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17 | <body> | |
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 | ||
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77 | <!-- Page published by Emacs Muse begins here --> |
78 | <h2><a name="sec1" id="sec1"></a> | |
3c59982c | 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 | ||
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217 | <p class="cke-footer">Jessie: i thought your beard took the oxygen from the air and made it |
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3c59982c | 219 | </p> |
220 | <p class="cke-timestamp">Last Modified: | |
221 | May 9, 2019</p> | |
222 | </body> | |
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