Judging from its title, this essay might appear to be a contribution to legal theory in the form of a method for the apprehension of those who unrightfully take the material property of others. Far from it. This is rather an investigation into the nature of a much more insidious type of thief: the concept-stealer. More specifically, this is a critical analysis of the article by Ronn Neff entitled "The Liar is a Thief." [1]

In this article, Neff first develops the "fallacy of the stolen concept." [2] In his own words, this is the violation of the principle that "if a concept is to be meaningful, its presuppositions must be accepted while that concept is being used."

Neff then introduces the Cretan Liar Paradox ("All Cretans always lie"), which admittedly is not a paradox until reformulated, viz., "This sentence is false." Neff mentions several attempted solutions of the paradox as reformulated--including, notably, Bertrand Russell's theory of types [3]--before attempting his own solution.

Neff's own 'solution' of the Cretan Liar Paradox entails the application of the stolen concept argument to the sentence: "This sentence is false." He alleges that such a sentence is actually false, because "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)."

But are either of these premises true? Are any of the reformulations or conversions of the Liar-sentence really meaningful? Indeed, does Neff's 'solution' actually do what it purports to do--namely, to solve the Cretan Liar Paradox? In a word: no. The whole discussion which Neff carries on regarding the truth or falsity of the Liar-sentence is futile, because neither truth nor falsity can be attributed to a meaningless sentence.

The Liar-sentence, as reformulated, is meaningless. And since the concepts of 'truth' and 'falsity' are genetically dependent upon the concept of 'meaningful,' they are thus inapplicable to the Liar-sentence. To establish these claims as true, it is necessary to make a cursory study of that area of epistemology which deals with meaning--i.e. the intentionality of consciousness.

Intentionality and Meaning

In her monograph Introduction to Objectivist Epistemology, Ayn Rand identifies the two fundamental attributes of every state of awareness: the content (object) of awareness and the action (processing) of consciousness in regard to that content. Implicit in these two attributes is a third attribute of consciousness: the directedness of the action of consciousness toward the object.

That is, every state of consciousness is characterized by the fact that it is directed toward some object. Conscious organisms select certain aspects of reality for mental processing; their consciousness is said to tend toward, to refer to, to represent, to signify, to mean, to intend some object which is its referent. Every state of consciousness is characterized by its meaning, its intentionality.

In particular, let us consider the process of cognition, the attempt to identify the facts of reality. A cognitive idea (cognitive content of consciousness) is a claim to have identified the facts of reality, it is a claim to knowledge of reality. When one's cognitive idea does in fact constitute recognition (correct, non-contradictory identification) of a fact of reality, one's idea constitutes knowledge and is true.

Knowledge is the product of a non-contradictory identification of the facts of reality; and truth is the attribute of that product, designating the character of the relation of that certain type of idea--namely, knowledge-to reality. Thus, the two concepts of 'truth' and 'knowledge' designate the same phenomenon--a non-contradictory identification of the facts of reality--from two complementary perspectives. In a very significant sense, then, knowledge is truth.

On the other hand, when one's cognitive idea (claim to knowledge) is an incorrect recognition of a fact of reality, one possesses ignorance and one's idea is false. Falsity is ignorance. But in either case--knowledge/truth or ignorance/falsity--one's cognitive idea is cognitively intentional, cognitively meaningful; it is a claim to knowledge of reality. Were it not such a claim, were it cognitively unmeaningful or non-intentional, it could not possibly be true or false.

Cognitive ideas, true or false, take the form of concepts, propositions and arguments. When concretized into linguistic forms, they are, respectively, words or phrases, sentences or clauses, and paragraphs.

These latter, material, linguistic tools of cognition are, qua tools of cognition and cognitive meaning and intention, clearly derivative from the former. Thus, if a given linguistic form is to be cognitively meaningful at all, it must be symbolic of (intend, mean, refer to, stand for) a corresponding cognitive idea (mental form). Without such correspondence, a linguistic form possesses no cognitive intentionality or meaning, and hence cannot be either true or false.

