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
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