John, List: JFS: By 1911, he realized that his earlier terminology was an obstacle, not an aid to understanding. To emphasize the necessary and sufficient core, he deliberately discarded most of his earlier terms.
He realized that *some*, perhaps even *much*, of his earlier terminology was an obstacle; but obviously not *all *of it. JFS: Peirce had been following Clifford's terminology by using the words 'spot' and 'line', but I suspect that by 1911 he was aware that common usage was moving away from that terminology. That may be one reason why he did not use the word 'spot' in 1911. He did not use "Spot" in the letter to Mr. Kehler, but he did use it in both R 669 and R 670, written only days earlier. Technically, something is not a Graph as defined by Clifford (and Sylvester) unless it includes both Spots and Lines. JFS: In presenting EGs, Peirce made one fatal mistake. He did not show the mapping from Alpha and Beta to his algebraic notation of 1885. Not systematically, which indeed would have likely been more effective than the 55 pages of "Prolegomena" turned out to be; but there are some manuscripts where he expressed the same Propositions using both notations, side by side. JFS: A peg is not a predicate. It's a point on a symbol that represents a relation. If the relation is N-adic that symbol will have N pegs where lines of identity may be attached. As I just posted in the other thread, Lines of Identity denote indefinite individuals, Spots (words) denote general concepts, and Pegs signify continuous predicates by which EGs as Propositions *attribute *concepts (Spots) to individuals (Lines). Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Sat, May 4, 2019 at 12:14 PM John F Sowa <s...@bestweb.net> wrote: > Jon, > > > JFS: I like the word peg, since it's iconic, and it doesn't > > conflict with any term in Peirce's writings, modern logic, > > linguistics, or mathematics. > > > > JAS: So do I; and I also like the words Graph, Spot, and Line > > for similar reasons. As we have discussed before, Peirce > > consistently employed these in accordance with his ethics of > > terminology. > > No. That does not follow from Peirce's ethics of terminology. > Peirce frequently changed his definitions during his career. > > But those changes did not violate his ethical principles. > He made the point that the person who coins a new term is bound > by those principles *if and only if* other people adopt and use > that term. > > For EGs, nobody but Peirce adopted his terminology during his > lifetime. By 1911, he realized that his earlier terminology > was an obstacle, not an aid to understanding. To emphasize the > necessary and sufficient core, he deliberately discarded most > of his earlier terms. > > To respect Peirce's decision, those terms should be relegated > to footnotes or to scholarly analyses of his development. > > > [CSP] I show that the only way is to make the spots represent > > relations and the lines the correlates. > > > > [JAS] it confirms my eventual decision to give up on straightforwardly > > interpreting Spots as subjects and Lines as predicates. It even > > conforms to how we routinely use diagrams in structural engineering > > -- Lines represent members, Spots (nodes) represent connections. > > Four comments: > > 1. Thank you for acknowledging that point. > > 2. But it's important to note that Peirce's algebraic notation > of 1885, with some alternate symbols by Peano, has become the > universal standard for predicate calculus. > > 3. Peirce was aware of those developments, and he did make some > concessions to the trends in his own choice of vocabulary in > later years. For example, he was using the word 'relation' > instead of 'relative'. > > 4. Your own use of the word 'node' in "Spots (nodes)" shows the > need for clarification for a modern audience. Peirce had been > following Clifford's terminology by using the words 'spot' and > 'line', but I suspect that by 1911 he was aware that common > usage was moving away from that terminology. That may be > one reason why he did not use the word 'spot' in 1911. > > In presenting EGs, Peirce made one fatal mistake. He did not > show the mapping from Alpha and Beta to his algebraic notation > of 1885. By 1900, all the major logicians and their students > were using Peirce's algebra as presented by Schröder and Peano. > > As Peirce said many times, he did not think in words. He thought > directly in diagrams and the operations upon them. Logicians from > Boole to the 21st c think in terms of algebraic diagrams. In order > to get them to understand the power of 2D diagrams, the words are > irrelevant. The only thing that matters is the mapping from the > 1D algebra to and from the 2D (or 3D) graphs. > > > [JFS] Since I'm trying to convert modern logicians to Peirce's > > notation, I have to juggle both sets of terms. I prefer to think > > in terms of the symbols and minimize the number of words used to > > describe them. > > > > [JAS] Understood; as I have repeatedly acknowledged, that approach > > makes sense for your purposes. > > Peirce had many purposes, and so do I. In order to understand > EGs on Peirce's own terms, it's essential to ignore the words > and to think directly in terms of the diagrams (1D, 2D, 3D...). > > For the best way to think about EGs the way Peirce did, banish > all words from your mind. That's what Peirce did. The words are > useful only as commentary. The thinking must be diagrammatic. > > > I still maintain that the meaning of any discrete predicate > > (Spot) can be analyzed into a hypostatically abstracted subject > > (word) and a continuous predicate (Peg); more to come on that > > in the other thread. > > Three points: > > 1. A peg is not a predicate. It's a point on a symbol > that represents a relation. If the relation is N-adic > that symbol will have N pegs where lines of identity may > be attached. > > 2. Continuous predicates are represented in the same way as > any other predicate: by a symbol with an appropriate number > of pegs. For example, the line of identity may be considered > as a string of any number of dyadic relation named 'is', each > of which has two pegs. > > 3. Hypostatic abstraction, which nominalizes some relation, is > always permissible, but it's only required when there is some > need to refer back to a particular instance of that relation. > For most purposes, it's better to say "Opium puts people to > sleep" than "Opium has dormitive virtue." > > For Peirce's own description of diagrammatic reasoning, see the > attached excerpt from NEM 4:275 -- diagrammatic.png. > > John >
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