[clinton/website/site/unknownlamer.org.git] / Term Logic.html

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    <h1>Term Logic</h1>
   <div class="contents">
<dl>
<dt>
<a href="#sec1">Definition</a>
</dt>
<dt>
<a href="#sec2">Propositions</a>
</dt>
<dd>
<dl>
<dt>
<a href="#sec3">Relations of Propositional Categories</a>
</dt>
<dd>
<dl>
<dt>
<a href="#sec4">A to E &mdash; Negation</a>
</dt>
<dt>
<a href="#sec5">I to O &mdash; Subcontradiction</a>
</dt>
<dt>
<a href="#sec6">A to I  / E to O&mdash; Implication</a>
</dt>
<dt>
<a href="#sec7">A to O / E to I &mdash; Contradiction</a>
</dt>
</dl>
</dd>
</dl>
</dd>
<dt>
<a href="#sec8">Syllogistic Dialectic</a>
</dt>
<dd>
<dl>
<dt>
<a href="#sec9">Modus Ponens (Affirming the Antecedent)</a>
</dt>
<dt>
<a href="#sec10">Modus Tollens (Denying the Consequent)</a>
</dt>
</dl>
</dd>
<dt>
<a href="#sec11">Sources</a>
</dt>
<dd>
<dl>
<dt>
<a href="#sec12"><em>Prior Analytics</em></a>
</dt>
</dl>
</dd>
</dl>
</div>


<!-- Page published by Emacs Muse begins here --><h2><a name="sec1" id="sec1"></a>
Definition</h2>

<p class="first">Term logic is the classical form of logic used by the followers of
Aristotle (i.e. all of Europe) prior to the advent of modern predicate
logic. A basic knowledge of it is fundamental to understanding
European and Greek philosophical texts written prior to around the
mid-1800s. I have written this page as a set of notes for myself to
assist with formulating the structure of the enthymemes presented in
<em>Rhetoric</em>.</p>


<h2><a name="sec2" id="sec2"></a>
Propositions</h2>

<p class="first">There are four categories of propositions in term logic</p>

<ul>
<li>A: Universal affirmative <!-- $\forall P \exists Q P
\rightarrow Q$--><img src="img/latex/latex2png-Term Logic__1820230203588184659.png" alt="latex2png equation" class="latex-inline" /></li>
<li>E: Universal negative <!-- $\forall P \exists Q P
\rightarrow \neg Q$--><img src="img/latex/latex2png-Term Logic__1990139104632252084.png" alt="latex2png equation" class="latex-inline" /></li>
<li>I: Particular affirmative <!-- $\exists P \exists Q P
\rightarrow Q$--><img src="img/latex/latex2png-Term Logic__1820230203585672063.png" alt="latex2png equation" class="latex-inline" /></li>
<li>O: Particular negative <!-- $\exists P \exists Q P
\rightarrow \neg Q$--><img src="img/latex/latex2png-Term Logic__1990136469440439988.png" alt="latex2png equation" class="latex-inline" /></li>
</ul>

<h3><a name="sec3" id="sec3"></a>
Relations of Propositional Categories</h3>

<h4><a name="sec4" id="sec4"></a>
A to E &mdash; Negation</h4>

<p class="first">Universal affirmatives and universal negatives stand in the most
important dialectical relationship: they cannot both be true.</p>


<h4><a name="sec5" id="sec5"></a>
I to O &mdash; Subcontradiction</h4>

<p class="first">Particular affirmatives and particular negatives <em>may</em> simultaneously be
true, but they cannot simultaneously be false.</p>


<h4><a name="sec6" id="sec6"></a>
A to I  / E to O&mdash; Implication</h4>

<p class="first">The universal affirmative implies the particular affirmative; likewise
for the universal and particular negative.</p>


<!-- \[ \forall P \exists Q P \rightarrow Q \vdash \exists P
      \exists Q P \rightarrow Q \]--><p><img src="img/latex/latex2png-Term Logic__662057013302028111.png" alt="latex2png equation" class="latex-display" /></p>