Specifically, if a sentence corresponds, not to a proposition, but to a non-propositional aggregation of concepts, then it is meaningless and hence cannot be either true or false. thus, as I stated above, neither truth nor falsity can be attributed to a (cognitively) meaningless sentence. To attempt to do so is to steal the concepts 'truth' or 'falsity'--to use them in contexts where they do not apply--to use them, while ignoring or contradicting the concept upon which they logically and genetically depend: the concept of 'meaningful.' [4]

What about the Liar-sentence, then? (I am referring, of course, to the reformulation "This sentence is false.") Is it or is it not a proposition? Is it or is it not meaningful, as intended? To answer these questions, we must consider the nature of propositions (regrettably, in brief fashion).

Propositions and Meaning

When concepts are arranged in a certain manner, they mean not only the natures and essences and the individual existents which they signify qua concepts. They also come to mean or designate certain things as being or existing. The kind of arrangement of concepts in which a designation of existence (or attribution) is made is a proposition.

An existence proposition (e.g., 'Existence exists', 'There are heroes') starts with the nature of its subject-concept assumed, and explicitly asserts the existence of the subject-concept's referents. A subject/predicate proposition (e.g., 'The Liar is a Thief', 'All cows eat grass'), by predicating certain attributes of the subject-concept's referents, implicitly asserts the existence of the subject-concept's referents.

The latter, subject/predicate propositions, mean that something exists by means of an asserted relation of identity between subject and predicate. This relation is designated by means of (some form of) the copula 'is', whether explicit or implicit. Examples of the former include: 'The Liar is a Thief', 'In the long run, we are all dead', 'Aristotle was a student of Plato.' Examples of the latter include: 'All cows eat grass' (which implies that all cows were eating, are eating, or will be eating grass), 'Aristotle taught philosophy' (which implies that Aristotle was teaching philosophy), and 'I will die some day' (which implies that I will be ceasing to live some day).

In general, for propositional truth to be possible, the subject-term(s) must designate something actually existing at the same time (the tense of the verb-copula must agree with the time-of-existence of the existent designated by the subject-term(s), and in the same respect (if the sense of the verb-copula is taken to be that pertaining to a physical object rather than a creation of the imagination, then the subject-term must designate something actually existing in the same manner) as the verb-copula indicates. (E.g., the sentences: 'The king of France is bald' and 'Unicorns exist' are definitely meaningful, but are as clearly false; they thus represent false propositions.

But for propositional meaning to be possible, the subject-term(s) must designate something actually existing at some time and in some respect. Only then--in the case of a subject/predicate proposition such as the Liar-sentence purports to be--can the subject- term(s) be asserted (rightly or wrongly) to be related by identity to a given predicate. Without such a referent for the subject-term(s), a propositional identity-relationship (i.e., a proposition) cannot even be asserted. If its subject-term(s) does not designate, an alleged proposition does not designate and is therefore non-intentional or meaningless, and is furthermore not a proposition.

Consider then the Liar-sentence (as reformulated): 'This sentence is false.' This sentence is not false, but meaningless, because the alleged proposition which it represents, 'This sentence is false'--or perhaps, 'This proposition is false'--is meaningless. (The following proof will deal with the former alternative, but will apply equally well to the second.) The alleged proposition is meaningless, because its subject-term "This sentence" designates nothing at all--nothing past, present, or future; nothing mental or physical, nothing period.

If it were said: 'This sentence: "I like rice" is false,' there would be propositional meaning, because there is designation by the terms "This sentence" of the sentence "I like rice." But without a specific sentence as designatum (object of designation) of the subject-term "This sentence," the alleged proposition 'This sentence is false' is meaningless (i.e., is not a proposition). and since the sentence 'This sentence is false' intends or represents a non-propositional (meaningless, non-intentional) group of concepts, the sentence, too, is meaningless.

