Jon, Gary f, John, list,
Formal logic represents an aspect of 'the simplest mathematics', the first
branch of mathematics as John outlines it in his diagram (John, your
extremely rich post arrived just as I was completing this message, and so I
have only had a chance to quickly read through it once and take a brief
look at your diagram of the classification of the sciences of discovery: at
first glance your diagram seems sound, although I would deeply question
your placing semeiotics below phaneroscopy in such a diagram--applications
of normative logic can occur in any science save mathematics. In any case,
I will have to reread and study your post before I can comment further).
So, again, mathematical logic *is* formal logic.
1902 | Minute Logic: Chapter III. The Simplest Mathematics | CP 4.240
Mathematical logic is formal logic. Formal logic, however developed, is
mathematics. Formal logic, however, is by no means the whole of logic, or
even its principal part. It is hardly to be reckoned as a part of
logic proper (in the *Commens *Dictionary).
"Logic proper" in this quotation, I take to be the normative science of
logic as semeiotic, and *most* especially it's central branch, critical
logic (Peirce sometimes calls this branch "logic as logic"), where the
'hard dualism' of propositions being found to be either true or false
prevails. But one sees its normative character (and aspects of dualism) in
the other two branches as well, for example, in that part of its third and
final branch, theoretical rhetoric where one finds the argument for the
structuring of a sound/complete inquiry developed, pragmaticism outlined
and developed, etc.
So, apart from mathematic's formal logic--a logic almost *too *simple to
represent, but which is most certainly present as the diagrams
mathematicians use to draw out the deductive consequences of their
hypotheses--logic is a normative science. While Peirce held with his
father, the great mathematician, Benjamin Peirce, that "mathematics is the
science which draws necessary conclusions" (this formulation framed by the
older Peirce in 1870), Peirce the younger often drew attention to an
essential step preceding such deductive reasoning, namely, the
quintessential act of the mathematician framing hypotheses. So, for example
we read:
1897 [c.] | On Multitude | MS [R] 26:1
Mathematics is a study of exact hypotheses, in so far as consequences can
be deduced from them. To limit mathematics to the deduction of those
consequences would be to separate from it some of the greatest of the
achievements of modern mathematicians, – achievements which nobody but
mathematicians could have performed, – such as the formation of the idea of
the system of imaginaries, and of the idea of Riemann surfaces. It must be
allowed, therefore, that the formation of the hypotheses is a part of the
business of mathematics.
And:
1895 [c.] | On the Logic of Quantity, and especially of Infinity | MS [R]
16:1
Mathematics may be defined as the study of the substance of exact hypotheses.
It comprehends
1st, the framing of hypotheses, and
2nd, the deduction of their consequences.
So, in a word, except for this formal, mathematical logic--which, to
repeat, represents an essential but 'simple' aspect of mathematical
reasoning (again, principally related to structuring the diagrams
mathematicians need to do their own deductive reasoning) and which "is
hardly to be reckoned as a part of logic proper," *all *other logic is
either normative logic--and since logic as semeiotic is a normative science
and, thus, a purely theoretical one--or applied logic (say, for example,
logic applied to a problem in physics or engineering).
It is my sense now that all the quasi-existential *content *of logic as
semeiotic (no need to add "normative" to that phrase in my opinion since,
according to Peirce, all three branches of logic as semeiotic are
normative, and I can't see why Gary f is disputing this), again, all the
content which semeioticians deal with is, in my opinion, derived (according
to what Richard Adkins terms "the principle of data") from sciences lower
in Peirce's classification of sciences, or from the ordinary thought and
experience of the logician. Of course, the findings of normative logic can
be used anywhere up or down the classification of sciences (including, I
would imagine, in the other two grand branches of science beyond Science of
Discovery, namely, Science of Review ("Retrospective Science," including
such matters as science digests, classifications of sciences and signs,
Philosophy of Science, etc.) and Practical Science (applied science).
Best,
Gary R
*Gary Richmond*
*Philosophy and Critical Thinking*
*Communication Studies*
*LaGuardia College of the City University of New York*
On Fri, Mar 8, 2019 at 1:11 PM Jon Alan Schmidt <[email protected]>
wrote:
> Gary F., List:
>
> Where did you get that idea? Again, Semeiotic is a generalization of
> Normative Logic, not formal/mathematical logic. The latter is limited to
> necessary reasoning (*logica utens*) from ideal hypotheses, and thus
> lacks the "hard dualism" of the former.
>
> CSP: Now the mathematician does not conceive it to be any part of his
> duty to verify the facts stated. He accepts them absolutely without
> question. He does not in the least care whether they are correct or not.
> (CP 3.559; 1898)
>
>
> Accordingly, I would classify the quote below as Normative Logic
> (Semeiotic), not formal/mathematical logic. It is an outcome of studying
> reasoning itself (*logica docens*), not simply drawing necessary
> conclusions.
>
> Regards,
>
> Jon Alan Schmidt - Olathe, Kansas, USA
> Professional Engineer, Amateur Philosopher, Lutheran Layman
> www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
>
> On Fri, Mar 8, 2019 at 11:33 AM <[email protected]> wrote:
>
>> Jon,
>>
>> So there is a *Formal Logic as Semeiotic* as well as a *Normative Logic
>> as Semeiotic*. I was unaware of that.
>>
>> Peirce says that “the normative sciences are thoroughly infused with
>> duality” (EP2:385). Is *Formal Logic as Semeiotic*, or any other aspect
>> of Semeiotic, free of this “hard dualism” (EP2:376)? For instance, how
>> would you classify the following statement from “Bedrock”: “on the
>> principle that logicians call ‘the *Nota notae*’ that the sign of a sign
>> of anything, X, is itself a sign of the very same X, the Phemic Sheet, in
>> representing the field of attention, represents the general object of that
>> attention, the Universe of Discourse.”
>>
>> Normative Logic? Formal? Neither? Or both?
>>
>> Gary f.
>>
>
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