Ancient Philosophy

Socrates, Plato, and Aristotle

Aristotle's Logic

The influence of Aristotle, significant in many domains, is most profoundly felt in the realm of logic. During the late classical period, when Plato still dominated metaphysics, Aristotle was recognized as the foremost authority in logic and remained so throughout the Middle Ages. It was only in the thirteenth century that Christian philosophers accorded him the same prominence in metaphysics. Aristotle's preeminence in metaphysics was largely lost during the Renaissance, yet his supremacy in logic endures. Even today, many Catholic instructors of philosophy, along with others, stubbornly reject the discoveries of modern logic, clinging tenaciously to a system that is as outdated as Ptolemy's astronomical model. This resistance complicates the possibility of fairly assessing Aristotle's contributions in historical context. In contemporary discourse, his influence often stands in opposition to clear reasoning, making it challenging to remember the monumental advancement he represented compared to his predecessors (including Plato), as well as how splendid and magnificent his logical system might appear had it continued as a progressive step rather than devolving into a dead end that resulted in over two millennia of stagnation.

When considering Aristotle’s predecessors, it is unnecessary to remind the reader that their works were not literally inspired; thus, they may be praised for their abilities and skills without the implication of agreeing with all their doctrines. The situation is different with Aristotle’s works, which continue to be the subject of debate, particularly regarding logic, and cannot be viewed solely from a historical perspective.

At the core of Aristotle's contributions to logic lies his doctrine of the syllogism. A syllogism is a form of proof composed of three parts: a major premise, a minor premise, and a conclusion. There are several modes of syllogism, each designated by scholastics. The most well-known is the mode termed "Barbara":

• All humans are mortal (major premise).
• Socrates is a human (minor premise).
• Therefore, Socrates is mortal (conclusion).

Alternatively:

• All humans are mortal.
• All Greeks are humans.
• Therefore, all Greeks are mortal.

(Aristotle does not distinguish between these two modes, which, as we shall see, is a mistake.)

Other modes include:

• No fish is rational; all sharks are fish; therefore, no shark is rational (this is the mode "Celarent").
• All humans are rational; some animals are humans; therefore, some animals are rational (this is the mode "Darii").
• No Greek is black; some people are Greeks; therefore, some people are not black (this mode is called "Ferio").

These four modes comprise the "first figure" of syllogism; Aristotle adds a second and third figure, while the scholastics introduce a fourth. It has been demonstrated that the latter three figures can be reduced to the first in various ways.

From a single premise, multiple conclusions can be drawn. From the premise "some humans are mortal," we may conclude that "some mortals are humans." According to Aristotle, this can also be derived from the premise "all humans are mortal." From the premise "no god is mortal," we can conclude that "no mortals are gods," but from the premise "not all humans are Greeks," it does not follow that "some Greeks are not humans."

Beyond such deductions, Aristotle and his followers believed that all deductive reasoning in strict formulation is syllogistic. By articulating all valid modes of syllogism and expressing any proposed proof in syllogistic form, one could avoid logical fallacies. This system marked the beginning of formal logic and, as such, was both remarkable and significant. However, when viewed as an endpoint rather than a starting point of formal logic, it is vulnerable to criticism along three lines:

1. Due to formal deficiencies within the system itself.
2. Because of an overestimation of the syllogism relative to other forms of deductive proof.
3. Due to an overestimation of deduction as a form of proof.

It is worthwhile to say a few words about each of these three lines of critique.

1. Formal deficiencies: Let us begin with the two statements "Socrates is a human" and "all Greeks are humans." A sharp distinction must be drawn between these two assertions, which is lacking in Aristotle's logic. The statement "all Greeks are humans" is typically interpreted as implying the existence of Greeks; without this hidden meaning, some of Aristotle’s syllogisms are unjustified. For example: "All Greeks are humans; all Greeks are white; therefore, some humans are white." This conclusion holds only if Greeks exist. If I were to assert, "all golden mountains are mountains; all golden mountains are golden; therefore, some mountains are golden," my conclusion would be false, even though, in a certain sense, my premises could be true. To clarify our statement, we must divide the single assertion "all Greeks are humans" into two: one being "Greeks exist" and the other "if something is a Greek, then it is a human." The latter remains purely hypothetical and does not imply that Greeks exist.

Thus, the statement "all Greeks are humans" is much more complex in form than the statement "Socrates is a human." In the statement "Socrates is a human," Socrates is the subject, whereas in the statement "all Greeks are humans," the phrase "all Greeks" is not the subject, as nothing is said about "all Greeks" in either "Greeks exist" or "if something is a Greek, then it is a human."

