, when we first affirm, or affirmatively >>> judge, the conjugate of premisses, the judgment of the conclusion has not >>> yet been performed. There then follows a real movement of thought in the >>> mind, in which that judgment of the conclusion comes to pass. Now surely, >>> speaking of the same A and B as above, it were absurd to say that a real >>> change of A into a sequent B consists in a state of things that should >>> consist in there not being an A without a B. For in such a state of things >>> there would be no change at all. (R 300:49[48], 1908) >>> >>> >>> Negation is not required to infer that if something is a tennis ball, >>> then it is a ball, or that if something is a kangaroo, then it is a >>> vertebrate. In each case, the consequent necessarily *follows *from the >>> antecedent because the concept of "tennis ball" *includes *the concept >>> of "ball" and the concept of "kangaroo" *includes *the concept of >>> "vertebrate." Negation comes into play only with the further inference that >>> there is no tennis ball that is not also a ball, or that there is no >>> kangaroo that is not also a vertebrate. While these different formulations >>> are equivalent in classical logic, they are not so in >>> intuitionistic/synechistic logic--the latter can be derived from the >>> former, but not vice-versa. >>> >>> Regards, >>> >>> Jon S. >>> >>> On Thu, Apr 8, 2021 at 1:04 PM Helmut Raulien <[email protected]> wrote: >>> >>>> >>>> Jon, List, >>>> >>>> ok, another argument, then I probably will have run out of them: In a >>>> no-identity- one-way- implication/inferation the implied/inferred-to is >>>> more primitive than the implier/inferred-from, as it must have fewer traits >>>> than the implier/inferred-from. The implier has more traits, some of which >>>> distinguish in the way, that the implied is not a kind of every kind of the >>>> implier. >>>> >>>> Example: "Tennis ball" implies "ball". "Ball" merely has the trait of >>>> being roughly spherical. This is more primitive than "tennis ball", which >>>> has additional traits, that lead to the fact, that not every ball is a >>>> tennis ball. >>>> >>>> Best, Helmut >>>> 08. April 2021 um 18:51 Uhr >>>> "Jon Alan Schmidt" <[email protected]> >>>> *wrote:* >>>> Helmut, List: >>>> >>>> >>>> HR: ... implication itself has been derived from double negation in a >>>> quasi-evolution, so double negation is more primitive. >>>> >>>> >>>> No, implication mirrors inference, which is more primitive than >>>> negation (single or double). >>>> >>>> Regards, >>>> >>>> Jon S. >>>> >>>> On Thu, Apr 8, 2021 at 9:27 AM Helmut Raulien <[email protected]> wrote: >>>> >>>>> Jon, List, >>>>> >>>>> I think, this is an example for reflection going the other way than >>>>> action, evolution: >>>>> >>>>> We can derive "vertebrate" from "kangaroo", but kangaroos are derived >>>>> (deriven?) from vertebrates, and vertebrates are (resp. were, when they >>>>> were not a class but merely a species) more primitive, than kangaroos are. >>>>> >>>>> In the same way, we, by reflection, can derive double negation from >>>>> implication, but implication itself has been derived from double negation >>>>> in a quasi-evolution, so double negation is more primitive. >>>>> >>>>> Best, Helmut >>>>> 08. April 2021 um 15:25 Uhr >>>>> "Jon Alan Schmidt" <[email protected]> >>>>> *wrote:* >>>>> Helmut, List: >>>>> >>>>> No, you had it right the first time. In intuitionistic/synechistic >>>>> logic, we can derive double negation (nested cuts/ovals) from implication >>>>> (scroll), but we cannot derive implication (scroll) from double negation >>>>> (nested cuts/ovals). Implication is primitive, single negation is derived >>>>> from it as the implication of falsity or absurdity, and double negation is >>>>> derived from it as a composite of two single negations. >>>>> >>>>> Regards, >>>>> >>>>> Jon Alan Schmidt - Olathe, Kansas, USA >>>>> Structural Engineer, Synechist Philosopher, Lutheran Christian >>>>> www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt >>>>> >>>>> On Thu, Apr 8, 2021 at 12:15 AM Helmut Raulien <[email protected]> >>>>> wrote: >>>>> >>>>>> >>>>>> Supplement: Oh-oh, I have mixed it completely up. Every implication >>>>>> is a double negation, but not every double negation is an implication, so >>>>>> double negation is the superclass, and thus more primitive than >>>>>> implication. >>>>>> Just like every kangaroo is a vertebrate, but not every vertebrate is >>>>>> a kangaroo, so vertebrate is the superclass, and more primitive. The >>>>>> first >>>>>> vertebrate is said to have been a fish-like creature with a single >>>>>> spine-bone. >>>>>> Jon, List, >>>>>> >>>>>> if we distinguish at all between implication and double negation, we >>>>>> are in the field of nonclassical logic. In intuitionalistic logic, every >>>>>> implication is a double negation, but not every double negation is an >>>>>> implication. So implication is the superclass, and double negation the >>>>>> subclass. >>>>>> the folllowing I derive from Stanley N. Salthe´s paper >>>>>> "Salthe12Axiomathes": In a subsumption (classification), the subclass has >>>>>> inherited the classifying traits from the superclass, and then developed >>>>>> additional traits, that distinguish it from other subclasses of the same >>>>>> superclass. So the subclass is more complex, less primitive than the >>>>>> superclass. So implication is more primitive than double negation, and >>>>>> double negation is derived from implication. But is single negation >>>>>> derived >>>>>> from double negation, or is single negation even more primitive than >>>>>> implication, and is just the combination of two negations derived from >>>>>> implication? >>>>>> >>>>>> Best, Helmut >>>>>> >>>>> _ _ _ _ _ _ _ _ _ _ ► 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 UNSUBSCRIBE PEIRCE-L in the >>> SUBJECT LINE of the message and nothing in the body. More at >>> https://list.iupui.edu/sympa/help/user-signoff.html . ► PEIRCE-L is >>> owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by >>> him and Ben Udell. >>> _ _ _ _ _ _ _ _ _ _ ► 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 UNSUBSCRIBE PEIRCE-L in the >>> SUBJECT LINE of the message and nothing in the body. More at >>> https://list.iupui.edu/sympa/help/user-signoff.html . ► PEIRCE-L is >>> owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by >>> him and Ben Udell. >>> _ _ _ _ _ _ _ _ _ _ >>> ► 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 UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of >>> the message and nothing in the body. More at >>> https://list.iupui.edu/sympa/help/user-signoff.html . >>> ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; >>> and co-managed by him and Ben Udell. >> >> >> >> -- >> "[..] events are primarily linguistic or cognitive in nature. That is, >> the world does not really contain events. Rather, events are the way by >> which agents classify certain useful and relevant patterns of change." >> Allen and Fergusson >> >> "No, no. *History of Eternity*. At first I wanted to find every single >> one of the buyers to apologize because of the book and also to thank them >> for what they had done. There is an explanation for that. If you think of >> thirty-seven people—those people are real, I mean every one of them has a >> face of his own, a family, he lives on his own particular street. Why, if >> you sell, say two thousand copies, it is the same thing as if you had sold >> nothing at all because two thousand is too vast—I mean, for the imagination >> to grasp. While thirty-seven people—perhaps thirty-seven are too many, >> perhaps seventeen would have been better or even seven—but still >> thirty-seven are still within the scope of one's imagination." >> >> http://www.theparisreview.org/interviews/4331/the-art-of-fiction-no-39-jorge-luis-borges >> _ _ _ _ _ _ _ _ _ _ ► 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 UNSUBSCRIBE PEIRCE-L in the >> SUBJECT LINE of the message and nothing in the body. More at >> https://list.iupui.edu/sympa/help/user-signoff.html . ► PEIRCE-L is >> owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by >> him and Ben Udell. >> > > > -- > "[..] events are primarily linguistic or cognitive in nature. That is, the > world does not really contain events. Rather, events are the way by which > agents classify certain useful and relevant patterns of change." > Allen and Fergusson > > "No, no. *History of Eternity*. At first I wanted to find every single > one of the buyers to apologize because of the book and also to thank them > for what they had done. There is an explanation for that. If you think of > thirty-seven people—those people are real, I mean every one of them has a > face of his own, a family, he lives on his own particular street. Why, if > you sell, say two thousand copies, it is the same thing as if you had sold > nothing at all because two thousand is too vast—I mean, for the imagination > to grasp. While thirty-seven people—perhaps thirty-seven are too many, > perhaps seventeen would have been better or even seven—but still > thirty-seven are still within the scope of one's imagination." > > http://www.theparisreview.org/interviews/4331/the-art-of-fiction-no-39-jorge-luis-borges > _ _ _ _ _ _ _ _ _ _ ► 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 UNSUBSCRIBE PEIRCE-L in the > SUBJECT LINE of the message and nothing in the body. More at > https://list.iupui.edu/sympa/help/user-signoff.html . ► PEIRCE-L is owned > by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and > Ben Udell. >
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