Aristotle’s lectures on what today we call logic were an outgrowth of the analysis of debate techniques taught by the Sophists, the first professional educators of the ancient world. His particular advance was to look at the syllogism, a pattern of reasoning in which the presence of a connecting idea in two separate sentences allows us to come up with a new sentence that will be true if the first two (the premises) are true.

The most famous syllogism of all is the model proposed by Aristotle himself:

All men are mortal.
Socrates is a a man.
Therefore, Socrates is mortal.
The connecting idea (or “middle term”) is “man.” Since there are a number of ways each statement could be developed (“Some men are mortal,” “No men are mortal,” etc.), Aristotle attempted to see which general patterns allowed a valid conclusion. What is especially important is that he saw that validity did not depend on the actual truth of the statements, as we can see from this example:

Everything white is sweet.
Salt is white.
Therefore, salt is sweet.
We have a valid but untrue conclusion, which is possible only because there was an untrue premise.

Aristotle’s categorical logic provided the standard for formal reasoning until this century, when gradually modern formal logic came to replace it. A key difference between the classical Greek logic and modern symbolic logic is the emphasis we put on purely hypothetical relationships--or conditionals. Because of this emphasis there is one major difference in how we see the relationship between statements such as “All unicorns are white” and “Some unicorns are white.” In Aristotle’s logic the first is seen as implying the second (or the second as following from the first), but in modern logic this is not so. We consider that the first will be automatically true if there are no unicorns at all (you cannot be proven wrong, then) while the second, which today is usually taken to imply the actual existence of unicorns, is presumedly false and so could not follow from the first.