The Liar Is a Thief

If a man contends that communication is impossible (and he is not speaking metaphorically or ironically) he contradicts himself, for he both affirms (in trying to communicate an idea) and denies (in what he tries to communicate) that communication is possible. This fallacy of generating a contradiction between use and meaning was discovered and identified by Ayn Rand who called it: "the fallacy of the stolen concept".

According to Objectivist epistemology, concepts are first formed by abstracting characteristics from percepts. Thereafter, concepts are integrated into wider concepts or subdivided into narrower concepts.1 Because of this process and because concepts are usually defined in terms of other concepts, concepts stand in hierarchical relationships, with concepts of irreducible primaries (such as "existence") and sensations — both of which are metaphysical primaries and are defined ostensively — standing at the base of man's knowledge — just as the referents of those concepts stand at the base of his experience. What is crucial for this essay is that the ordering of this hierarchy is logical, reflecting which concepts must be grasped before certain other concepts can be grasped.2 If a concept is to be meaningful, its presuppositions must be accepted while that concept is being used.

Since the whole of man's knowledge must conform to it, this principle is easily exemplified. The concept "to eat" presupposes and depends on the existence of such concepts as: "living being" and "hunger"; the concept "to lift" presupposes and depends on the existence of the concept "motion"; the concept "slavery" presupposes and depends on the existence of such concepts as: "man" "coercion", and "ownership". The nature of this dependence can be more thoroughly appreciated when one realizes that, for example, divorced from the concepts "man", "coercion", or "ownership", "slavery" would never arise and would be meanless. Even its metaphorical value would be lost. The concept "metaphorical" arises only in contradistinction to the concept "literal", and the two presuppose one another. Any metaphorical value of "slavery" derives from that concept's having literal content, and divorced from the mentioned concepts "slavery" can have no literal content. Generally, if a concept is dependent on another concept, the referent of the first is metaphysically dependent on the referent of the second. Thus, slavery could not exist if there were no men to do the enslaving, no coercion to be initiated by them, or no such thing as ownership claimed by men over men.

The presuppositions of a concept are like the goose of fairy-tales: when the goose was killed the golden eggs it produced vanished. The fallacy of the stolen concept consists in not accepting the appropriate presuppositions while using a concept, i.e. in killing the goose, but wanting to keep the eggs. It resembles the fallacy of circularity: circularity is the use of a concept to validate itself (e.g. defining lines and points in terms of coordinate systems, forgetting that coordinate systems presuppose lines and points), the stolen concept is the use of a concept to invalidate itself.

To examine the fallacy in closer detail, consider the statement "All concepts are stolen." This sentence commits the fallacy in at least three different ways: (1) A stolen concept is an invalid concept. If all concepts are stolen, then all concepts are invalid, from which it follows that the concept "stolen concept" is invalid. Since logic does not permit the use of invalid concepts, the speaker may not use the concept "stolen concept"; he has already affirmed its invalidity, and logically must agree that he ought not use it. (2) The concept "invalid concept" presupposes the concept "valid concept", to which it is intended to stand in opposition. If, as the sentence implies, there are no valid concepts, there would be no concepts from which to differentiate invalid ones; there would only be concepts, and the question of validity would never arise. Nevertheless, the statement relies on this distinction to obliterate one of the components of the distinction, thus obliterating entirely the distinction on which the statement depends. (3) The sentence itself can be intelligible only if it is composed of valid concepts, and this contradicts the content of the sentence. All these contradictions accrue because of a single fallacy, and because they do accrue, the sentence generating them is, to say the least, indisputably false.

One of the 'problems' posed in ancient philosophy is a subtle instance of the stolen concept called the "Liar Paradox". Its first formulation emitted from Epimenides the Cretan (c. 600 B.C.E.) who asserted: "All Cretans always lie." Actually this is not a paradox. To be sure, if the sentence is true a contradiction does result — for then all Cretans always lie, from which we can deduce that Epimenides the Cretan is lying, and his sentence is false, i.e., if it is true it's false — no paradox obtains if the assertion is false, as, we may be sure, it is.3 Other philosophers have 'corrected' Epimenides' error with such formulations as: "This sentence is false" (hereafter, TSIF). The Principle of Bivalence holds that all sentences are either true or false, but in either case a contradiction is alleged to result.4 If TSIF is true, what it says is true. What it says is that a certain sentence is false, so if it is true, that sentence is false. The sentence is TSIF, so if TSIF is true, TSIF is false. On the other hand, if TSIF is false, what it says is false. It says that a certain sentence is false, so if TSIF is false, the sentence of which it speaks is true. That sentence is TSIF, so if TSIF is false, TSIF is true. Thus, a contradiction results whether the sentence is true or false.

There have been a number of attempts to solve this paradox, to locate its origin and discover some principle the sentence violates. A ready 'solution' is the denial of the Principle of Bivalence, to assert that some sentences are neither true nor false, but have instead the status of requests, commands, etc. The error of this 'solution' is too obvious and mean to warrant discussion. Far more respectable was the solution of Diodorus Cronus, who, according to an apocryphal tale, hanged himself after failing to solve the paradox.

