The assault on man’s conceptual faculty has been accelerating since Kant, widening the breach between man’s mind and reality.  The cognitive function of concepts was undercut by a series of grotesque devices—such, for instance, as the “analytic-synthetic” dichotomy which, by a route of tortuous circumlocutions and equivocations, leads to the dogma that a “necessarily” true proposition cannot be factual, and a factual proposition cannot be “necessarily” true.


The above quotation is from Ayn Rand’s Introduction to Objectivist Epistemology (p. 77).  It seems apparent that Rand did not approve of Kant—a few pages later she likens his system to “a hippopotamus engaged in belly dancing” (p. 80).  My interest is not in defending Kant, but rather in examining the Objectivist criticism of the “analytic-synthetic dichotomy.

First of all, that is this dichotomy, in plain English?  Basically it is a distinction between two kinds of logic, deductive and inductive, and of the strengths and limitations of each.

Deductive logic consists of taking two or more statements and “deducing” their implications.  An example is the following:  “All Germans love music.  Mr. Schmidt is a German.  Therefore Mr. Schmidt loves music.”  There are other variations of the pattern, but for present purposes this one will do.

How does it work?  It is a process of working from the general to the specific.  You have two premises:  “All Germans love music,” the major, because more inclusive, premise, and “Mr. Schmidt is a German,” the minor, less inclusive, premise, followed by the conclusion, “Mr. Schmidt loves music.”  If the premises are true the conclusion has to be true.  There is no other possibility.  That is the strength of deductive reasoning; the conclusions are certain.  Its weakness is that it is concerned only with the implications of statements, not with whether they are true or false.  If one of the premises is false—if, for instance, Mr. Schmidt is actually a Czech—then the conclusion is false, although I suppose we must allow for music-loving Czechs.

Inductive works in precisely the opposite way, from the specific to the general.  If twenty times in a row your dog barks when the doorbell rings, you conclude that he will bark every time the doorbell rings.  Your conclusion is not necessarily correct.  If on the twenty-first ring, or the thirty-third ring, the dog merely raises his head, looks bored and goes back to sleep, then your conclusion is false.  However, if the conclusion is correct then it becomes a means of predicting the dog’s future behavior.  Its predictive power is its strength.

This is pretty much the standard views of deductive and inductive logic, the sort of thing you would most probably hear in an introductory college course in philosophy.  The differences seem fairly obvious—except that the Objectivists want to argue that there are no grounds on which to distinguish “analytic” (read “deductive”) from “synthetic” (read “inductive” or “empirical”) propositions.”  Witness the following quotation from an article by Leonard Peikoff in the same book:


Whether one states that “A man is a rational animal,” or that “A man has only two eyes”—in both cases, the predicated characteristics are true of man and are, therefore, included in the concept “man.”  The meaning of the first statement is: “A certain type of entity, including all its characteristics (among which are rationality and animality) is:  a rational animal.”  The meaning of the second is:  “A certain type of entity, including all of its characteristics (among which is the possession of only two eyes) has:  only two eyes.”  Each of these statements is an instance of the Law of Identity; each is a “tautology”’ to deny either is to contradict the meaning of the concept “man,” and thus to endorse a self-contradiction. (p. 100)


Note that Peikoff begins by designating “man” as a “concept”—not, of course, “man” as an actual physical object but “man” as an idea.  So what is a “concept” when it’s at home?  A “concept” is first of all an intellectual construct.  It doesn’t exist as an object in the world but as a thought in the mind.  And most concepts, including the concept of “man,” are intellectual grab bags of empirical observations, things we learned at our mother’s knee, prejudices, etc.  Probably my concepts differs from yours in lots of significant ways, simply because my experience of life has been different from yours.  Our concepts are private accumulations, like the contents of our attics, only of ideas rather than of furniture and luggage.

I remember my mother telling me, when I was very young, that “most people are honest.”  This is part of my grab bag of ideas about “man.”  It exists in my mind as an empirical observation, the accuracy of which is open to question.

The point is that all of our notions of “man” are, at least in theory, empirical propositions which are subject to confirmation and rejection on the basis of subsequent experience.  They are not part of a “definition.”

