John S., List: JFS: I would also add that phenomenology is not a normative science. But Peirce used logic to analyze and specify the phenomenological categories. That application of logic is prior to normative science, and it establishes the theory of semiotic.
I agree that phenomology is not a Normative Science, and that is precisely why it is misleading to say that "Peirce used logic [which *is *a Normative Science] to analyze and specify the phenomenological categories." On the contrary, that was an application of *mathematics*--including "the Mathematics of Logic," "the simplest mathematics," "dichotomic mathematics"--as *every *science *must *be. CSP: Indeed all formal logic is merely mathematics applied to logic. (CP 4.228; 1902) JFS: But you have to distinguish formal logic from logic applied to something other than mathematics. This juxtaposition makes evident a fundamental error--mathematics is applied to logic, and to *every *other science; but logic is *not *applied to mathematics *at all*, nor is *any *other science. Moreover, the context of that Peirce quote--a chapter of the "Minute Logic" entitled "The Simplest Mathematics," thereby indicating its primary subject matter--sheds additional light on this. CSP: In this chapter, I propose to consider certain extremely simple branches of mathematics which, owing to their utility in logic, have to be treated in considerable detail, although to the mathematician they are hardly worth consideration. In Chapter 4, I shall take up those branches of mathematics upon which the interest of mathematicians is centred, but shall do no more than make a rapid examination of their logical procedure. In Chapter 5, I shall treat formal logic by the aid of mathematics. There can really be little logical matter in these chapters; but they seem to me to be quite indispensable preliminaries to the study of logic. It does not seem to me that mathematics depends in any way upon logic. It reasons, of course. But if the mathematician ever hesitates or errs in his reasoning, logic cannot come to his aid. He would be far more liable to commit similar as well as other errors there. On the contrary, I am persuaded that logic cannot possibly attain the solution of its problems without great use of mathematics. Indeed all formal logic is merely mathematics applied to logic. It was Benjamin Peirce, whose son I boast myself, that in 1870 first defined mathematics as "the science which draws necessary conclusions." (CP 4.227-229; 1902) As Peirce put it later in the same manuscript, "mathematics is the science which *draws* necessary conclusions," while logic is the (normative) "science of *drawing *necessary [and other] conclusions" (CP 4.239; 1902). Metaphysics and the Special Sciences depend on the latter, but *no other* sciences do--not mathematics, phenomenology, esthetics, or ethics. Again, all of these rely entirely on our *logica utens*, not our *logica docens*. CSP: Mathematical logic is formal logic. Formal logic, however developed, is mathematics. Formal logic, however, is by no means the whole of logic, or even its principal part. (CP 4.240; 1902) JFS: That principal part, which is critical for evaluating truth in any actual application, is methodeutic. Here you claim that Methodeutic is the "principal part of logic," but even in your chart it is the third branch of the Normative Science of Logic as Semeiotic, which you previously characterized as logic only from "a partial and narrow" standpoint. Which is it? Once again the context of the Peirce quote is instructive. CSP: But, indeed, the difference between the two sciences is far more than that between two points of view. Mathematics is purely hypothetical: it produces nothing but conditional propositions. Logic, on the contrary, is categorical in its assertions. True, it is not merely, or even mainly, a mere discovery of what really is, like metaphysics. It is a normative science. It thus has a strongly mathematical character, at least in its methodeutic division; for here it analyzes the problem of how, with given means, a required end is to be pursued. This is, at most, to say that it has to call in the aid of mathematics; that it has a mathematical branch. But so much may be said of every science. There is a mathematical logic, just as there is a mathematical optics and a mathematical economics. Mathematical logic is formal logic. Formal logic, however developed, is mathematics. Formal logic, however, is by no means the whole of logic, or even its principal part. It is hardly to be reckoned as a part of logic proper. Logic has to define its aim; and in doing so is even more dependent upon ethics, or the philosophy of aims, by far, than it is, in the methodeutic branch, upon mathematics. We shall soon come to understand how a student of ethics might well be tempted to make his science a branch of logic; as, indeed, it pretty nearly was in the mind of Socrates. But this would be no truer a view than the other. Logic depends upon mathematics; still more intimately upon ethics; but its proper concern is with truths beyond the purview of either. (CP 2.240; 1902) Here Peirce explicitly stated that logic "is a normative science" that, like every other science, "has a mathematical branch," but "is even more dependent upon ethics." He also said that *formal *logic, as *mathematical *logic, "is hardly to be reckoned as part of logic proper." How much more definitive could he have been? Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Sat, Sep 15, 2018 at 12:31 PM, John F Sowa <[email protected]> wrote: > Jerry R, Helmut, and Jon AS, > > This note is rather long, but each of your questions requires > a lot of explanation supported by quotations. > > JR > >> But my reservation about not treating bacteria as quasi-mind remains. How >> is this even possible? >> > > I'll answer that question with another question: A brain is a colony > of one-celled neurons. How would it be it possible for a brain to > support a mind unless each cell had at least a quasi-mind? > > See the attached intention.gif. Note the Following comment: > >> A bacterium swimming upstream in a glucose gradient marks >> the beginning of goal-directed intentionality. >> > > That kind of behavior is possible with living things as simple > as a bacterium. But it's not possible with a rock, which Peirce > said had an 'effete mind'. By comparison, a bacterium would have > a far more robust quasi-mind. > > Remember that I'm just trying to explain what Peirce said. > I agree with him, but one could define mind in different ways > that are not Peircean. But I trust Peirce's intuition -- > especially when it's supported by modern experts, such as Lynn M. > > HR > >> linguistics can only be better developed than biosemiotics, if it is >> not a branch of it´s, i.e. if there are inanimate things that speak. >> > > Linguistics is *not* based on psychology or biology. Linguists have > always derived grammars from large corpora of examples. There were > no native speakers of ancient Greek, Latin, or Egyptian, but there > were thousands of documents in Greek and Latin, including many more > examples of how they evolved over the centuries. > > For Egyptian, they discovered the Rosetta Stone, which had parallel > texts in Greek, Egyptian hieroglyphics, and a later notation called > demotic. > > As a starting point, they made a guess that the Coptic language, > which was still in use for church services, evolved from ancient > Egyptian. That proved to be true. And they were able to derive > the meaning, the grammar, and even the pronunciation of Egyptian. > Of course, their pronunciation would be closer to Coptic than the > way the Pharaohs actually spoke. But that's good enough. > > HR > >> Mathematics is only the basis of it all, if it is more than mere >> tautology, but then it would be dependent on new experience too >> > > Pure mathematics is indeed "mere tautology". If you're using > Peirce's rules of inference, the proof of every mathematical > theorem begins with a blank sheet of paper. Next, draw a double > negation around a blank. That produces an EG of the form "If blank, > then blank". Next, insert the hypothesis and all the axioms into > the If-area. From that derive the conclusion in the Then-area. For > examples, see slides 31 to 41 of the intro to existential graphs: > http://jfsowa.com/talks/egintro.pdf > > Re experience: Pure mathematics is independent of any other subject. > But every science, including common sense. is applied mathematics. > It begins with some observations and assumptions, selects an appropriate > version of pure math, and links the actual entities to the If-part of > some theorem. The conclusion in the Then-part is a prediction about > those actual entities. > > By methodeutic, test that conclusion to see if it's true. If all the > predictions turn out to be true, then you can have some confidence > that the pure theorem, when applied to the actual subject matter, > makes reliable predictions about that subject. You can call it a law. > > HR > >> I doubt, that classification of sciences makes sense at all. >> > > That classification is central to everything that Peirce wrote. > If you're not convinced, please read more by Peirce and by other > authors who explain what Peirce meant > > JAS: Peirce repeatedly made it very clear that he considered Logic >> as Semeiotic to be a Normative Science, not a branch of phenomenology. >> JFS: No. He explicitly said that logic is a branch of mathematics. >> > > I would also add that phenomenology is not a normative science. > But Peirce used logic to analyze and specify the phenomenological > categories. That application of logic is prior to normative science, > and it establishes the theory of semiotic. > > JAS > >> Please provide a citation for this claim. The first branch of >> mathematics is "the Mathematics of Logic" (CP 1.185), not "formal logic" >> > > There are 106 instances of 'formal logic' in CP. See below for > a few that explain these issues. In particular, CP 4.226: > >> Indeed all formal logic is merely mathematics applied to logic. >> > > JAS > >> He wrote elsewhere that "mathematics has such a close intimacy with one >> of the classes of philosophy, that is, with logic, that no small acumen >> is required to find the joint between them" (CP 1.245; 1902). However, >> note that here logic is still not a branch of mathematics, but of >> philosophy. >> > > Yes. But you have to distinguish formal logic from logic applied > to something other than mathematics. Note CP 4.420 quoted below: > >> Formal logic... is mathematics. Formal logic, however, is by no >> means the whole of logic, or even its principal part. >> > > That principal part, which is critical for evaluating truth in > any actual application, is methodeutic. As pure math, formal > logic is independent of any possible experience. But methodeutic > requires both perception and action -- observation and testing. > That application is not be part of mathematics. > > John > _________________________________________________________________ > > 3.92 Indeed, logical algebra conclusively proves that mathematics > extends over the whole realm of formal logic; and any theory of > cognition which cannot be adjusted to this fact must be abandoned. > We may reap all the advantages which the mathematician is supposed > to derive from intuition by simply making general suppositions of > individual cases. > > 3.418 What is commonly called logical algebra differs from other formal > logic only in using the same formal method with greater freedom. I may > mention that unpublished studies have shown me that a far more powerful > method of diagrammatisation than algebra is possible, being an extension > at once of algebra and of Clifford's method of graphs; but I am not in > a situation to draw up a statement of my researches. > > 4.226 Indeed all formal logic is merely mathematics applied to logic. > > 4.240 Mathematical logic is formal logic. Formal logic, however > developed, is mathematics. Formal logic, however, is by no means the > whole of logic, or even its principal part. >
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