Re: [PEIRCE-L] Existential Graphs in 1911
John, During your repeated debates with Jon an experience I had as a freshman philosophy kept knocking at my doors of perception. It was the first meeting in which each of the students had to read a passage of Hegels logic. I was the first to read and started with the first alinea in which logic is defined as being concerned with the idea in the formal element. Just having had my first course in logic, I relied on what I learned and started talking about that, i.e. as logic trying to lay down the rules of formal thought, the formal element. And met with serious opposition from the teachers present. I recall that it took them some time to get me to realize that the emphazis is on "'idea' in the formal element" and not on the formal element severed from any actuality. It is a line of thought I can see leading to what Jon wrote. Jon A. wrote: In this particular case, my purpose is the same as Peirce's--analyzing reasoning into its most fundamental and irreducible elements. Even more specifically, I am currently exploring intuitionistic/constructive/synechistic logic using EGs, consistent with Peirce's own skepticism of excluded middle. John can speak for himself, but it is clear by now that he does not share these same objectives. -- Logical positivism could restrict itself to logic regarded sub species eternitate (Tractatus), we know for certain that Peirce was not of like opinion. His view on logic is multi-facetted. He is not just concerned with, I cite: John wrote: For mathematicians and logicians, clarity and precision are essential. The formal structure is everything, and the words are of minor interest. The fewer, the better. -- For him, as far as I understood his thought, the formal structure is not everything. It only is "the formal structure as it operates in a living intelligence". It did not prevent him from focussing exclusively on the formal structure, as his formal work shows. But he was aware of the limitations. You seem to be less so. It is in this light that I find the negation - ilation debate of interest. Kant gives the erroneous view that ideas are presented separated and then thought together by the mind. This is his doctrine that a mental synthesis precedes every analysis. What really happens is that something is presented which in itself has no parts, but which nevertheless is analyzed by the mind, that is to say, its having parts consists in this that the mind afterward recognizes those parts in it. Those partial ideas are really not in the 1rst idea, in itself, though they are separated out from it. It is a case of destructive distillation. CP 1.384 I think that this quote backs up Jon's approach from a systematic perspective. Systematic here to be taken in the philosophical sense, not the logical. Best, Auke > Op 29 januari 2021 om 5:51 schreef "John F. Sowa" : > > Auke> I was thinking in terms of goals, i.e. what is the object you > try to understand, not credentials. I can connect Jon's answer to my > question with his line of reasoning and I did like that. There might > be differences in the goals and then it is always better to asses and > value the differences, instead of fighting about who is right. > > I have been doing research and teaching in logic, computer science, > computational linguistics, and artificial intelligence for many > years. In 1976, I had published an article on Conceptual Graphs in > the IBM Journal of Research and Development. > > Then in 1978, I came across Don Roberts' book on EGs, and it was > exactly what I was looking for. Peirce's EGs were far more elegant > and powerful than the AI research in the 1970s. (including my own). > I immediatetly adopted it as the foundation for the book I published > in 1984. I continued reading Peirce's other writings and various > publications about Peirce since then. > > Then in 2001, I came across Michel Balat's transcription of a first > draft of L231 (mistakenly classified as R514). I realized that it > was an excellent introduction to EGs, and I posted a copy with > commentary on my web site: http://jfsowa.com/peirce/ms514.htm . > > I also realized that this version was far superior to Peirce's > earlier versions. In particular, I used it to solve a previously > unsolved research problem from 1988. I published the solution in > Semiotca in 2011: http://jfsowa.com/pubs/egtut.pdf . > > In April 2015, I presented a lecture on related issues at a Peirce > Session at the APA conference in Vancouver. In December of 2015, I > presented an extended version at a workshop that Zalamea sponsored in > Bogota. And in 2018, I publishted a 76-page version that spelled out > all the details. > > The following slides are minor revisions of the 2015 version: > http://jfsowa.com/talks/ppe.pdf . Slide 2 has a link to the 2018 > publication in
Aw: Re: [PEIRCE-L] Scroll vs Nested Ovals (was Existential Graphs in 1911)
