Jon AS, Auke, Gary F, and Kirsti,
This thread started with what I thought was an uncontroversial
diagram that summarized Peirce's classification of the sciences.
Your questions, objections, and citations have been very helpful
in forcing me to fill in the gaps, to correct some points, and
to state the issues more clearly.
But I suspect that the difference between pure mathematics and
applied mathematics has been a stumbling block that has caused
this thread to drag on interminably:
1. Pure mathematics consists of all possible theories that begin
with any assumptions whatever and derive all possible conclusions.
2. The set of all consistent theories specify everything in Peirce's
"universe of possibilities" and the set of all theorems in them
specify everything in the "universe of necessity".
3. Therefore, when Peirce said that every science depends on
mathematics, he meant that every theory applied to any subject
whatever is a copy of some theory of pure mathematics. The only
change is to make the labels point to something actual instead
of merely possible.
JAS
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.
I agree. For De Morgan, Peirce, and modern logicians, formal logic
has been identified with deductive logic.
All three fall under Critic, the middle branch of the Normative
Science of Logic as Semeiotic;
I agree. But I would add that every theory, including theories of
induction and abduction, are copies of theories of pure mathematics
(possibly with some change of names or labels).
Peirce, logic was already "a normative science" in 1902.
OK. I stand corrected about the dates.
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.
JAS: 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.
No disagreement: We both read that quote in exactly the same way.
AvB
I can't recall having written...
I apologize for making a mistake in attribution.
AvB
Putting Emil Post in the Speculative Grammar domain, is not quite
what I expected and I see no bridge at all.
Formal grammar is the modern name for the pure mathematical theory.
Peirce used the name 'speculative grammar' for the application
to normative logic.
GF
abduction and induction — the generation and empirical testing of
hypotheses — are the important types of argument for all positive
sciences (including both cenoscopy and idioscopy).
I certainly agree.
GF
This is quite different from saying that all theories can be stated
in formal-logical terms, because those terms are not indexically
anchored to the objects of scientific theories, as inductive logic is.
I agree. Pure mathematical theories have no indexical anchors
to anything actual. But their copies, when relabeled for any
application, are anchored to the subject matter.
By the way, modern mathematicians consider two theories that differ
only in the choice of names or labels to be identical. I believe
that Benjamin and Charles made the same assumption.
KM
English has more and more become the new Latin of scientists and
scholars. Thus perpetuating a new uniformity within ways of thinking.
Uniformity is the death of creativity. Benjamin taught Charles Latin,
Greek, and mathematics from a very early age. I believe that was
critical for his ability to discover, relate, and synthesize a wide
range of diverse ideas and points of view.
KM
Peirce named Tetens Kant's teacher... and especially pointed out
that he used his concept of FEELING in the same sense that it was
used and developed by Tetens.
That's important. I did a bit of googling, and I think Tetens may
have influenced Peirce's highly generalized view of quasi-mind.
KM
no Peircean should do the error of taking the mind as the same as
consciousness, whatever one may mean by that. Husserlian philosophy
was designed as a philosophy of consciousness, it aimed to answer to
the modern question of knowledge, not the ancient or medieval one.
That would be a reason why Peirce replaced the term 'phenomenology'
with 'phaneroscopy'. Peirce's version of phenomenology seems to
be identical with his phaneroscopy. But unlike Husserl, Peirce
considered "present to the mind" to include the extremely important
unconscious influences: *present* does not imply *aware*.
John
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