Clashing Symbols by Peter Kreeft


Clashing Symbols

The Loss of Aristotelian Logic & the Social, Moral & Sexual Consequences
by Peter Kreeft

When I started teaching logic, in 1962, most of the textbooks taught traditional Aristotelian logic rather than the (then still fairly new) "symbolic logic," also called "mathematical logic" or "propositional calculus." Forty years later, there are only two full-length texts of traditional Aristotelian logic in print. One of them is my own recently published logic textbook, Socratic Logic (St. Augustine's Press), from which much of the middle part of this article is taken. All the other logic texts, over 500 of them, teach symbolic logic, or else informal logic (rhetoric).

By the 1970s, most of the English-speaking philosophical establishment had cast in its lot with "analytic philosophy" and the symbolic logic that was its methodological complement. I still vividly remember the reaction of outrage, fear, and loathing that came from that establishment when Henry Veatch published his attack on the new logic (The Two Logics). The book was a bit verbose, bombastic, and intemperate, but it possessed the three most important (and most rare) qualities any book of philosophy should have: it was interesting, it was rational, and it was right. That's why the establishment "went postal." People will forgive you for being wrong, but they will never forgive you for being right.

But this change in logic is not just a technical, in-house issue for philosophers. It concerns everyone, and it has serious social, moral, and even sexual implications, and it is one of the unrecognized indirect causes of "the culture of death," as I shall try to show in this article.

A Prophetic Phone Call

I realized this only reluctantly. What first buzzed my inner alarm was a phone call I received about 25 years ago from a man who was quite famous (but not with me: I have forgotten his name). He had written a book attacking the computer revolution. The book had been on the New York Times best-seller list for a number of weeks and had elicited high praise. The author had been called "one of the ten most intelligent men in the world." He thought he had found in me an ally for his cyber-Luddite philosophy because he had read some personal complaint against computers in one of my books. (Yes, I do hate the arrogant little bastards. They are robbers, tricksters, and snobs. "I hate them with perfect hatred, I count them mine enemies.")

The caller tried to persuade me of this apocalyptic scenario: The use of computers, he claimed, was imperceptibly changing the very structure of human thought into a geometrically increasing left-brain dominance and right-brain atrophy; so that, as we became more and more willing servants of more and more elaborate calculating machines, our acts of ordinary intuitive understanding were becoming rarer and harder. He seemed to me an extremist and a conspiracy theorist, and I mentally labeled him a crank and a crackpot. But he offered me three pieces of empirically verifiable evidence for his hypothesis, each of them testable by anyone who had taught logic for the last thirty years.

The first was the general prediction that students would become increasingly incapacitated in Aristotelian logic as they became increasingly capable in symbolic logic. The second was more specific: that they would be increasingly unable to understand analogies, and analogical terms. (For understanding analogies is one thing digital computers cannot do. It is an intuitive, "right-brain" act.) The third prediction was the most specific of all, and, I thought, the most absurd: the Scholastic Aptitude Test (SAT), taken by nearly every applicant to college in America, would soon abolish its entire section on analogies because upcoming students would no longer be able to understand them. (These tests had never been substantively changed in fifty years, though they had been repeatedly "dumbed down.")

A few years, later, the third prediction literally came true. Remembering the other predictions, I got out some of my oldest, easiest logic tests, from 1962, and gave them to my current logic students. They failed quite spectacularly, especially the questions about analogical terms. For instance, only three students in a class of 75 understood that in the sentence "He pointed with his right hand to the hands of the clock," the word "hands" is analogical. Very few had had any trouble with that in 1962.

But, you may say, this is only a change in abstract logical thinking; where are the social, moral, and sexual consequences that my title claims?

To explain this, I need to give you a very short course in the history of logic and modern philosophy.

The Rise of Symbolic Logic

About 350 years before Christ, Aristotle wrote the world's first logic textbook. It was actually six books, which collectively came to be known as the Organon, or "Instrument." From then until 1913, when Bertrand Russell and Alfred North Whitehead published Principia Mathematica, the world's first classic of mathematical or symbolic logic, all students in all universities in the world learned Aristotelian logic. The only other "new logic" for 24 centuries had been a seventeenth-century improvement on the principles of inductive logic and scientific method by Francis Bacon, the Novum Organum ("New Organon"), and another by John Stuart Mill in the nineteenth century. But today, "logic" virtually means "symbolic logic."

