Kent Worthington on Inference and Proof

How Ideas Work Review Series: Part IV

G. Stolyarov II

A Journal for Western Man-- Issue XLIV-- December 20, 2005

Note: This is the fourth of five articles discussing Kent Worthington’s innovative book, How Ideas Work. The first three articles are “Kent Worthington on Consistency and Contradiction,” “Kent Worthington on Similarity and Difference,” and “Kent Worthington on Cause and Effect.”

            In the preceding chapters of How Ideas Work, Mr. Worthington discussed the proper methods for forming accurate concepts—abstraction—and accurate propositions—grammar. In Chapter 4, “Inference and Proof,” he explains the process of inference, used to form the next and final level of idea: conclusions. Conclusions may appear similar to propositions in that they are contained in a sentence or series of sentences unified by the structures of grammar. However, they go beyond each individual proposition in that they organize a multiplicity of them to thereby derive an otherwise inaccessible insight (95). Inference is the process which enables one to organize propositions to form further knowledge than each proposition can provide in isolation.

            While inference enables one to form a conclusion, proof works in the other direction: one begins at a conclusion and then seeks to validate it. The process of proof consists of tying an already existing idea to its evidence (95). Mr. Worthington uses an instructive analogy to illustrate the relationship between inference and proof:

            Inference and proof are like a subway, where the train reaches the end of the line and simply heads back the other way. Same line, same train, same method of operation. And same engineer—you. The motion is in one direction or the other, depending on your purpose. Are you forming a conclusion or validating one? Are you heading uptown or downtown? Like the engineer at the controls of the subway train, you operate in both directions (95).   

The way to initiate the process of inference begins with premises—which are “any proposition[s] used to form a conclusion” (95-96). Every conclusion has a universal premise—applicable to all entities with given characteristics. The universal premise behind a given conclusion is not always immediately evident, but there is a sure way to discover it: the syllogism.

            The syllogism is a critical and indispensable part of the process of inference. It consists of at least two propositions, from which the conclusion is derived. The first of these propositions must be a universal proposition. This is the structure of every valid syllogism:
            The universal proposition.

            A second proposition (sometimes more).

            The conclusion. (98)

Mr. Worthington gives an example of how a crucial real-world conclusion can only be reached through syllogistic reasoning:

            When no traffic is coming, it is safe to cross.

            No traffic is coming now.

            Therefore, it is safe to cross now. (97)

In this case, the universal premise is “When no traffic is coming, it is safe to cross.” This premise applies to all instances anywhere where there is no traffic coming—past, present, and future. The United States, too, was founded on the basis of a syllogism—thereby becoming the only nation in history whose government was initially justified via a rational basis. Mr. Worthington presents the syllogism implicit in Thomas Jefferson’s Declaration of Independence:

            Men institute governments in order to secure their rights. [Universal premise]

            This government (the British) has failed to secure rights.

            Therefore, this government’s authority is dissolved. (102)

The reason why the Declaration of Independence was a groundbreaking document is precisely its syllogistic nature, which implied an understanding of the universal purpose of government: an absolute standard to which all governments everywhere were bound—whether or not they recognized it—and by which any government that failed to protect all its individual constituents’ rights could be deemed illegitimate.

The syllogism always renders explicit the universal premise leading to a given conclusion. But the syllogism alone is not enough to validate the conclusion. It only shows that the conclusion does, indeed, follow from the universal premise behind it. Once the universal premise is known, it, too, must be shown to be true. This is the second step of the proof—the renowned “problem of universals,” which anti-rational thinkers throughout the ages have portrayed as unsolvable, thereby seeking to negate the possibility of genuine knowledge.  Mr. Worthington does not fall into this trap, however; he provides a solution to this problem, which derives from the nature of propositions and conclusions and the fact that one is not identical to the other.

