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THE ANALYTIC-SYNTHETIC DICHOTOMY

Aristotle Discovers Formal Logic

One of the greatest philosophers of ancient Greece was from an aristocratic family in Stagira in northeastern Greece. He was Aristotle (384-322 B.C.E.). One of his greatest accomplishments was to initiate the study of formal logic.

All of us reason informally. We silently and automatically use calculating processes in our heads to number, plan, and make decisions. How many pencils do I have in my hand? Can I get across the street before that car comes? Should I invite my mother for Christmas?

But Aristotle wrote a series of works on logic explaining how one can make decisions explicitly; check that those decisions are correct; and so defend them (demonstrate one's reasoning) to others.

This is very important.

Supposedly, you and I possess a mental faculty called reason which separates us from the other earthly animals. We use that faculty, and the process of its thinking -- also called reason -- extensively. But all of us want to know that we are, in fact, reasoning correctly. We want, also, to be able to prove that we have reasoned correctly. If we can prove that we have reasoned correctly we can perhaps win the trust of others, persuade them to do what we want them to. In rhetoric this is called making a rational appeal.

Reasoning is difficult. Most of us don't do it very well (study any political debate, if you don't believe me).

So how can we practically test our ideas, and prove that they are true?

Aristotle analyzed (broke down) the kinds of sentences in which we make assertions. He then established rules for determining if the conclusions in our reasonings were valid. The rules in Aristotle's logical works (and later additional rules devised by later logicians in Greece, Rome, Europe, and the Americas) help us to use and improve our reasoning.

Among Aristotle's treatises on logic were the Topics, the Categories, the Prior Analytics, and the Posterior Analytics. These were later lumped together by editors under the title the Organon. This meant instrument, because the Organon treatises were the instrument by which one could understand formal logic.

In the Organon Aristotle discovered and published what were thought until the late 19th century to be formal logic's fundamental laws. Indeed, they were thought to be the very laws of thought itself. Thus the British mathematician and logician George Boole (1814-1864) titled his famous 1854 book on logic (in which he invented Boolean algebra, a kind of symbolic logic that helps to check formal logic for correctness) An Investigation Into The Laws of Thought.

Aristotle's concern was with how we can argue, as we would say today, logically.

The Sophists

About forty years before Aristotle's birth, a loosely associated group of philosophers began arriving in Athens. One leading light was Gorgias (circa 485-ca. 380 B.C.E.) of Leontini in Sicily; a brilliant orator, he invented cadenced prose. Gorgias arrived in Athens in 427 B.C.E. as an ambassador and dazzled the Athenians with a speech. Later he returned to the city, and set up as a teacher of rhetoric. His ideas were fundamental to the group. He is said to have believed that

Nothing exists.
If anything did exist it could not be known.
If anything did exist and were known, it could not be communicated.

Forget Gorgias's ideas for now. They don't make a lot of sense. After all,

If Gorgias believed that nothing could be communicated, why was he attempting to communicate his ideas?
If nothing could be known, why did he think he knew his ideas to be true?
And if nothing exists, why did Gorgias seem to exist, and seem to act as if the Athenians existed?

Gorgias's ideas are mostly interesting because they give some sense of the group to which he belonged. (The French philosopher Jacques Derrida (b. 1930), who believes that nothing can be communicated, seems in some ways the Gorgias of our day.)

Protagoras Invents Relativism

A slightly later member of the group of philosophers was Protagoras of Abdera (480?-411? B.C.E.). He gave the group its name, Sophists (i.e., experts, wise men, masters). Protagoras believed that nothing was absolutely good or bad, false or true; everything was relative: in other words, truth was not, as we would say, objective¹ but only a matter of opinion. Each person, Protagoras thought, had to decide his own beliefs. "Man," Protagoras famously said, "is the measure of all things."

The Sophists had other challenging, original, philosophical doctrines. But the belief which most challenged Athenian philosophers, the one that hit them where they lived, was the Sophists' conviction that philosophy should be ruthlessly practical. Unlike other Athenian philosophers, the Sophists (starting, apparently, with Protagoras) demanded payment for their teaching.

Now this was revolutionary. Prior to this time philosophy in Athens had been a kind of dilettantish amateur study among wealthy aristrocratic males. They lived, a small minority, on top of a ruthlessly patriarchal slave society.

In return for their wage, the Sophists offered to teach Athenian males skill in persuasive speech, what today we call rhetoric. In this way the Sophists' Athenian students would win their law cases and other disputes, become effective speakers in the Assembly, and become generally successful.

Perhaps because of the example of the Sophists, Aristotle was deeply concerned with the need to discover and communicate real truth. For despite the apparent value of what the Sophists seemed to offer -- success in daily life -- Athenian public opinion gradually turned against them. Sophists were gradually felt to be persons without any moral beliefs. Socrates, Plato, and Aristotle attacked their doctrines; the latter two also objected to their mercenary nature. (The Sophists' very name has come to denote "hypocritical, deceiving speakers".) It came to be believed that there was something (we would say) "invalid" or "unfair" about the way the Sophists argued. Sure, they made superficially plausible arguments, but were these arguments really true? Or were they just mere bamboozling "sophistry"?