There are at least three good reasons for the current triumph of symbolic logic over Aristotelian logic. But each comes at a price.

The first and most obvious is that the new logic really is superior to the old in efficiency for expressing long and complex arguments, much as Arabic numerals are superior to Roman numerals, or a digital computer to an analog computer, or writing in shorthand to writing in longhand.

However, longhand is superior to shorthand in other ways: for instance, it has more beauty and elegance, it is intelligible to more people, and it gives a more personal touch. That is why most people write in longhand. It is similar in logic: most people "argue in longhand," i.e., ordinary language, and Aristotelian logic stays close to ordinary language. That is why it is more useful for beginners.

The Insufficiency of Symbolic Logic

A second reason for preferring symbolic logic is its more exact, scientific form. Symbolic logic is mathematical logic. "Modern symbolic logic has been developed primarily by mathematicians with mathematical applications in mind," says one of its defenders, Henry C. Byerly in A Primer of Logic (Harper & Row, 1973).

Mathematics is a wonderful invention for saving time and empowering science, but it is not very useful in ordinary or philosophical conversations. In fact, the more important the subject matter, the less useful mathematics seems to be. Its forte is not quality but quantity. It is the only totally clear, totally unambiguous language in the world, but it cannot say anything very interesting about anything very important.

The philosophical god of symbolic logicians, Ludwig Wittgenstein himself, admitted in his Philosophical Investigations that "because of the basic differences between natural and artificial languages, often such translations (from natural-language sentences into artificial symbolic language) are not even possible in principle." That is why Stephen N. Thomas said, in 1973, that "many logicians now agree that the methods of symbolic logic are of little practical usefulness in dealing with much reasoning encountered in real-life situations" (Practical Reasoning in Natural Language).

And in philosophy!

However helpful symbolic logic may be as a tool of the . . . sciences, it is useless as a tool of philosophy. Philosophy aims at insight into principles and into the relationship of conclusions to the principles from which they are derived. Symbolic logic, however, does not aim at giving such insight. (Andrew Bachhuber, Introduction to Logic [New York, 1957])

Two Unfashionable Assumptions

There is a third reason for the triumph of symbolic logic among philosophers, and this one is philosophical, or ideological. Aristotelian logic was scorned by most twentieth-century philosophers because it rests on two unfashionable, though commonsensical, philosophical assumptions. The technical terms for them are "epistemological realism" and "metaphysical realism." These two assumptions were believed by nearly all philosophers for nearly 2,000 years (roughly, from Socrates until the eighteenth century), and they are still believed by most ordinary people today, but not by most of the influential philosophers of the twentieth century.

The first assumption, epistemological realism, says that the object of human reason, when reason is working naturally and rightly, is objective reality; that human reason can know things as they really are, and can sometimes know them with certainty; that when we say, "Two apples plus two apples must always be four apples," or "Apples grow on trees," we are saying something true about the universe, not just about how we think or use symbols.

There are two main reasons why many twentieth-century philosophers were skeptical of this belief: in two words, Hume and Kant, the two most influential eighteenth-century "Enlightenment" philosophers.

Hume's Fatal Assumption

David Hume inherited from his empiricist predecessor, John Locke, the fatal assumption that the immediate object of human knowledge is our own ideas. Locke had naively assumed that we could know that these ideas "corresponded" to objective reality, somewhat like photos; but it is difficult to know how we can be sure any photo accurately corresponds to the real object of which it is a photo if the only things we can ever know directly are photos and not real objects. Hume drew the logical conclusion of skepticism from Locke's premise.