The 'solution' most widely accepted today is Bertrand Russell's theory of types, which asserts that a sentence must not be a part of the subject-matter of itself, i.e., a sentence must refer to a collection of things in which it is not included. This 'solution', however, commits the very error it should have corrected, and in so doing commits its adherents to the fallacy of self-exclusion. When a man talks about all men, he includes himself; likewise, a sentence about all sentences refers to itself. Type theory ignores this fact. The theory of types is expressed by the sentence: "All sentences must refer to collections of which they are not members, i.e., in which they are not included." But is that sentence to be bound by the theory of types, or can it refer to collections in which it is included? That it does refer to such a collection is incontrovertible; why then is it supposed to be exempt from the theory of types? Either it is included in the theory of types, in which case it violates the fundamental principle of the theory, or it is not included, in which case the principle it expresses is false, for it says that all sentences must have a certain characteristic which it, a sentence, does not have. If a sentence expressing type theory is true, type theory is false. It follows from that sentence's being the expression of type theory that if type theory is true, then type theory is false. Type theory cannot be proved, because to prove it, it must first be named, and to name it one must contradict himself. The type-theorist must hold a theory to be true while violating the fundamental principle of that theory. His assertion of the theory's nature contradicts that nature.

To uncover the Liar's secret, it is necessary to examine the concepts of which it makes use. These are: "particularity" (in the word "this"), "sentence" (and, hence, "language"), and "truth" and "falsity". The crucial concept, the one whose generic roots are denied, is: "sentence".

A sentence is an assertion. To assert is to assert as a fact. When one makes an assertion he claims what he asserts as fact, whether it is a fact or not. Such qualifications on assertions as expressions of belief, possibility, or probability do not alter this view. When one asserts that something is probably (or possibly) the case, he does not assert as fact that it is the case, but he does assert as fact that it probably (or possibly) is the case. If one asserts that he believes that something is the case, he does not assert as fact that it is the case, but he does assert as fact that he believes it. That to assert is to assert as fact makes such phrases as: "It is true that…." and "It is the case that…." redundant. Thus, TO ASSERT IS TO ATTRIBUTE TRUTH.

To attribute truth to that which is asserted does not, of course, guarantee that what is asserted is true; men are not omniscient and can mistakenly attribute characteristics to existents; truth, being a characteristic of some sentences, also may be mistakenly attributed. But there is no escaping the attributing of truth to a sentence that has been asserted; the attribution is entailed in the act of asserting. If this were not so the rejoinders "That's not true" and "That's false" would be senseless, for most assertions contain no explicit claim to to truth. Those rejoinders, however, even if not coherent as philosophical or scientific theses, are at least coherent as rejoinders, regardless of what sentence they are meant to contest.

That to assert is to attribute truth makes communication possible. Consider how rapidly man's knowledge and technology could advance if saying attributed falsity to what was said. If Einstein wished to publish his discovery that E equals mc², he would have to write "E does not equal mc²," and his assertion would impute falsity to the published claim. A fellow physicist would read "E does not equal mc²" and would think: "Aha, since he has said it he means it to be false, so he means that E does equal mc². But since I've said that, I mean that he doesn't mean that E equals mc²…." It readily becomes apparent that if to assert were to attribute falsity, man could never encounter this particular problem: he could never even reach a level of knowing what "E" stood for; or even learn that to assert was to attribute falsity. No man could ever consider another's ideas because no one could think about his own ideas long enough to discover in what form he should express them that others might consider them.

Even if only some sentences were such that to assert them were to attribute falsity to them, rational discourse would be impossible, for there would be no means of discovering which sentences were and which sentences were not of the nature that to assert them was to attribute falsity to them. Any principle distinguishing these would itself be open to the question of whether to assert it was to attribute falsity to it; the principle itself could not be invoked to answer this question, since what an assertion of the principle meant would be what was in question. The same difficulty would obtain with respect to any principle answering this latter question. Moreover, any sentence of such a nature that to assert it was to attribute falsity to it would be closed to consideration because of the regress that would inherently accompany any attempted consideration. This would be tantamount to asserting that the truth of such a sentence is unknowable in principle, a self-contradictory claim.5

Nor can it be that the asserting of a sentence attributes neither truth nor falsity to the asserted sentence. In that case, one could never express agreement or disagreement; he would have no way of knowing whether his agreement was with the assertion as true or as false (and likewise for disagreement), since, as has been said, most assertions contain no explicit claim to truth or falsity.

There is yet another important implication of assertions. From any assertion that something is it follows that it is possible (if it were not possible, it could never have been). From an assertion that two different things are the case, it follows that they both be the case. Since to assert that something is and that it is not (at the same time in the same respect) is to assert a contradiction, it follows that to so assert is to assert that contradictions. Because contradictions are not possible, the assertion of a contradiction is false.

