John S., List: JAS: 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). JFS: Those additions put words in Peirce's mouth.
Peirce said here that *deductive *logic is "the science of drawing necessary conclusions," but he elsewhere (and repeatedly) also recognized *inductive *and *retroductive *logic as having their own validity, despite drawing conclusions that are *not *necessary. All three fall under Critic, the middle branch of the Normative Science of Logic as Semeiotic; in fact, as I quoted previously, Peirce stated explicitly *in the very next paragraph* that logic "is a normative science" (CP 4.240; 1902). JFS: Since he wrote that classification in 1902, he probably wasn't as careful about the his 1903 distinction between formal logic and normative logic ... Since Peirce wrote this passage in 1902 -- before he classified (non-formal) logic as a normative science -- he was talking about formal logic. Again, these statements are *directly falsified* by CP 4.240; for Peirce, logic was already "a normative science" in 1902. CSP: The logician does not care particularly about this or that hypothesis or its consequences, except so far as these things may throw a light upon the nature of reasoning. (CP 4.239; 1902) JFS: That is the opposite of the normative logician, who cares very much about hypotheses and their consequences. That seems like a clear misreading of the quote. In context, Peirce was talking about *mathematical *hypotheses and their consequences, which need not (and often do not) have any bearing on Reality whatsoever. Mathematicians just want to derive those consequences as efficiently as possible, but the *normative *logician studies "the nature of reasoning"--i.e., "deliberate thinking"--in minute detail. 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 5:28 PM, John F Sowa <s...@bestweb.net> wrote: > Auke and Jon AS, > > In my previous note, I forgot to reply to this point: > > AvB > >> if speculative grammar, with alternative name semiotics is not the >> first of the normative logic branch anymore, what occupies this spot >> instead? >> > > Formal grammars, as a branch of mathematics, were developed in the > 20th c. by Emil Post and others. Chomsky adopted "Post production > rules" as a formal notation, which branched off into both linguistics > and computer science. As with Formal logic, formal grammars can be > used descriptively (in linguistics) or normatively (in education) > to distinguish "good grammar" from "bad grammar". > > Peirce did not use the term "formal grammar', since it was coined > many years later. But his framework supports the distinction. > > AvB > >> You seem to argue that because semiotic is not normative it cannot >> be part of normative logic. >> > > Note that Peirce's "depends on" relation is transitive. Since > normative science depends on both mathematics and phenomenology, > any theory of either one may be adopted and adapted normatively. > > AvB > >> I see no problem in a sub-branch of a normative science that >> itself cannot properly be called normative. >> > > Grammars could certainly be used (applied) normatively, but > formal grammar is a branch of mathematics. Since all the > sciences depend on math, they can apply grammar for any purpose. > > Peirce did not use the term "formal grammar', since it was coined > many years later. But his framework supports the distinction. > > JAS > >> 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." >> > > Yes. I agree that I should have said that *formal* logic is used > to specify the phenomenological categories. And as Peirce himself > said, those three terms are synonyms: mathematical logic, the logic > of mathematics, and formal logic. > > For normative science, the "principal part" is methodeutic. This is > an application of *both* phenomenology and formal logic to develop > the normative extensions. > > AvB > >> logic is not applied to mathematics at all, nor is any other science. >> > > Since formal logic is a branch of mathematics, the use of formal logic > to analyze the foundations of mathematics (as Hilbert and many others > did) is an application of one branch of mathematics to another. > > But Peirce differed from Hilbert & Co. because he insisted that > mathematics is prior to formal logic. Boole was a mathematician > who applied algebra to logic. De Morgan, Hamilton, Jevons, and > Peirce continued that tradition. See "Peirce the logician" by > Putnam: http://jfsowa.com/peirce/putnam.htm > > JAS > >> 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," >> > > I agree that I should have said 'formal logic'. My only excuse is > that I usually talk to audiences in computer fields, where the terms > 'logic' and 'formal logic' are usually treated as synonyms. > > 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. >> >> JAS: mathematics is applied to logic, and to every other science; but >> logic is not applied to mathematics at all, nor is any other science. >> > > Peirce in 1902 was making the same omission that I often make: not > using the adjective 'formal' in front of the second occurrence of > 'logic'. > > Since he wrote that classification in 1902, he probably wasn't > as careful about the his 1903 distinction between formal logic > and normative logic. > > 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). >> > > Those additions put words in Peirce's mouth. See below for the > complete paragraph 4.239. > > Note the following point in that paragraph (I added a space before it): > >> The logician does not care particularly about this or that hypothesis >> or its consequences, except so far as these things may throw a light >> upon the nature of reasoning. >> > > That is the opposite of the normative logician, who cares very much > about hypotheses and their consequences. Since Peirce wrote this > passage in 1902 -- before he classified (non-formal) logic as a > normative science -- he was talking about formal logic. > > 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. >> JAS: 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. >> > > Good question. I took those words from CP 1.573: > >> Logic, regarded from one instructive, though partial and narrow, point >> of view, is the theory of deliberate thinking. >> > > That implies that there is a more complete and broader point of view. > > In any case, CP 191 on normative science is sufficient to distinguish > normative logic from formal logic: > >> Logic is the theory of self-controlled, or deliberate, thought; and >> as such, must appeal to ethics for its principles. It also depends >> upon phenomenology and upon mathematics. >> > > To avoid the controversy, I'll delete the phrase "partial and narrow" > and replace it with a line that says normative logic is the "theory > of self-controlled or deliberate thought". > > John > _______________________________________________________________________ > > CP 4.239. The philosophical mathematician, Dr. Richard Dedekind, > holds mathematics to be a branch of logic. This would not result from > my father's definition, which runs, not that mathematics is the science > of _drawing_ necessary conclusions -- which would be deductive logic -- > but that it is the science which _draws_ necessary conclusions. It is > evident, and I know as a fact, that he had this distinction in view. > At the time when he thought out this definition, he, a mathematician, > and I, a logician, held daily discussions about a large subject which > interested us both; and he was struck, as I was, with the contrary > nature of his interest and mine in the same propositions. > > The logician does not care particularly about this or that hypothesis > or its consequences, except so far as these things may throw a light > upon the nature of reasoning. The mathematician is intensely interested > in efficient methods of reasoning, with a view to their possible > extension to new problems; but he does not, quâ mathematician, trouble > himself minutely to dissect those parts of this method whose correctness > is a matter of course. The different aspects which the algebra of logic > will assume for the two men is instructive in this respect. The > mathematician asks what value this algebra has as a calculus. Can it > be applied to unravelling a complicated question? Will it, at one > stroke, produce a remote consequence? The logician does not wish > the algebra to have that character. On the contrary, the greater number > of distinct logical steps, into which the algebra breaks up an > inference, will for him constitute a superiority of it over another > which moves more swiftly to its conclusions. He demands that the > algebra shall analyze a reasoning into its last elementary steps. > Thus, that which is a merit in a logical algebra for one of these > students is a demerit in the eyes of the other. The one studies the > science of drawing conclusions, the other the science which draws > necessary conclusions.
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