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

* Definition

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
*Rhetoric*.


* Propositions

There are four categories of propositions in term logic

 - A: Universal affirmative <math inline>\forall P \exists Q P
   \rightarrow Q</math>
 - E: Universal negative <math inline>\forall P \exists Q P
   \rightarrow \neg Q</math>
 - I: Particular affirmative <math inline>\exists P \exists Q P
   \rightarrow Q</math>
 - O: Particular negative <math inline>\exists P \exists Q P
   \rightarrow \neg Q</math>

** Relations of Propositional Categories

*** A to E -- Negation

Universal affirmatives and universal negatives stand in the most
important dialectical relationship: they cannot both be true.

*** I to O -- Subcontradiction

Particular affirmatives and particular negatives *may* simultaneously be
true, but they cannot simultaneously be false.

*** A to I  / E to O-- Implication

The universal affirmative implies the particular affirmative; likewise
for the universal and particular negative.


      <math>\forall P \exists Q P \rightarrow Q \vdash \exists P
      \exists Q P \rightarrow Q</math>

      <math>\forall P \exists Q P \rightarrow \neg Q) \vdash \exists P
      \exists Q P \rightarrow \neg Q</math>

*** A to O / E to I -- Contradiction

The universal affirmative contradicts the particular negative;
likewise for the universal negative and the particular positive.

; fix notation? -- is \not \vdash proper ... I don't think so
      <math>\forall P \exists Q P \rightarrow Q \not \vdash \exists P
      \exists Q P \rightarrow \neg Q</math>

      <math>\forall P \exists Q P \rightarrow \neg Q \not \vdash
      \exists P \exists Q P \rightarrow Q</math>

* Syllogistic Dialectic

      <math>
      \begin{array}{lcl}
      A & \text{R} & B \\
      C & \text{R} & A \\
      C & \text{R} &  B
      \end{array}
      </math> 

Where **R** is one of the aforementioned relations.

** Modus Ponens (Affirming the Antecedent)

      <math>P \rightarrow Q, Q \vdash P</math>

** Modus Tollens (Denying the Consequent)

      <math>P \rightarrow Q, \neg Q \vdash \neg P</math>

* Sources

** *Prior Analytics*

 - [[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
Commit	Line	Data
09816bb9	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