Imran, List, You suggested that I had concluded "that minimal negation operators are not related to Peirce’s mathematical work"
I didn't conclude that at all, but rather that Jon should make some minimal attempt to show that relation. In truth, I think it might be more productive than this back and forth with me for you to discuss that relation with Jon on the List (this is apparently the first time(s) you've posted to Peirce-L). IM: You ask: "why this conclusion is so overwhelming that it called for threatening to ban Jon rather than engage the relevant subject matter on list." The topic of "minimal negation operators" is just the current subject of JA's posts. And, btw, if you are so interested in the topic, then why don't you "engage the relevant subject matter"? That might resolve the whole issue. I do wonder why you have suddently become the voice of Jon's 'defense' rather than Jon himself, especially since -- as far as I know -- you haven't discussed any of this relation -- or, really anything -- with him on Peirce-L. And I am *not* "threatening" Jon, but *respectfully* requesting, as I have done again and again (and as Joe Ransdell did repeatedly) to make clear the Peirce-related relevance of his posts. I'm not "singling Jon out" as you claim -- except perhaps in the sense that I haven't had this issue with any other participant on the List, including those with whom I'm at loggerheads. But I am increasingly frustrated that he can't meet this minimum request: to clearly show the relevance of his posts to the theme of "a list called "PEIRCE-L: The Philosophy of Charles Peirce." This is a Peirce-related discussion forum. Can we please return to that purpose? Best, Gary Richmond (writing as List moderator) “Let everything happen to you Beauty and terror Just keep going No feeling is final” ― Rainer Maria Rilke *Gary Richmond* *Philosophy and Critical Thinking* *Communication Studies* *LaGuardia College of the City University of New York* On Mon, Sep 27, 2021 at 10:01 PM Imran Makani <[email protected]> wrote: > Gary, > > Then please explain how it is that you concluded through your independent > study of Jon’s work that minimal negation operators are not related to > Peirce’s mathematical work, and why this conclusion is so overwhelming that > it called for threatening to ban Jon rather than engage the relevant > subject matter on list. > > Imran > > Sent from my iPhone > > On Sep 27, 2021, at 8:43 PM, Gary Richmond <[email protected]> > wrote: > > > Imran wrote: > > Respectfully, it seems to me as though Jon is being unfairly targeted > merely because the subject matter of his contributions in this case are > outside the scope of your expertise and interests, not Peirce’s. Again, > this is just my impression and I don’t mean it disrespectfully. > > > You are certainly free to have your *not* 'disrespectful' opinion of > my "expertise and interests." But, in fact, you have absolutely *no* > knowledge of my understanding of the topics which Jon takes up. Indeed, I > studied his work in earnest for the first decade in which I was aware of > it, including, and especially, his cactus graphs. I finally came to the > conclusion that Peirce's existential graphs were a superior-- and more > iconic -- way of diagramming matters 'logical'. That I currently have > little to no interest in what Jon is posting has nothing to do with my > request that he make it clear how his posts are Peirce-related. > > Now, it seems to me. that Jon more or less repeats what he has already > analyzed for decades (that, of course, is just my opinion, and he may be > introducing 'subtleties' to his earlier work which I am simply not > interested in considering). But that is not at all why I expect him -- and > *every > *participant in this forum -- to demonstrate the relevance of what they > post to this forum. > > So, despite your not disrespectful opinion to the contrary, I am not > singling Jon out at all. In truth, he singles himself out -- as he did > earlier when Joe Ransdell was moderator of Peirce-L -- as someone who is > unwilling or unable to respect this forum's purpose and culture. And, > consequently, most often -- or so it seems to me -- his 'discussions' (when > they occur at all) are not with Peirce-L participants. > > Best, > > Gary Richmond (writing as Peirce-L moderator) > > “Let everything happen to you > Beauty and terror > Just keep going > No feeling is final” > ― Rainer Maria Rilke > > *Gary Richmond* > *Philosophy and Critical Thinking* > *Communication Studies* > *LaGuardia College of the City University of New York* > > > > > > > > On Mon, Sep 27, 2021 at 8:56 PM Imran Makani <[email protected]> wrote: > >> Gary, >> >> >> Thank you for this background. But it remains unclear to me how you >> concluded that minimal negation operators are not related to Peirce’s >> mathematical work. In his first post on this thread Jon clearly says >> that they they were developed from Peirce’s alpha graphs for propositional >> calculus and that he has even outlined the history of this early >> development in a previous series of posts. >> >> >> It’s also unclear to me why Jon should have to preemptively preface all >> of his posts with a reasonable explanation for why their subject matter >> should be under discussion on this list, rather than respond with this only >> when it is reasonably requested of him, since other members are not >> required to provide this preemptively for their posts. >> >> >> Respectfully, it seems to me as though Jon is being unfairly targeted >> merely because the subject matter of his contributions in this case are >> outside the scope of your expertise and interests, not Peirce’s. Again, >> this is just my impression and I don’t mean it disrespectfully. >> >> >> Best, >> >> >> Imran >> >> Sent from my iPhone >> >> On Sep 27, 2021, at 7:06 PM, Gary Richmond <[email protected]> >> wrote: >> >> >> Imran, List, >> >> As Joe Ransdell wrote on the Peirce-L page of Arisbe when he created both >> Peirce-L and Arisbe: >> >> Discussion should be Peirce-related but not necessarily on Peirce, and >> the working test for relevance would simply be a plausible explanation of >> why the topic in question should be under discussion on a list called >> "PEIRCE-L: The Philosophy of Charles Peirce", given that people subscribe >> to such lists with some more or less definite expectations about >> subject-matter in mind. *https://arisbe.sitehost.iu.edu/PEIRCE-L/PEIRCE-L.HTM >> <https://arisbe.sitehost.iu.edu/PEIRCE-L/PEIRCE-L.HTM>* >> >> >> As I wrote earlier today, it is not and should not be required of any >> member of the List, including the Moderator, to have to ask for the >> relevance of a post; that is the responsibility of the poster. And I should >> add that it has been only when Jon has posted several consecutive posts >> that did not meet this minimum requirement that either Joe or I intervened. >> Too many of Jon's posts do not meet the criterion of relevance to the forum. >> >> As a matter of the history of Peirce-L, Jon is one of only two people who >> Joe Ransdell removed from the List in his many years as Moderator and for >> the very reason that Jon was not willing to offer that self-same relevance. >> Some long term forum participants may recall that history, and I know that >> the co-manager with me of Peirce-L and Arisbe, Ben Udell, does indeed >> recall it as he and I discussed it not very long ago. >> >> As did Joe, I have tried off-list and on-list to encourage Jon to post >> only relevant messages to Peirce-L, but for whatever reason, he resists >> doing so. When he has been relevant, as have you, I too have valued his >> contributions even when we weren't in agreement on a given issue. I would, >> in fact, very much like to see Jon connect *in a substantive **way* >> posts relevant to Peirce's