Saturday, September 30, 2006

Frame's Summary of Van Til's OMA

In his lecture outline The Thought of Cornelius Van Til, John Frame gives an informal overview of Van Til's reasoning for thinking that the Christian doctrine of the "trinity" is needed in order to solve the problem of universals. Here we have, from one of the master apologist's own star pupil's, a denuded rendition of the so-called "one-many argument," a variant of the "transcendental argument for the existence of God." In the brief sketch that Frame provides, we can spot several major misconceptions about the nature of abstraction, so much so that it reads essentially as a primer on how not to treat concepts.

Frame's lecture outline itself is quite long - spanning some 36 pages on my downloaded version. The section which appears below can be found on page 10 - under the sub-heading 4. Trinity of section V. Metaphysics of Knowledge . It consists of the following:

d. The Trinity and the One-and-Many

(i) We cannot identify particulars and distinguish them from one another, without uniting them by universal terms.
(ii) But the universal terms exclude particularities ("dog" and "Fido"). So they cannot explain all particularities.
(iii) We cannot define the universals, either, except by means of particularities. But particularities, individuals, are not universal; so whence comes universality?
(iv) So there are no pure particulars or pure universals.

(A) But if every universal is relative to particulars, how can it serve as an explanatory principle? Insofar as it is particular, it requires further explanation.
(B) And if every particular is defined by universals, how can it be distinguished from them so as to be explained by them?

(v) VT: the Trinity explains this situation.

(A) God is both perfectly particular and perfectly universal, many and one.
(B) The world is made in his likeness.
(C) The correlativity of one and many in the world is like the correlativity of these in God; hence there is mystery.
(D) Van Til's "solution" does not give us pure universals or pure particulars, or the kind of exhaustive knowledge that these would bring us. Rather, it calls us to trust that he has a perfect understanding, both of himself, and of his world.

Frame's basic procedure here has a simple two-step formula: first the nature of the problem (as Van Til-Frame conceive it) is presented, then the "solution" (namely the triune god of Christianity) is presented. In presenting the problem (premises i-iv), two of the premises (i & iii) are concerned with what we "cannot" do, and the remaining premises (ii & iv) provide us with a glimpse of the presuppositionalist understanding of the nature of universals and their relationship to particulars. In proposing Christianity's notion of the trinity as the solution to the problem outlined in premises i-iv, certain vague and dubious statements are provided to support the view that the problem of universals requires the Christian god to solve it, even though it is apparently stipulated that "mystery" rather than understanding is the final outcome so far as man is concerned.

In my analysis below I will show how the way in which the problem is conceived suffers from its own debilitating problems, thus calling into grave question the position that a theistic solution is required. Also, I will show how the solution that presuppositionalism proposes is arbitrary and thus useless.

The Problems with Van Til's Understanding of the Problem

To expose the fundamental errors of the Vantillian conception of the nature of universals, let us review the premises that Frame presents in outlining the problem as presuppositionalism conceives of it.

Premise (i):

We cannot identify particulars and distinguish them from one another, without uniting them by universal terms.

This is wrong. A child's initial verbal identifications are of particulars which he names specifically, either by proper names (e.g., Jack, Bill, Alice, Fido, etc.) or by titles (such as 'Mommy', 'Daddy', 'Uncle', etc.) which are used in the same manner as proper names (i.e., to name something specific rather than a class of entities united under one term). By use of proper names and titles, both of which are not universalistic, one can both identify particulars and distinguish between one and another. A child, for instance, can perceive his mother and his little brother, and he can distinguish between them by calling the one Mommy and the other by using his first name Jack. A child does not begin his task of identifying the objects around him with fully constituted concepts already in place. So I would have to contest what Frame states here rather strongly. Even as adults, we can identify and distinguish particulars from one another by use of proper names as opposed to universal terms. In fact, we use universal terms (that is, concepts) in order to treat a group of particulars as a group. And even when we use concepts to distinguish between particulars which those concepts subsume, we find that we must use qualifiers which isolate one particular from another or group of like objects. For instance, I might say "this book as opposed to that book" to identify and distinguish particulars. So even when we use universal terms to refer to specific particulars, we have to modify them. It is disappointing that Van Til-Frame could be so off on this point. And yet this is where the presuppositionalist starts his argument!