<!-- \[ \forall P \exists Q P \rightarrow \neg Q) \vdash \exists P
      \exists Q P \rightarrow \neg Q \]--><p><img src="img/latex/latex2png-Term Logic__2257733438607490157.png" alt="latex2png equation" class="latex-display" /></p>


<h4><a name="sec7" id="sec7"></a>
A to O / E to I &mdash; Contradiction</h4>

<p class="first">The universal affirmative contradicts the particular negative;
likewise for the universal negative and the particular positive.</p>


<!-- \[ \forall P \exists Q P \rightarrow Q \not \vdash \exists P
      \exists Q P \rightarrow \neg Q \]--><p><img src="img/latex/latex2png-Term Logic__930112774001846957.png" alt="latex2png equation" class="latex-display" /></p>

<!-- \[ \forall P \exists Q P \rightarrow \neg Q \not \vdash
      \exists P \exists Q P \rightarrow Q \]--><p><img src="img/latex/latex2png-Term Logic__1000903687973200244.png" alt="latex2png equation" class="latex-display" /></p>


<h2><a name="sec8" id="sec8"></a>
Syllogistic Dialectic</h2>

<!-- \[ 
      \begin{array}{lcl}
      A & \text{R} & B \\
      C & \text{R} & A \\
      C & \text{R} &  B
      \end{array}
       \]--><p><img src="img/latex/latex2png-Term Logic__1578431659330548867.png" alt="latex2png equation" class="latex-display" /></p>

<p>Where <strong>R</strong> is one of the aforementioned relations.</p>

<h3><a name="sec9" id="sec9"></a>
Modus Ponens (Affirming the Antecedent)</h3>

<!-- \[ P \rightarrow Q, Q \vdash P \]--><p><img src="img/latex/latex2png-Term Logic__1704608037914088017.png" alt="latex2png equation" class="latex-display" /></p>


<h3><a name="sec10" id="sec10"></a>
Modus Tollens (Denying the Consequent)</h3>

<!-- \[ P \rightarrow Q, \neg Q \vdash \neg P \]--><p><img src="img/latex/latex2png-Term Logic__598849921279338722.png" alt="latex2png equation" class="latex-display" /></p>


<h2><a name="sec11" id="sec11"></a>
Sources</h2>

<h3><em><a name="sec12" id="sec12"></a>Prior Analytics</em></h3>

<ul>
<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>
</ul>


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<p class="cke-footer">"Karen loved animals. Unfortunately the cheetahs betrayed her trust,"
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Commit	Line	Data
3c59982c	1	<?xml version="1.0" encoding="utf-8" ?>
	2	<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
	3	"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
	4	<html xmlns="http://www.w3.org/1999/xhtml">
	5	<head>
	6	<title>Term Logic</title>
	7	<meta name="generator" content="muse.el" />
	8	<meta http-equiv="Content-Type"
	9	content="text/html; charset=utf-8" />
	10	<link href="https://feeds.unknownlamer.org/rss/site-updates"
	11	rel="alternate" type="application/rss+xml" title="Updates Feed" />
	12
	13	<link rel="stylesheet" href="default.css" />
	14	</head>
	15	<body>
	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 — Negation</a>
	34	</dt>
	35	<dt>
	36	<a href="#sec5">I to O — Subcontradiction</a>
	37	</dt>
	38	<dt>
	39	<a href="#sec6">A to I / E to O— Implication</a>
	40	</dt>
	41	<dt>
	42	<a href="#sec7">A to O / E to I — 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 — 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 — 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— 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 — 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> — <a href="http://creativecommons.org/licenses/by-nc-sa/2.5/au/">CC by-nc-sa</a> licensed translation</li>
184	</ul>
185
186
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213
214	<p class="cke-footer">"Karen loved animals. Unfortunately the cheetahs betrayed her trust,"
215	Libot said.
216	</p>
217	<p class="cke-timestamp">Last Modified:
218	May 9, 2019</p>
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220	</html>