work. That certainly would be a valuable >> contribution to the forum. >> >> You may have noticed that Jon cross-posts to many lists, none of which is >> Peirce-related in the sense in which Ransdell described it in the quotation >> above. And it seems to me that some of these lists are serving principally >> -- if not exclusively -- as repositories of posts rather than being active >> discussion groups such as Peirce-L is. Since I have copied the addresses of >> these lists below, you might consider joining one or more of them so that >> you can be assured of following Jon's messages uninterruptedly. >> >> Cybernetic Communications <[email protected]>, >> Laws of Form <[email protected]>, >> Ontolog Forum <[email protected]>, >> Structural Modeling <[email protected]>, >> SysSciWG <[email protected]> >> >> >> Best, >> >> Gary Richmond (writings as List manager) >> >> >> “Let everything happen to you >> Beauty and terror >> Just keep going >> No feeling is final” >> ― Rainer Maria Rilke >> >> *Gary Richmond* >> *Philosophy and Critical Thinking* >> *Communication Studies* >> *LaGuardia College of the City University of New York* >> >> >> >> >> >> >> >> On Mon, Sep 27, 2021 at 6:24 PM Imran Makani <[email protected]> wrote: >> >>> Gary, >>> >>> Jon clearly said he indeed would be the one to provide this relevance >>> when you request it of him on list. >>> >>> I for one value his contributions here. >>> >>> Best, >>> >>> Imran >>> >>> Sent from my iPhone >>> >>> On Sep 27, 2021, at 3:17 PM, Gary Richmond <[email protected]> >>> wrote: >>> >>> >>> Jon, >>> >>> JA: I don't do off-list communication. >>> >>> GR: Well, that is something new. In any event, Joe Ransdell established >>> the practice of writing a list participant off-list before bringing the >>> issue in question to the list. I follow this precedent. >>> >>> JA: If you have questions about the relevance of my posts >>> to Peirce's lifelong work in logic, mathematics, and >>> semiotics and to the development of pragmatic thought >>> in general, please be so kind as to ask them on List. >>> >>> No. It is you who needs to provide the relevance of your posts to >>> Peirce-L, not I nor anyone else. >>> >>> Best, >>> >>> Gary Richmond (writing to you about this matter for the last time on or >>> off-list) >>> >>> “Let everything happen to you >>> Beauty and terror >>> Just keep going >>> No feeling is final” >>> ― Rainer Maria Rilke >>> >>> *Gary Richmond* >>> *Philosophy and Critical Thinking* >>> *Communication Studies* >>> *LaGuardia College of the City University of New York* >>> >>> >>> >>> >>> >>> >>> >>> On Mon, Sep 27, 2021 at 4:08 PM Jon Awbrey <[email protected]> wrote: >>> >>>> Dear Gary, >>>> >>>> I don't do off-list communication. >>>> >>>> If you have questions about the relevance of my posts >>>> to Peirce's lifelong work in logic, mathematics, and >>>> semiotics and to the development of pragmatic thought >>>> in general, please be so kind as to ask them on List. >>>> >>>> Regards, >>>> >>>> Jon >>>> >>>> On 9/27/2021 3:46 PM, Gary Richmond wrote: >>>> > off List >>>> > >>>> > Jon, >>>> > >>>> > Please remove Peirce-L from your list of sites if your messages aren't >>>> > Peirce-L related in the sense in which the forum is conceived. If you >>>> can't >>>> > do that, given that I've repeatedly asked you to do so on and off >>>> List, >>>> > then either leave the List or we'll do it for you if you prefer. >>>> > >>>> > I've Cc'd this note to Ben Udell. >>>> > >>>> > Gary Richmond (writing off-list as moderator) >>>> > >>>> > “Let everything happen to you >>>> > Beauty and terror >>>> > Just keep going >>>> > No feeling is final” >>>> > ― Rainer Maria Rilke >>>> > >>>> > *Gary Richmond* >>>> > *Philosophy and Critical Thinking* >>>> > *Communication Studies* >>>> > *LaGuardia College of the City University of New York* >>>> > >>>> > >>>> > >>>> > >>>> > >>>> > >>>> > >>>> > On Mon, Sep 27, 2021 