John, List: JFS: Jon objected that Peirce never used the term 'normative logic'.
I have never raised any such objection; as I recall, Gary F. did so several months ago, when I myself used the term "normative logic" as a shorthand way of distinguishing the Normative Science of Logic (i.e., Semeiotic) from formal/mathematical logic. JFS: Formal semeiotic would have to be an application of mathematics to the study of signs, as they appear in the phaneron. Therefore, it is not a branch of pure mathematics. I agree; but according to Peirce, "the study of signs, as they appear in the phaneron" is the first branch (Speculative Grammar) of Logic, which is the third branch of Normative Science. It does not fall within Phenomenology, which is the study of the phaneron *itself*, encompassing qualities (1ns) and reactions (2ns) as well as signs (3ns). JFS: This definition cannot include normative science because esthetics and ethics would include quite a large amount of human thought. On the contrary, the subject matter of Esthetics is feeling (1ns) and that of Ethics is action (2ns). The only Normative Science whose subject matter is thought (3ns) is Logic as Semeiotic--and as Peirce said, it studies not merely *human* thought, but thought *in general*, which is semeiosis. JFS: For more evidence, look at CP v. 1 book 3. That has the title "phenomenology", it uses formal logic to analyze the phaneron, and it generates the monads, dyads, and triads of logic and formal semeiotic. As I keep pointing out over and over, the title and specific content of CP v1 b3 are irrelevant, because the CP editors chose both--not Peirce himself. In any case, Phenomenology indeed uses formal/mathematical logic to analyze the phaneron; it does not use the Normative Science of Logic, which is Semeiotic. JFS: That produces three versions of logic: the logic of mathematics, which is the first branch of pure mathematics; the logic used in CP v1 b3, which is used to analyze the phaneron to produce the categories; and the logic that depends on all of the above plus esthetics and ethics. Peirce only identified *two* versions of logic--formal/mathematical logic, which is a *logica utens* that depends on nothing else and is used in every science, including Phenomenology; and the Normative Science of Logic as Semeiotic, which is a *logica docens* that depends on Mathematics, Phenomenology, Esthetics, and Ethics, and is used in Metaphysics and every Special Science. There is no warrant in his writings for the claim that there is a *third* version of logic used specifically in Phenomenology. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Tue, Sep 10, 2019 at 1:05 PM John F. Sowa <s...@bestweb.net> wrote: > > Ben, Jon, List > That is an important distinction: > BU: Peirce adopted the old distinction between /logica docens/ and > /logica utens/ and made no notable modification in it. Logica docens is > formal and systematic, while logica utens is informal and is not > systematically studied. > Yes. 'docens' would imply a kind of logic that is being taught , and > 'utens' would imply a kind of logic that is generally used or useful. That > suggests the distinction formal/informal. But to emphasize the position of > logica utens under the normative branch, a better option would be to put > the adjective 'normative' in front of the noun 'logic'. That gives us the > term 'normative logic'. Jon objected that Peirce never used the term > 'normative logic'. That's true, but irrelevant. Both words were used by > Peirce, and common English usage sanctions that syntactic and semantic > combination. The quotations (copied below) that Ben selected say that > logic (without any preceding adjective) "will be defined as formal > semiotic." But Peirce also said that this definition is > "non-psychological". > Further issues: Pure mathematics is a study of pure form without any > application to any subject matter. But every sign has a perceptible mark > (or tone). Formal semiotic would have to be an application of mathematics > to the study of signs, as they appear in the phaneron. Therefore, it is > not a branch of pure mathematics. But NEM 4:54 (copied below) says "Logic > is formal semiotic... This definition no more involves any reference to > human thought than does the definition of a line as the place within which > a particle lies during a lapse of time. It is from this definition that I > deduce the principles of logic by mathematical reasoning." This definition > cannot include normative science because esthetics and ethics would include > quite a large amount of human thought. Therefore logic as formal semiotic > would have to come after phenomenology, but before the normative > sciences. For more evidence, look at