It is simple enough to validate universal propositions referring to a known limited number of entities. For example, if one were to say, “Everyone in the room is wearing a red shirt,” one would only need to examine every individual in the room and see whether he is wearing a red shirt. If this is the case for every single person one examines, the universal statement is validated. The “problem of universals” applies to propositions referring “to all the entities of a given concept” (105). When one claims for example, “Any mutually parallel lines will never intersect,” one presents such a universal claim—which, if correct, will be true of all parallel lines everywhere—whether or not they are in one’s present capacity to individually examine. This type of universal claim is a generalization, “a proposition that refers to all the entities of a concept that is not modified to the perceptual level” (106).

The key to solving the “problem of universals” with generalizations is knowing that a proposition is not a conclusion; the two are arrived at in fundamentally different ways. A generalization is a proposition, and its truth is verified by the criterion for the truth of all propositions: the actual existence of the relationship between the subject and the predicate.

For a generalization, it is impossible to take an inventory of all individual entities the generalization encompasses in order to verify its truth. However, another method is accessible to man: the verification of whether “[t]he predicate is essential to the subject” (108). An essential relationship is one without which the subject of the proposition would not be what it is. The universal statement, “Any mutually parallel lines will never intersect” exhibits such a relationship. Never intersecting—the predicate—is essential to parallel lines—the subject. If two lines intersect, they do not have that essential quality which makes them parallel. Euclid himself never explicitly recognized the logical validation of this proposition—though he held to it as true. Mr. Worthington’s system confirms the validity of Euclid’s parallel postulate—sweeping away mounds of untrue, unrealistic speculation by mathematicians on the possibility of “Non-Euclidean” systems of geometry.

So it is with governments: securing every constituent individual’s rights (the predicate) is essential to government (the subject). When a government fails to do this, its essential nature is altered: it ceases to be a benevolent protector and becomes an intrusive, abusive tyranny, thriving at the expense of its constituents and their rights. Taking an inventory of all actual governments throughout history to verify this proposition would be grievously fallacious—because most historical “governments” were abusive tyrannies, either of the few or of the many.  Rather, one should examine the universally valid essential purpose that a proper government ought to serve—and judge all historical governments, past and present, with that purpose as the standard.

The reason for the historical difficulty with generalizations is past thinkers’ misapprehension of generalizations as types of conclusions, not propositions. When generalizations are treated as conclusions, absurdities result. One such absurdity is the so-called “inductive method,” whose utter silliness Mr. Worthington reveals in the following illustration:

This crow has wings.

That crow has wings.

And another and another.

Every crow seen in China.

Every crow reported from the 17th century.

Every crow ever reported has wings.

Therefore, all crows have wings. (110)

The above is not a true syllogism, though it attempts to mimic the syllogism’s structure in order to pass off the generalization, “All crows have wings,” as a conclusion. All the “inductive method” provides is an inventory of particulars, “taken by examining and counting—with a conclusion tacked on at the end” (110). Because the inductive method ignores the operation of essentials, it can never arrive at a complete validation of any generalization. Rather, all it can do is say, “Every crow we have seen so far has wings. It is quite possible and conceivable that the next crow we encounter will not.” This does not suffice if one’s aim is to obtain genuine knowledge. All one will get via the “inductive method” are statistical inventories whose purpose is unclear, because it is not—and cannot be—to obtain knowledge.

            The “inductive method” has been accepted as an unchallengeable orthodoxy in today’s realm of “scientific research,” which—writes Mr. Worthington—undercuts the pursuit of genuine truth:

Sadly, this unfortunate “method of generalizing” has been institutionalized today by what is called the statistical method. Modern statistics has enshrined the method of sampling, of taking inventory, by insisting that it leads to generalizations. It does not!... [B]ecause generalizations are not conclusions, they can’t be explained by an inventory with a conclusion attached, or any other veiled form of inference. Any such attempt will deteriorate into a contorted and futile manipulation of statistics. This, in fact, has been the fate of induction as a method of inference. (111)

 Mark Twain was brilliantly insightful when he wrote that there are three types of lies: lies, damned lies, and statistics. He might not have known that this is not a mere quip, but an absolute truth. Statistics can never arrive at valid generalizations, and using them to “prove” such generalizations implies a fundamentally false methodology.

