No, my last mail is an error. Regards Mauro Il ven 9 apr 2021, 19:06 Mauro Bertani <[email protected]> ha scritto:
> 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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