All, I think, the difference is not the meaning, but what it is. Though the double negation´s meaning is the same as the conclusion´s meaning, the double negation has the form of a proposition, or a definition, which is secondness: "There is not a featherless biped that is not a human" may be classificationally instantated from exclusion of exclusion to definition: "A human is a featherless biped". The conclusion "If it is a featherless biped then it is a human" may be individually instantated to an argument; "It is a human because it is a featherless biped". It is thirdness, a rule or law. Which of both is more fundamental? Both mean the same, so if one changes, the other changes too. But which is more likely to change? The law "If it is a featherless biped then it is a human" cannot change just so, by itself. But the situation, the secondness, the truth of the proposition "There is not a featherless biped that is not a human" can easily change, and make the law obsolete, e.g. if an ape quits using its arms for walking, or if a dog sadly has two legs amputated, or if a chicken, due to a mutation, is born without feathers. So, is the double negation more fundamental, because it breaks the law? People will say, that the ape is just stupid, the chicken and the dog are just handicapped, exceptions only corrobate the rule, and all people who claim that the law is no longer in charge are heretics. A law (3ns) is more tenacious than actualities (2ns), that first have to prove worthwile one by one to add up to a certain measure, so is it more fundamental? Helmut Freitag, 29. Januar 2021 um 00:49 Uhr "Jon Alan Schmidt" wrote: John, List, All: In this post, I will simply respond to the numbered items below rather than quoting them. 1. I am not aware of any evidence that Peirce ever explicitly denied that illation is essential for deduction or rejected the use of the scroll for that purpose in EGs. The absence of these specific terms in his relatively sparse writings during the last 34 months of his life does not outweigh their abundance in his voluminous output over the preceding decades. Again, my hypothesis is that in June 1911 he merely decided to simplify his presentation of EGs for the uninitiated by omitting the derivation of negation (oval) from consequence (scroll). 2. The psychological process of noticing a difference or distinction in perception does seem to be more primitive than the linguistic process of verbalizing the inference of modus ponens, but as Peirce repeatedly affirmed, the logical relation of negation is absolutely not more primitive than the logical relation of consequence. Moreover, "We do not derive these notions [universal elementary relations of logic] from observation, nor by any sense of being opposed, but from our own reason" (CP 8.352, EP 2:485, 1908). 3. I have repeatedly acknowledged that in classical logic, which is what Peirce obviously had in mind in 1911, a scroll is indeed equivalent to a nest of two ovals. Although he anticipated intuitionistic logic in several remarkable ways, including his explicit statements in R 300 (1908) that analyzing a consequence as a composite of two negations is erroneous, unfortunately he did not take the additional steps that would have been necessary to formalize it. Otherwise, we might today be calling it synechistic logic instead. 4. According to Peirce, "I have a complete theory of this process [logical analysis], including its methodeutic, which I base upon my existential graphs which is my chef d'oeuvre" (NEM 3:885, 1908). Whether it was logical analysis or EGs that he considered to be his masterpiece, it is clear that they are closely linked. In the context of logical analysis, he repeatedly defines "more analytical" as "breaking up inferences into the greatest possible number of steps" (CP 4.373, 1902). In every single classical or intuitionistic proof that involves negation, deriving it from a consequence with "the essence of falsity" as its consequent is technically a necessary additional step. As Bellucci and Pietarinen rightly put it, "Taking the idea of negation as primary is philosophically inaccurate." 5. Peirce was obviously not advocating that we add unnecessary steps, and he generally sought to minimize the number of axioms. For example, he eagerly embraced non-Euclidean geometry as demonstrating that the parallel postulate is not essential for a consistent system. I believe that he likewise would have endorsed intuitionistic logic as demonstrating that excluded middle and its corollaries are not essential for a consistent system, had he managed to work out the details himself--or had he lived to see Brouwer and Heyting do so, despite undoubtedly disagreeing with them about the philosophical motivations. In that sense, non-Euclidean geometry is more analytical than Euclidean geometry and intuitionistic logic is more analytical than classical logic, because in each case the former requir
Re: Aw: Re: [PEIRCE-L] Scroll vs Nested Ovals (was Existential Graphs in 1911)
