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MyWikiBiz, Author Your Legacy — Friday September 27, 2024
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The example that Edelman gives (1988, Fig. 10.5, p. 194) involves sets of stimulus patterns that can be described in terms of the three features "round" <math>u\!</math>, "doubly outlined" <math>v\!</math>, and "centrally dark" <math>w\!</math>.  We may regard these simple features as logical propositions <math>u, v, w : X \to \mathbb{B}.</math>  The target concept <math>\mathcal{Q}</math> is one whose extension is a polymorphous set <math>Q\!</math>, the subset <math>Q\!</math> of the universe <math>X\!</math> where the complex feature <math>q : X \to \mathbb{B}</math> holds true.  The <math>Q\!</math> in question is defined by the requirement:  "Having at least 2 of the 3 features in the set <math>\{ u, v, w \}\!</math>".
 
The example that Edelman gives (1988, Fig. 10.5, p. 194) involves sets of stimulus patterns that can be described in terms of the three features "round" <math>u\!</math>, "doubly outlined" <math>v\!</math>, and "centrally dark" <math>w\!</math>.  We may regard these simple features as logical propositions <math>u, v, w : X \to \mathbb{B}.</math>  The target concept <math>\mathcal{Q}</math> is one whose extension is a polymorphous set <math>Q\!</math>, the subset <math>Q\!</math> of the universe <math>X\!</math> where the complex feature <math>q : X \to \mathbb{B}</math> holds true.  The <math>Q\!</math> in question is defined by the requirement:  "Having at least 2 of the 3 features in the set <math>\{ u, v, w \}\!</math>".
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Taking the symbols <math>u\!</math> = "round", <math>v\!</math> = "doubly outlined", <math>w\!</math> = "centrally dark", and using the corresponding capital letters to label the circles of a venn diagram, we get a picture of the target set <math>Q\!</math> as the shaded region in Figure 1.  Using these symbols as "sentence letters" in a truth table, let the truth function <math>q\!</math> mean the very same thing as the expression "(<math>u\!</math>&nbsp;and&nbsp;<math>v\!</math>) or (<math>u\!</math>&nbsp;and&nbsp;<math>w\!</math>) or (<math>v\!</math>&nbsp;and&nbsp;<math>w\!</math>)".
    
<pre>
 
<pre>
Taking the symbols u = "round", v = "doubly outlined", w = "centrally dark",
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and using the corresponding capitals to label the circles of a venn diagram,
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we get a picture of the target set Q as the shaded region in Figure 1.  Using
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these symbols as "sentence letters" in a truth table, let the truth function q
  −
mean the very same thing as the expression "{u and v} or {u and w} or {v and w}".
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