Once he limited the objects of knowledge to our own ideas, Hume then distinguished two kinds of ideas, which he called "(sense) impressions" and "ideas" (in the narrow sense), and two corresponding kinds of knowledge, which he called "matters of fact" and "relations of ideas." By "relations of ideas" he meant basically what Kant later called "analytic propositions" or what logicians call "tautologies": propositions that are true by definition, true by form rather than by content, true only because their predicate merely repeats all or part of their subject—e.g., "Trees are trees" or "Unicorns are not non-unicorns" or "Unmarried men are men."

On the other hand, by "matters of fact" Hume meant basically what Kant later called "synthetic propositions," propositions whose predicate adds some new information to the subject—e.g., "Some trees never shed their leaves" or "No Englishman is 25 feet tall." Hume argued that this kind of proposition can be known only by sense observation. They are always particular, like "These two men are bald," rather than universal, like "All men are mortal," for we do not sense universals like "all men," only particulars like "these two men."

The Denial of Certain Knowledge

Common sense tells us that we can be certain of some universal truths, like "All men are mortal," and that we can be certain of the particular conclusions we validly deduce from them, like "Socrates is mortal." But according to Hume, we can not be certain of universal truths, because the only way we can come to know them is by generalizing from particular sense experiences; and since we cannot sense all men, we cannot be certain that all men are mortal.

Since these general principles can only be probable, the particular conclusions we deduce from them can only be probable. If it is only probably true that all men are mortal, it is only probably true that Socrates is mortal. The fact that the sun has risen every day for millions of years does not prove it rises every day, and therefore we cannot know it will rise tomorrow.

Hume's conclusion from this analysis was skeptical: there is no certain knowledge of the real world ("matters of fact"), only of tautologies ("relations of ideas"). Even science lacks certainty, because science assumes the general principle of causality, and this principle, according to Hume, is not a universal objective truth but only a subjective association of ideas in our mind. Because we have seen a "constant conjunction" of birds and eggs, because we have so often seen eggs follow birds in time, we naturally assume that birds cause eggs. But we do not see causality itself; we see only birds and eggs. We do not see universals, and we do not see the universal principle that effects come from causes. So, Hume concluded, we do not really have the knowledge of objective reality that we naturally believe we have. We must be skeptics, if we are only Humean beings.

Kant's "Copernican Revolution"

Immanuel Kant accepted most of Hume's epistemological analysis but said, in effect, "I, Kant, accept your skeptical conclusion." He thought he avoided the conclusion by denying the assumption that human reason is supposed to conform to objective reality and fails to do its job. Kant said, instead, that human reason's job is to form or construct its object, as an artist forms or constructs his artwork. The knowing subject determines the known object rather than vice versa. Human reason does its job quite well, but its job is not to discover what is, but to make it—to shape it, to structure it, to impose form on matter, unconsciously and ubiquitously. Kant distinguished three levels of such structuring: (1) the two "forms of perception," space and time; (2) twelve abstract logical "categories," including causality, necessity, substance, and relation; and (3) three "ideas of pure reason," God, self, and world.

Thus, the world of experience is determined by our knowing it rather than our knowing being determined by the world. Kant called this idea his "Copernican revolution in philosophy." It is also called "epistemological idealism" or, more properly, "Kantian idealism." ("Epistemological idealism" is sometimes used in a broader sense, to mean the belief that ideas rather than objective realities are the objects of our knowledge; in that sense, Locke and Hume are also epistemological idealists.)

The bottom line for logic is that, if you agree with either Hume or Kant, logic becomes the mere manipulation of our symbols, not the principles for a true and orderly knowledge of an ordered world. Categories like "relation" and "quality" and "substance," and perhaps even "time" and "self" and "God," are not real features of the world we discover, only mental classifications we make.

Metaphysical Realism vs. Nominalism

In such a logic, "genus" and "species" mean only any larger class and smaller sub-classes that we mentally construct. But in Aristotelian logic, a "genus" is the general, or common, or universal part of a thing's real essential nature—e.g., "animal" is man's "genus." And a "species" is the whole essence—e.g., "rational animal" is man's "species." So for Aristotle, a genus is part of (the internal meaning of) a species rather than a species being part of (the external population of) a genus.