Now let’s take a look at the two statements in question.  “A man is a rational animal” is presented as a purported example of a definition and “A man has only two eyes” is presented as a purported “synthetic” (read “inductive” or “empirical”) proposition.

The initial statement, “A man is a rational animal” is not a very good definition because, in the first place, a person born severely retarded is not capable of reason but is still human, and, in the second, man may not be the only rational animal.  There is a certain amount of evidence that whales are capable of higher intellectual functions.  This may be true or it may be false—since none of us have much of a command of Whalese it’s hard to say—but it is certainly possible, in which case either whales are human or the definition of man as a “rational animal” is not defining of that class of creatures which are human.

Rand addresses this particular problem, not with reference to whales but to “a Martian who had a rational mind, but a spider’s body,” and her conclusion is that “the differences between him and man would be so great that the study of one would scarcely apply to the other and, therefore, the formation of a new concept to designate the Martians would be objectively mandatory.” (p. 73)  The problem is that previously she had posited “A rational animal” as “the one and only valid definition of man, within the context of his knowledge and of all mankind’s knowledge to date.” (p. 44)  So, according to that definition the rational Martian is a man:


“Man” is defined as “a rational animal.”

A Martian is a “rational animal.”

Therefore a Martian is a “man.”



There is no evading the conclusion—and what would be required in this instance is a new concept of “man,” not of the Martian.  Rand’s conclusion is the triumph of wishful thinking over logic.

In the second statement, it is possible to imagine someone being born with one eye or even three or more.  I have seen a photograph of an Indian baby who was born with two faces and four eyes.  In her village she was worshipped as the incarnation of some Hindu goddess.  Since the baby is human the statement fails as both a definition and an empirical proposition.

But neither of these little collisions with reality are the main problem with the Objectivists’ attempt to blur the distinction between deductive and empirical statements.  In fact, both of these statements are empirical.  That man is a rational animal had to have started as an observation, probably dating from about the time that someone somewhere arrived at an understanding of what reason might be.  That man has only two eyes was also something observed, possibly only after we first climbed down from the trees—possibly even before.

The problem is that deductive and inductive logic are two different types of operations and yield two different kinds of results.  And a definition is neither the one nor the other. 

As an example of the character of deductive logic, consider the following syllogism:


      Major Premise:            All Porphidliae are gnorcatious.

      Minor Premise:            Borphatz is a Porphidlia.

      Conclusion:                 Borphatz is gnorcatious.


You don’t know what these words mean?  Neither do I and I made them up.  The point is that as “concepts,” if you insist on using such terminology, they are entirely empty.  They don’t have any referents.  However, the syllogism is still perfectly valid.  The conclusion is unarguable.

This is the nature of deductive logic.  It isn’t about the qualities or contents of  either “existents” or “concepts,” only about the implications of statements.  “Prophidliae” (the plural form) are defined as being “gnorcatious.”  “Borphatz: is defined as being “Porphidlia.”  Therefore “Borphatz” is “gnorcatious.”  If the major and minor premises are accepted, even if they are meaningless, then the conclusion has to be true.  Its truth is dependent on nothing outside the closed system of the syllogism itself.

How does this different from mathematics?  It doesn’t, because mathematics uses a range of “concepts” which do not exist in the world of experience.  For instance, in geometry a “line” is defined as having only one dimension.  It has neither width or depth, only length.  We have no real world experience of “lines” so defined because it is impossible to imagine an object that isn’t three-dimensional.  The same is true of numbers.  We have all seen two of something, but there is no object in reality which is simply “two.”

Mathematics is a useful tool, but, being deductive, it is not necessarily perfect as a description of the world of experience.  For instance, consider the Greek pre-Socratic Zeno’s paradox about the arrow shot at a tree.  The arrow goes half the distance, then half the remaining distance, etc.  The point is that the arrow approaches the tree but never hits it.  The distance between the arrow’s point and the surface of the tree becomes infinitesimally small but never entirely disappears.

Zeno thought he was demonstrating that motion is an illusion; however, since we all know that, unless the archer is simply a bad shot, the arrow does reach the tree, what he did demonstrate is that mathematics cannot be accepted as, in every case, a model for understanding reality.  It has been pretty clear, at least since Russell and Whitehead, that mathematics is a subspecies of deductive logic, and as Einstein said, “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”  Mathematics, strictly speaking, is not about the world.  It is about itself.

