Hi,
A couple of days ago (while jogging, of course), a thought occurred to me
that the syllogism may fit the category diagram (also called the
'commutative triangle') I have been using so often on these lists. I
checked the idea just now by diagramming it on a piece of paper and found
that it indeed seems to work as expected:
f g
Major Premise --------> Minor Premise --------> Conclusion
|
^
|
|
|______________________________________|
h
Figure 1. The syllogism as a category, with the structure-preserving
mappings defined as f = natural process, g = mental process, and h =
correspondence.
These mappings are thought to satisfy the commutative
condition, f x g = h.
I am now wondering if this commutative triangle can be viewed as the
simplest unit of "reasoning" in human thought. If so, we may be justified
to state that:
"We think in categories."
(05202-15-1)
which would be synonymous with
"We think in signs."
(05202015-2)
since the Peirceasn sign is itself a commutative triangle, i.e., a category.
This leads me to ask whether it would be reasonable to divide all the signs
that we use on these lists into three classes -- (i) words (W) (used in
most of the posts, e.g., Ben, Edwina, Jeff, Jerry, Gary, Steven, etc.),
(ii) diagrams (D) (e.g., Jon, Howard, Edwina, me, etc.), and (iii)
mathematical formulas (M) (e.g., mostly me, e.g., see Table 1 below).
This WDM trichotomy is an observed fact on these lists and not a
theoretical construct. For example, we can readily recognize these three
elements in Table 1:
W = at least 50% of the symbols appearing in the 6 x 4 table
D = the 6 x 4 table itself
M = the 8 equations appearing in the table
Table 1. A possible relation among entropy, quanta, and information
1. Concept
*Entropy* (1)
*Quanta *(2)
*Information *(3)
2. Field of inquiry
Thermodynamics
Quantum mechanics
Informatics
3. Experiment/Measurement
S = ΔQ/T
Blackbody radiation spectra
Selecting m out of n possibilities
4. Statistical mechanical
formulation
S = - k∑ pi log pi
*Boltzmann-Gibbsentropy *(1866)
U(λ, T) = (2πhc2/λ5)/(ehc/λkT – 1)
*Planck radiation equation*
(PRE) (1900) [1]
IP = log2(AUC(P)/AUC(G))
where IP = Planckianinformation [2], AUC = area under the curve, P = PDE,
and G = *Gaussian-like equation* [3]
y = Ae–(x - µ)^2/(2*σ^2)
5. Mathematical formulation
H = - K∑ pi log pi
*Shannon entropy*(1948)
y = (a/(Ax+B)5)/(eb/(Ax + B)– 1)
*Planckian distribution equation* (PDE) (2008) [2]
I = A log2 (n/m)
*a unified theory of the amount of information*(UTAI) (2015) [4]
6. Emerging Concept
A measure of*DISORDER*
Quantization of action needed for*ORGANIZATION*
A measure of the *ORDER*of an organized system
It would be a challenge (and should be possible) to map the WDM trichotomy
to the three trichotomies of signs in Peircean semiotics.(
https://www.marxists.org/reference/subject/philosophy/works/us/peirce2.htm).
All the best.
Sung
--
Sungchul Ji, Ph.D.
Associate Professor of Pharmacology and Toxicology
Department of Pharmacology and Toxicology
Ernest Mario School of Pharmacy
Rutgers University
Piscataway, N.J. 08855
732-445-4701
www.conformon.net
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