This involves the second commonsensical Aristotelian assumption, metaphysical realism, which is the belief that essences, or universals (like "man," "animal," or "substance"), are objectively real. The two assumptions are mutual corollaries: epistemological realism says that intelligence knows reality, and metaphysical realism says that reality is intelligible; that reality is ordered; that when we say "Man is a rational animal," we are not just imposing an order on a reality that is really unknowable, formless, random, or chaotic; that universal categories are taken from reality into thought and language, not imposed on reality from thought and language.

(There are two versions of metaphysical realism. Plato believed that universals were real things in themselves, while Aristotle believed, more commonsensically, that they were real aspects of things which we mentally abstracted from things.)

The opposite of metaphysical realism is nominalism, the belief that universals are only names (nomina). William of Ockham (1285–1349) is the philosopher who is usually credited (or debited) with being the founder of nominalism. G. K. Chesterton refuted nominalism with his usual economy and wit when he argued, "If, as the nominalist says, 'all chairs are different,' how can he call them all 'chairs'?"

Aristotle's "Acts of the Mind"

Aristotelian logic assumes both epistemological realism and metaphysical realism because it begins with "the first act of the mind," the act of understanding a universal or a nature, or an essence, such as the nature of "apple" or "man." These universals, or essences, or natures, are known by concepts and expressed by what logic calls terms. Then, in "the second act of the mind," the act of judgment, two of these terms are related as subject and predicate of a proposition—e.g., "Apples are fruits" or "All men are mortal." And in "the third act of the mind," the act of reasoning, a further proposition (the "conclusion") is deduced from two previous propositions (the "premises")—e.g., "All men are mortal, and Socrates is a man; therefore, Socrates is mortal."

"Aristotle never intended his logic to be a merely formal calculus (like mathematics). He tied logic to his ontology (metaphysics): thinking in concepts presupposes that the world is formed of stable species" (R. Lenoble, Essai sur la notion de l'experience, 1943).

An Ape Plus a Computer?

Symbolic logic, in contrast, is a set of symbols and rules for manipulating them without needing to know their meaning and content, or their relationship to the real world, their "truth" (in the traditional, commonsensical sense of "truth"). A computer can do symbolic logic. It is purely quantitative, not qualitative. It is digital, it is reducible to zero-sum mathematics.

Symbolic logic is also called "propositional logic" because it begins with propositions, not with terms. For terms like "man" and "apple" and "mortal" express universals, or essences, or natures; and to admit that these are real would be to admit the reality of universals (metaphysical realism), and that we can know them as they are (epistemological realism).

Typically modern philosophers criticize that assumption as naïve, but it seems to me a very reasonable assumption and not naïve at all. Is it naïve to assume that we know what an apple is? I would not want to go to your house for lunch if you really believe that you do not know what an apple is.

Symbolic logic has no way of knowing, and prevents us from saying, what anything is! But that was the essential Socratic question about everything. Symbolic logic would make Socrates impossible.

The very nature of reason itself is understood differently by symbolic logic than it was by Aristotelian logic. The ancients used "reason" to mean all that distinguished man from the beasts, including intuition, understanding, wisdom, moral conscience, and aesthetic appreciation, as well as calculation. But beginning with Descartes, it is only the last of these powers that we think of when we think of "reason."

That is why there are philosophers today who actually believe there is no fundamental difference between "natural intelligence" and "artificial intelligence," that is, between humans and computers. In other words, man is nothing but an ape plus a computer. Having met some of these philosophers at Harvard and MIT, I must admit that their self-description sometimes seems quite accurate.

Shrunken Language, Shrunken Thought

The new logic is like Orwell's "Newspeak" in 1984: it shrinks language rather than expanding it. In this logic, we can no longer ask the Socratic question of "what" something is, what its essence is. But if we cease to say a thing, we will soon cease to think it, for there will be no holding-places in our language for the thought. Language is the house of thought, and homelessness is as life-threatening for thoughts as it is for people.

If we should begin to speak and think only in nominalistic terms, that would be a monumental historic change. It would be the reversal of the evolutionary event by which man rose above the animal in gaining the ability to know abstract universals. It would be the mental equivalent of going naked on all fours, living in trees, and eating bugs and bananas. (Could monkeys have evolved by natural selection from nominalists?)

