Gary, List: GR: It makes clear why you titled this new thread "The Proper Way in Logic," which, when I first read it, sounded quite shocking.
Of course, that characterization is Peirce's own, again written in late 1908 (NEM 3:885) when he evidently adopted it rather suddenly and decisively. Throwing everything possible into the subject recognizes the *indexical *nature of most words--functioning much like proper names, since one must already be acquainted with their objects in order to understand them--and leaves only the pure/continuous predicate as the *iconic *part of the proposition. By contrast, standard first-order predicate logic goes the other way, throwing everything possible into the predicate and leaving only quantified variables as the subjects. Peirce himself endorses that approach in some earlier writings. CSP: The most perfectly thorough analysis throws the whole substance of the Dicisign into the Predicate. (CP 2.318, 1903) CSP: It has been shown that in the formal analysis of a proposition, after all that words can convey has been thrown into the predicate, there remains a subject that is indescribable and that can only be pointed at or otherwise indicated, unless a way, of finding what is referred to, be prescribed. (CP 5.525, c. 1905) CSP: Take the proposition "Burnt child shuns fire." ... On this view, the predicate is, "is either not a child or has not been burned, or has no opportunity of shunning fire or does shun fire"; while the subject is "any individual object the interpreter may select from the universe of ordinary everyday experience." (CP 5.473, 1907) "Cain killed Abel" becomes "there exists an *x* and there exists a *y* such that *x* is Cain and *y* is Abel and *x* stands in the relation of killing to *y*." It is an interesting historical fact that the usual abbreviated notation for such formulations is derived from one developed by Peirce--for these two examples, ∀*x* (¬C*x* ∨ ¬B*x* ∨ S*x*) = ∀*x* ((C*x* ∧ B*x*) → S*x*) and ∃*x *∃*y *(C*x* ∧ A*y* ∧ K*xy*). Still, notice how compact the natural language expressions are, by virtue of utilizing syntax that iconically matches the flow of causation instead of spelling everything out with symbols. Likewise, as Frederik Stjernfelt observes on pages 138 and 172 of his 2022 book, *Sheets, Diagrams, and Realism in Peirce*, EGs are more iconic than the corresponding algebraic expressions in the specific sense that each indefinite individual--now a line of identity instead of a variable--always appears *exactly once*, instead of at least twice; in these cases, four and three times, respectively. [image: image.png] Technically, in "burnt child shuns fire," shunning is a *dyadic *relation whose additional correlate is fire. That makes the algebraic notation ∀*x* ∀ *y* (¬C*x* ∨ ¬B*x* ∨ ¬F*y* ∨ S*xy*)) = ∀*x* ∀*y* ((C*x* ∧ B*x* ∧ F*y*) → S *xy*). Throwing everything possible into the predicate, there are now two subjects (lowercase letters) and four predicates (uppercase letters). Throwing everything possible into the subject, there are six subjects--four general concepts (names) and two indefinite individuals (lines of identity)--and a single pure/continuous predicate (syntax). [image: image.png] Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Sat, Feb 10, 2024 at 4:12 PM Gary Richmond <gary.richm...@gmail.com> wrote: > Jon, > > Your post sheds light on both associated matters that you discussed in it. > This snippet of a quotation -- and which I've reflected on a number of > times previously -- represents for me something of a succinct summary of > the matter, especially as emphasizing the need for collateral knowledge. > > CSP: A proposition can be separated into a predicate and subjects in more > ways than one. But the proper way in logic is to take as the subject > whatever there is of which sufficient knowledge cannot be conveyed in the > proposition itself, but collateral experience on the part of its > interpreter is requisite. ... The result is that everything in a > proposition that possibly can should be thrown into the subjects, leaving > the *pure *predicate a mere form of connection, such as 'is,' 'possesses > (as a character),' 'stands in the dyadic relation ___ to ___ ,' 'and' = 'is > at once ___ and ___ ,' etc. > > > It makes clear why you titled this new thread "The Proper Way in Logic," > which, when I first read it, sounded quite shocking. But it becomes > understandable that "a proposition may have any number of subjects but > can have but one predicate which is invariably general, namely, a *pure * > or *continuous *predicate that cannot be analyzed further and expresses > the logical relations between the subjects." > > > As to your question: JAS: "Where do these different constituent signs > within a proposition fit into Peirce's late taxonomies? > > You answered: JAS: They are distinguished in his trichotomy according to > the mode of presentation of the *immediate* object, as he explains in > another late 1908 writing." > > This will require a bit more study on my behalf. But this summary sentence > is clear enough: > > JAS: When a proposition is expressed linguistically in a sentence, the > subjects that denote its objects are either *descriptive* names or > *designative* pronouns or gestures, while the pure/continuous predicate > that signifies its interpretant is often a *copulant* sign. > > > Equally clear is the question of "a sentence like "Cain killed Abel," > which includes no words except those serving as its subjects," Peirce's > answer, given in this lovely passage, explains it quite nicely (within the > context of the entire quotation, of course). > > CSP: What, then, is left to serve as Predicate? Nothing but the *flow of > causation*. It is true that we are more acquainted even with that in > Experience. When we see a babe in its cradle bending its arms this way and > that, while a smile of exultation plays upon its features, it is making > acquaintance with the flow of causation. So acquaintance with the flow of > causation so early as to make it familiar before speech is so far acquired > that an assertion can be syntactically framed, and it is embodied in the > syntax of every tongue. > > > Finally, the whole matter is tied up in your concluding paragraph which > begins with this idea. > > JAS: Pure/continuous predicates are sometimes conveyed entirely by > *syntax*, which in natural languages tends to reflect "the flow of > causation." > > > In conclusion: Jon, I did not expect such a complete response to my > request for an explication of this comment in your last post: > > JAS: *The necessity of collateral experience/observation for any sign* to > be understood is one of Peirce's most notable insights. It leads to the > recognition that *every name in a proposition is a subject that > indexically denotes one of its objects*, while *its syntax is the pure > predicate that iconically signifies its interpretant as the general form of > their logical relations*. (I've added the emphasis I put in this > quotation as a kind of "more iconic" diagram for the purpose of studying > your post today. GR). > > Again, much appreciated. Thank you for taking the time and making the > effort to explain at length that which was succinctly -- albeit abstractly > -- posited in that single sentence I just added emphasis to above. As > usual, quotations and examples proved extremely helpful. > > Best, > > Gary Richmond >
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