It might be claimed that there actually is a sentence designated by "This sentence," and that the sentence so designated is everything within the single-quotation marks: 'This sentence is false.' But if this be the case, then we should be able to express it in a standard form: 'This sentence: "A is B" is false.' Substituting into this formula, we obtain: 'This sentence: "This sentence is false" is false.' Now observe that the outer sentence's subject designates another, inner sentence, all right, but that the inner sentence's subject designates nothing!

Thus, this ploy has not escaped the predicament at all, that being the meaninglessness of the Liar-sentence. If the same process be repeated, no matter how many times, the result is essentially the same:

'This sentence: "This sentence: "'This sentence: ""This sentence:.....

......is false,"" is false,'" is false," is false.'

That is, the subject cannot be expressed; indeed, the Liar-sentence has no definite, finite subject at all. To repeat: "This sentence" designates nothing, no actually existing thing (infinity does not actually exist). The Liar-sentence: 'This sentence is false," is therefore meaningless.

The same analysis applies to the other form of the Paradox cited by Neff:

G: Sentence H is false.

H: Sentence G is true.

Neither of the sentences G or H represents an actual proposition. The subject of sentence G, "Sentence H", designates sentence G, whose subject designates sentence H, etc., etc. And vice versa. For neither sentence is there an actual, existent proposition, for there is no definite, finite subject. E.g.:

G: Sentence H: Sentence G: Sentence H:....?....Sentence G: Sentence H:....

is false, is true, is false, ....?....is false, is true, is false.

From this, it is but a short step to stating our conclusions here. I would be remiss, however, if I were to neglect to comment on the issue surrounding Russell's theory of types and the fallacy of self-exclusion--an issue treated in a most cavalier fashion by Neff in his article.

Logic, Intentionality, and Self-Exclusion

Throughout the history of philosophy, there have been basically two approaches as to the nature of logic: (1) the intentional view, which is the basis behind the Aristotelian Realist school (e.g., the medieval Scholastics, Henry Veatch, and the Randian Objectivists); and (2) the non-intentional view, which supports various Conventionalist theories of logic, most notably modern mathematical logic and the propositional calculus (e.g., Bertrand Russell and Alfred North Whitehead, Ludwig Wittgenstein, Rudolph Carnap, Kurt Goedel, Alfred Tarski, W. V. Quite, etc.)

As Professor Henry B. Veatch pointed out in his book Intentional Logic (upon which I rely greatly with respect to approach, if not terminology, during this section), the basic difference between the two positions is that the former recognize that the subject matter of logic includes both linguistic tools (e.g., words, sentences, etc.) as well as the mental tools (e.g., concepts, propositions, etc.) which the linguistic tools must intend or refer to if they are to be meaningful. The Conventionalists, on the other hand, focus strictly upon the nature of the linguistic tools and operations. Let us observe how this basic difference manifests itself when each position tries to deal with the Cretan Liar Paradox in the face of the fallacy of exclusion.

(1) The Conventionalists (including Russell) have failed to understand that a mental tool can, in a very special manner, hold itself as its object--that we can have a concept of all concepts which is itself a concept, or a proposition of all propositions which is itself a proposition. Failing to understand this fact about intentionality and cognitive tools, they have denied the existence of self-membered classes, i.e., of concepts or propositions which include themselves among their referents. This has led them either to theories about meta-languages and metalogics or, in Russell's case, to a theory of a hierarchy of types.

In the latter case, an arbitrary rule was formulated which excludes a priori and by fiat all self-membered classes: "All sentences must refer to collections of which they are not members, i.e., in which they are not included." Or, "No sentence may be included in a collection to which it refers." Or, "No sentence may be included in its own subject."

