Logic’s Conceptual Nature
Since man’s sum of knowledge is something he develops throughout the course of his life as he learns about reality and confirms or disconfirms things which he has learned, his knowledge has a hierarchical structure. Since his knowledge takes the form of conceptual integration, the general nature of this structure has certain requisite features, such as its base in perceptual awareness. Our initial concepts (including of course axiomatic concepts) are formed on the basis of perceptual input. Concepts so formed can of course be integrated into higher abstractions, but only subsequently, after these initial, “lower-level” concepts have been formed, for they would first need to exist in order to serve as units for further integration. Man’s higher-level knowledge, then, rests on the validity of his lower-level knowledge, which in turn stands on the perceptual level of his awareness. Peikoff’s own illustrative description of the hierarchical nature of knowledge is worth noting:
Human knowledge is not like a village of squat bungalows, with every room huddling down against the earth’s surface. Rather, it is like a city of towering skyscrapers, with the uppermost story of each building resting on the lower ones, and they on the still lower, until one reaches the foundation where the builder started. The foundation supports the whole structure by virtue of being in contact with solid ground. (Objectivism: The Philosophy of Ayn Rand, p. 130)
But not only is logic’s purpose bound to developing man’s conceptual hierarchy, its very principles are conceptual in nature and so is the suitability of their application to this task. The law of identity, for instance, would not be available to man for this purpose if he could not first form the concept ‘identity’. The concept ‘identity’ is an axiomatic concept. And as a concept, it is open-ended, which means it can apply to anything which exists. The standard equational formulation of the law of identity, i.e., A is A, is so useful because the term A can represent anything which exists. For example, a rock is a rock, a river is a river, goats are goats, financial institutions are financial institutions. This open-endedness of the concept ‘identity’ and all other concepts (including those which inform logical principles) is its universality, which is a product of the abstraction process known as measurement-omission. Briefly, this is the process by which the specifics of the objects which we perceive are treated as variables which must exist, but can exist in any quantity, thus allowing those objects to be integrated with other objects which are similar in some relevant way to form a concept. The concept ‘man’, for instance, includes men who are 5’2” tall as well as those who are 6’4” tall, those who weigh 120 lbs as well as those who weigh 320 lbs, those with light skin as well as those who have dark skin, those who are twenty-two years old as well as those who are sixty-two years old, those who live today as well as those who lived two millennia ago, etc. The open-endedness or universality of conceptual knowledge is specific to man’s consciousness because he is neither omniscient nor infallible. It is this understanding of universality which lead Ayn Rand to discover the mathematical nature of conceptual knowledge:
The basic principle of concept-formation (which states that omitted measurements must exist in some quantity, but may exist in any quantity) is the equivalent of the basic principle of algebra, which states that algebraic symbols must be given some value, but may be given any value. In this sense and respect, perceptual awareness is arithmetic, but conceptual awareness is the algebra of cognition… The relationship of concepts to their constituent particulars is the same as the relationship of algebraic symbols to numbers. In the equation 2a = a + a, any number may be substituted for the symbol “a” without affecting the truth of the equation. For instance: 2 X 5 = 5 + 5, or 2 X 5,000,000 = 5,000,000 + 5,000,000. In the same manner, by the same psychoepistemological method, a concept is used as an algebraic symbol that stands for any of the arithmetical sequence of units it subsumes. (Introduction to Objectivist Epistemology, p. 18)
Premise: All men are mortal.
Premise: Socrates is a man.
Conclusion: Therefore, Socrates is mortal.
But the conceptual aspects of logical syllogism do not stop there. Notice that the very form of the argument can be used to argue other conclusions by replacing its terms with other terms. For instance:
Premise: All cats are mammals.
Premise: Morris is a cat.
Conclusion: Therefore, Morris is a mammal.
Premise: All accounts of UFO sightings are true.
Premise: Marshall Applewhite’s account is an account of a UFO sighting.
Conclusion: Therefore, Marshall Applewhite’s account is true.
Premise: All theistic arguments are sound.
Premise: TAG is a theistic argument.
Conclusion: Therefore, TAG is sound.
There are, then, various key aspects of logic, including its universality, its two-fold purpose and its suitability to the non-omniscient, fallible nature of man’s mind, which are directly related to its conceptual nature. A good understanding of concepts will bring these points out so that we can recognize them explicitly and understand how they apply to man’s mind in general and logic’s applicability in man’s quest for knowledge. And it is precisely this understanding which seems completely absent from presuppositionalism’s case for associating logic with the Christian god.