Premise (ii):

But the universal terms exclude particularities ("dog" and "Fido"). So they cannot explain all particularities.

This is wrong. Universal terms, if they are formed properly, include all particularities subsumed under the class of objects which they name. The concept 'dog' for instance includes specific animals such as Fido, Spot, Bowser, etc., as well as sub-classes, such as dachshund, beagle, golden retriever, etc. This is because the concept 'dog', when unqualified by context-specific modifiers (e.g., adjectives, adjectival phrases and clauses, specific context, etc.), includes in its scope of reference all dogs (and all kinds of dogs) past, present and future. Also, it is unclear what Frame has in mind when he wants to conclude (on the basis of this erroneous assumption or otherwise) that "universal terms... cannot explain all particularities." The purpose of concepts ("universal terms") is not to explain the objects which they name, but to enable a thinker to treat a whole class of objects, regardless of however many there might be, as a unit. These classes in turn can be used in informing explanations, but by themselves they are not intended to serve as explanations.

Premise (iii):

We cannot define the universals, either, except by means of particularities. But particularities, individuals, are not universal; so whence comes universality?

This is wrong: We can - and do - define universals in terms of other universals (save in the case of axiomatic concepts). Of course, to understand the purpose of definitions and the way in which they are properly formulated (for instance, there is a difference between a definition and a description), one needs a good understanding of concepts (I've asked Christians, to no avail, where such understanding might be found in the bible), and as part of the theory of concepts the recognition that essence is epistemological (religious philosophy tends to treat essences as if they were metaphysical). According to an objective theory of concepts, essence is a property of concepts, not of particular entities which exist independent of our consciousness of them. This theory holds that

the essence of a concept is that fundamental characteristic(s) of its units on which the greatest number of other characteristics depend, and which distinguishes these units from all other existents within the field of man's knowledge. Thus the essence of a concept is determined contextually and may be altered with the growth of man's knowledge. (Ayn Rand, Introduction to Objectivist Epistemology, p. 52.)

In defining a concept, the concern is to identify the nature of the units it subsumes and "to distinguish a concept from all other concpets and thus keep its units differentiated from all other existents." (Ibid., p. 40.) Thus it is appropriate to identify the essential characteristic which the units subsumed under a concept have in common, and doing this requires (except in the case of axiomatic concepts) the use of other concepts. How could we formulate a definition for the concept 'lemon', for instance, without using the concept 'fruit'?

It is encouraging to see Frame asking the question "whence comes universality?" for he will not find the answers to such questions in the bible. When it comes to such issues, religion provides no answers and leaves its adherents epistemologically stranded in the Dark Ages. The implication of presuppositionalism is that this is such a stumper question that we're all supposed to throw up our hands in bewilderment exclaiming "I donno!" and thus point to the Christian god as the "explanation."

From the foregoing, Frame seems to draw as a sub-conclusion his Premise (iv):

So there are no pure particulars or pure universals.

It is not clear what this statement is supposed to mean or how it is supposed to follow from what Frame has stated up to this point. What is a "pure particular" as opposed something that is not a "pure particular"? Similarly, what is a "pure universal" as opposed to something that is not a "pure universal"? Is a rock a "pure particular" or something other than a "pure particular"? Is the concept 'rock' a "pure universal" or something other than a "pure universal"? It's not apparent what these expressions could possibly mean, and I wonder if Frame explains them anywhere. Perhaps Frame simply does not understand what distinguishes a particular from a universal, or maybe he hopes his readers don't. Any specific rock, like the one I dug up in my garden last week, is a particular object, not a partially particular object, not a quasi-particular object, not a half-particular, half-non-particular object. Also, the unqualified concept 'rock' applies to all rocks, and in this sense, that is in the sense of referential scope, it is wholly universal. So again, it's not clear what Frame means here, but I admit that it's quite difficult to shake the impression that he's simply trying to muddy the waters to make them appear deep.

