Ben, Jon, List
That is an important distinction:
BU: Peirce
adopted the old distinction between /logica docens/ and /logica
utens/ and made no notable modification in it. Logica docens is formal
and systematic, while logica utens is informal and is not systematically
studied.
Yes. 'docens' would imply a kind of logic that is being
taught , and 'utens' would imply a kind of logic that is generally used or
useful. That suggests the distinction formal/informal.
But to
emphasize the position of logica utens under the normative branch, a
better option would be to put the adjective 'normative' in front of the
noun 'logic'. That gives us the term 'normative logic'.
Jon
objected that Peirce never used the term 'normative logic'. That's true,
but irrelevant. Both words were used by Peirce, and common English usage
sanctions that syntactic and semantic combination.
The quotations
(copied below) that Ben selected say that logic (without any preceding
adjective) "will be defined as formal semiotic." But Peirce
also said that this definition is
"non-psychological".
Further issues: Pure mathematics is
a study of pure form without any application to any subject matter. But
every sign has a perceptible mark (or tone). Formal semiotic would have
to be an application of mathematics to the study of signs, as they appear
in the phaneron. Therefore, it is not a branch of pure
mathematics.
But NEM 4:54 (copied below) says "Logic is formal
semiotic... 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."
This
definition cannot include normative science because esthetics and ethics
would include quite a large amount of human thought. Therefore logic as
formal semiotic would have to come after phenomenology, but before the
normative sciences. For more evidence, look at CP v. 1 book 3. That has
the title "phenomenology", it uses formal logic to analyze the
phaneron, and it generates the monads, dyads, and triads of logic and
formal semiotic.
That produces three version of logic: the logic of
mathematics, which is the first branch of pure mathematiics; the logic
used in CP v1 b3, which is used to analyze the phaneron to produce the
categories; and the logic that depends on all of the above plus esthetics
and ethics. Summary:1. Logic as a branch of pure mathematics, formal
logic (AKA logica docens),
2. Logic as used to analyze the phaneron to
derive the categories, formal semeiotic.
3. Logic as a normative
science that depends on esthetics and ethics, informal logic (AKA logic
utens) -- or normative logic.
This terminology is consistent with
what Peirce wrote *and* with 21st c. practice in teaching (docens) and
using (utens)
logic.
John
__________________________________________________________Ben,
quoting from Final Version of the Carnegie application - MS L75.363-364
>>> 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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