John, List: I have taken the liberty of adding Francesco Bellucci (who has posted to Peirce-L in the past) and Ahti-Veikko Pietarinen to the cc: line, since their names keep coming up. I earnestly invite them to share their thoughts on this exchange, as well as the previous one (e.g., https://list.iupui.edu/sympa/arc/peirce-l/2021-05/msg00117.html and https://list.iupui.edu/sympa/arc/peirce-l/2021-05/msg00121.html).
JFS: If you look through the literature of math & logic, different authors often derive exactly the same theories by starting with different choices of primitives and definitions. But as long as every definition in one is an equivalence in the other, the two theories are identical. They are identical from a *formal *standpoint within the *same *system of logic--classical in this case--but not from a *philosophical *standpoint, especially once we recognize and seek to accommodate *different *systems of logic. Practical efficiency in carrying out classical proofs is not the *only *purpose worth pursuing within the field of logic. As Peirce attests repeatedly, it was at most a secondary consideration for him when inventing EGs, which he intended primarily to facilitate studying logic itself. There are plenty of good reasons for exploring non-classical alternatives, such as intuitionistic logic and modal logic. "*Do not block the way of inquiry*" (CP 1.135, EP 2:48, 1898; bold in original). JFS: Since every Alpha or Beta EG and every proof with the EGs can be mapped directly to the new version, there is no logical or philosophical idea expressed with the old version that cannot be expressed as well or better with the new version. On the contrary, the derivation of negation from the implication of falsity is obviously a "logical or philosophical idea ... that cannot be expressed as well or better with the new version," since the latter treats negation as if it were primitive for the sake of convenience. Rejecting excluded middle, resulting in intuitionistic logic rather than classical logic, is another "logical or philosophical idea ... that cannot be expressed as well or better with the new version," since "not-A or B," "if A then B," and "not-(A and not-B)" are no longer equivalent. Representing modal propositions by scribing EGs with broken cuts is a third "logical or philosophical idea ... that cannot be expressed as well or better with the new version." JFS: But some people have claimed that there are certain stylistic features, such as a preference for an "illative sign" that is omitted in the new version. As Bellucci, Pietarinen, and others have written at considerable length, this is not a mere "stylistic feature," it is a fundamental logical and philosophical idea that Peirce maintained throughout his life. Anyone is free to *disagree *with him about this, but not to attribute a *different *view to him. As I apparently keep having to repeat, even to the person who posted it in the first place ( https://list.iupui.edu/sympa/arc/peirce-l/2021-05/msg00045.html), "nobody can claim that anything other than an exact quotation is what Peirce intended." *Omission is not rejection.* JFS: Unfortunately, he went far beyond Whately in considering that "illative conjunction" to be an obligation, rather than a stylistic convention. Deeming this approach "unfortunate" is obviously nothing more than a personal opinion. I join others like Bellucci and Pietarinen in finding it extremely insightful and fruitful from a *philosophical *standpoint. After all, as Pietarinen's title for his comprehensive collection of Peirce's writings about EGs indicates, we are interested in exploring the logic of the *future*, not getting stuck in the logic of the *past*. JFS: Every logical or philosophical idea that can be explained in terms of the earlier EGs can be explained with greater clarity, precision, and generality with the EGs of 1911. Nobody has ever found a single exception. Such sweeping generalizations are unbecoming of someone who is purportedly a scholar, especially since they are blatantly inaccurate. There can be no question that the "logical or philosophical idea" of inference being primitive and corresponding to the formal relation of implication, such that negation is properly derived from it rather than treated as a primitive itself, *cannot *"be explained with greater clarity, precision, and generality with the EGs of 1911." In fact, so far, "Nobody has ever found a single exception" to my own observation that there is no evidence in any text by Peirce that he *rejected *this idea. Again, *omission is not rejection.* Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Mon, May 24, 2021 at 12:03 AM John F. Sowa <s...