This purely formal error has been a source of misconceptions in metaphysics and epistemology. Let us analyze the establishment of our knowledge in light of the two assertions: "Socrates is mortal" and "all humans are mortal." To determine the truth of the statement "Socrates is mortal," most of us are satisfied with oral testimony; yet, if that testimony is reliable, it must lead us back to someone who knew Socrates and saw him dead. A single observed fact—a dead body of Socrates—along with the knowledge that it was called "Socrates" is sufficient to convince us of Socrates' mortality. However, when the claim is made that "all humans are mortal," the situation changes. The question of our knowledge of such general statements is very complex. Sometimes they are merely verbal: for instance, the truth of "all Greeks are humans" is known because nothing is called a Greek unless it is a human. Such general assertions can be verified through a dictionary. They convey no information about the world, aside from how the words are employed. However, "all humans are mortal" is not of that nature. There is nothing logically contradictory about the concept of an immortal human. We believe in the truth of the above statement based on induction, as there is no fully verified case of a human living longer than, say, 150 years; yet this makes the statement merely probable, not certain. It cannot be deemed certain as long as there are living humans.

Metaphysical errors arise from the assumption that "all men" serves as the subject of the judgment "all men are mortal" in the same sense that "Socrates" serves as the subject of the judgment "Socrates is mortal." This allows for the assertion that, in some sense, the expression "all men" denotes an essence of the same kind as that denoted by the word "Socrates." This led Aristotle to assert that, in some sense, species is substance. He accompanies this assertion with qualifications, yet his followers, particularly Porphyry, exhibited less caution.

Another mistake into which Aristotle falls, due to this same misconception, is the thought that the predicate of a predicate can also serve as a predicate for the original subject. If we say "Socrates is a Greek; all Greeks are men," Aristotle believes that "men" is a predicate for "Greek," just as "Greek" is a predicate for "Socrates," thus it seems evident that "men" is also a predicate for "Socrates." However, in reality, "men" is not a predicate for "Greek." The distinction between names and predicates, or, in the language of metaphysics, between individuals and universals, thus becomes blurred, with disastrous consequences for philosophy. One of the confusions arising from this was the assumption that a class with a single member is identical to that member. This rendered an accurate theory of the number one impossible and led to endless misguided metaphysical reasoning regarding unity.

The overvaluation of the syllogism follows. The syllogism is but one type of deductive proof. In mathematics, which is wholly deductive, syllogisms are rarely encountered. Certainly, one could rewrite mathematical proofs in the form of syllogisms, yet this would be exceedingly artificial and would not make them more persuasive. Take arithmetic, for instance. If I purchase an item costing 16 shillings and 3 pence and offer a banknote of 1 pound in payment, how much change am I owed? To represent this simple arithmetic problem in the form of a syllogism would be absurd and would obscure the true nature of the proof. Furthermore, logic contains non-syllogistic inferences, such as "a horse is an animal; therefore, the head of a horse is the head of an animal." Correct syllogisms are merely one form of valid deductions and hold no logical superiority over others. The attempt to privilege the syllogism in deduction misled philosophers regarding the nature of mathematical reasoning. Kant, recognizing that mathematics is non-syllogistic, concludes that it employs super-logical principles, which he nevertheless considers to be as determinate as the principles of logic. Like his predecessors, albeit in a different manner, Kant was misled by a reverence for Aristotle.

The overvaluation of deduction must also be addressed. The Greeks generally attributed greater significance to deduction as a source of knowledge than do modern philosophers. In this, Aristotle is not so much to blame as Plato; he repeatedly acknowledged the importance of induction and devoted considerable attention to how we establish the initial premises from which deduction must proceed. Nevertheless, he, like other Greeks, assigned an unduly high place to deduction in his theory of knowledge. We might agree that, say, Mr. Smith is mortal, and we can freely assert that we know this because we know that all men are mortal. Yet in reality, we do not know that "all men are mortal," but rather something like: "all men born more than one hundred and fifty years ago are mortal, and so are almost all men born more than one hundred years ago." This serves as our basis for believing that Mr. Smith will die. However, this proof is inductive rather than deductive. It possesses less persuasive power than deduction, yielding only probabilistic rather than certain knowledge; yet, on the other hand, it provides new knowledge that deduction does not furnish. All significant inferences outside of logic and pure mathematics are inductive rather than deductive; the sole exceptions are jurisprudence and theology, each deriving its foundational principles from an undisputed text, namely from a code of laws or from sacred scriptures.

Besides the "Prior Analytics," which treats of the syllogism, Aristotle's other logical works also hold significant importance in the history of philosophy. One of these is the brief treatise "Categories." The Neoplatonist Porphyry wrote a commentary on it, which exerted a notable influence on medieval philosophy. However, let us set aside Porphyry and limit ourselves to Aristotle.

What precisely is meant by the word "category" in the contexts of Aristotle, Kant, and Hegel is, I must confess, something I have never fully grasped. Personally, I do not believe that the term "category" can be of any utility in philosophy as it attempts to convey a clear idea. Aristotle lists ten categories: substance, quantity, quality, relation, place, time, position, state, action, and passion. Only a single definition of "categories" is provided: they are "expressions that do not denote anything complex in any way," followed by the aforementioned list. The essence of this definition seems to be that each word, whose meaning is not compounded from the meanings of other words, signifies an essence, or quantity, or something else. There are no indications of any principle upon which the list of ten categories was compiled.

