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, 12:36, 17 April 2009→Commentary Note 11.19
===Commentary Note 11.19===
===Commentary Note 11.19===
Up to this point in the LOR of 1870, Peirce has introduced the "number of" measure on logical terms and discussed the extent to which this measure, ''v'' : ''S'' → '''R''' such that ''v'' : ''s'' ~> [''s''], exhibits a couple of important measure-theoretic principles:
Up to this point in the 1870 LOR, Peirce has introduced the "number of" measure on logical terms and discussed the extent to which this measure, <math>v : S \to \mathbb{R}</math> such that <math>v : s \mapsto [s],</math> exhibits a couple of important measure-theoretic principles:
Peirce next takes up the action of the "number of" map on the two types of, loosely speaking, "additive" operations that we normally consider in logic.
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| <p>The "number of" map exhibits a certain type of ''uniformity property'', whereby the value of the measure on a uniformly qualified population is in fact actualized by each member of the population.</p>
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| <p>The "number of" map satisfies an ''order morphism principle'', whereby the illative partial ordering of logical terms is reflected up to a partial extent by the arithmetical linear ordering of their measures.</p>
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Peirce next takes up the action of the "number of" map on the two types of, loosely speaking, ''additive'' operations that we normally consider in logic.
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{| align="center" cellspacing="6" width="90%" <!--QUOTE-->
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It is plain that both the regular non-invertible addition and the invertible addition satisfy the absolute conditions. (CP 3.67).
<p>It is plain that both the regular non-invertible addition and the invertible addition satisfy the absolute conditions.</p>
<p>(Peirce, CP 3.67).</p>
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