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Tables 53.1 and 53.2 show three different ways of coding the elements of an ER and the features of a LIR, respectively, for the world set <math>W = W(\text{A}, \text{B}),\!</math> that is, for the set of objects, signs, and interpretants that are common to the sign relations <math>L(A)\!</math> and <math>L(B).\!</math> Successive columns of these Tables give the ''mnemonic code'', the ''pragmatic code'', and the ''abstract code'', respectively, for each element.
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Table 53.1 Elements of ER (W)
Table 53.1 Elements of ER (W)
Mnemonic Element Pragmatic Element Abstract Element
Mnemonic Element Pragmatic Element Abstract Element
"i" s3 w5
"i" s3 w5
"u" s4 w6
"u" s4 w6
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Table 53.2 Features of LIR (W)
Table 53.2 Features of LIR (W)
Mnemonic Feature Pragmatic Feature Abstract Feature
Mnemonic Feature Pragmatic Feature Abstract Feature
i s3 w5
i s3 w5
u s3 w6
u s3 w6
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If the world of A and B, the set W = {A, B, "A", "B", "i", "u"}, is viewed abstractly, as an arbitrary set of six atomic points, then there are exactly 26 = 64 "abstract properties" (APs) or "potential attributes" (PAs) that might be applied to or recognized in these points. The extensions of these APs are the subsets of W, otherwise known as members of the "power set" Pow (W). In order to make this way of talking about properties consistent with the previous definition of reality, it is necessary to say that one potential property is never realized, since no point has it, and its extension is the empty set {}. All the "natural" properties of points that one observes in a concrete situation, properties whose extensions are known as "natural kinds", can be recognized among the "abstract", "arbitrary", or "set theoretic" properties that are systematically generated in this way. Typically, however, many of these abstract properties will not be recognized as falling among the more natural kinds.
If the world of A and B, the set W = {A, B, "A", "B", "i", "u"}, is viewed abstractly, as an arbitrary set of six atomic points, then there are exactly 26 = 64 "abstract properties" (APs) or "potential attributes" (PAs) that might be applied to or recognized in these points. The extensions of these APs are the subsets of W, otherwise known as members of the "power set" Pow (W). In order to make this way of talking about properties consistent with the previous definition of reality, it is necessary to say that one potential property is never realized, since no point has it, and its extension is the empty set {}. All the "natural" properties of points that one observes in a concrete situation, properties whose extensions are known as "natural kinds", can be recognized among the "abstract", "arbitrary", or "set theoretic" properties that are systematically generated in this way. Typically, however, many of these abstract properties will not be recognized as falling among the more natural kinds.