Helmut - if you read Peirce's cosmological outlines [6.203 and 1.412], he begins with 1ns, moves on to the instantiations of 2ns, and then, into the developing habits of 3ns. So, the 'actualization' of the modes in spatiotemporal existence is linear. But - all three modes are potential and necessary, therefore, I don't think that one can say that any one of them is 'more fundamental'. And I'm not sure how a singular description of a variable [A human is a featherless biped] can be transformed into a sound deductive argument [IF it is a featherless biped THEN it is human]. As you point out, the connection of the attribute [featherless biped] might not always apply to the variable of 'human'. Edwina On Fri 29/01/21 11:02 AM , Helmut Raulien h.raul...@gmx.de sent: All, I think, the difference is not the meaning, but what it is. Though the double negation´s meaning is the same as the conclusion´s meaning, the double negation has the form of a proposition, or a definition, which is secondness: "There is not a featherless biped that is not a human" may be classificationally instantated from exclusion of exclusion to definition: "A human is a featherless biped". The conclusion "If it is a featherless biped then it is a human" may be individually instantated to an argument; "It is a human because it is a featherless biped". It is thirdness, a rule or law. Which of both is more fundamental? Both mean the same, so if one changes, the other changes too. But which is more likely to change? The law "If it is a featherless biped then it is a human" cannot change just so, by itself. But the situation, the secondness, the truth of the proposition "There is not a featherless biped that is not a human" can easily change, and make the law obsolete, e.g. if an ape quits using its arms for walking, or if a dog sadly has two legs amputated, or if a chicken, due to a mutation, is born without feathers. So, is the double negation more fundamental, because it breaks the law? People will say, that the ape is just stupid, the chicken and the dog are just handicapped, exceptions only corrobate the rule, and all people who claim that the law is no longer in charge are heretics. A law (3ns) is more tenacious than actualities (2ns), that first have to prove worthwile one by one to add up to a certain measure, so is it more fundamental?Helmut Freitag, 29. Januar 2021 um 00:49 Uhr "Jon Alan Schmidt" wrote: John, List, All: In this post, I will simply respond to the numbered items below rather than quoting them. 1. I am not aware of any evidence that Peirce ever explicitly denied that illation is essential for deduction or rejected the use of the scroll for that purpose in EGs. The absence of these specific terms in his relatively sparse writings during the last 34 months of his life does not outweigh their abundance in his voluminous output over the preceding decades. Again, my hypothesis is that in June 1911 he merely decided to simplify his presentation of EGs for the uninitiated by omitting the derivation of negation (oval) from consequence (scroll). 2. The psychological process of noticing a difference or distinction in perception does seem to be more primitive than the linguistic process of verbalizing the inference of modus ponens, but as Peirce repeatedly affirmed, the logical relation of negation is absolutely not more primitive than the logical relation of consequence. Moreover, "We do not derive these notions [universal elementary relations of logic] from observation, nor by any sense of being opposed, but from our own reason" (CP 8.352, EP 2:485, 1908). 3. I have repeatedly acknowledged that in classical logic, which is what Peirce obviously had in mind in 1911, a scroll is indeed equivalent to a nest of two ovals. Although he anticipated intuitionistic logic in several remarkable ways, including his explicit statements in R 300 (1908) that analyzing a consequence as a composite of two negations is erroneous, unfortunately he did not take the additional steps that would have been necessary to formalize it. Otherwise, we might today be calling it synechistic logic instead. 4. According to Peirce, "I have a complete theory of this process [logical analysis], including its methodeutic, which I base upon my existential graphs which is my chef d'oeuvre" (NEM 3:885, 1908). Whether it was logical analysis or EGs that he considered to be his masterpiece, it is clear that they are closely linked. In the context of logical analysis, he repeatedly defines "more analytical" as "breaking up inferences into the greatest possible number of steps" (CP 4.373, 1902). In every single classical or intuitionistic proof that involves negation, deriving it from a consequence with "the essence of falsity" as its consequent is technically a necessary additional step. As Bellucci and Pietarinen rightly put it, "Taking the idea of negation as primary is philosophically inaccurate." 5.
