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Let's examine Peirce's example of a conjunctive term, "spherical, bright, fragrant, juicy, tropical fruit", within a lattice framework.  We have these six terms:
 
Let's examine Peirce's example of a conjunctive term, "spherical, bright, fragrant, juicy, tropical fruit", within a lattice framework.  We have these six terms:
   −
: ''t''<sub>1</sub> = ''spherical''
+
{| align="center" cellspacing="6" width="90%"
: ''t''<sub>2</sub> = ''bright''
+
|
: ''t''<sub>3</sub> = ''fragrant''
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<math>\begin{array}{lll}
: ''t''<sub>4</sub> = ''juicy''
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t_1 & = & \operatorname{spherical}
: ''t''<sub>5</sub> = ''tropical''
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\\
: ''t''<sub>6</sub> = ''fruit''
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t_2 & = & \operatorname{bright}
 +
\\
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t_3 & = & \operatorname{fragrant}
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\\
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t_4 & = & \operatorname{juicy}
 +
\\
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t_5 & = & \operatorname{tropical}
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\\
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t_6 & = & \operatorname{fruit}
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\end{array}</math>
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|}
   −
Suppose that ''z'' is the logical conjunction of these six terms:
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Suppose that <math>z\!</math> is the logical conjunction of these six terms:
   −
: ''z'' = ''t''<sub>1</sub> ''t''<sub>2</sub> ''t''<sub>3</sub> ''t''<sub>4</sub> ''t''<sub>5</sub> ''t''<sub>6</sub>
+
{| align="center" cellspacing="6" width="90%"
 +
|
 +
<math>\begin{array}{lll}
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z & = & t_1 \cdot t_2 \cdot t_3 \cdot t_4 \cdot t_5 \cdot t_6
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\end{array}</math>
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|}
    
What on earth could Peirce mean by saying that such a term is "not a true symbol", or that it is of "no use whatever"?
 
What on earth could Peirce mean by saying that such a term is "not a true symbol", or that it is of "no use whatever"?
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