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6 <title>Term Logic
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17 <div class=
"contents">
20 <a href=
"#sec1">Definition
</a>
23 <a href=
"#sec2">Propositions
</a>
28 <a href=
"#sec3">Relations of Propositional Categories
</a>
33 <a href=
"#sec4">A to E
— Negation
</a>
36 <a href=
"#sec5">I to O
— Subcontradiction
</a>
39 <a href=
"#sec6">A to I / E to O
— Implication
</a>
42 <a href=
"#sec7">A to O / E to I
— Contradiction
</a>
49 <a href=
"#sec8">Syllogistic Dialectic
</a>
54 <a href=
"#sec9">Modus Ponens (Affirming the Antecedent)
</a>
57 <a href=
"#sec10">Modus Tollens (Denying the Consequent)
</a>
62 <a href=
"#sec11">Sources
</a>
67 <a href=
"#sec12"><em>Prior Analytics
</em></a>
75 <!-- Page published by Emacs Muse begins here --><h2><a name=
"sec1" id=
"sec1"></a>
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>
88 <h2><a name=
"sec2" id=
"sec2"></a>
91 <p class=
"first">There are four categories of propositions in term logic
</p>
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>
104 <h3><a name=
"sec3" id=
"sec3"></a>
105 Relations of Propositional Categories
</h3>
107 <h4><a name=
"sec4" id=
"sec4"></a>
108 A to E
— Negation
</h4>
110 <p class=
"first">Universal affirmatives and universal negatives stand in the most
111 important dialectical relationship: they cannot both be true.
</p>
114 <h4><a name=
"sec5" id=
"sec5"></a>
115 I to O
— Subcontradiction
</h4>
117 <p class=
"first">Particular affirmatives and particular negatives
<em>may
</em> simultaneously be
118 true, but they cannot simultaneously be false.
</p>
121 <h4><a name=
"sec6" id=
"sec6"></a>
122 A to I / E to O
— Implication
</h4>
124 <p class=
"first">The universal affirmative implies the particular affirmative; likewise
125 for the universal and particular negative.
</p>
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>
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>
135 <h4><a name=
"sec7" id=
"sec7"></a>
136 A to O / E to I
— Contradiction
</h4>
138 <p class=
"first">The universal affirmative contradicts the particular negative;
139 likewise for the universal negative and the particular positive.
</p>
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>
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>
151 <h2><a name=
"sec8" id=
"sec8"></a>
152 Syllogistic Dialectic
</h2>
160 \]--><p><img src=
"img/latex/latex2png-Term Logic__1578431659330548867.png" alt=
"latex2png equation" class=
"latex-display" /></p>
162 <p>Where
<strong>R
</strong> is one of the aforementioned relations.
</p>
164 <h3><a name=
"sec9" id=
"sec9"></a>
165 Modus Ponens (Affirming the Antecedent)
</h3>
167 <!-- \[ P \rightarrow Q, Q \vdash P \]--><p><img src=
"img/latex/latex2png-Term Logic__1704608037914088017.png" alt=
"latex2png equation" class=
"latex-display" /></p>
170 <h3><a name=
"sec10" id=
"sec10"></a>
171 Modus Tollens (Denying the Consequent)
</h3>
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>
177 <h2><a name=
"sec11" id=
"sec11"></a>
180 <h3><em><a name=
"sec12" id=
"sec12"></a>Prior Analytics
</em></h3>
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