ONT Re: Differential Logic A -- Discussion
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DLOG A. Discussion Note 10
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| Such reasonings and all reasonings turn upon the idea that if one exerts
| certain kinds of volition, one will undergo in return certain compulsory
| perceptions. Now this sort of consideration, namely, that certain lines
| of conduct will entail certain kinds of inevitable experiences is what
| is called a "practical consideration". Hence is justified the maxim,
| belief in which constitutes pragmatism; namely,
|
| In order to ascertain the meaning of an intellectual conception one should
| consider what practical consequences might conceivably result by necessity
| from the truth of that conception; and the sum of these consequences will
| constitute the entire meaning of the conception.
|
| C.S. Peirce, "Pragmatism" (c. 1905), 'Collected Papers', CP 5.9
This particular formulation of the pragmatic maxim is personally important
to me, as it's the version that linked up my studies in algebra, automata,
computer simulation, cybernetics, dynamical systems, and formal languages
all through the 1980's to the streams of psychology literature that I was
exploring in parallel at the same time.
Here is how I was accustomed to picture a "machine with input" in those days:
| a b c d | a b c d | a b c d
T_1 : | T_2 : | T_3 : |
V c d d b V b a d c V d c d b
This parameterized set of transformations is given more compactly in Table 1.
Table 1. Finite Transducer, or Machine with Input
o---------o---------o---------o---------o---------o
| | | | | | |
| | | a | b | c | d |
| V | | | | |
o=========o=========o=========o=========o=========o
| | | | | |
| T_1 | c | d | d | b |
| | | | | |
| T_2 | b | a | d | c |
| | | | | |
| T_3 | d | c | d | b |
| | | | | |
o---------o---------o---------o---------o---------o
I copied this out of Ashby's 'Cybernetics', 4/1,
except for replacing his letter "R" with my "T".
Jon Awbrey
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http://www.cs.bsu.edu/homepages/mighty/history.html
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