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IOE, The Analytic-Synthetic Dichotomy

by David Ross

Date: 26 Mar 1992
Forum: Moderated Discussion of Objectivist Philosophy
Copyright: David Ross

The final section of IOE is an essay by Leonard Peikoff entitled "The Analytic-Synthetic Dichotomy". In it, Peikoff presents the dichotomy and criticizes it, on the basis of the theory that Rand has developed in the prior 8 chapters. In this posting, my purpose is to discuss the dichotomy for the purpose of re-invigorating the discussion of it that was curtailed when the IOE project began: I shall rely on Peikoff's essay, but the central topic is the dichotomy itself, not Peikoff's analysis of it.

The analytic-synthetic dichotomy, according to its advocates, subdivides true propositions into two classes; those whose truth can be established simply by an analysis of the meanings of the constituent concepts, and those whose truth can be established only by checking the facts of the case, i.e., by consulting reality. The former are called analytic truths, the latter synthetic truths. A standard example of an analytic truth would be:

Ice is a solid.

An example of a synthetic truth would be:

Ice floats on water.

In order to complete these examples, let me supply a definition of 'ice', courtesy of Webster's Unabridged Dictionary

ice. the solid form of water.

Peikoff presents several features of the distinction between the two types of propositions, which I'll summarize.

a. To deny an analytic truth is to endorse a self-contradiction, but to deny a synthetic truth is merely to endorse a falsehood.

b. Analytic truths are necessary, they could not have been otherwise. Synthetic truths, by contrast, are contingent. States of affairs that contradict those described by synthetic truths are conceivable, or imaginable, or logically possible.

c. Analytic truths are independent of experience. Synthetic truths depend on experience, they must be established by reference to specific facts.

d. Analytic truths provide no information about reality, they follow from mere linguistic convention. Synthetic truths do provide information about reality, and are therefore unprovable.

It is advisable, when assessing a theory, to consult a presentation by its advocates. Detractors, no matter how well-intentioned, may find it difficult to give a convincing, objective presentation of the theory. After all, they think it's wrong. A lucid discussion of the dichotomy is given by John Hospers - an advocate - in "An Introduction to Philosophical Analysis" (1953, p.90). The exchange between Hospers and Tibor Machan, an Objectivist, in The Personalist, may also be of interest (Hospers, 1970. Machan, 1970). An unbiased and characteristically clear presentation is contained in Jones's book (1970, Chap. 2), in the context of a discussion of Kant's attempt to refute Hume's skepticism.

Before we begin, let me try to clarify the point of disagreement. Certainly, once one has defined a concept, it is possible to distinguish between properties that the concept's referents have in virtue of the concept's defining characteristic(s), and other properties. It is even simpler to identify propositions that are essentially restatements of the definition - analytic statements. The point at issue is whether this distinction has any real cognitive significance. The onus here falls on the advocates of the dichotomy. As Machan (1970, p.249) has put it, regarding logical possibility, 'What Hospers & Co. must do is show that the distinction they are opting for does in fact serve to differentiate two radically different kinds of possibilities, while showing that both are still possibilities proper. To date, they have not done so'.


The crucial point on which Objectivists, and many other Aristotelians, differ from advocates of the dichotomy is the question of what constitutes the meaning of a concept. Advocates of the dichotomy hold that the definition of a concept specifies its meaning in its entirety. Objectivists hold that the units integrated by the concept constitute its meaning. I'll say more about this in the final section, here I'll just focus on the relation of definitions to concepts.

Let us look in on a group of Aristotelians working at defining the concept 'man'. One suggests that 'entity' should be the genus. Another points out that, while it's true that men are entities, this is too broad a genus. "Living being" is then proposed and dismissed for the same reason. After "animal" has been discussed, analyzed, and accepted as the genus, they go on to the differentia. Here, abundant proposals are made. The use of language, erect posture, the use of tools, the ability (or need) to blush, the possession of a rational faculty, the playing of symphonies, the appreciation of baseball, and some other properties of man, are suggested as differentia. All of these, it is agreed, are in fact properties of man. Some, however, are not unique to man, and thus are disqualified as differentia. For example, a biologist points out that wild chimps have been found to fashion and use tools. Other properties, e.g., language-having, baseball-loving, and music-playing, are rejected because they fail the test of fundamentality (Rand, 1990, p.45); in fact, they can be explained by another property that has been proposed. Rationality begins to look like the best candidate. But an anthropologist points out that this property is not unique to the creatures we call 'men', that a rudimentary form of rationality was possessed by Neanderthals. Some discussion of context ensues, and it is decided that while specialists may have to distinguish between homo sapiens neanderthalenis and homo sapiens sapiens, this is unnecessary for the average man. "The rational animal", it is agreed, is the proper definition of "man".