at 2:45 PM Jon Awbrey <[email protected]> wrote: >>>> > >>>> >> Cf: Minimal Negation Operators • 4 >>>> >> >>>> https://inquiryintoinquiry.com/2017/09/01/minimal-negation-operators-4/ >>>> >> >>>> >> All, >>>> >> >>>> >> I'm including a more detailed definition of minimal negation >>>> operators >>>> >> in terms of conventional logical operations largely because readers >>>> of >>>> >> particular tastes have asked for it in the past. But it can easily >>>> be >>>> >> skipped until one has a felt need for it. Skimmed lightly, though, >>>> it >>>> >> can serve to illustrate a major theme in logic and mathematics, >>>> namely, >>>> >> the Relativity of Complexity or the Relativity of Primitivity to the >>>> >> basis we have chosen for constructing our conceptual superstructures. >>>> >> >>>> >> ⁂ ⁂ ⁂ >>>> >> >>>> >> Defining minimal negation operators over a more conventional basis >>>> >> is next in order of exposition, if not necessarily in order of every >>>> >> reader’s reading. For what it’s worth and against the day when it >>>> may >>>> >> be needed, here is a definition of minimal negations in terms of ∧, >>>> ∨, >>>> >> and ¬. >>>> >> >>>> >> Formal Definition >>>> >> ================= >>>> >> >>>> >> To express the general form of νₙ in terms of familiar operations, >>>> >> it helps to introduce an intermediary concept. >>>> >> >>>> >> Definition. Let the function ¬ₘ : Bⁿ → B be defined for each >>>> >> integer m in the interval [1, n] by the following equation. >>>> >> >>>> >> • ¬ₘ(x₁, …, xₘ, …, xₙ) = x₁ ∧ … ∧ xₘ₋₁ ∧ ¬xₘ ∧ xₘ₊₁ ∧ … ∧ xₙ. >>>> >> >>>> >> Then νₙ : Bⁿ → B is defined by the following equation. >>>> >> >>>> >> • νₙ(x₁, …, xₙ) = ¬₁(x₁, …, xₙ) ∨ … ∨ ¬ₘ(x₁, …, xₙ) ∨ … ∨ ¬ₙ(x₁, >>>> …, xₙ). >>>> >> >>>> >> We may take the boolean product x₁ ∙ … ∙ xₙ or the logical >>>> conjunction >>>> >> x₁ ∧ … ∧ xₙ to indicate the point x = (x₁, …, xₙ) in the space Bⁿ, in >>>> >> which case the minimal negation νₙ(x₁, …, xₙ) indicates the set of >>>> points >>>> >> in >>>> >> Bⁿ which differ from x in exactly one coordinate. This makes νₙ(x₁, >>>> …, xₙ) >>>> >> a discrete functional analogue of a point-omitted neighborhood in >>>> ordinary >>>> >> real analysis, more precisely, a point-omitted distance-one >>>> neighborhood. >>>> >> Viewed in that light the minimal negation operator can be recognized >>>> as >>>> >> a differential construction, an observation opening a very wide >>>> field. >>>> >> >>>> >> The remainder of this discussion proceeds on the algebraic convention >>>> >> making the plus sign (+) and the summation symbol (∑) both refer to >>>> >> addition mod 2. Unless otherwise noted, the boolean domain B = {0, >>>> 1} >>>> >> is interpreted for logic in such a way that 0 = false and 1 = true. >>>> >> This has the following consequences. >>>> >> >>>> >> • The operation x + y is a function equivalent to the exclusive >>>> >> disjunction of >>>> >> x and y, while its fiber of 1 is the relation of inequality >>>> between x >>>> >> and y. >>>> >> >>>> >> • The operation ∑ₘ xₘ = x₁ + … + xₙ maps the bit sequence (x₁, …, xₙ) >>>> >> to its parity. >>>> >> >>>> >> The following properties of the minimal negation operators >>>> >> νₙ : Bⁿ → B may be noted. >>>> >> >>>> >> • The function ν₂(x, y) is the same as that associated with >>>> >> the operation x + y and the relation x ≠ y. >>>> >> >>>> >> • In contrast, ν₃(x, y, z) is not identical to x + y + z. >>>> >> >>>> >> • More generally, the function νₙ(x₁, …, xₙ) for k > 2 >>>> >> is not identical to the boolean sum ∑ₘ xₘ = x₁ + … + xₙ. >>>> >> >>>> >> • The inclusive disjunctions indicated for the νₙ of more than >>>> >> one argument may be replaced with exclusive disjunctions without >>>> >> affecting the meaning since the terms in disjunction are already >>>> >> disjoint. >>>> >> >>>> >> 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 >>> [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.