Frame offers the following two points, either as somehow supporting the sub-conclusion that "there are no pure particulars or pure universals," or at any rate as implications to be reckoned with:

(A) But if every universal is relative to particulars, how can it serve as an explanatory principle? Insofar as it is particular, it requires further explanation.
(B) And if every particular is defined by universals, how can it be distinguished from them so as to be explained by them?

Here we see Frame repeating the notion that universals are intended to explain the particulars which they name. But as I pointed out above, this is not their purpose. The purpose of concepts is to provide man's consciousness with the economical means he needs in order to expand his consciousness beyond the perceptual level. Concepts accomplish this task by providing him a conscious means of treating all members of a class of entities, attributes, actions, qualities, relationships, etc., as a single unit, thus equipping his mind with a kind of mental shorthand which can be used in referencing an open-ended range of units both perceived and unperceived, whether they exist in the present, in the past or in the future. The concept 'man', for instance, is not intended to "explain" either one man or all men; rather, its purpose is to allow the human mind to treat all men - regardless of their number or individual attributes - as a unit unto its own.

Moreover, it is unclear what Frame means by universals being "relative to particulars." Objectively formed concepts are based ultimately on the objects which we perceive firsthand. Thus the tie between our knowledge, which takes the form of concepts, and the reality to which our knowledge relates, is a faculty which in fact has an objective nature. That is, perception is not informed volitionally; we do not get to choose what we perceive. We perceive what we perceive, whether we like it or not. It is in this sense - i.e., in the sense that perception is not an invention of consciousness - that it has an objective nature. Our volition comes into play when we make the choice to think or to evade thinking. We also make choices when it comes to forming concepts as well, whether to integrate the objects we perceive into mental units, or to remain stranded at the perceptual level (cf. concrete-bound), attempting to identify each particular object with its own specific title, and never graduating beyond the mentality of a toddler.

Next Frame asks a question which turns on the assumption that particulars are "defined by universals." This, too, is mistaken. We define concepts, not the specific entities or attributes which they name. We are not defining the particular entities or attributes that we name when we include them in a larger, mental unit that includes similar entities or attributes; these things do not need us to define them, since they exist independent of consciousness. To exist already means to be something specific, so the notion of "defining a particular" makes no sense: an entity is distinct from other entities, not by virtue of some conscious act of defining it, but by virtue of the fact that it exists. Definition, on the other hand, is the final step in concept-formation, and pertains to entity classes and other abstractions residing on the higher rungs of the conceptual hierarchy. An objective conceptual theory, then, must be consistent with an objective metaphysical orientation.

(Related to this is the common error among theists and other thinkers who treat meaning as if it were metaphysical. On the contrary, meaning is epistemological, that is, having to do with the content of our concepts, their relationship to the objects to which they refer, and the statements we build from them. Just as definition is a property of (properly formed) concepts rather than of particular entities which exist in the universe, the concept 'meaning' applies to visual and verbal symbols we use to represent concepts in our thought and communication. Another common error is to confuse the concept 'meaning' with other concepts, such as purpose or significance.)

Frame's concern at this point is in distinguishing particulars from universals. In fact, this constitutes an insuperable problem for theists, and it is interesting that Frame even comes so far as to pose the question in the first place. The reason why distinguishing particulars from universals is problematic for theists is the same reason why Vantillian apologists so habitually confuse "presuppositions" with metaphysical conditions. The problem originates in the blurring of the subject-object relationship, a bad habit which lies at the very core of the religious view of the world. By reversing the orientation of the subject-object relationship, thereby granting metaphysical primacy to the subject side of the relationship (cf. an omnipotent consciousness which creates existence and can manipulate the nature of entities at will), theism starts off on the wrong footing from the very get-go, booby-trapping the cognitive operations of those who accept its false premises, thus fatally undermining truth and every valid concept in one fell swoop at the very beginning of the philosophical enterprise. Basing philosophy on the recognition that the primacy of existence is absolute and incontrovertible, a genuinely rational philosophy avoids these kinds of problems. By recognizing the proper orientation of a subject to its objects, the primacy of existence consistently acknowledges the distinction between the metaphysical (the world of concrete particulars which exist independent of consciousness) and the epistemological (the means by which man's consciousness identifies and integrates what he perceives into open-ended classes or mental units).

