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It may come as some comfort to GMAT preppers puzzling over the Critical Reasoning section of the test to know that they are continuing a tradition of hoary antiquity, going back to Ancient Greece.

This tradition reaches at least as far as the philosopher Plato, but certainly to his disciple Aristotle, in the 4th century B.C.E. The kind of disciplined thinking needed to tackle Critical Reasoning is closely paralleled in a foundational field of philosophy called ‘formal logic’. Aristotle was undoubtedly the founding father of this field, and the system he elaborated remained uncontested for almost two millennia, (until the development of modern logic, which has taken issue with a number of Aristotle’s principles). Aristotle’s own term for formalizing logical statements was ‘the syllogism’ (sullogismos in Greek) – variously translated as ‘deduction’, ‘conclusion’, or ‘inference’. Sounds familiar?

The basic form of the syllogism is that of  two statements or premises, which necessarily lead to a conclusion. In Aristotle’s words:

A deduction (sullogismos) is speech (logos) in which, certain things having been supposed, something different from those supposed results of necessity because of their being so. (Prior Analytics I.2, 24b18-20)

So we see that we are not so far afield from the basic form of Critical Reasoning arguments, in which we identify a number of premises, and a conclusion. The most famous syllogism from Aristotle’s writings is the following:

All men are mortal. Socrates is a man. Therefore, Socrates is mortal.

In this syllogism we have two categorical statements (premises) and one conclusion. Three terms are used in the syllogism: men, Socrates, and mortal. The connecting idea (or “middle term”) is “men.” Aristotles also showed that there are a number of ways one could develop each of the basic statements – for example by negating the terms (“No men are mortal,”) or particularizing one of them (“Some men are mortal”). One could shuffle around the position of the three terms in the different statements (is it in the subject or predicate position of the statement?).

Aristotle was interested in showing which general patterns allowed a valid conclusion. All in all, when combining the different patterns and possibilities, logicians have shown that there are 256 possible forms of syllogism, but only 19 of them present valid conclusions. This can help us realize why Critical Reasoning questions are challenging – there are many more ways of stating something illogical than there are of presenting a logical argument. And some of those invalid argument can appear quite persuasive (they are called fallacies), unless we hone our minds to detect the flaws.

Validity versus Truth

The key idea, without which we cannot really understand what formal logic is all about – is that validity does not depend on the actual truth of the statements. The following syllogism illustrates this:

Everything metal is heavy. A pin is metal. Therefore, a pin is heavy.

Here we have a formally valid but untrue conclusion, which is possible only because there was an untrue premise. So, in essence, we can only say that a conclusion is true, if the premises are true. However, we can affirm the validity of a deduction/syllogism regardless of whether the ‘facts’ in the story are true. This is important for preparing oneself for the Critical Reasoning questions, because , again, here we are only interested in what is valid, not it what is true. This is also why we are told to set aside our own knowledge and understanding of the world when we approach Critical Reasoning- whether a statement is true is irrelevant for solving the problem.

Although Aristotle developed a rather abstract and formal system of classifying syllogisms, some scholars maintain that he did not ‘invent’ the syllogism but merely discovered a feature of the human mind – the ways in which it reasons. They point to examples in the work of Aristotle’s mentor – Plato – which show that this form of reasoning was already practiced and exercised before Aristotle. In Plato, the syllogism isn’t formally defined, but syllogisms may be recognized, although they are clothed in a narrative form – much like the Critical Reasoning questions we encounter, which present us with a little scenario or situation from life.

Here’s an example from one of Plato’s dialogues, in which Socrates, after being sentenced to death by an Athenian tribunal, discusses the nature of the afterlife with his student, Cebes. Of course, the one asking the question is Socrates – Cebes is responding:

And what do we call the principle which does not admit of death? The immortal, he said. And does the soul admit of death? No. Then the soul is immortal? Yes, he said. And may we say that this is proven? Yes, abundantly proven, Socrates, he replied.

Phaedo 105e2-7,

Although this argument appears in dialog format, it can quite easily be recast in the classic form of a three-part syllogism

Premise 1: Anything that does not admit of death is immortal

Premise 2: The soul does not admit of death.

Conclusion: THEREFORE, the soul is immortal.

If Socrates gave scores for correct answers, and Cebes, Phaedo and friends could mention their dialogue with Socrates at his deathbed in their resumes, I’m sure they would have made for very glamorous MBA candidates (that is, if Aristotle’s academy offered MBA degrees). Now that’s quite a hypothetical syllogism right there. But let’s flashforward back to the present and ask – can our appreciation of the ancient art of syllogistic reasoning help us at all on the GMAT? We’ll look at that question in a future post.