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
<http://www.LinkedIn.com/in/JonAlanSchmidt> -
twitter.com/JonAlanSchmidt <http://twitter.com/JonAlanSchmidt>
On Tue, Sep 3, 2019 at 7:58 PM Ben Udell <baud...@gmail.com
<mailto: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