Frame, of course, wants to point to the Christian god as the "solution" to these alleged problems (which, it should now be clear, are the result of dramatic misconceptions). Isn't it nifty how apologists always find the solution to problems in the god they imagine?

An Arbitrary Solution to an Arbitrarily Conceived Problem

When apologists point to the Christian god as the solution to philosophical problems associated with universals, we need to keep in mind the fact that claims about invisible magic beings are ultimately untestable and incapable of being validated, essentially because they are at root arbitrary. An arbitrary claim is one which constitutes a fundamental departure from reality. One can claim anything he wants about an entity that no one can perceive; how is one to confirm what he says about it? How is one to disconfirm whatever he says about it? How can one reliably distinguish between what a theist claims and what he is only imagining? Theists of every stripe and creed will insist that they are not merely imagining, emphatically asserting that what they claim is not only actually true, but also binding on all human beings.

With these points in mind, consider the Vantillian "solution" to the problem of universals as presuppositionalism characterizes it.


God is both perfectly particular and perfectly universal, many and one.

Statements like this ultimately come to us on an "I'll take your word for it" basis; they are claims which are intended to be accepted uncritically on the speaker's say so, not examined for their sensibility. There is no way to look out at reality and observe something which confirms the claim that Frame states here.

That having been said, one can understand the idea of something being both particular and universal from an objective standpoint. (This of course rules out subjective worldviews which premise reality on the intentions of an invisible magic being.) For instance, Objectivism's very starting point - 'existence exists' - subsumes every particular and applies universally, literally all particulars in a single plenum, the ultimate many in the one. Existence is particular in the sense that to exist is to be something specific, i.e., particular. Existence is universal in the sense that anywhere you go in the universe, you'll find something that exists. We can say this because 'universe' means the sum total of all that exists. Thus by definition existence exists everywhere in the universe. Also, the axiomatic concept 'existence' is a universal including every entity and attribute that exists (by virtue of the fact that those entities and attributes exist), and the axiom 'existence exists' applies universally (e.g., there is no place in the universe where this is not true). So as rational thinkers, Objectivists begin with a fully informed one-and-many that is perfect in the sense that there are no exceptions in reality to which its fundamental truth does not apply.

But can any of this be said about the Christian god? Again, one can claim anything about something that resides only in one's imagination, for in this fake environment it is very easy for the arbitrary to serve as one's guide and standard. If one is determined not to be constrained by facts and reason, what is to serve as a barrier to his concoctions? Since theism constitutes a fundamental departure from facts and reason, effectively severing the mind of the believer from the reality in which he lives, we know that a theistic worldview's pronouncements cannot be true. Does it make sense to claim that a single entity is both particular and universal? If these concepts are formed on the basis of imaginative fabrication as opposed to objective inputs, why not? After all, doesn't Bugs Bunny look quite at home in his cartoon universe, a universe where a master designer has final say on what exists and what happens?


The world is made in his likeness.

Affirmations such as this indicate that those who want to stand by them do not fully grasp what it is they are saying. For one thing, the subjectivist implications are difficult to miss. It is essentially saying that the world is a product of conscious activity - that a subject created it, that the world is a product of the unconstrainable wishing of a cosmic, omnipotent consciousness. What could possibly serve as evidence for such a position? Theists have throughout history attempted to concoct some way of finally substantiating such claims, but from what I have examined they all fail to deal with the question at hand: How can consciousness can hold metaphysical primacy over its objects? Theists have to assume the opposite, in effect borrowing from a non-Christian viewpoint, to assert and defend such a view as truth, since the concept 'truth' is squarely premised on the principle that the entities we perceive exist independent of a person's wishing. On Christianity's premise of granting primacy to a subject of consciousness, one has no objective basis to make any truth claims. He has basically pulled the rug out from underneath himself.

