Chrysippus cofounded The Stoics (later adhered to by the Roman Emperor Marcus Aurelius (121-10)). Stoics were very much concerned with the use of language, contributing to the origins of Logic as much as Aristotle (384-322 BC), but little known for this.

Chrysippus made the choice which most characterized Logic: base it upon declarative sentences which can be evaluated as "True" or "False". This bivalency is usually attributed to Arisotle, so that "semanticists" who disagree with its limitations erroneously speak of "Aritotleian Logic".

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PHILO OF MEGARA (fl. 4th cent. BC)

From the "implication" notion of Philo we derive our present "conditional" operator.

This is a declarative (a..k.a. statement, proposition) of the form, "If _, then _", where the first blank is filled in by a premise or precedent statement and the second blank by a consequent statement. Clearly,

• a true precedent can imply a true consequent;
• a true precedent cannot imply a false consequent;
• a false precedent can imply a false consequent.
• But can a false precedent imply a true consequent?

Philo ruled that it can. (The mathematician-philosopher Bertrand Russell (1872-1970) said, "A stopped watch is correct twice a day.") This choice has been generally accepted down to our time, except for certain adherents to "modal logic".

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THEOPHRASTUS (c. 370-c. 287 BC)

This student of Aristotle endowed us with our most powerful logical proof, known usually by the Latin name, modus ponens (MP, "method or mode of the bridge"):

				(A & (A É B) ÉB

MP is also labeled "Rule of Detachement" for this reason:

• given a statement such as A as an axiom or proven theorem;
• given the above argument;
• you may then detach B as a proven theorem. MP is the only rule of proof need for statement logic or zero predicate logic; and MP, along with The Rule of Substitution, are sufficient to prove all higher levels of the predicate calculus. Truly a great endownment, for which we should give thanks.