Term Logic.muse

   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