Bahnsen’s Mishandling of Universality in Logic
Very often, the “case” for logic having its foundations in the Christian deity takes the form of a false dichotomy, where the pro-Christian side is affirmed with little explanation and the contra-Christian side is denigrated to such a degree that no one would want to affirm it. Greg Bahnsen’s views on the topic are not atypical in this regard:
If the laws of science, the laws of logic, and the laws of morality are not seen as expressions of the unchanging mind of God, then the notion of universal and absolute “laws” or the concept of order in the contingent, changing world of matter makes no sense whatsoever. In what way could anything truly be universal and law-abiding when every event is isolated and random? If universality is supposed to be objective, then there is no justification for holding to it on the basis of man’s limited experience, whereas if universality is subjective (internal to man’s thinking), then it is arbitrarily imposed by man’s mind on his experience without warrant. (Van Til’s Apologetic: Readings & Analysis, p. 110n.65.)
It is important to note that Bahnsen is simply wrong to imply that all facts in the universe are “changing.” There is no reason why a non-Christian philosophy cannot identify certain fundamental facts which in fact do not change. For instance, the fact that the universe exists does not change; if it changed, none of us would be able to worry about these matters in the first place. But other facts in the universe do not change. For instance, the fact that the objects of consciousness exist independent of consciousness does not change. The fact that man needs to breathe in order to live does not change. The fact that an appropriate amount of heat will cause water to boil does not change. The fact that cows have eyes does not change. The fact that paper is made of some substance found in the universe does not change. There are many constants available to us right here in the realm in which we live, since there are so many facts which do not change.
Also, observe how Bahnsen fails to support his initial statement here, namely his claim that “if the laws of science [etc.] are not seen as expressions of the unchanging mind of God, then the notion of universal and absolute ‘laws’… make no sense whatsoever.” Instead of offering an argument to support this claim, he follows it first with a question, and then a universally negative assertion which again is not supported with an argument. Let’s examine these in turn.
Bahnsen asks the question: “In what way could anything truly be universal and law-abiding when every event is isolated and random?” The question is phrased in a manner such that it seems to answer itself. Presumably if “every event is isolated and random,” then nothing could “truly be universal and law-abiding” (save perhaps the supposition that “every event is isolated and random”?). Again, notice how Bahnsen’s point here assumes an either-or scenario: either the Christian god exists, or we’re faced with a “changing world of matter” where “every event is isolated and random.” And even though this dichotomy is not defended by Bahnsen (he simply assumes it), his statements and questions make no sense without it. But as I pointed out above, I see no reason why non-believers would be forced into supposing that the world is ever-changing, and that “every event is isolated and random.” In fact, just to categorize something as an event means that whatever it is that one is so categorizing satisfies certain criteria, such as the fact that it has happened, that it has a causal basis, that it is an event as opposed to something else (like a hairball or chocolate bar, etc.). So the “random” part here (if it is supposed to mean “occurring without cause”) can be rejected here (while the apologist’s insistence on it amounts to deliberate misrepresentation of a rival position). And why suppose that “every event is isolated”? Again, Bahnsen does not say why non-theism necessarily leads to such a view. I certainly don’t think it does. We can recognize connections between events, such as the sun shining on the earth and the temperature rising, a car running out of gas and the need to push it to the nearest gas station, or the rise of the Third Reich and World War II.
But perhaps Bahnsen is trying to say that without the existence of his god, such conceptualized connections could not be made. In such a case, we can rightly ask: What does the “God” part have to do with it? If his response is that his god is needed for universality in cognition, then we can safely put this mistaken notion to rest. This brings us to Bahnsen’s universally negative statement:
If universality is supposed to be objective, then there is no justification for holding to it on the basis of man’s limited experience…
But suppose that the theist explains this to mean that his god is aware of every member belonging to every category, that its direct awareness of things is literally universal. Say for instance that when the history of the earth is all said and done, there will have been exactly one trillion human beings which have lived. The theist of course would claim that his god would have direct awareness of all these individuals (let’s call this “comprehensive awareness”) and that this is most likely what Bahnsen would have had in mind as the alternative to “man’s limited experience.” Fine, let’s say that this is what Bahnsen may have had in mind. But even here it’s clear that it’s alleged experience would still be limited, specifically to those (hypothetical) one trillion human beings, and not “unlimited.”
The presuppositionalist may concede this point but say it gains no significant ground for the non-theist. He may point out that Bahnsen believed that universality presupposed such comprehensive awareness of individuals. But does it? Is it really the case that universality is possible only so long as there’s a mind which does have such comprehensive awareness? If that were the case, and the Christian god is that mind which enjoys such maximal awareness, how does that give man universal categories? It seems that this is where presuppositionalism is destined to fall apart, for it fails to offer a clear account of how man forms universal categories in the first place.
