Term Logic.html

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  18     <h1>Term Logic</h1>
  19    <div class="contents">
  20 <dl>
  21 <dt>
  22 <a href="#sec1">Definition</a>
  23 </dt>
  24 <dt>
  25 <a href="#sec2">Propositions</a>
  26 </dt>
  27 <dd>
  28 <dl>
  29 <dt>
  30 <a href="#sec3">Relations of Propositional Categories</a>
  31 </dt>
  32 <dd>
  33 <dl>
  34 <dt>
  35 <a href="#sec4">A to E &mdash; Negation</a>
  36 </dt>
  37 <dt>
  38 <a href="#sec5">I to O &mdash; Subcontradiction</a>
  39 </dt>
  40 <dt>
  41 <a href="#sec6">A to I  / E to O&mdash; Implication</a>
  42 </dt>
  43 <dt>
  44 <a href="#sec7">A to O / E to I &mdash; Contradiction</a>
  45 </dt>
  46 </dl>
  47 </dd>
  48 </dl>
  49 </dd>
  50 <dt>
  51 <a href="#sec8">Syllogistic Dialectic</a>
  52 </dt>
  53 <dd>
  54 <dl>
  55 <dt>
  56 <a href="#sec9">Modus Ponens (Affirming the Antecedent)</a>
  57 </dt>
  58 <dt>
  59 <a href="#sec10">Modus Tollens (Denying the Consequent)</a>
  60 </dt>
  61 </dl>
  62 </dd>
  63 <dt>
  64 <a href="#sec11">Sources</a>
  65 </dt>
  66 <dd>
  67 <dl>
  68 <dt>
  69 <a href="#sec12"><em>Prior Analytics</em></a>
  70 </dt>
  71 </dl>
  72 </dd>
  73 </dl>
  74 </div>
  75
  76
  77 <!-- Page published by Emacs Muse begins here -->
  78 <h2><a name="sec1" id="sec1"></a>
  79 Definition</h2>
  80
  81 <p class="first">Term logic is the classical form of logic used by the followers of
  82 Aristotle (i.e. all of Europe) prior to the advent of modern predicate
  83 logic. A basic knowledge of it is fundamental to understanding
  84 European and Greek philosophical texts written prior to around the
  85 mid-1800s. I have written this page as a set of notes for myself to
  86 assist with formulating the structure of the enthymemes presented in
  87 <em>Rhetoric</em>.</p>
  88
  89
  90
  91 <h2><a name="sec2" id="sec2"></a>
  92 Propositions</h2>
  93
  94 <p class="first">There are four categories of propositions in term logic</p>
  95
  96 <ul>
  97 <li>A: Universal affirmative <!-- $\forall P \exists Q P
  98 \rightarrow Q$--><img src="img/latex/latex2png-Term Logic__1820230203588184659.png" alt="latex2png equation" class="latex-inline" /></li>
  99 <li>E: Universal negative <!-- $\forall P \exists Q P
 100 \rightarrow \neg Q$--><img src="img/latex/latex2png-Term Logic__1990139104632252084.png" alt="latex2png equation" class="latex-inline" /></li>
 101 <li>I: Particular affirmative <!-- $\exists P \exists Q P
 102 \rightarrow Q$--><img src="img/latex/latex2png-Term Logic__1820230203585672063.png" alt="latex2png equation" class="latex-inline" /></li>
 103 <li>O: Particular negative <!-- $\exists P \exists Q P
 104 \rightarrow \neg Q$--><img src="img/latex/latex2png-Term Logic__1990136469440439988.png" alt="latex2png equation" class="latex-inline" /></li>
 105 </ul>
 106
 107 <h3><a name="sec3" id="sec3"></a>
 108 Relations of Propositional Categories</h3>
 109
 110 <h4><a name="sec4" id="sec4"></a>
 111 A to E &mdash; Negation</h4>
 112
 113 <p class="first">Universal affirmatives and universal negatives stand in the most
 114 important dialectical relationship: they cannot both be true.</p>
 115
 116
