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1 | * Definition |
2 | |
3 | Term logic is the classical form of logic used by the followers of |
4 | Aristotle (i.e. all of Europe) prior to the advent of modern predicate |
5 | logic. A basic knowledge of it is fundamental to understanding |
6 | European and Greek philosophical texts written prior to around the |
7 | mid-1800s. I have written this page as a set of notes for myself to |
8 | assist with formulating the structure of the enthymemes presented in |
9 | *Rhetoric*. |
10 | |
11 | |
12 | * Propositions |
13 | |
14 | There are four categories of propositions in term logic |
15 | |
16 | - A: Universal affirmative <math inline>\forall P \exists Q P |
17 | \rightarrow Q</math> |
18 | - E: Universal negative <math inline>\forall P \exists Q P |
19 | \rightarrow \neg Q</math> |
20 | - I: Particular affirmative <math inline>\exists P \exists Q P |
21 | \rightarrow Q</math> |
22 | - O: Particular negative <math inline>\exists P \exists Q P |
23 | \rightarrow \neg Q</math> |
24 | |
25 | ** Relations of Propositional Categories |
26 | |
27 | *** A to E -- Negation |
28 | |
29 | Universal affirmatives and universal negatives stand in the most |
30 | important dialectical relationship: they cannot both be true. |
31 | |
32 | *** I to O -- Subcontradiction |
33 | |
34 | Particular affirmatives and particular negatives *may* simultaneously be |
35 | true, but they cannot simultaneously be false. |
36 | |
37 | *** A to I / E to O-- Implication |
38 | |
39 | The universal affirmative implies the particular affirmative; likewise |
40 | for the universal and particular negative. |
41 | |
42 | |
43 | <math>\forall P \exists Q P \rightarrow Q \vdash \exists P |
44 | \exists Q P \rightarrow Q</math> |
45 | |
46 | <math>\forall P \exists Q P \rightarrow \neg Q) \vdash \exists P |
47 | \exists Q P \rightarrow \neg Q</math> |
48 | |
49 | *** A to O / E to I -- Contradiction |
50 | |
51 | The universal affirmative contradicts the particular negative; |
52 | likewise for the universal negative and the particular positive. |
53 | |
54 | ; fix notation? -- is \not \vdash proper ... I don't think so |
55 | <math>\forall P \exists Q P \rightarrow Q \not \vdash \exists P |
56 | \exists Q P \rightarrow \neg Q</math> |
57 | |
58 | <math>\forall P \exists Q P \rightarrow \neg Q \not \vdash |
59 | \exists P \exists Q P \rightarrow Q</math> |
60 | |
61 | * Syllogistic Dialectic |
62 | |
63 | <math> |
64 | \begin{array}{lcl} |
65 | A & \text{R} & B \\ |
66 | C & \text{R} & A \\ |
67 | C & \text{R} & B |
68 | \end{array} |
69 | </math> |
70 | |
71 | Where **R** is one of the aforementioned relations. |
72 | |
73 | ** Modus Ponens (Affirming the Antecedent) |
74 | |
75 | <math>P \rightarrow Q, Q \vdash P</math> |
76 | |
77 | ** Modus Tollens (Denying the Consequent) |
78 | |
79 | <math>P \rightarrow Q, \neg Q \vdash \neg P</math> |
80 | |
81 | * Sources |
82 | |
83 | ** *Prior Analytics* |
84 | |
85 | - [[http://etext.library.adelaide.edu.au/a/aristotle/a8pra/index.html][HTML]] -- [[http://creativecommons.org/licenses/by-nc-sa/2.5/au/][CC by-nc-sa]] licensed translation |