@bestweb.net> wrote: > In my previous note (copy below) I showed that the only factual > information available shows that Peirce summarized his earlier EGs in R669, > developed a new version in R670, and wrote a more polished version at the > beginning of a long letter (L231) to Mr. Kehler, a member of Lady Welby's > Significs group. > > Since every Alpha or Beta EG and every proof with the EGs can be mapped > directly to the new version, there is no logical or philosophical idea > expressed with the old version that cannot be expressed as well or better > with the new version. > > But some people have claimed that there are certain stylistic features, > such as a preference for an "illative sign" that is omitted in the new > version. That idea may have been influenced by what Peirce read 60 years > earlier. > > When Peirce was 12 years old, he read his brother's copy of Whately's > Elements of Logic. A Google Books copy of the 9th edition (1855) can be > found on the WWW. (CSP probably read the 8th edition.) On p. 86 Whately > wrote > > "If the Conclusion be stated last (which is the strict logical form, to > which all Reasoning may be reduced) then, that which is employed to prove > it is called the premisses, and the Conclusion is then introduced by some > illative conjunction, as 'therefore.' " > > The terminology, spelling, and style of writing apparently had a strong > influence on the young CSP. Unfortunately, he went far beyond Whately in > considering that "illative conjunction" to be an obligation, rather than a > stylistic convention. > > Nobody knows exactly why Peirce replaced the R669 EGs with the new version > of R670 and L231. But a comparison of the two shows that Peirce had > finally freed himself from Whately's influence. > > The attached R669.png shows Peirce's assumption of a "sign of illation" (a > scroll for material implication) as primitive, and the steps of deriving > negation from a scroll plus a blot (pseudograph). But the steps from Fig. > 24 to Fig 27 are ad hoc. They do not follow the rules of inference, which > were substantially unchanged from 1896 to 1911. In R670 and L231 and > later, negation is primitive and material implication does not require a > definition: a nest of two negations is equivalent to a scroll. > > Further evidence of Peirce's new freedom from Whately's influence, is the > three permissions (rules of inference) in R670. In R669, the first two > were called illative permissions, and the third (double negation) was not > considered illative. But he realized that all of the rules depend only on > negation; none of them depend on an illative sign. > > Every logical or philosophical idea that can be explained in terms of the > earlier EGs can be explained with greater clarity, precision, and > generality with the EGs of 1911. Nobody has ever found a single exception. > > John > _______________________________________________________ > > Before getting into any speculation, I'll mention some undeniable facts: > > 1. R699 has the title "Assurance through reasoning", it begins with a > paragraph about necessary deduction and probable deduction, and it contains > a summary of the EG system from the early days up to and including > recto/verso semantics. It also includes a story about a paradise without > negation as support for deriving negation from a scroll (for material > implication) plus a blot (representing the pseudograph) that shrinks to a > invisble, but still present dot. > > 2. Five days after finishing (or stopping) R669, Peirce began R670 with > the same title and a similar opening paragraph. But the system omits many > features of R699, and replaces them with a new foundation, which Peirce > presents in a clean presentation in L231, which he begins five days after > finishing R670. > > This is my summary, and I'm stating it only to highlight the critcal > points in two brief paragraphs. But every sentence in it could be replaced > by excerpts from the threee MSS. > > When I used the title "Peirce's own tutorial" in my 2011 article in > Semiotica, I was misled by the erroneous date of 1909 on R514, which I used > instead of L231. But now that we know the correct date and provenance, all > available evidence shows that L231 is Peirce's best and final version. > > There is only one minor objection that is easily dismissed: Some people, > including Ahti, have used the derivation of negation from a scroll plus > pseudograph in some writings. But that point is irrelevant. In > mathematics (which includes formal logic), any proof that starts with a > definition of A as B can be carried out in exactly the same steps by > starting with a statement that A is equivalent to B. > > If you look through the literature of math & logic, different authors > often derive exactly the same theories by starting with different choices > of primitives and definitions. But as long as every definition in one is > an equivalence in the other, the two theories are identical. > > There may be some people who need a bit of explanation of these points, > but there is no mathematician or logician on earth who could refute them. >
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