So deductive logic simply works out the implications of concepts and definitions.  It does not generate information about the world.  Doing that is the province of inductive logic.

By way of explanation, allow me to tell a story.  The high school I attended was in another town, several miles away from where I lived.  Therefore, at least until I got my driver’s license, I had to ride my bicycle down to El Camino Real (a distance of 1 mile, if you must know) and then wait at the bus stop.  When this routine first started I worried a lot about missing the bus.  What if it came early?  But even at thirteen it didn’t take very long for me to figure out that the bus wasn’t going to come early.  This conclusion was the result of observation.  I would arrive at the bus stop early and the bus would show up either right on time or a few minutes late.  Day after day after day.

This is how inductive reasoning operates.  If a particular phenomenon repeats itself a given number of times you begin to think that this is a pattern which will go on into the future.  It was of course always logically possible that one day the bus would arrive early, but it never did.  Probably to this moment, over fifty years later, the bus is still arriving at my bus stop either on time or late.

Induction is predictive, and the power to predict how events will unfold has been our key to the whole enterprise of being human.

Of course, as I said, the bus may one day arrive early.  A conclusion arrived at inductively can always be disproved by further evidence.  The history of science is full of examples of conclusions that turn out to the false, or, at least, in need of modification.  Newtonian physics held sway for well over two hundred years, and then along came Einstein.

But does it matter that a scientific and/or observational conclusion cannot be “necessarily” true?  I think not.  I personally have no doubts about, for instance, the law of gravity—I don’t expect to start floating up toward the ceiling anytime soon.  The inductive method does not require anyone to doubt a well-established conclusion, only the accept the logical possibility that some future information might refute it.

Although it was not codified in the West until the 19th Century, inductive reasoning was understood and studied in the Arab world as early as the 12th Century.  It is not only the logic of science; it is one of the basic patterns of human thought, one all of us use every day of our lives.  It is how our understanding of reality was and is generated.  It is the means by which we form our expectations about the world.

Consider once again the Objectivist definition of “man” was a “rational animal.”  As we’ve already seen, such a definition may need to be revised, just as the definition of man as a “tool maker” had to be revised after Jane Goodall observed chimpanzees stripping tree branches to make something with which to probe into ant hills.  Probably definitions of “human” (I prefer that term) based on behavior are always going to be a little dodgy.  Probably the only defining property of human beings is the genetic pattern encoded in their DNA, which was something discovered, via the scientific (read “inductive”) method only as long ago as the mid 20th Century.

And remember the Objectivist argument quoted above, to the effect that the statement “man has only two eyes” “is an instance of the Law of Identity” and as such is “a ‘tautology’” to deny which “is to contradict the meaning of the concept ‘man,’ and thus to endorse a self-contradiction.”  These days, at least if you’re an Objectivist, you may consider it a tautology to say “man has a particular DNA structure,” but that certainly wasn’t the case in 1953.  No discovery starts out as a tautology.  To argue that there is no difference in kind between conclusions arrived at deductively and inductively is simply absurd.

So why do the Objectivists make an issue out the analytical-synthetic distinction?  It is only in the Conclusion of his essay that Peikoff absolutely spills the beans on that score:


The ultimate result of the theory of the analytic-synthetic dichotomy is the following verdict pronounced on human cognition:  if the denial of a proposition is inconceivable, if there is no possibility that any fact of reality can contradict it, i.e. if the proposition represents knowledge which is certain, then it does not represent knowledge of reality.  In other words, if a proposition cannot be wrong, it cannot be right.  A proposition qualifies as factual only when it asserts facts which are still unknown, i.e., only when it represents a hypothesis; should a hypothesis be proved and become a certainty, it ceases to refer to facts and ceases to represent knowledge of reality.  If a proposition is conclusively demonstrated–so that to deny it is obviously to endorse a logical contradiction—then, in virtue of this fact, the proposition is written off as a product of human convention or arbitrary whim. (pp. 118-19)


This is a grotesque distortion of the empirical method.  The very point of an empirical proposition is that it is predictive, that “it asserts facts which are still unknown.”  It is confirmed not only by the data that led to his formulation but by all future data that can fall within the proposition’s range.  If future data contradict it, then it has either to be revised or discarded.  The history of science is a chronicle of propositions being either confirmed or denied by new information.  An empirical proposition can reach a point at which so much confirming data has accumulated that no one doubts its validity, but it can never be “conclusively demonstrated.”  It cannot become  absolutely certain the way a mathematical proposition is certain.  There is always at least the logical possibility that new information will overthrow it.