To investigate the Christian claim that the world was "made" in the likeness of the Christian deity further, we can compare what the world is like to the claims theists make about their god, and see if in fact there is any "likeness" which obtains between the two in some way. But this exercise will certainly spell death for such theistic views. For this likeness would have to be borne out on a general level in order to be signifant enough to give any credibility to such a claim, and yet it is precisely on the level of general characteristics that such a likeness simply does not exist. For instance, observe the fundamental antinomies between Christianity's "God" and the world in which we exist:

  • "God" is said to be infinite, but the world is not infinite
  • "God" is said to be immaterial, but the world is not immaterial
  • "God" is said to be supernatural, but the world is not supernatural
  • "God" is said to be incorruptible, but the world is not incorruptible
  • "God" is said to be perfect, but the world is not perfect
  • "God" is said to be immutable, but the world is not immutable
  • "God" is said to be divine, but the world is not divine

With such dramatically contrastive opposites as these (and others could be cited, e.g., the Christian god is said to be both omniscient and infallible, but the world is neither of these, etc.), the notion that the one was made in the likeness of the other is quite far-fetched, to say the least. Where is the "likeness"? The world is full of deficiencies. Theists themselves, in their attempts to argue for their god, regularly point to the world as a ever changing place of "constant flux," while their god is said to be the diametric opposite of this. Given these fundamentally divisive incongruities, how can one say it was "created" by a "perfect creator"? How can one say that this world, made of dirt and rock and other crude elements which break down and reform into new shapes and relationships, is in any way "like" the god of Christianity? Is the god of Christianity like a barren desert, an overgrown jungle, or an inhospitable polar ice cap? That's what we find in the world. At best, the Vantillian can claim some highly abstract "likeness" - one which allows him to ignore these vast and pervasive dissimilarities, and settle in his mind that this abstract "something" - again a phenomenon which cannot be reliably distinguished from his imagination - connects this world to the supernatural consciousness he wants to worship.

Frame wants to say that

(C) The correlativity of one and many in the world is like the correlativity of these in God; hence there is mystery.

But as should be clear now, the correlativity between concepts and the objects they identify and integrate has nothing to do with the Christian god. Indeed,it is a mathematic relationship, akin to the relationship between a variable term in an equation and an integer which can stand in its place. With an objective understanding of concepts, there is no mystery here. In fact, if all that Christianity can do in the end when attempting to offer a solution to the problem of universals amounts to throwing up one's hands and saying "it's all a mystery!" what good is that solution? It gets one no further than where he started.

Frame concludes his summary of Van Til's apologetic use of the problem of universals with the following:

(D) Van Til's "solution" does not give us pure universals or pure particulars, or the kind of exhaustive knowledge that these would bring us. Rather, it calls us to trust that he has a perfect understanding, both of himself, and of his world.

Van Til's "solution" brings us no closer to an understanding of how the human mind forms concepts than if presuppositionalists simply took a vow of silence. Indeed, a genuine understanding of how the mind works is not something they want men to have. On the contrary, so long as their minds remain mysterious to themselves, men will be in a better position to be seduced and controlled by those who seek to catch them in their nets. Van Til's "solution" calls for "trusting" in an invisible magic being, precisely because it offers no enlightenment to begin with. Those who are enlightened do not need to put their trust blindly in the hands of an invisible magic being which refuses to show itself, hold a rational dialogue with those who are supposed to be willing to sacrifice their very lives for it, or simply allow human beings to live for their own sake. Van Til's "solution" requires us to accept religious sloganeering in place of critical thought. It is not intended to be understood, it is intended to be accepted unquestioningly. If it is such a worthy solution, why doesn't Van Til-Frame offer something better?

by Dawson Bethrick