Logical thinking, formal thinking in general, is constructed on the basis of the deductive method, proceeding from a more general syllogism through a number of premises to the necessary conclusion. Such a chain of syllogisms is called a sorites.

– Trotsky, Writings, 1939-40

Aristotle was the first one to write a systematic account of both dialectics and formal logic, as methods of reasoning. The purpose of formal logic was to provide a framework to distinguish valid from invalid arguments. This he did in the form of syllogisms. There are different forms of syllogism, which are really variations on the same theme.

Aristotle in his Organon, names ten categories – substance, quantity, quality, relation, place, time, position, state, action, passion – which form the basis of the dialectical logic, later given its full expression in the writings of Hegel. This side of Aristotle’s work on logic is frequently ignored. The British philosopher Bertrand AW Russell (1872-1970), for example, considered these categories to be meaningless. But since logical positivists like Russell have written off practically the whole history of philosophy (except the bits and pieces that coincide with their dogmas) as “meaningless”, this should neither surprise nor trouble us too much.

The syllogism is a method of logical reasoning, which may be variously described. The definition given by Aristotle himself was as follows: “A discourse in which, certain things being stated, something other than what is stated follows of necessity from their being so.” The simplest definition is given by AA Luce: ” A syllogism is a triad of connected propositions, so related that one of them, called the Conclusion, necessarily follows from the other two, which are called the Premises.“[49]

The mediaeval Schoolmen focused their attention on this kind of formal logic, which Aristotle developed in The Prior and Posterior Analytics. It is in this form that Aristotle’s logic came down from the Middle Ages. In practice, the syllogism consists of two premises and a conclusion. The subject and the predicate of the conclusion each occur in one of the premises, together with a third term (the middle) that is found in both premises, but not in the conclusion. The predicate of the conclusion is the major term; the premise in which it is contained is the major premise; the subject of the conclusion is the minor term; and the premise in which it is contained is the minor premise. For example,

a) All men are mortal. (Major premise)
b) Caesar is a man. (Minor premise)
c) Therefore, Caesar is mortal. (Conclusion)

This is called an affirmative categorical statement. It gives the impression of being a logical chain of argument, in which each stage is derived inexorably from the previous one. But actually, this is not the case, because “Caesar” is already included in “all men”. Kant, like Hegel, regarded the syllogism (that “tedious doctrine”, as he called it) with contempt. For him, it was “nothing more than an artifice” in which the conclusions were already surreptitiously introduced into the premises to give a false appearance of reasoning.[50]

Another type of syllogism is conditional in form (if…then), for example: “If an animal is a tiger, it is a carnivore.” This is just another way of saying the same thing as the affirmative categorical statement, i.e., all tigers are carnivores. The same in relation to the negative form –”If it’s a fish, it’s not a mammal” is just another way of saying “No fishes are mammals”. The formal difference conceals the fact that we have not really advanced a single step.

What this really reveals is the inner connections between things, not just in thought, but in the real world. “A” and “B” are related in certain ways to “C” (the middle) and the premise, therefore, they are related to each other in the conclusion. With great profundity and insight, Hegel showed that what the syllogism showed was the relation of the particular to the universal. In other words, the syllogism itself is an example of the unity of opposites, the contradiction par excellence, and that, in reality, all things are a “syllogism”.

The heyday of the syllogism was in the Middle Ages, when the Schoolmen devoted their entire lives to endless disputations on all manner of obscure theological questions, like the sex of angels. The labyrinthine constructions of formal logic made it appear that they were really involved in a profound discussion, when, in fact, they were arguing about nothing at all. The reason for this lies in the nature of formal logic itself. As the name suggests, it is all about form. The question of the content does not enter into it. This is precisely the chief defect of formal logic, and its Achilles’ heel.

By the time of the Renaissance, that great re-awakening of the human spirit, dissatisfaction with Aristotelian logic was widespread. There was a growing reaction against Aristotle, which was not really fair to this great thinker, but stemmed from the fact that the Church had suppressed all that was worthwhile in his philosophy, and preserved only a lifeless caricature. For Aristotle, the syllogism was only part of the process of reasoning, and not necessarily the most important part. Aristotle also wrote on the dialectic, but this aspect was forgotten. Logic was deprived of all life, and turned, in Hegel’s phrase, into “the lifeless bones of a skeleton”.

The revulsion against this lifeless formalism was reflected in the movement towards empiricism, which gave a tremendous impetus to scientific investigation and experiment. However, it is not possible to dispense altogether with forms of thought, and empiricism from the beginning carried the seeds of its own destruction. The only viable alternative to inadequate and incorrect methods of reasoning is to develop adequate and correct ones.

By the end of the Middle Ages the syllogism was discredited everywhere, and subjected to ridicule and abuse. Rabelais, Petrarch and Montaigne all denounced it. But it continued to trundle along, especially in those Catholic lands, untouched by the fresh winds of the Reformation. By the end of the 18th century, logic was in such a bad state that Kant felt obliged to launch a general criticism of the old thought forms in his Critique of Pure Reason.

Hegel was the first one to subject the laws of formal logic to a thoroughgoing critical analysis. In this, he was completing the work commenced by Kant. But whereas Kant only showed the inherent deficiencies and contradictions of traditional logic, Hegel went much further, working out a completely different approach to logic, a dynamic approach, which would include movement and contradiction, which formal logic is powerless to deal with.

  1. Luce, A. op. cit., p. 83 (our emphasis).

  2. Kant, I. Critique of Pure Reason, p. 99, footnote.