This formulation obviously does commit the fallacy of self-exclusion, as Neff so rightly pointed out. Its subject, the concept 'sentence,' does include within itself the very sentence of which it is the subject (that sentence being a unit of the concept 'sentence'). I.e., the rule is included in its own subject, contradicting what it asserts. Its very existence and content make it a false assertion. (Please note, though, that it is a meaningful assertion, as I will demonstrate shortly, and thus is capable of being true or false, i.e., of being self-consistent or self-contradictory.)

Thus, the Conventionalist position taken by Russell is not a solution of the Cretan Liar Paradox, but rather an embarrassingly arbitrary and self-contradictory evasion of the problem. (The same applies with regard to other variants of the Conventionalist position, as Professor Veatch proves in his book.)

(2) The more consistent of the Aristotelian Realists, on the other hand, affirm the existence of self-membered classes. Because cognitive tools can themselves become the object of cognition, they too can be referents of the concepts 'concept' and 'proposition' and 'argument', and of propositions about all concepts, propositions, and arguments, etc.

More specifically, all propositions are references of the concept 'proposition', including propositions about all propositions. That is, a proposition about all propositions: e.g., 'All propositions are composed of concepts' has the concept 'proposition' as its subject-term. And such a proposition, insofar as it is a proposition, is included within its subject-term, the concept 'proposition.' thus can the Aristotelian affirm what the Conventionalists choose to deny, namely, 'Some propositions may be included in their own subject.'

At the same time, they also realize that it is impossible for a proposition to be its own subject, that any attempt to formulate such a proposition leads unavoidably to an infinite regress (as we saw above). To designate a particular, presently existing proposition, one uses the phrase "This proposition" or "This particular here-and-now existent proposition" or some other equivalent. But in the context of any group of concepts in the form 'This proposition is X', there is no particular here-and-now existent proposition for the subject-term "This proposition" to designate. It is in this manner that an Aristotelian Realist deals with the Cretan Liar Paradox (as reformulated), by applying the rule: 'No proposition may be its own subject.'

Now let us briefly note the difference between the Conventionalist rule and the intentional rules of Aristotelian-Realism. The Conventionalist claims that no proposition is included in its own subject. But the Aristotelian-Realist holds that while some propositions are included in their own subjects, no proposition is its own subject.

The difference between a proposition's being included in its subject and a proposition's being its subject amounts to the difference between a proposition's being able to satisfy a non-specific, indefinite conceptual reference to itself and a proposition's being able to satisfy a specific, definite concrete reference to itself. Whereas the former is possible, the latter is simply not.

The concept of 'proposition' refers to all propositions, past and present (already existing, or actual) and future (not-yet-existing, or potential). The qualifiers "All" and "Some" and "No" thus set up indefinite references to a number of propositions, some of which are already actually existing. Yet they also allow indefinite future reference to a number of propositions which do not yet exist, including most importantly here, the propositions in which they are used (which are in the process of being actualized).

On the other hand, the qualifier "This" sets up a reference to a definite, specific proposition--a here-and-now particular existent proposition--which cannot refer to the proposition in which it is used, since that proposition does not exist here-and-now, but (since it is still in the process of being actualized) only in the future.

Thus, when a group of concepts with "All propositions" or "Some propositions" or "No propositions" as its subject includes itself in its own subject, it does not result in an infinite regress since there are other presently existent propositions fitting the designation and which can relieve it of the burden of serving as the presently existing designatum of the subject. The group of concepts can later, once completely organized, be seen to be a specific referent of themselves--and thus to have been one of their non-specific referents, while they were in the process of being organized. This allows one to complete the organization of such concepts into a proposition, without having had to chase one's tail in search of a specific referent.

