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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