One of the more impressive features of Ayn Rand’s theory of concepts is its illustration of how the human mind can form concepts on the scant basis of only two units. Far from needing the kind of comprehensive awareness mentioned above, the objective theory of defines a concept as “a mental integration of two or more units which are isolated according to a specific characteristic(s) and united by a specific definition” (Introduction to Objectivist Epistemology, p. 10, emphasis added). Take the concept ‘ball’ for example. On the Objectivist account, a child needs to have awareness of only two specific balls to form a concept integrating them into a mental unit. Say one is a basketball, and the other a ping pong ball. Both have similarity in the fact that they both exist, they are both round, they both roll on the floor, they both bounce, etc. They are also dissimilar in certain ways: the basketball is much larger than the ping pong ball, he can carry the ping pong ball in one hand, but needs two to carry the basketball, the ping pong ball is white and has very little mass while the basketball is orange with black stripes and heavy, etc. The child forms the concept ‘ball’ by integrating these two units by reference to a specific characteristic which they share and omitting specific measurements which distinguish them from one another. This allows him to integrate new units which he’ll discover later, such as tennis balls, baseballs, billiard balls, etc., into the same concept. Because the concept does not specify the quantities in which the omitted measurements must exist, the concept is open-ended such that later-discovered units can be integrated along with these previously observed units without contradiction. It is, roughly, in this way that even a child is capable of forming universal categories. He did not need “comprehensive awareness” of each and every ball in existence in order to do this. In fact, it is because man’s experience is limited, because man is not omniscient, because he does not have “comprehensive awareness,” that universality is both possible and important to him. Universality treats a potential infinity of units as a single whole. It is because man’s awareness is limited that he requires a mode of cognition which allows him to treat a potential infinity as a single unit. Man’s mind can hold only so much in his immediate awareness at any given time, and concepts allow him to economize his cognition. No one knows how many balls exist, have existed and will exist, but this knowledge is not required to form the concept ‘ball’. And if someone did have such knowledge, concepts would be useless to him, since he’d have “comprehensive awareness” of every unit, making the economizing virtues of conceptualized awareness of no value whatsoever. Man’s justification for universality, then, is not Christian god-belief, but the objective theory of concepts. Bahnsen’s notion that a supernatural, omniscient mind is needed to explain or “account for” universality, is a case of missing the point in the grandest scale imaginable.
As for Bahnsen’s understanding of what universality is as it pertains to human knowledge, all that seems important to him is that it’s only available if his god exists. Beyond this it is unclear, especially when he entertains the proposal that “if universality is subjective…, then it is arbitrarily imposed by man’s mind on his experience without warrant.” His parenthetical “(internal to man’s thinking”) is of little help here. Is he denying that universality is an aspect of the conceptual level of cognition? But again, the charge of subjectivism can be answered here by the objective theory of concepts: If universality is the result of an objective process of abstraction on the basis of perceptual input (as the objective theory of concepts teaches), then as an aspect of concepts it is object-bound, i.e., objective rather than subjective. In such a case, universality is not “arbitrarily imposed by man’s mind on his experience,” but an important component of a method of cognition which is consistent with the primacy of existence metaphysics.
The chief point here is that logic is conceptual in nature, which in turn leads to three relevant truths. Because logic is conceptual in nature:
(i) the basis of logic is the facts of the universe as they are grasped by a consciousness which possesses its knowledge in conceptual form (as opposed to something which is only imaginary);
(ii) it is not the case that logic could find its basis in a mind which would not possess its knowledge in conceptual form. (See my blog Would an Omniscient Mind Have Knowledge in Conceptual Form?)
(iii) a good theory of concepts is crucial to a good understanding of the meta-nature of logic.
Impact on Theistic Arguments
It is important to understand how a lack of a good understanding of the nature of concepts can enable bad theistic arguments. The presuppositionalist argument that logic presupposes the Christian god is a case in point. Below we will observe how such an argument might proceed in action.
As we have seen in the foregoing and in my examination of presuppositionalist statements about logic, the overall scheme of arguments for logic presupposing the Christian god generally takes a two-part format: first it is stated that logic poses insurmountable philosophical tangles for the non-believer due to certain positions (usually inserted by apologists into the non-believer’s mouth) which allegedly follow as a necessary result from non-belief; then it is stated that logic finds its basis in the nature of the Christian god given various attributes which it is said to possess, such as its eternality, its immutability, its inability to lie, its absoluteness, etc.