The other side of the historical coin of treating generalizations as conclusions has been the “deductive method,” which—though it was correct in its employment of syllogisms to reach conclusions—was lacking in the ability to validate starting premises, including universal ones. Yet proper conclusions depend on true premises, and, without a way to validate those premises, the deductive method “will deteriorate into a contorted and futile manipulation of symbols. This, in fact, has been the fate of deduction as a method of inference” (112).

Indeed, the induction/deduction dichotomy is a false one. One side of the dichotomy denies man’s reason in favor of his observational faculty—the other denies man’s observational faculty in favor of his reason. Neither is proper to an individual wishing to live in a reality which he must both observe and reason about. Mr. Worthington shatters the induction/deduction dichotomy by presenting a unitary method of inference as an alternative:

Inference is a single method, not two. It is the method of explaining all conclusions. But it is not a method of explaining any generalization. There is only one method of inference, [o]nly one cause of valid conclusions, only one explanation of how they actually work. Inference involves two steps: Assert your premises, and then organize them properly. Consequently, there is only one process of proof, of validating a conclusion. In involves two steps: Check your organization, and then check your premises. (112)

During the process of inference, one must constantly refer back to the propositions one employs to ensure that each individual one is true. This is done not by “induction” or “deduction,” but by the ascertainment of essential relationships between the subject and predicate of each proposition.

            Mr. Worthington links his discussion of inference to his system of causality, showing how every causal relationship “can be expressed as an explicit generalization” (115) and can thus be used as an essential ingredient in forming conclusions. If a condition is necessary but not sufficient to a given action, then one can form the following valid conclusions:

            If the action occurred, then the condition was present.

            If the condition was not present, then the action did not occur.

If a condition is sufficient but not necessary to a given action, the following conclusions are valid:

            If the condition was present, the action occurred.

            If the action did not occur, the condition was not present.

If a given condition is both necessary and sufficient for an action, then all four of the above conclusions are valid. The statement that the condition is either necessary or sufficient to the action, or both, is the generalization; the statements inferred from it are conclusions.

            Kent Worthington goes beyond the insights of Ayn Rand—who never had a systematic theory of propositions, generalizations, causality, and inference. Rand, too, was vulnerable to the induction/deduction dichotomy, and her idea of the derivation of the fundamentals of her system was always a shaky “balance” between the two—which happened to arrive at the proper conclusions because Rand did not, unlike most thinkers, altogether reject one method in favor of the other. She did, however, maintain that an essential difference between induction and deduction existed and that there were two methods of inference, not one. Mr. Worthington has removed that trap, however, by showing that generalizations are propositions, not conclusions, and can be validated by reference to essentials—whereafter syllogistic reasoning leads from generalizations to the conclusions that follow.

You can order How Ideas Work at

G. Stolyarov II is a science fiction novelist, independent filosofical essayist, poet, amateur mathematician and composer, contributor to organizations such as Le Quebecois Libre, Enter Stage Right, and the Autonomist.  Mr. Stolyarov is the Editor-in-Chief of The Rational Argumentator and a Senior Writer for the Liberal Institute ( He can be contacted at

This TRA feature has been edited in accordance with TRA's Statement of Policy.

Click here to return to TRA's Issue XLIV Index.

Learn about Mr. Stolyarov's novel, Eden against the Colossus, here.

Read Mr. Stolyarov's comprehensive treatise, A Rational Cosmology, explicating such terms as the universe, matter, space, time, sound, light, life, consciousness, and volition, here.

Read Mr. Stolyarov's four-act play, Implied Consent, a futuristic intellectual drama on the sanctity of human life, here.

Visit TRA's Principal Index, a convenient way of navigating throughout the issues of the magazine. Click here.