But there is no such relief for any group of concepts with "This proposition" as subject-term. When one attempts to pursue the will-o'-the-wisp of making that group be its own specific, presently existing referent, one merely stunts (indeed, halts) the propositional growth of the mental process employing those concepts--one never gets 'closer' to the end of an infinite regress! [5]

To conclude this section, let us make the following observations:

(1) The Conventionalist rule, 'No proposition (sentence) may include itself within its own subject', is meaningful and is a proposition, for it does not try to be its own subject. It is, however, included in its own subject, and is incompatible with its own content. It is therefore self-contradictory and false, by the fallacy of self-exclusion.

(2) The Aristotelian-Realist rule, 'No proposition may be its own subject', is meaningful and is a proposition, for it does not try to be its own subject. and although it is included in its own subject, it is compatible with its own content. It is therefore self- consistent and is true, since its content is in accord with the impossibility of making a proposition be its own subject (due to an infinite regress, as we saw above).

(3) The Cretan Liar Paradox, in its reformulation ('This sentence is false') is meaningless, and thus is not a proposition, and also cannot be true or false. This is because it purports to be its own subject.

(4) The Cretan Liar Paradox, as originally formulated ('All Cretans always lie' or 'All propositions by Cretans are false') is meaningful and is a proposition. While it does include itself within its own subject and is incompatible with its own content, it does not purport to be its own subject. Although it is meaningful, however, it is self-contradictory and false, by the fallacy of self-exclusion.

Conclusion

I have adequately, I hope, substantiated my earlier claim that the series of words 'This sentence is false', is cognitively meaningless, and therefore cannot be either true or false. The sentence purports to be its own subject, in flagrant violation of the requirements of the intentionality of cognition. The subject "This sentence" implores us to tend to, to look at (to make into an object of our cognitive awareness) some actual existent sentence, a sentence which just does not exist. Hence, the Liar-sentence (as reformulated) is a cognitively meaningless expression, one to which truth or falsity cannot be attributed.

This is what we originally set out to do, to refute the Cretan Liar Paradox. But in the process of doing so, it has become crystal clear that Mr. Neff has committed some grave errors, errors which must not go unidentified. Specifically, not only has he falsely accused the Liar of the epistemological crime of concept-stealing; but he has engaged in that very crime himself! [6]

First of all, the Liar (in the original formulation of the Paradox) was not a concept-stealer. He perfectly recognized the antecedents of all the concepts he used, and he arranged them in a perfectly meaningful manner: 'All propositions by Cretans are false.' And in fact, only by making a meaningful utterance could the Cretan actually be said to "lie" and to be a "Liar". (A lie is a knowingly false statement, a knowingly self-contradictory statement, which requires that it first be a knowingly meaningful statement.)

Secondly, the reformulation of the Paradox, 'This sentence is false', is properly attributed by Neff not to the Cretan Liar, but to later philosophers. It is these shadowy figures who comprise the Epistemological Syndicate--perhaps we should call them Epistemological Crime Incorporated!--which are the ones who are engaged in concept- stealing. [7] They have stolen not the concept 'sentence', however, but rather the concept 'false', using it to apply to a meaningless utterance, a non-existent proposition, a non- propositional sentence. And they most certainly are not liars.

And thirdly, Neff, who attacks the Paradox as reformulated, claims that the reformulators are attributing truth to their utterance. "To assert is to attribute truth," he asserts. Through a series of linguistic contortions, he finally concluded that the utterance is actually false after all, since it is (he claims) self-contradictory.

Thus, Neff himself steals the concept 'false', becoming the Epistemological Syndicate's unwitting partner in (epistemological) crime. Furthermore, in his claim that "To assert is to attribute truth", he also steals the concept 'truth'. To wrench some of Neff's own words out of their original context: "This sort of thing (concept-stealing) is more common than many philosophy students realize!!" Truer words were never spoken.

Mr. Neff has attacked not Liar, then, but a Pack of Thieves. And by his method of attack, he has further deceived himself into believing that he has 'licked em', when in reality he has merely 'joined em'.

