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Figure 1. Polymorphous Set Q
Figure 1. Polymorphous Set Q
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In other words, the proposition q is a truth-function of the 3 logical variables u, v, w,
In other words, the proposition <math>q\!</math> is a truth-function of the 3 logical variables <math>u\!</math>, <math>v\!</math>, <math>w\!</math>, and it may be evaluated according to the "truth table" scheme that is shown in Table 2. In this representation the polymorphous set <math>Q\!</math> appears in the guise of what some people call the "pre-image" or the "fiber of truth" under the function <math>q\!</math>. More precisely, the 3-tuples for which <math>q\!</math> evaluates to true are in an obvious correspondence with the shaded cells of the venn diagram. No matter how we get down to the level of actual information, it's all pretty much the same stuff.
and it may be evaluated according to the "truth table" scheme that is shown in Table 2.
In this representation the polymorphous set Q appears in the guise of what some people
call the "pre-image" or the "fiber of truth" under the function q. More precisely,
the 3-tuples for which q evaluates to true are in an obvious correspondence with
the shaded cells of the venn diagram. No matter how we get down to the level
of actual information, it's all pretty much the same stuff.
<pre>
Table 2. Polymorphous Function q
Table 2. Polymorphous Function q
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With the pictures of the venn diagram and the truth table before us,
With the pictures of the venn diagram and the truth table before us, we have come to the verge of seeing how the word "model" is used in logic, namely, to distinguish whatever things satisfy a description.
we have come to the verge of seeing how the word "model" is used in
logic, namely, to distinguish whatever things satisfy a description.
In the venn diagram presentation, to be a model of some conceptual
In the venn diagram presentation, to be a model of some conceptual description <math>\mathcal{F}</math> is to be a point <math>x\!</math> in the corresponding region <math>F\!</math> of the universe of discourse <math>X\!</math>.
description !F! is to be a point x in the corresponding region F
of the universe of discourse X.
In the truth table representation, to be a model of a logical
In the truth table representation, to be a model of a logical
proposition f is to be a data-vector !x! (a row of the table)
proposition <math>f\!</math> is to be a data-vector <math>\mathbf{x}\!</math> (a row of the table) on which a function <math>f\!</math> evaluates to true.
on which a function f evaluates to true.
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This manner of speaking makes sense to those who consider the ultimate meaning of
This manner of speaking makes sense to those who consider the ultimate meaning of
a sentence to be not the logical proposition that it denotes but its truth value
a sentence to be not the logical proposition that it denotes but its truth value