Logic vs. Sophistry

Aristotle was therefore concerned with how he could distinguish what we would today call "logical," "valid," and "sound" arguments from sophistry.

Aristotle therefore had to work out what logical arguments were, and how they worked. In the Organon Aristotle explains several forms of argument which -- if you handle them correctly -- make, he believes, true and powerful arguments. He even invents several kinds of criteria of truth, namely what logicians today call "validity" and "soundness".

Among the logical forms of argument Aristotle explains is the syllogism. Everyone is familiar with syllogisms, right? Here's a classic, boring, traditional example, updated for less-sexist times:

All humans are mortal. (This is traditionally called the major premise of the syllogism.)
Socrates is a human. (This is traditionally called the minor premise.)
Therefore, Socrates is a mortal. (This is traditionally called the conclusion.)

In syllogisms, words like "all men", "mortal", "Socrates", "a man" and "a mortal" are traditionally called terms. (Presumably this is because they appear at the ends, both ends, of each sentence in the syllogism (Latin terminus, "end").

Of course, the meaning of each term is important. Aristotle describes how to explain the meaning of a term, namely, by making a definition. One makes a definition of a term by finding a group (called a species) of which the term is a member, and then a short phrase (traditionally called a differentia) which explains how the term differs from other members of the species.

An example:

In the definition of "Aristotle", say, namely "Aristotle was a Greek philosopher who lived from 384 to 322 B.C.E.," "Greek philosopher" is the species and "who lived from 384 to 322 B.C.E." is the differentia.

Aristotle and later philosophers observed that, from a definition, one seems immediately to know certain facts.

For example:

Take "man". Suppose the meaning of "man" (the definition) is "a featherless biped". From this it is obvious that a man (at least, if he hasn't had an amputation) has but two legs. Or if the definition is "a rational creature" (meaning: has the power of rationality or reason), then it is obvious that a man has the power of reason. One is practically just restating the definition.

The German philosopher Immanuel Kant (1724-1804) seems to have invented and named the analytic-synthetic dichotomy. Centuries before Kant philosophers (Aristotle, for example) had noticed that some facts seemed to be true from the definition of terms. (A term is a word -- a noun -- especially when thought of as appearing within a logical form as, for example, a syllogism.) Philosophers had argued that, if you studied the meaning of a term, you could understand some facts about the term. Further, these facts wouldn't be just true, they would be necessarily and absolutely and certainly true.

For example, the truths of mathematics.

Mathematical sums and remainders and products and dividends -- the results of adding, subtracting, multiplying, and dividing in arithmetic -- are (according to these traditional philosophers) absolutely true. They're true by definition. They will always be true. 2 + 2 = 4 just because of what 2 and + and = mean. You know this to be certainly true, just from analyzing the terms of this simple equation. The same is true for 8 - 2 = 6, 4 x 4 = 16, and 21 divided by 7 = 3. All of these equations are true by analysis, that is, on examination by definition.

I hope you got that, because it's crucial to what follows.

Such mathematical sentences (which, like sentences in formal logic, are called propositions) are called analytic or necessary; this means, like I said above, that you verify them just by analyzing their terms and meaning. By doing that, you know that an analytic or necessary proposition is necessarily true (which means, true in all times and places, forever).

But there is said to be another kind of proposition.

If I say, "My mother ate porridge yesterday," how do you know whether that sentence/logical proposition is true or false? Not, most people would say, simply by analyzing the meaning of the terms "mother", "porridge", "ate", and so on. No. That wouldn't be enough. You'd actually have to look her up and ask her, or at least try to find someone who knew what she had eaten and ask that person. You'd have to, one way or another, check out the facts. You'd have to gather and examine the evidence for the truth or falsehood of alleged maternal porridge-eating.

This seems to be a different kettle of porridge from just being able to analyze the meanings of 2 = 2 and 21 divided by 7.

Right?

So philosophers call this type of proposition -- one where, to see whether it's true, you have to go and check out the facts -- mere analysis of terms not being enough -- a synthetic or contingent proposition.

BORING BUT NECESSARY SUMMARY (SO FAR)

There are supposed to be two (2) types of propositions (sentences in mathematics or formal logic). One type is called analytic or necessary; you check its truth by analyzing the meaning of its terms (i.e., its important words). Analytic or necessary truths are absolutely true, and true forever and everywhere. They can never be refuted.

The other kind of proposition is called synthetic or contingent; you check the truth of this second kind by looking at the facts of reality. Synthetic or contingent truths can be refuted by the evidence, by a single new observation that contradicts them.

Okay?

On with our show.

The Two Worlds of Immanuel Kant

In 1781 Immanuel Kant published his book The Critique of Pure Reason.

[To Be Continued and Revised]

Notes

¹"Objective" means "out there," in common exterior reality (where anyone -- theoretically -- can see it); "thrown in front of you like an object in your path."

Sources

Microsoft Corporation. "Aristotle". Article. Microsoft Encarta Encyclopedia Deluxe 2000.

------. "Logic". Article. Ibid.

------. "Sophists". Article. Ibid.

Last modified: 1:30 PM 12/22/2001