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Revision as of 03:34, 11 November 2012
, 03:34, 11 November 2012→6.27. Differential Logic and Group Operations
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<pre>+1. There is a frame of observation that affords, determines, or arranges for a sequence of observations on a system.+2. There is an observable property or logical feature x that can be true or false of the system at any given moment t of observation.+3. There is a pair <t, t'> of succeeding moments of observation.+
−Relative to a setting of this kind, the rules of SI are exemplified by the schematism shown in Table 41.
+
===6.27. Differential Logic and Group Operations===
===6.27. Differential Logic and Group Operations===
−This section isolates the group-theoretic content of the previous series of Tables, using it to illustrate the following principle: When a geometric object, like a graph or digraph, is given an intensional representation (IR) in terms of a set of logical properties or propositional features, then many of the transformational aspects of that object can be represented in the ''differential extension'' of that IR.
−This section isolates the group theoretic content of the previous series of Tables, using it to illustrate the following principle: When a geometric object, like a graph or digraph, is given an IR in terms of a set of logical properties or propositional features, then many of the transformational aspects of that object can be represented in the "differential extension" (DEX) of that IR.
−One approach to the study of a temporal system (TS) is through the paradigm/ principle of "sequential inference" (SI).
+One approach to the study of a temporal system is through the paradigm or principle of ''sequential inference''.
−Principle of "sequential inference" (SI). An SI rule is operative in any setting where the following list of ingredients can be identified.
+Principle of ''sequential inference''. A sequential inference rule is operative in any setting where the following list of ingredients can be identified.
−# There is a frame of observation that affords, arranges for, or determines a sequence of observations on a system.
+# There is an observable property or a logical feature <math>x\!</math> that can be true or false of the system at any given moment <math>t\!</math> of observation.
+# There is a pair <math>(t, t')\!</math> of succeeding moments of observation.
−Relative to a setting of this kind, the rules of sequential inference are exemplified by the schematism shown in Table 41.
−<br>
−<pre>
Table 41. Schematism of Sequential Inference
Table 41. Schematism of Sequential Inference
Initial Differential Inferred
Initial Differential Inferred
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(x) @ t dx @ t x @ t'
(x) @ t dx @ t x @ t'
(x) @ t (dx) @ t (x) @ t'
(x) @ t (dx) @ t (x) @ t'
+</pre>
+<pre>
It may be thought that a notion of real time (t C R) is needed at this point to fund the account of sequential processes. From a logical point of view, however, I think it will be found that it is precisely out of such data that the notion of time has to be constructed.
It may be thought that a notion of real time (t C R) is needed at this point to fund the account of sequential processes. From a logical point of view, however, I think it will be found that it is precisely out of such data that the notion of time has to be constructed.
