Ben U., List: Thanks for this correction; I need to remember to include NEM whenever I undertake terminological searches in the future. Fortunately for me, these earlier passages (1902) are consistent with what I have been saying all along--Formal Semeiotic is simply how Peirce defined Logic, which is the third branch of Normative Science in his 1903 classification. It certainly *does not* fall under Phenomenology.
No one is claiming that "the mathematics of logic" or "mathematical logic" is limited to *deductive *logic. It is simply the *logica utens* that is required for *every *science, including the other branches of Mathematics, Phenomenology, Esthetics, and Ethics. Logic proper--Formal Semeiotic--provides a *logica docens* by studying the process of reasoning (semeiosis), including the relation between signs and the end of truth, which is why it is a *Normative *Science. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Tue, Sep 3, 2019 at 7:58 PM Ben Udell <baud...@gmail.com> wrote: > Jon A.S., John F.S., list, > > On 9/3/2019 1:53 PM, Jon Alan Schmidt wrote: > > JAS: [...] there is no passage whatsoever where he employed the term > "Formal Semeiotic," [....] > > *Au contraire* (variant spellings notwithstanding), > > http://www.iupui.edu/~arisbe/menu/library/bycsp/L75/ver1/l75v1-05.htm > > QUOTE: > Final Version of the Carnegie application - MS L75.363-364 > MEMOIR 12 > ON THE DEFINITION OF LOGIC > > 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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