Substance, above all, is that which cannot be either a predicate of any subject or reside within a subject. It is said that a thing "exists in a subject," and although it is not a part of the subject, it cannot exist without it. What examples are given? A sample of grammatical knowledge residing in the mind, and a certain whiteness that a body may possess. Substance, in the aforementioned primary sense, is an individual thing, a person or an animal. However, in a secondary sense, a species or genus, that is, "man" or "animal," may also be termed a substance. This secondary sense seems indefensible and has allowed later writers to embark upon a multitude of misguided metaphysical speculations.

The "Posterior Analytics" primarily addresses the question that should concern any deductive theory: how are initial premises obtained? Since deduction must derive from something, we must begin with something unproven, known in some manner other than through immediate demonstration. I shall not detail Aristotle's theory, as it relies on the concept of essence. A definition, he asserts, is a statement of the essence of the nature of a thing. The concept of essence has been an elusive part of every philosophical system since Aristotle, until we reach the modern era. I find this concept hopelessly confounding, yet its historical value compels me to say a few words about it.

Evidently, the concept of the "essence" of a thing refers to "those of its properties that cannot be changed without it ceasing to be itself." Socrates may sometimes be happy, sometimes sad; sometimes healthy, sometimes ill. Since these qualities, these properties, can change, and he does not cease to be Socrates, they do not constitute part of his essence. Yet it is assumed that Socrates' essence is that he is a man, though a Pythagorean who believes in the transmigration of souls would not accept this. In reality, the question of "essence" is a question of how to use words. We use the same name in various instances for quite diverse phenomena, which we regard as manifestations of the same "thing" or "person." In fact, however, this is merely a verbal convention. Socrates' "essence," therefore, consists of such properties that must be absent for the name "Socrates" to be applicable. This question is purely linguistic: a word may possess essence, but a thing cannot.

The concept of "substance," much like that of "essence," is a transference into the realm of metaphysics of what is merely a linguistic convention. In our descriptions of the world, we find it convenient to depict certain occurrences as events in the life of "Socrates," while others we categorize as events in the life of "Mr. Smith." This inclination leads us to think of "Socrates" or "Mr. Smith" as signifying something that exists over the course of many years, something that is, in a certain sense, more "durable" and "real" than the events that transpire with them. If Socrates is ill, we consider that at another time he is healthy; thus, the existence of Socrates does not depend on his illness. Conversely, the illness requires the existence of someone who is ill. However, while Socrates need not be unwell, something must indeed happen to him if he is regarded as existing. Therefore, in reality, he is no more "durable" than the events that occur to him.

Taking "substance" seriously gives rise to insurmountable difficulties. It is posited that substance is the bearer of properties, something distinct from all its properties. Yet when we discard these properties and attempt to conceive of substance in isolation, we find that nothing remains of it. Let us pose the question differently: what distinguishes one substance from another? It is not the difference in properties, for according to the logic of substance, a distinction in properties presupposes a numerical distinction between the "substances" under discussion. Thus, two substances must be precisely two, not being distinguishable by any means in and of themselves. How, then, can we ascertain that there are two?

In fact, "substance" is merely a convenient method of tying events together into cohesive units. What can we know about "Mr. Smith"? When we observe him, we perceive a specific arrangement of colors; when we listen to his speech, we hear a series of sounds. We believe that, like us, he harbors thoughts and feelings. But what is "Mr. Smith," taken apart from all these phenomena? Merely an imagined hook upon which, it is assumed, the phenomena should hang. In reality, such phenomena do not require a hook, just as the earth does not need an elephant upon which to rest. Anyone can observe from geography that a term such as "France" is but a linguistic convenience, and that there exists no entity called "France" beyond and apart from its various parts. The same applies to "Mr. Smith"; it is a collective name for a range of phenomena. If we take it to signify something more, it will denote something utterly unknowable and thus unnecessary for expressing what we know.

In summary, the concept of "substance" is a metaphysical error stemming from the transference of the structure of the world into the structure of a proposition composed of a subject and a predicate.

In conclusion, I assert that the doctrines of Aristotle that we have explored in this chapter are entirely false, save for the formal theory of the syllogism, which holds little significance. In our day, anyone wishing to study logic would waste their time by reading Aristotle or any of his disciples. Nevertheless, Aristotle's works on logic are testament to great talent and would have been beneficial to humanity had they emerged during a time when intellectual originality was still substantial. Unfortunately, they appeared at the tail end of the creative period of Greek thought, and thus were accepted as undisputed tenets. By the time originality in logic was revived, two millennia of Aristotelian dominance made it exceedingly difficult to dethrone it. Throughout the entire modern era, practically every advancement in science, logic, or philosophy has had to be wrested from the resisting followers of Aristotle.