CP v. 1 book 3. That has the title > phenomenology", it uses formal logic to analyze the phaneron, and it > generates the monads, dyads, and triads of logic and formal semiotic. > That produces three version of logic: the logic of mathematics, which is > the first branch of pure mathematiics; the logic used in CP v1 b3, which > is used to analyze the phaneron to produce the categories; and the logic > that depends on all of the above plus esthetics and ethics. Summary:1. > Logic as a branch of pure mathematics, formal logic (AKA logica docens), > 2. Logic as used to analyze the phaneron to derive the categories, formal > semeiotic. > 3. Logic as a normative science that depends on esthetics and ethics, > informal logic (AKA logic utens) -- or normative logic. > This terminology is consistent with what Peirce wrote *and* with 21st c. > practice in teaching (docens) and using (utens) logic. > John > __________________________________________________________Ben, > quoting from Final Version of the Carnegie application - MS L75.363-364 > >>> Logic will here be defined as formal semiotic. A > >>> definition of a sign will be given which no more refers > >>> to human thought than does the definition of a line as > >>> the place which a particle occupies, part by part, during > >>> a lapse of time. Namely, a sign is something, A, which > >>> brings something, B, its interpretant sign determined or > >>> created by it, into the same sort of correspondence with > >>> something, C, its object, as that in which itself stands > >>> to C. It is from this definition, together with a > >>> definition of "formal", that I deduce mathematically the > >>> principles of logic. I also make a historical review of > >>> all the definitions and conceptions of logic and show not > >>> merely that my definition is no novelty, but that my > >>> non-psychological conception of logic has virtually been > >>> quite generally held, though not generally recognized. > >>> > >>> > > From Draft D - MS L75.235-237 > >>> I define logic very broadly as the study of the formal > >>> laws of signs, or formal semiotic. I define a sign as > >>> something, A, which brings something, B, its > >>> interpretant, into the same sort of correspondence with > >>> something, C, its object, as that in which itself stands > >>> to C. > [....] > >>> END QUOTE > >>> > >>> These passages are in New Elements of Mathematics, which > >>> includes a passage (absent from Joe Ransdell's version of the > >>> Carnegie application) that Jon Awbrey likes to quote (e.g., > >>> he put it into the Peirce Wikipedia article on Peirce): > >>> > >>> No. 12. /On the Definition of Logic/ [Earlier Draft] > >>> > >>> QUOTE: > >>> Logic is /formal semiotic./ A sign is something, A, > >>> which brings something, B, its /interpretant/ sign, > >>> determined or created by it, into the same sort of > >>> correspondence (or a lower implied sort) with something, > >>> C, its object, as that in which itself stands to C. This > >>> definition no more involves any reference to human > >>> thought than does the definition of a line as the place > >>> within which a particle lies during a lapse of time. It > >>> is from this definition that I deduce the principles of > >>> logic by mathematical reasoning, and by mathematical > >>> reasoning that, I aver, will support criticism of > >>> Weierstrassian severity, and that is perfectly evident. > >>> The word 'formal' in the definition is also defined. > >>> (NEM 4, 54). > >>> END QUOTE. > >>> > >>> As regards mathematics of logic, it's been unclear to me just > >>> what it consists of. It's not enough to say, it's all and > >>> only the deductive logic. There is deductive math applied in > >>> philosophy, according to Peirce, e.g. applied as the doctrine > >>> of chances (probability theory). Are the existential graphs > >>> logic applied in philosophy, or are they in Peirce's first > >>> part of math, called mathematics of logic? Is maths of logic > >>> just an algebra of two values /v, f,/ that could stand for > >>> Caesar, Pompey, (Peirce said something like that), just as > >>> well as for true (/verum/) and false? There's a passage about > >>> that where Peirce goes on to discuss triadic mathematics, > >>> which I didn't understand, I'm no mathematician. There is to > >>> keep in mind is that the mathematics of logic is not > >>> necessarily fully the selfsame thing as the logic of > >>> mathematics. Peirce often discusses how mathematics USES > >>> diagrammatic reasoning, but usually says that mathematics > >>> needs, and anyway has taken, no help FROM logic except in a > >>> few cases, involving infinities if I recall aright. > >>> > >>> Best, Ben >
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