Nice comments, Jerry. If we are to evaluate some introductory books on logic,
I'll repeat my support for Harry Gensler's Introduction to Logic and also, D.Q.
McInerny, 'Being Logical'. Both are excellent, the latter is less of a
practical teaching tool than Gensler's and more of a very clear conceptual
analysis of both formal and informal logic. I like them better than Graham
Priest's 'A very short Introduction' (which I have). And Howard DeLong's 'A
profile of Mathematical Logic' is also very good both for its introductory and
also, its more advanced outlines.
Edwina
----- Original Message -----
From: Jerry LR Chandler
To: Peirce List
Sent: Sunday, July 06, 2014 11:29 PM
Subject: Re: [PEIRCE-L] Burgin's Fundamental Triads as Peirceasn Signs. On
the nature of a syllogism
On Jul 5, 2014, at 5:46 PM, Sungchul Ji wrote:
The logic behind my syllogism is as follows:
Major premise: A = B
Minor premise: A = C
Conclusion: C = B
where A = Burign's fundamental triad, B = the unification of mathematics;
and C = the Peircean triad.
List:
This is an example of the mathematical concept of substitutions of equals for
equals.
It is not an Aristotelian syllogism.
Sung prefers to create a unique perspective of a metaphysical system
expressed in the language of physics.
A syllogism consists of three propositions contains exactly three terms with
three copula.
The conclusion of a syllogism contains exactly two terms with one copula.
The logic of a syllogism depends on removing exactly one of the three terms
contained in the premises, leaving two terms in the conclusions.
Thus, from a mathematical perspective, the net consequence of a syllogism is
a SUBTRACTION, not a SUBSTITUTION.
Many other differences between mathematics and syllogisms are known.
And, of course, many other logics are well known.
For an excellent introduction (but rather biased from my perspective) see:
Graham Priest, A Very Short Introduction to Logic, Oxford University Press.
It is also apparent the the logic of chemistry is not described by syllogisms
or mathematics.
If one starts with two terms, such as: Oxygen exists, and, Hydrogen exists,
one CONCLUDES that water exists.
Thus from two or more terms representing atoms (atomic numbers), one
symbolically generate a third term, the name of the molecule as the some of the
parts of the whole.
This is the creativity of chemistry that CSP puzzled about for decades and,
eventually, led to his philosophy of diagrammatic logic and the beta-
existential graphs.
Further, please note,
from a modern perspective,
that even if the logic of chemistry is not understood
(outside of the strict closure of chemical notation based on the atomic
numbers,)
many of the MATHEMATICAL relations between physics and chemistry are well
understood
and mutually consistent and supportive of one-another.
(I have intentionally formatted this sentence, which consists of many terms
and many conceptual relationships, with the intent to separate out the
associative logic between disciplines.)
Cheers
Jerry
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