The point of this story in the context of the analytic-synthetic dichotomy is that an immense amount of information about the units subsumed by a concept must be analyzed in the process of arriving at a definition of the concept. The truth of propositions such as 'men use tools', 'so do chimps', 'men play music', 'men have the capacity to blush' and our ability to know that these propositions are true, precedes the construction of a definition. In fact, the genus/species structure of a definition and the rule of fundamentality require that we be able to identify relationships between the units of a concept and units of other concepts, and that we be able to identify causal dependencies between properties of units, before we can make a definition. "A definition is a condensation of a vast body of observations-and stands or falls with the truth or falsehood of these observations" (Rand, 1990, p.48).

Given the priority of this "vast body of observations", there seems to be no basis for attributing to a concept's definition and restatements of it, some preferred 'truth' status.


On several occasions, I've heard it suggested that the statement "A is A", the propositional-form shorthand for the law of identity, is an analytic truth or "tautology" that Objectivists take as a starting point for formal deduction. It is not. In the context of logic, it is a formal statement of the law of identity, an abstract identification of the form that true propositions take. A true proposition about an existent - "A" - will say of this existent that it is one or more of the things that, in fact, it is: "Man is a mortal animal", "Man is a rational animal","Man is gravitationally attracted to the earth",...

On the correspondence theory of truth, the proposition "Man is a rational animal" is true because the referents of the concept "man" do, in fact, have the property of rationality, just as the proposition "man is gravitationally attracted to the earth" is true because the referents of the concept "man" are, in fact, gravitationally attracted to the earth. Let us imagine someone who utters the sounds "Man is a rational animal", and who claims that this is true because the definition of "man" is "a rational animal", so that his utterance implicitly has the form "A rational animal is a rational animal" or "A is A". If his claim for the truth of his utterance is based solely on its form, and not on any correspondence to fact, then I should say that he is mistaken. Truth and Falsity are properly predicated of propositions in virtue of their correspondence (or failure thereof) to reality. If this fellow has constructed an utterance that conforms to some formal rules, intending no reference to reality, then he is engaged in an endeavor in which truth and falsity play no role.


One piece of evidence that advocates of the dichotomy offer for its legitimacy is the 'imaginability' or 'conceivability' of the opposite of a synthetic truth. We can imagine, they say, an ice cube sinking in water, or a lead bar floating on it, or a cat giving birth to pups, but we cannot imagine ice that is not solid, or a cat that is not a carnivore (cat. any of several carnivores of the family Felidae. (Again, thanks to Webster)). Initially, there is a certain persuasiveness to this argument. Indeed, we could, for example, construct an animated cartoon of what would look like an ice cube sinking in water, or a cat giving birth to pups. We could not construct such a cartoon presenting something that would look like non-solid ice. However, the objection to this argument is clear. Why should we regard imagination as the arbiter of logical classification? Our ability to 'imagine' an ice cube sinking in water says nothing about the nature of ice and water.

Peikoff (Rand, 1990, p.116) points out that "In a serious, epistemological sense of the word, a man cannot conceive the opposite of a proposition he knows to be true (apart from propositions dealing with man-made facts)". Indeed, in order for us to understand just what is intended by this 'argument from imagination', its advocates would have to clarify and define terms like 'imaginable' and 'conceivable'. (Worthwhile insights on this point are presented by Machan (1970) and Rasmussen (1983).) Let us consider the example of ice sinking in water. Given my knowledge that the specific gravity of ice is less than that of water, and my further knowledge that a solid of a given specific gravity will not sink in a liquid of greater specific gravity (I am not going to bother with a detailed specification of the experimental conditions), in what would it consist for me to 'imagine' a piece of ice sinking in water? Just what cognitive machinations must I perform in order to 'imagine' sinking ice, given my knowledge of the physics of the situation?

