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 <[email protected]
<mailto:[email protected]>> 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