While it may seem "extremist" to suggest it, such a mental "devolution" is not impossible. And the use of computers is not unrelated to it. Already, "internet logic," the logic of spontaneous association by "keywords," is replacing genus and species logic, the logic of an ordered hierarchy of objectively real categories that express natural essences.

In fact, to most modern minds, the last seven nouns and adjectives of the previous sentence already seem as archaic as alchemy or feudalism. And those that do understand them often label them ideologically dangerous. They contend that classifications like "Hittites," and universal statements about classes like "Hittites could not read Hebrew," constitute stereotyping, judgmentalism, prejudice, oppression, or even "hate speech."

Weak on Substance

Logic and social change are not unrelated. (Logic is not unrelated to anything.) Our society no longer thinks about the fundamental metaphysical question, the question of what something is, the question of the "nature" of a thing. Instead, we think about how we feel about things, how we can use them, how they work, how we can change them, how we see them behave, and how we can predict and control their behavior by technology.

But none of this raises us above the animal level in kind, only in degree. The higher animals, too, have feelings about things, use things, understand how some things work and how they can change them, see them behave, and can predict and even control their behavior by a kind of primitive technology. For the act of hunting is technological; it is an art of predicting and controlling the behavior of other animals.

What does man have that no other animal has? The very thing that is vilified by many modern philosophers: abstract concepts. We can abstract and understand universals. That is the power Aristotelian logic is founded on, and that is the thing symbolic logic ignores or denies.

The old logic was like the old classic movies: strong on substance rather than on sophistication. The new logic is like the typically modern movies: strong on "special effects" but weak on substance, on theme, character, plot, and language; strong on "bells and whistles" but weak on the engine; strong on the technological side, weak on the human side. But logic should be a human instrument. Logic was made for man, not man for logic.

Consensus Undone

Symbolic logic is essentially a logic of "if . . . then . . .", a logic of antecedent and consequent propositions; and it is a mathematical logic, a logic of quantity. These two features perfectly fit and foster utilitarianism in ethics because utilitarianism is essentially an ethics of "if . . . then . . .", an ethics of consequences; and it is also an ethics of quantity. For its fundamental principle is that an act is ethically good if its foreseeable consequences constitute "the greatest happiness for the greatest number." (This is a version of "the end justifies the means," though that formula is somewhat ambiguous.)

In contrast, Aristotelian logic naturally fits and fosters a natural-law ethics because its basic unit is a term, which expresses a nature or essence, and its basic judgment is "all S is P," which is a statement of universal truth or law about the nature or quality of S (as expressed in P). It is essentially a logic of natures, of universal kinds and categories, of qualities and essences, and the principles of natural-law ethics are based on and abstracted from the universal nature of man.

Before symbolic logic, Western culture, despite its pluralism and creativity, displayed a strong, deeply rooted, nearly universal, and rarely questioned consensus—and not just a consensus but an understanding—about most of the basic aspects of the universal, natural moral law, about what was natural and what was unnatural to man. There probably was not a greater obedience to this law in the past, but there certainly was a much greater knowledge of it and belief in it.

More Sexual than Logical

By far the most radically changed area of morality in both belief and practice is sex. We routinely speak of "the sexual revolution." We do not use that word for any other aspect of ethical change. For today, most people find the traditional language about "unnatural acts" not only politically incorrect and offensive, but literally incomprehensible. This is because they no longer accept the legitimacy of the very question of the "nature" of a human act—the thing symbolic logic disallows.

Who today still debates issues like homosexuality, contraception, masturbation, divorce, adultery, or even incest, pedophilia, and bestiality, in terms of the "nature" of sexuality, the "nature" of femininity and masculinity, and the "nature" of marriage? Traditional Roman Catholics. No one else. It is not a far-fetched suspicion that the most powerful force driving the new logic is more sexual than logical.

I will therefore conclude with a prediction, in the spirit of my prophetic phone call. I predict that when the sexual wisdom of Pope John Paul II's "theology of the body" becomes known and accepted, there will also be a restoration of Aristotelian logic. •