So it appears that even though the concept-stealing is, in Mr. Neff's case, apparently unintended (no pun intended!), some cognitive rehabilitation is definitely prescribed. And since anyone else who accepted his argument as valid is equally an accessory to the (epistemological) crime of stealing the concepts of 'truth' and 'falsity', the same applies to them as well.

For this purpose, I recommend two excellent books: Logic As A Human Instrument by Francis Parker and Henry B. Veatch, and Intentional Logic by Henry B. Veatch. Despite some apparent errors in their treatment of the relationship of signs and symbols to intentionality, their works nevertheless comprise a valuable adjunct to Rand's Introduction to Objectivist Epistemology and Leonard Peikoff's course on The Objectivist Theory of Knowledge, if read critically and in close conjunction with the latter.

Finally, to be a successful epistemologist, one must have much more than good intentions ('intention1': to refute the Cretan Liar Paradox; 'intention2': to possess the rationally valuable tool which is the recognition of the fallacy of the stolen concept). One must also consistently concretize that good intention--i.e. one must (1) give an authentic and valid refutation of the Cretan Liar Paradox, not one which commits the same error; and one must (2) properly use the logical tool which is the recognition of the stolen concept fallacy.

Only then can one avoid the epistemological injustice of concept-stealing. Only then can one avoid being "notoriously inept" in the epistemological branch of dikeology (the study of philosophy of justice), as Mortimer Adler is in the political branch. [8] And only then can one be a successful (epistemological) crime-fighter, with no hidden conflict of interests to reduce one's effectiveness.

Postscript Comments

Neff claims correctly that "to assert is to assert as a fact," and that "to assert is to attribute truth." Recognize further, however, that to assert is to mean something, to intend to convey something cognitively meaningful; and to assert as fact is to mean that something is a fact. If a given utterance is meaningless, then, it cannot be considered to be an assertion, in the proper sense of the word; it is a meaningless utterance. Thus, it is not an assertion, and does not attribute truth.

But Neff claims that "all sentences are assertions" and are thus meaningful, clearly an invalid claim from our examination of intentionality. He then infers that to "assert a sentence is to attribute truth to it." Here the ambiguity of the verb 'assert' (to 'say' something, irrespective of its meaning vs. to 'meaningfully say' something) comes into play to obscure his invalid inference. It is definitely not the case that to 'assert' (say) any old sentence, irrespective of whether or not it is meaningful, is to attribute truth to it. If what one 'asserts' (says) is meaningless, one is not 'asserting' (meaning) anything, and one is thus not attributing truth or falsity to it--not validly, anyway. And when one attempts to do so--as both reformulators of the Paradox and Mr. Neff have done--it is precisely the concepts of 'truth' and 'falsity' which one is stealing.

This ambiguity of the verb 'assert' is but one example of the conceptual sloppiness pervading Neff's paper. It is true that to (meaningfully) assert a sentence is the prerequisite of communication; but it is not necessarily true that to assert (say) a sentence will make communication possible, for the sentence may well be meaningless. And whereas it is true that to (meaningfully) assert a sentence is to attribute truth to it, it is not true at all that to assert (say) a sentence is to attribute truth to it, for one is not necessarily attributing even meaning to it.

There are two final aspects of Neff's article on which I will comment. The first is Neff's assertion that his 'refutation' of the Cretan Liar is similar to that published in the late 1400s by Jean Buridan in Sophismata. We now can see that they are not the same 'solution' at all. Buridan is speaking of propositions (and, thus, meaningful sentences only), whereas Neff makes his claims about all sentences. [9] Furthermore, Buridan deals with the meaningful but false original form of the Paradox, whereas Neff deals with meaningless formulations. (Buridan cites, as his example, Socrates' proposition: 'No proposition is true.') Thus, although Buridan escapes the charge of concept-stealing, he has not refuted the reformulation of the Paradox either.