Aw: Re: Re: [PEIRCE-L] Scroll vs Nested Ovals (was Existential Graphs in 1911)
Edwina, yes, "a human is a featherless biped" might be understood as singular description. I meant it as definition, so it is better to say "a human is defined as featherless biped", which is a proposition, a description of a status, and not yet a law. The semiosis of habit-formation goes 1-2-3, and the semiosis of reflexion the other way, so, yes, I agree, that it neither is correct that 2ns is more fundamental than 3ns, nor the other way. But I think logic is reflexion, so in this case 3ns (law, conclusion, the scroll) is primary to 2ns (actuality, proposition, nested ovals). With "more fundamental" I just was refering to the question in this thread about what is primary to what. I still am quibbling with the reason for intuitionalistic logic. But it is somwhat hard to show a primarity that cannot be illustrated with examples, as there is no loss or gain in meaning, merely a by me suspected academic rule, that logic is reflexion, and in reflexion 3ns comes before 2ns. But all in all I am merely suspecting and tentatively trying this and that. Best, Helmut 29. Januar 2021 um 18:19 Uhr "Edwina Taborsky" wrote: Helmut - if you read Peirce's cosmological outlines [6.203 and 1.412], he begins with 1ns, moves on to the instantiations of 2ns, and then, into the developing habits of 3ns. So, the 'actualization' of the modes in spatiotemporal existence is linear. But - all three modes are potential and necessary, therefore, I don't think that one can say that any one of them is 'more fundamental'. And I'm not sure how a singular description of a variable [A human is a featherless biped] can be transformed into a sound deductive argument [IF it is a featherless biped THEN it is human]. As you point out, the connection of the attribute [featherless biped] might not always apply to the variable of 'human'. Edwina On Fri 29/01/21 11:02 AM , Helmut Raulien h.raul...@gmx.de sent: All, I think, the difference is not the meaning, but what it is. Though the double negation´s meaning is the same as the conclusion´s meaning, the double negation has the form of a proposition, or a definition, which is secondness: "There is not a featherless biped that is not a human" may be classificationally instantated from exclusion of exclusion to definition: "A human is a featherless biped". The conclusion "If it is a featherless biped then it is a human" may be individually instantated to an argument; "It is a human because it is a featherless biped". It is thirdness, a rule or law. Which of both is more fundamental? Both mean the same, so if one changes, the other changes too. But which is more likely to change? The law "If it is a featherless biped then it is a human" cannot change just so, by itself. But the situation, the secondness, the truth of the proposition "There is not a featherless biped that is not a human" can easily change, and make the law obsolete, e.g. if an ape quits using its arms for walking, or if a dog sadly has two legs amputated, or if a chicken, due to a mutation, is born without feathers. So, is the double negation more fundamental, because it breaks the law? People will say, that the ape is just stupid, the chicken and the dog are just handicapped, exceptions only corrobate the rule, and all people who claim that the law is no longer in charge are heretics. A law (3ns) is more tenacious than actualities (2ns), that first have to prove worthwile one by one to add up to a certain measure, so is it more fundamental? Helmut Freitag, 29. Januar 2021 um 00:49 Uhr "Jon Alan Schmidt" wrote: John, List, All: In this post, I will simply respond to the numbered items below rather than quoting them. 1. I am not aware of any evidence that Peirce ever explicitly denied that illation is essential for deduction or rejected the use of the scroll for that purpose in EGs. The absence of these specific terms in his relatively sparse writings during the last 34 months of his life does not outweigh their abundance in his voluminous output over the preceding decades. Again, my hypothesis is that in June 1911 he merely decided to simplify his presentation of EGs for the uninitiated by omitting the derivation of negation (oval) from consequence (scroll). 2. The psychological process of noticing a difference or distinction in perception does seem to be more primitive than the linguistic process of verbalizing the inference of modus ponens, but as Peirce repeatedly affirmed, the logical relation of negation is absolutely not more primitive than the logical relation of consequence. Moreover, "We do not derive these notions [universal elementary relations of logic] from observation, nor by any sense of being opposed, but from our own reason" (CP 8.352, EP 2:485, 1908). 3. I have repeatedly acknowledged that in classical logic, which is what Peirce obviously had in mind in 1911, a scroll is indeed equivalent to a nest of two ovals. Although he anticipated intuitionistic logic in
[PEIRCE-L] Re: Animated Logical Graphs
