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 <gary.richm...@gmail.com> 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 <jawb...@att.net> 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 <jawb...@att.net> 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 peirce-L@list.iupui.edu > . > ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu > 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 peirce-L@list.iupui.edu . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu 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.