 117 <h4><a name="sec5" id="sec5"></a>
 118 I to O &mdash; Subcontradiction</h4>
 119
 120 <p class="first">Particular affirmatives and particular negatives <em>may</em> simultaneously be
 121 true, but they cannot simultaneously be false.</p>
 122
 123
 124 <h4><a name="sec6" id="sec6"></a>
 125 A to I  / E to O&mdash; Implication</h4>
 126
 127 <p class="first">The universal affirmative implies the particular affirmative; likewise
 128 for the universal and particular negative.</p>
 129
 130
 131 <!-- \[ \forall P \exists Q P \rightarrow Q \vdash \exists P
 132       \exists Q P \rightarrow Q \]--><p><img src="img/latex/latex2png-Term Logic__662057013302028111.png" alt="latex2png equation" class="latex-display" /></p>
 133
 134 <!-- \[ \forall P \exists Q P \rightarrow \neg Q) \vdash \exists P
 135       \exists Q P \rightarrow \neg Q \]--><p><img src="img/latex/latex2png-Term Logic__2257733438607490157.png" alt="latex2png equation" class="latex-display" /></p>
 136
 137
 138 <h4><a name="sec7" id="sec7"></a>
 139 A to O / E to I &mdash; Contradiction</h4>
 140
 141 <p class="first">The universal affirmative contradicts the particular negative;
 142 likewise for the universal negative and the particular positive.</p>
 143
 144
 145 <!-- \[ \forall P \exists Q P \rightarrow Q \not \vdash \exists P
 146       \exists Q P \rightarrow \neg Q \]--><p><img src="img/latex/latex2png-Term Logic__930112774001846957.png" alt="latex2png equation" class="latex-display" /></p>
 147
 148 <!-- \[ \forall P \exists Q P \rightarrow \neg Q \not \vdash
 149       \exists P \exists Q P \rightarrow Q \]--><p><img src="img/latex/latex2png-Term Logic__1000903687973200244.png" alt="latex2png equation" class="latex-display" /></p>
 150
 151
 152
 153
 154 <h2><a name="sec8" id="sec8"></a>
 155 Syllogistic Dialectic</h2>
 156
 157 <!-- \[
 158       \begin{array}{lcl}
 159       A & \text{R} & B \\
 160       C & \text{R} & A \\
 161       C & \text{R} &  B
 162       \end{array}
 163        \]--><p><img src="img/latex/latex2png-Term Logic__1578431659330548867.png" alt="latex2png equation" class="latex-display" /></p>
 164
 165 <p>Where <strong>R</strong> is one of the aforementioned relations.</p>
 166
 167 <h3><a name="sec9" id="sec9"></a>
 168 Modus Ponens (Affirming the Antecedent)</h3>
 169
 170 <!-- \[ P \rightarrow Q, Q \vdash P \]--><p><img src="img/latex/latex2png-Term Logic__1704608037914088017.png" alt="latex2png equation" class="latex-display" /></p>
 171
 172
 173 <h3><a name="sec10" id="sec10"></a>
 174 Modus Tollens (Denying the Consequent)</h3>
 175
 176 <!-- \[ P \rightarrow Q, \neg Q \vdash \neg P \]--><p><img src="img/latex/latex2png-Term Logic__598849921279338722.png" alt="latex2png equation" class="latex-display" /></p>
 177
 178
 179
 180 <h2><a name="sec11" id="sec11"></a>
 181 Sources</h2>
 182
 183 <h3><em><a name="sec12" id="sec12"></a>Prior Analytics</em></h3>
 184
 185 <ul>
 186 <li><a href="http://etext.library.adelaide.edu.au/a/aristotle/a8pra/index.html">HTML</a> &mdash; <a href="http://creativecommons.org/licenses/by-nc-sa/2.5/au/">CC by-nc-sa</a> licensed translation</li>
 187 </ul>
 188
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