The second aspect which needs to be clarified is Neff's reference to the Principle of Bivalence. Properly formulated, it should read: 'Every cognitively meaningful sentence is either true or false.' Thus, some sentences are neither true nor false-- specifically, cognitively meaningless sentences such as questions, commands, and utterances such as 'This sentence is false'. So denying that this principle applies to the Cretan Liar Paradox--far from being a 'solution' whose "error...is too obvious and mean to warrant discussion"--is indeed a sound step toward the proper refutation of the Cretan Liar Paradox! If this be a far less "respectable" solution than that of Diodorus Cronus (who hanged himself after failing to solve the Paradox), as Neff claims it is, I nevertheless invite him to join me and make the most of it! [10]

Endnotes

[1] Individualist, May 1971, Vol. 3, No. 6, pp. 10-13.

[2] Historically, the original recognition of this fallacy was by Aristotle in his Metaphysics, 1006a, line 16. To my knowledge, the first modern mention of this fallacy was made by Ayn Rand in her novel Atlas Shrugged; while Nathaniel Branden gave a formal treatment of it in his article "The Stolen Concept," The Objectivist Newsletter, Vol. 2, No.1.

[3] As Neff describes it, Russell's theory of types "asserts that a sentence must not be a part of the subject-matter of itself, i.e., that a sentence must refer to a collection of things in which it is not included." He contends that Russell's 'solution' is invalid because it commits the fallacy of self-exclusion, a contention which we shall examine in more detail later.

[4] Please note, however, that even though they do not correspond to any proposition, meaningless sentences are still sentences. Though linguistic forms (e.g., sentences) are derived from mental forms (e.g., propositions), they can be filled with all kinds of meaningless stuff or manipulated in all sorts of meaningless ways. Because a sentence is a material, concretized form of thought, it must take on some particular material form, some particular arrangement of words (whether spoken, written, printed, or whatever). And it is easy for someone who desires to, to focus on manipulating the material forms, ignoring their original connection to and source in mental forms of thought. A meaningless sentence, then, is a sentence which corresponds to no proposition, but merely a propositionally meaningless aggregation of concepts, which does conform to the proper material arrangement of its constituent words, that arrangement, however, not representing any propositional arrangement of concepts.

[5] This, then, reveals more clearly the special way in which tools of cognition can hold themselves among others in an indefinite reference, which is made definite only in retrospect, by a separate, later act of focus. And for the same reason, it is impossible for a tool of cognition to cognize only itself. The very reason that "a consciousness conscious of nothing but itself is a contradiction in terms" (Ayn Rand, Atlas Shrugged, p. 694, pb), is that an infinite regress makes it impossible for a given conscious process to achieve cognition of itself as its sole definite, finite object.

[6] 1997 note: In his published reply, Neff protests that I say he has "unjustly" accused the Liar Paradox of concept-stealing, and that I "complain that [he has] falsely maligned the Liar Paradox..." Not at all. I say that he has unjustly accused the Liar--i.e. the Cretan Liar in the original, non-paradoxical version. He does so in the title of his essay, "The Liar is a Thief." However, it is also true that he falsely accuses the original version of the Paradox of concept-stealing, as he does in this passage: "One of the 'problems' posed in ancient philosophy is a subtle instance of the stolen concept called the 'Liar Paradox.'" Since it was not reformulated as a truly concept-stealing version until medieval times, my claim stands.

[7] 1997 note: Incredibly, Neff says of me that "...if he is correct that 'This sentence is false' is meaningless, then because it makes use of the concept 'false', which presupposes meaning, there is, in fact, an instance of concept-stealing here. In other words, Bissell's own position would entail that this Liar-propagating sentence is an example of a stolen concept." That is precisely the point I make, in so many words, in this paragraph, which makes me wonder whether he even read it! (If he did, he should have said so, rather than taking credit for my observation.)

[8] See Adler's statist-oriented books The Time of Our Lives and The Common Sense of Politics.

