| 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 |