With the foregoing knowledge at hand, the Liar can be successfully cross-examined. The content of "This sentence is false" asserts that a particular sentence is false; at the same time, the nature of the sentence attributes truth to that same sentence. The sentence therefore says that one and the same sentence is both true and false. It asserts a contradiction, from which it follows that contradictions are possible. But since contradictions are not possible, the sentence is false. Contrary to an earlier argument, it does not follow from TSIF's being false that TSIF is true. That resulted from the position that since the sentence is false, what it says is false, and that it says a particular sentence is false. But that is not all TSIF says! It says that a particular sentence is true and that that sentence is false. To infer from TSIF's asserted truth and falsity that TSIF is true is just illicit. Analogous would be the argument that, since it is false that God exists and so does the world, God exists (or: the world doesn't exist). The Liar can therefore be judged to be false without generating any paradox.

The Liar has taken many guises, and this analysis is adequate to deal with them all. One is:

G: Sentence H is false.
H: Sentence G is true.

G, a sentence, asserts: (a) that G is true (because it is an assertion and truth must be attributed to it), (b) that H is false, from which it follows (c) that G is false. G thus asserts a contradiction and is false. Once again, it cannot be inferred that H is true, for H's falsity is only one of at least three things that G asserts, and from G's falsity it does not follow that all three of them are false. H, in fact, is also false. It asserts: (a) that H is true (because it is an assertion), (b) that G is true, and therefore (c) that H is false, thus asserting a contradiction. (Once G is determined to be false, H is false even without the contradiction it generates: it asserts that G is true. But neither this nor something similar would obtain if H had been shown false before G; H says that H is false, and that much of what it says is true.)

The only way any of the Liar-propagating sentences can be understood as false, without falling into contradiction in so maintaining, is by understanding that to use a concept (in this case, to use sentences) one must accept the presuppositions of the concept (in this case, that to assert a sentence is to attribute truth to it). Failure to do this constitutes the fallacy of the stolen concept, and can only result in a myriad of contradictions. That he commits this particular fallacy is the Liar's subtlety; for centuries he has confessed himself a liar, and philosophers have believed him, not questioning his ethical nature further. Had they, they would have found him to be a thief as well.

Author's Note

The preceding is derived from discoveries I made during the summer of 1969, and the solution itself is original with me, though it is based on principles discovered by Ayn Rand and Nathaniel Branden, and published in "Introduction to Objectivist Epistemology" and The Objectivist Newsletter, Volume 2 Number 1 ("The Stolen Concept"). I was aided in the writing of the essay by my friend Michael Ferguson.

I discovered after having solved the paradox that, though my solution is original in that I independently formulated it, it is not chronologically original. A similar solution was published in the late 15th century in Sophismata by Jean Buridan. In Chapter VII, Section D, subsection 7, he writes:

…Every proposition virtually implies another proposition, so that of the subject standing for it, there is affirmed this predicate "true". I say it implies virtually just as an antecedent implies that which follows from it. Thus, any proposition is not true, if in this consequent affirmation, the subject and predicate do not stand for the same. For example, we could posit that this proposition of Socrates "No proposition is true" is properly called by the name "C". And then it follows that no proposition is true; therefore C is not true. And thus, unless it is as is signified by this consequent, it follows that the predicate in the given proposition was virtually implied in that proposition. The proposition is not true.

It is a sad commentary, but many modern logicians simply are not familiar with the work done in logic between the 4th century B.C.E. and the 17th century C.E., and those that are ignore it. (One of my own professors had a hand in producing a current translation of Sophismata, yet he teaches type theory and not Buridan.) This is unfortunate, as a great deal of work must now be rediscovered that otherwise would have been readily available, as the existence of this essay testifies. Not only did Buridan correctly solve the Liar Paradox six centuries ago (though he failed to integrate it into a correct epistemology), but his discussion of it was so thorough that he corrected an error I had made in an early draft of this essay.

I suspect that this sort of thing is more common than many philosophy students realize, and they would do well to read Mortimer Adler's The Conditions of Philosophy. Though Adler is notoriously inept in dealing with ethics and dikeology (— the philosophy or study of justice) his other works are very instructive. He does an excellent job of identifying the nature of philosophy, and his admonishments for its conduct, had they been known and heeded in the 17th century, could have spared the world a great deal of philosophical woe.

Footnotes

1. For a brief presentation of the Objectivist epistemology, see Ayn Rand's "Introduction to Objectivist Epistemology".
2. Though I have used the temporal term "before", this ordering is not to be construed as chronological. The concept "justice" may be grasped temporally before the concept "surgery"; this does not mean that the one is dependent on the other. "Justice", however, does depend on such concepts as "to judge", "character", and "man", and these must be grasped before "justice" can be understood.
3. Interesting to note is that this assertion was supposedly known to St. Paul, who considered it to be true. See Titus I, 12-13.
4. "Sentence" is understood in this context to refer only to declarative sentences, and not to questions, prayers, commands, etc.
5. See Nathaniel Branden, "Are Certain Things Unknowable?" The Objectivist Newsletter, Volume 2 Number 1.

Ronn Neff is an anarchist-Objectivist theoretician. His articles have appeared in The Individualist, The Libertarian Connection, and Invictus.