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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 — Negation</a> |
| 36 | </dt> |
| 37 | <dt> |
| 38 | <a href="#sec5">I to O — Subcontradiction</a> |
| 39 | </dt> |
| 40 | <dt> |
| 41 | <a href="#sec6">A to I / E to O— Implication</a> |
| 42 | </dt> |
| 43 | <dt> |
| 44 | <a href="#sec7">A to O / E to I — 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 — 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 — 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— 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 — 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> — <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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| 220 | <p class="cke-timestamp">Last Modified: |
| 221 | May 9, 2019</p> |
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