Now let us look at the issue from another perspective. Presuming that we can 'imagine' ice sinking, why can we not 'imagine' non-solid ice, or a married bachelor, or a four-sided triangle? (Douglas Rasmussen (1983, p.531) develops this line of thought nicely, illustrating it with a picture of a four-sided triangle!) If we are taking our ability to form mental images - not our knowledge of the actual properties of entities - as the standard of 'logical possibility', on what basis can it be argued that it is impossible to imagine, say, non-solid ice? Suppose I claim to have in my mind a mental picture of a piece of non-solid ice. Before you tell me that I can't have such a mental image, ask yourself whether your objection is based on the nature and inherent capacity of my imagination, or on what you know about ice. If you are invoking facts about ice, then you are not taking our ability to form mental images as the standard of 'logical possibility'.


Views on the validity of the analytic-synthetic dichotomy reflect views on the larger question of just what logic is. Advocacy of the dichotomy implies a view of logic as restricted; claims such as that the sinking of ice in water is 'logically possible' although it is, in fact, impossible, imply that there is some cognitive mechanism other than logic through which we become aware of the actual impossibility of ice sinking. This is contrary to the Objectivist, and more generally the Aristotelian view of what logic is.

According to Ayn Rand (1961, p.125), logic is "The art of non- contradictory identification". This is consonant with the traditional Aristotelian designation of logic as the "Organon", the instrument of human knowledge (see, e.g., Veatch, 1974, p. 162). Logic, as an art, is the skill of acquiring knowledge of reality. This skill involves, not just some limited techniques, e.g. deductive inference, but the full range of rational endeavor, including things like concept formation, definition construction, inductive generalization, integration of ideas, and reduction of ideas to perceptual data. To stress this point, let me say that in this context, I should include applied mathematics - the art of identifying quantitative relationships - as a subfield of logic.

Logic as a science studies the structures and techniques that are the means of non-contradictory identification. It studies things like concepts, propositions and arguments. Aristotelians, notably the modern philosopher Henry Veatch (1952), use the concept "intention" to analyze the nature of logic. Concepts, propositions, and arguments are "intentions" or "formal signs" (Veatch, 1952, p.11); their entire identity consists in signifying something else. A formal sign, e.g., a concept, is distinguished from an instrumental sign, e.g., a traffic sign. To become aware of the significatum - say a sharp curve in the road - of the traffic sign, an instrumental sign, one must first become aware of the sign itself. However with a formal sign, say a concept, awareness of the sign IS awareness of its significata. The concept is nothing but the instrument of our awareness of its referents. Rasmussen (1983, p. 534) has summed this up nicely; "concepts do not have meanings; they are meanings". Peikoff (1990, p.98) puts it similarly "the meaning of a concept consists of the units - the existents - which it integrates, including all of the characteristics of these units".

On this view, there is no justification for the analytic-synthetic dichotomy.


There is much to say on the topic of the analytic-synthetic dichotomy, I have said very little of it. In particular, there are several arguments made by the dichotomy's advocates, and several distinctions that are drawn by them, of which I am aware, but which I've chosen not to address (those of you who consult Hosper's paper (1970) will encounter some of these). Time is limited. I just wanted to point out, to devotees of such arguments and distinctions, that my intention was not to construct a straw man, and if you think I've done so, please present your view and we'll take it from there.


Hospers, J., An Introduction to Philosophical Analysis, Englewood Cliffs, Prentice-Hall, 1953.

Hospers, J., Reply to Mr. Machan on 'Logical Possibility', The Personalist, 51, 1970.

Jones, R.T., A History of Western Philosophy IV: Kant and the Nineteenth Century, San Diego, Harcourt, Brace, Jovanovich, 1975.

Machan, T., Another Look at 'Logical Possibility', The Personalist, 51, 1970.

Rand, A., Introduction to Objectivist Epistemology. New York, Meridian, 1990.

Rand, A., For the New Intellectual. New York, Meridian, 1961.(Reprint of Galt's Speech)

Rasmussen, D., Logical Possibility, an Aristotelian Essentialist Critique. The Thomist, 47, 1983.

Veatch, H. B., Aristotle, Bloomington, Indiana University Press, 1974.

Veatch, H. B., Intentional Logic, New Haven, Yale University Press, 1952.

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