Term Logic.html

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