Cf: Survey of Animated Logical Graphs • 3 https://inquiryintoinquiry.com/2020/08/23/survey-of-animated-logical-graphs-3/ All, I updated my last Survey page on Animated Logical Graphs and added links to the series of posts on CSP, GSB, & Me. https://inquiryintoinquiry.com/2017/07/19/charles-sanders-peirce-george-spencer-brown-and-me/ https://inquiryintoinquiry.com/2017/07/20/charles-sanders-peirce-george-spencer-brown-and-me-1/ https://inquiryintoinquiry.com/2017/07/21/charles-sanders-peirce-george-spencer-brown-and-me-2/ https://inquiryintoinquiry.com/2017/07/31/charles-sanders-peirce-george-spencer-brown-and-me-3/ ••• https://inquiryintoinquiry.com/2017/08/25/charles-sanders-peirce-george-spencer-brown-and-me-10/ https://inquiryintoinquiry.com/2021/01/18/charles-sanders-peirce-george-spencer-brown-and-me-11/ https://inquiryintoinquiry.com/2021/01/25/charles-sanders-peirce-george-spencer-brown-and-me-12/ https://inquiryintoinquiry.com/2021/01/26/charles-sanders-peirce-george-spencer-brown-and-me-13/ Regards, Jon _ _ _ _ _ _ _ _ _ _ ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu with no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Existential Graphs in 1911
Auke, I agree with your observation, and the conclusion: "It is a line of thought I can see leading to what Jon wrote." Charles' father Benjamin Peirce gave him a thorough training in mathematics from early childhood, and Charles devoured Whateley's logic book in a week when he was 13. He insisted that metaphysics should be based on mathematics, not on Hegel-style verbiage. Jon's method of focusing on the words is a kind of literary criticism that would be more appropriate for analyzing Shakespeare than Peirce. John _ _ _ _ _ _ _ _ _ _ ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu with no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Existential Graphs in 1911
John Sowa wrote: JFS: Jon's method of focusing on the words is a kind of literary criticism that would be more appropriate for analyzing Shakespeare than Peirce. I found this comment as useless and, frankly, as absurd as this earlier one of yours in this thread. JFS: As for Jon's comments about earlier versions, any quotations prior to June 1911 are irrelevant. Please do not recommence these preposterous -- in their gross generality -- or ad hominem attacks that were so disruptive last year and, indeed, part of the year before. Please stick to discussing substantive content. We have really had more than enough of this on the List for a lifetime. Best, Gary Richmond (writing as List moderator) "Time is not a renewable resource." gnox *Gary Richmond* *Philosophy and Critical Thinking* *Communication Studies* *LaGuardia College of the City University of New York* On Fri, Jan 29, 2021 at 6:35 PM John F. Sowa wrote: > Auke, > > I agree with your observation, and the conclusion: "It is a line of > thought I can see leading to what Jon wrote." > > Charles' father Benjamin Peirce gave him a thorough training in > mathematics from early childhood, and Charles devoured Whateley's logic > book in a week when he was 13. He insisted that metaphysics should be > based on mathematics, not on Hegel-style verbiage. > > Jon's method of focusing on the words is a kind of literary criticism > that would be more appropriate for analyzing Shakespeare than Peirce. > > John > _ _ _ _ _ _ _ _ _ _ ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu with no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Existential Graphs in 1911
Gary R, My remarks were ad rem, not ad hominem. Mathematics is like music. A mathematician or a musician thinks only in terms of the patterns, the operations on those patterns, and their relationship to whatever notation is used to represent them. The words used to describe those patterns are useful for communication among teachers, students, and critics. But those words are absent from the minds of the artists (musical or mathematical) who are imagining and creating novel patterns. Peirce was a great mathematical/logical artist. In June 1911, he had a new insight into the melodies of logic. Any logician can "hear" an exciting new melody in R670 and L231 that was not present in R669 or the Monist article of 1906. Peirce didn't have to write a "note to self" about the change. He just did it. And any logician can "hear" it. But I realize that many people can't feel or hear the difference. I plan to post the 1906 version and the 1911 version on my web site, and I'll point out exactly where the differences occur and their implications. I'll post that in the next two days. And I won't refer to any other person's comments or opinions on the subject. Meanwhile, I recommend the following slides and their quotations of mathematicians, logicians, and linguists about their subject: http://jfsowa.com/talks/ppe.pdf . The application of Peirce's EGs to Euclidean diagrams is easy with the 1911 EGs, but not with the earlier versions. That application is one of the strongest arguments in support of Peirce's claim that EGs represent "the action of the mind in thought." John _ _ _ _ _ _ _ _ _ _ ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu with no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
