# 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]

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