[Let's do a quick re-cap of the Greek
syllogism for those of you who either played hooky or slept through that
lecture in Philosophy 101. I dug out my yellowing notes. It seems I was awake
that day. Here's what those aging notes still record in crude undergraduate scrawl. Ahem . . . ]
“The logic upon which the Western world and Western society has been built traces back to ancient Greece about 2,500 years ago. There the ancient thinkers, of whom Socrates, Plato, and Aristotle are but a few, built an edifice of rational thinking which has survived far more intact than the art and architecture of the era.
“All the rules we use today for rational thought trace back to these ancient times. Those rules have withstood the scrutiny of the finest minds of the last 2½ millennia and have proven their sturdiness. These rules form the basis of all logical thinking and mathematics which has built Western society to the pinnacles (or depths depending your point of view) that Western society has reached today.
“One of the central tenants of these rules of logic is what we today call the syllogism. This is a logical proof consisting of three statements. The first two statements contain known or given propositions. These two propositions partially overlap in some fashion which leads to a deduced or proven third statement.
“In bare-bones logic this becomes: If A implies B, and B implies C, then A implies C. Symbolic logic states it as:
If A => B
and B => C
then A => C
“This is considered proof that if you establish A and B, then C must also be true. Note, however, that this does not include the opposite, known as the converse. If you establish C, it does not necessarily mean that A has been established. This is a one-way street. The only thing which is proved is C, and it is proved only if A and B are established first. The most common verbal example of the syllogism cited is as follows:
A. Socrates is a man.
B. All men are mortal.
C. Therefore, Socrates is mortal.
“The mortality of Socrates, therefore, is logically proven simply by establishing his humanity. No further proof of Socrates' mortality is necessary. Note that the converse, all mortals are Socrates, is not proven. One consequence of this exercise is that the execution of Socrates can be concluded to be a logical redundancy as the syllogism had already inconvertibly established the mortality of Socrates prior to any ingestion of hemlock.
“A more recent treatment of the implications of the syllogism will be studied by those of you planning to take Philosophy 206, An Introduction to 19thCentury European Philosophers, in which, inter alia, the Greek syllogism is examined in depth as the logical foundation out of which Hegel developed his dialectic of thesis, antithesis, and synthesis, which in turn led us to Marxism and the Soviet Union's empire (a development unlikely to have been anticipated by the ancient Greek philosophers) . . .”
[The lecture at this point drifted off into a rambling discussion of the logical fallacy of argument ad hominem, a subject foreshadowing the invention (many years later) of the internet and its amusing diversions of usenet flame wars. Nota bene: I really did takes notes when I was freshman at college . . . well at least some of the time . . . at least before the beer and pizza arrived on Fridays.]