But what the above quotation does make clear is that the Objectivists will settle for nothing less than absolutely certain knowledge of reality.  They won’t settle for the truth of experience.  They want metaphysical truth.  As Peikoff goes on to say:


We can know only the “phenomenal,” mind-created realm, according to Kant; in regard to reality, knowledge is impossible.  We can be certain only within the realm of our own conventions, according to the moderns; in regard to facts, certainty is impossible. (p. 120)


Kant receives a lot of bad press from the Objectivists, so it might be worthwhile to summarize  his conclusions about the possibilities of knowledge.

Kant drew a distinction between the world as we experience it through the senses, which he called the “phenomenal” world, and the world as it actually is apart from our experience of it, which he called the “noumenal” world.  His point was that we can never know the precise relation between these two worlds.  They might be identical and they might not.  And the reason for questioning their identity is that there are certain ideas—time, extension, cause and effect, etc.—without which we are incapable of imagining what reality would be like.  What would a world be like without time?  What would objects be like if they didn’t have height, width and depth?  How can we imagine any event that simply happens of its own accord, without something acting as a cause?  These ideas seem to be hardwired into the human mind, so how do we know that they are properties of reality, properties of the world as it is apart from our experience of it, instead of ideas we bring to experience?  The answer is, we don’t.  We never can.  We are trapped in our senses, which are the only instruments through which we can approach reality.  We can only know the world as we experience it.

This view is to some degree confirmed by science that was unavailable to Kant.  Consider the case of sound.  Sound is a pattern of compression and decompression in the air or other media caused by a vibration of some sort.  The pattern in the air vibrates the ear drum, which causes the nerve cells to fire and send an electro-chemical signal to the brain.  We interpret his signal as sound, but is it not imaginable that it could be interpreted by the brain as something else?  We could experience it as some other sensory experience, such a sensation somewhere on the spectrum between pleasure and pain or as moving patterns visible in the air.  The point is that the nervous system interprets the vibration and what we experience is the interpretation, not the original stimulus.  Another example:  the human eye is only capable of registering a certain number of colors at a time—I think the number is 256, but I’m not certain.  Thus it is perfectly possible that our perceptions of the world don’t correspond the real qualities of objects in the noumenal world, to what Kant calls “the thing in itself” in ways we don’t recognize and may never be able to recognize.

Now, does any of this matter in our daily lives?  Apparently not.  We live in the phenomenal world, that “mind-created realm” as Peikoff calls it, and seem to be perfectly comfortable there.  Our senses seem to give us sufficiently accurate information to navigate.  And for Kant the problem presented by his phenomenal versus noumenal distinction lies not in scientific enquiry or getting to work on time but in the realm of metaphysics.  For instance, God.  We don’t have any sensory experience of God.  Moses apparently had conversations with him, but I never have and neither has anyone reading this article.  God, if we assume that He exists, is in the noumenal world and therefore outside of our experience and outside of our capacity to know anything at all about Him, with the result that all the statements theologians have been generating about Him over the past few thousand years are just so much gibberish.  In fact, by the prevailing canons of epistemology (a little thing called Ockham’s Razor, “don’t multiply entities beyond necessity”), since there is nothing in experience that requires us to assume His existence, we are bound to conclude that He does not exist.  However, Kant remained a good Lutheran all his life.  Go figure.

The Objectivists, on the other hand, want knowledge to be absolutely certain.  I conclude that they must think the world of experience precisely coincides with the world as it is in fact, apart from our experience of it.  But how do they know this?  So far as I am aware, no one has ever come up with a successful refutation of Kant’s argument.  The fact that Ayn Rand and her followers find it uncomfortable doesn’t constitute a refutation.  All the Objectivists seem able to do is ignore it, and that isn’t good enough.