# Aristotle
(Αριστοτἑλης)

## Notes

Aristotle's presentation in "*De Interpretatione*"
([Aristotle,
DE])
and
([Aristotle,
Pr. Anal.])
is prose, not actually symbolic logic. Lemmon and Scott
[Lemmon and Scott,
1977, Historical Introduction]
give a presentation in modern symbology with this page (mostly follows)

Since the discussion was not in the form of a minimal axiomatic basis,
the list below has redundancy.

## Based on

(Some changes in notation to match the rest of these pages. -JH)

- Operators
- Ip : p is impossible.
- Mp : p is possible. (if p is assumed, it has no impossible consequences)
- Qp : p is not necessary, and has not impossible consequences
- ~p : p is false.
- p>q : p implies q
- p == q : p is (logically) equivalent to q
- p&q : p and q are both true.

- Rules
- Uniform substitution (US) [Assumed]
- Modus Ponens for > (MP>) [explicit]

- Axioms
- 1) Lp>Mp
- *2) Mp>M~p
*(not in final system, Causes Modal collapse (Lp==p) with axiom 1)*
- 3) Lp>p
- 4) p>Mp
- 5) Ip == L~p
- 6) Ip == ~Mp
- 7) Qp == (~Lp & ~Ip)
- 8) Mp == ~Ip
- 9) Qp == Q~p
*(This replaces what he originally used axiom 2 for)*
- 10) Qp > Mp
- 13) L(p>q) >L(Mp > Mq)
- 14) L(p>q) >L(Lp > Lq)
- 21) Lp == ~M~p
*(LS states as implicit)*
- 22) Mp == ~L~p
*(LS states as implicit)*

As reported in [Lemmon and Scott,
1977, Historical Introduction]

## Basis for

# Go to ...

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© Copyright 2005 by John Halleck, All Rights Reserved.
This page is http://www.cc.utah.edu/~nahaj/logic/structures/systems/aristotle.html
This page was last modified on August 6th, 2006.
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