[9] 1997 note: Neff says that Buridan's "basic position, however, is that every sentence (or proposition) entails another sentence (or proposition) to the effect that the original sentence (usually named by that sentence's own quotation) is true. And this is exactly the principle that I employed in my solution. Mr. Bissell may cry that I have misused it, but I have, nonetheless, used it; and I fail to see what is accomplished by insisting otherwise." I nowhere "insisted" that Neff did not use Buridan's principle; he did, indeed, use it, but it is not the correct principle to use in analyzing the Liar's Paradox reformulations. Instead, it is the analogous principle that every sentence entails another sentence to the effect that the original sentence is meaningful. Or, to put it in terms of the concepts used: any attempted propositional attribution of truth or falsity to a sentence presupposes the attribution of meaningfulness to that same sentence. And if the latter attribution is mistaken, the use of the concept of 'truth' or 'falsity' is stolen, in Rand's terminology. (Furthermore, we can extend the stolen concept fallacy by analogy to sentences or propositions by observing that whenever an utterance is meaningless, not only every concept used in the utterance is stolen, but also the form of the sentence or proposition itself!)

[10] 1997 note: Neff concedes that there are sentences which are neither true nor false, not because they are commands, wishes, etc., but because they are meaningless--and, presumably, that the Principle of Bivalence does not apply to them. He just doesn't agree that Liar-propagating sentences are included in this category of meaningless sentences, while offering no refutation of my argument that they are. He also says that he was aware of Veatch's (and my) approach to solving the Liar paradox when he wrote his paper, but that "he did not discuss it in the body of the paper, because it would have involved much tedious discussion of intentionality and the nature of propositions, and made the essay entirely too long..." (From this, one might draw the inference that Neff mentioned Veatch in a bibliography or a footnote, but he did not. One might also draw the inference that Neff thought my discussion of intentionality and the nature of propositions was "tedious" and, as a result, my essay "entirely too long." A satisfactory discussion might well have been less tedious and more compact than mine, but some such discussion seems vitally necessary for properly dealing with the Liar paradox reformulations.) Curiously, Neff further says that he determined our approach to be "basically ad hoc"--which suggests that he thought that it was a correct solution, merely one that employed no useful general principle, as against his other comment that he agreed with the general principle Veatch and I invoke about meaningless sentences being neither true nor false, but disagreed with our invoking it in the case of the reformulations of the Liar paradox. Against both of this misreadings of our approach, I will simply reaffirm my own confident belief that it is correct and refer the reader to Note 6 above for an additional and most interesting principle that is invoked. In any case, Neff says, he did not intend our approach to be the target of his criticism of those who claim the Principle of Bivalence does not apply to the Liar paradox. (There is a fine distinction here: Veatch and I are not "mean" or unrespectable in suggesting that reformulations of the Liar Paradox are meaningless and thus neither true nor false--just wrong! Or "ad hoc." It is not completely clear which.) What Neff seems to be getting at is that commands, wishes, prayers, questions, etc., can be reformulated as cognitively meaningful sentences (which are thus true or false) by spelling out the implicit belief or desire that accompany them as part of their standard intended meaning (E.g., The question: "Why are you doing that?" could be reformulated as the sentence: "I want you to tell me why you are doing that.")-- and thus that trying to dismiss the Principle of Bivalence when considering such is at least an error, if not a sophistical maneuver. While I agree, however, and now realize that my referring to commands, wishes, etc., as cognitively meaningless was in error, I still think that those whom Neff criticized for saying that the Liar Paradox reformulations are not subject to the Principle of Bivalence were being led by very sound instincts!

This essay first appeared in Individualist, July/August 1971, pp. 32-37. Individualist was a publication of the old Society for Individual Liberty, which lives on as an international organization. For information, click on this link: International Society for Individual Liberty website Or, contact ISIL at 836-B Southampton Rd, #299, Benicia, CA, 94510 Tel: (707) 746-8796 Fax: (707) 746-8797