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The answer to the “problem of universals” lies in Ayn Rand’s discovery of the relationship between universals and mathematics. Specifically, the answer lies in the brilliant comparison she draws between concept-formation and algebra.
This is more than a mere comparison, as she shows, since the underlying method in both fields is the same.
The basic principle of concept-formation (which states that the omitted measurements must exist in some quantity, but may exist in any quantity) is the equivalent of the basic principle of algebra, which states that algebraic symbols must be given some numerical value, but may be given any value. In this sense and respect, perceptual awareness is the arithmetic, but conceptual awareness is the algebra of cognition.
The relationship of concepts to their constituent particulars is the same as the relationship of algebraic symbols to numbers. In the equation 2a = a + a, any number may be substituted for the symbol “a” without affecting the truth of the equation. For instance: 2 x 5 = 5 + 5, or: 2 x 5,000,000 = 5,000,000 + 5,000,000. In the same manner, by the same psycho-epistemological method, a concept is used as an algebraic symbol that stands for any of the arithmetical sequence of units it subsumes.
Let those who attempt to invalidate concepts by declaring that they cannot find “manness” in men, try to invalidate algebra by declaring that they cannot find “a-ness” in 5 or in 5,000,000.
For centuries, rationalist philosophers have venerated mathematics as the model of cognition. What they have admired about the discipline is its deductive method. Objectivism, too, regards mathematics as an epistemological model, but for a different reason.
The mathematician is the exemplar of conceptual integration. He does professionally and in numerical terms what the rest of us do implicitly and have done since childhood, to the extent that we exercise our distinctive human capacity.
Mathematics is the substance of thought writ large, as the West has been told from Pythagoras to Bertrand Russell; it does provide a unique window into human nature. What the window reveals, however, is not the barren constructs of rationalistic tradition, but man’s method of extrapolating from observed data to the total of the universe.
What the window of mathematics reveals is not the mechanics of deduction, but of induction. Such is Ayn Rand’s unprecedented and pregnant identification in the field of epistemology.
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How, then, do we know that man has volition? It is a self-evident fact, available to any act of introspection.
You the reader can perceive every potentiality I have been discussing simply by observing your own consciousness. The extent of your knowledge or intelligence is not relevant here, because the issue is whether you use whatever knowledge and intelligence you do possess. At this moment, for example, you can decide to read attentively and struggle to understand, judge, apply the material — or you can let your attention wander and the words wash over you, half-getting some points, then coming to for a few sentences, then lapsing again into partial focus. If something you read makes you feel fearful or uneasy, you can decide to follow the point anyway and consider it on its merits — or you can brush it aside by an act of evasion, while mumbling some rationalization to still any pangs of guilt. At each moment, you are deciding to think or not to think. The fact that you regularly make these kinds of choices is directly accessible to you, as it is to any volitional consciousness.
The principle of volition is a philosophic axiom, with all the features this involves. It is a primary — a starting point of conceptual cognition and of the subject of epistemology; to direct one’s consciousness, one must be free and one must know, at least implicitly, that one is. It is a fundamental: every item of conceptual knowledge requires some form of validation, the need of which rests on the fact of volition. It is self-evident. And it is inescapable. Even its enemies have to accept and use it in the process of any attempt to deny it. Let us see why…
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There is no question more crucial to man than the question: what is man? What kind of being is he? What are his essential attributes?
Many thinkers and artists have sought to answer this question. They have looked at men and then offered a report on man’s nature. Their reports have clashed through the ages. Aristotle defined man as the “rational animal.” Plato and the medievals described other-worldly souls trapped in a bodily prison. Shakespeare dramatized man as an aspiring but foolish mortal, defeated by a “tragic flaw.” Thomas Hobbes described a mechanistic brute. Kant saw man as a blind chunk of unreality, in hock to the unknowable. Hegel saw a half-real fragment of the state. Victor Hugo saw a passionate individualist undercut by an inimical universe. Friedrich Nietzsche saw a demoniacal individualist run by the will to power. John Dewey saw a piece of flux run by the expediency of the moment. Sigmund Freud spoke of an excrement-molding pervert itching to rape his mother.
Ayn Rand looked at men and saw…
Excerpt
Those who reject the principle of selfishness will find in the history of ethics two main alternatives. One is the primordial and medieval theory that man should sacrifice himself to the supernatural. The second is the theory that man should sacrifice himself for the sake of other men. The second is known as “altruism,” which is not a synonym for kindness, generosity, or good will, but the doctrine that man should place others above self as the fundamental rule of life.
I shall not attempt in this book to identify the contradictions and evils of these two theories. Ayn Rand has covered this ground too well — in theory, in practice, in history, and from every aspect I can think of. If her works have not already convinced you that the morality of self-sacrifice is the morality of death, nothing I can add will do so, either.
I shall confine myself here to one polemical observation.
The advocates of self-sacrifice, in either version, have never demanded consistency. They have not asked men to sacrifice their goods, pleasures, goals, values, and ideas as a matter of principle. Even the saints had to eschew such a course, which would be tantamount to instant suicide. The moralists of self-lessness expect a man to go on functioning, working, achieving — else he would have no values to give up. They expect him to exercise his mind for his own sake and survival, and then to deny his judgment as the spirit moves them. They expect him to be ruled by whim, the whim of the relevant authority or beneficiary, whenever it injects itself into the process and demands to be paid off.
These moralists expect you to live your life on a part-time basis only, while trying to get away on the side with sundry acts of self-immolation, just as drug addicts pursue some regular nourishment while trying to get away with their periodic fixes.
Neither of these contradictions, however, is practicable. Man’s life does require adherence to principle. Nor is the above a distortion of the theory of self-sacrifice. It is what that theory actually means. Short of suicide, this is all that can be denoted in reality by the notion of a living entity practicing “anti-egoism.”…