In developing their case, apologists often treat logical principles as mental laws which hold by some mysterious force called “necessity.” The implication here, it is said, is that these “mental laws” (because they are “necessary”) would obtain even if no human beings were around to mentally grasp them. People come and go, live and die, but these “mental laws” continue indefinitely. They’re “eternal” (e.g., they won’t “die” with us) as well as “universal” (they’re true for everyone, everywhere), and thus they are “necessary” (magically binding?). Dominic Tennant, who defends such an argument, takes it up as follows:
At first blush, the argument presented here seems as poignant as it is simple: mental laws require a mind, and since those mental laws are universal and necessary, it follows that they entail the existence of a universal and necessary mind. This universal and necessary mind is “an aseitic God” – i.e., an eternally and necessarily existing supernatural mind.
…mental laws do imply a mind. By definition, the mental entails a mind; and so universal, necessary mental laws therefore must imply a universal, necessary mental mind. We could otherwise phrase this by saying that such laws must imply an aseitic God. A necessarily existent, noncontingent, underived, and immaterial Mind exists.
To be sure, this ointment catches many flies.
The problem is that its seeming poignancy and simplicity are merely a disguise for its disastrous superficiality. Aside from the fact that this argument commits the fallacy of non sequitur (it does not follow that because mental laws are universal and necessary, they “therefore must imply a universal, necessary mental mind”), what’s lacking is a good theory of concepts as well an understanding of objectivity in terms of the subject-object relationship. In fact, it is in both these areas which certain key confusions are exploited by such arguments in order to make their theistic conclusions seem cogent. In regard to objectivity here, briefly, I will point out that the objective theory of truth assumes the metaphysical primacy of existence, for this is the metaphysical position which recognizes that the objects of consciousness exist independent of the intentions of the knowing subject. It is this fundamental truth – that the objects of consciousness exist independent of the subject of consciousness – which underlies statements like “wishing doesn’t make it so.” But already theism is at a grave disadvantage here, since theism and the primacy of existence (i.e., the principle of objectivity) are in fundamental conflict. (In regard to this latter topic, see my several blogs on the topic.)
But the problems for such arguments do not stop there. We have yet to see how a poor understanding of concepts can make arguments such as Tennant’s seem so compelling. To expose this, let’s explore his reasoning a little deeper.
The example of “mental laws” which Tennant cites is the old Socrates syllogism which we saw above:
Premise 1: All men are mortal.
Premise 2: Socrates is a man.
Conclusion: Therefore, Socrates is mortal.
But to his credit, Tennant does at least attempt to develop the matter a little further. He continues, saying that we are “immediately aware” of the relationship between the argument’s premises “through introspection,” and thus “we believe Socrates is mortal because of the premises.” The words “because of” here indicate “a causal relationship between the premises and the conclusion.” So we have here, according to Tennant, a causal relationship between different mental phenomena, which he characterizes as “a real, non-physical relationship between these premises and the conclusion.”
It is at this point that Tennant invokes a composition fallacy to fend off the anticipated objection of the facts that human brains are physical and a necessary precondition for any human mental activity:
None of this denies that our mental states may correlate to physical states in our brains. But we cannot reduce the mental states to these physical states, because we would then remove truth and intentionality completely, since they are non-physical things. Similarly, we cannot say that the mental states are caused by physical states, because then the only real causation would be physical causation while the mental states are just along for the ride, having no actual influence on what happens. But we have just established that mental states do really have causal influence on other mental states. If they don’t, then logical inference does not actually take place, and the relationship between premises and conclusions does not really exist.
Tennant says something else which seems incorrect:
we agree that this relationship does exist. What is interesting about it, however, is that, although it entails a mind (because it is a mental relationship), it does not entail our minds. We could none of us exist, and yet we must acknowledge that this mental relationship would still hold.
All this is not to say that the existence of human beings is necessary for any facts to obtain, where facts are essentially understood as mind-independent data existing in reality and available for us to discover. But even here, there is a context to keep in mind. What I understand Tennant to be essentially saying is that at least some truths, such as the laws of logic, are timeless, and that they are objective. Since these truths apply for everyone, they do not entail or presuppose any specific human mind’s existence, but since they are “mental” they necessarily presuppose the existence of some mind. Why it cannot be the human mind as such (an abstraction which includes every human mind which exists, has existed and will exist) is not explained. But it seems to me that the laws of logic do necessarily presuppose the human mind, for reasons which I presented in my previous blog, specifically that logic as a method which guides cognition is suited to minds which are neither omniscient nor infallible, which possess knowledge in conceptual form, and whose process of acquiring and validating knowledge is not automatic. These conditions certainly do not suggest the Christian god.
We can say that the laws of logic are timeless because they are abstract. Remember that concepts are formed by a process of abstraction which allows measurements to exist in any quantity. (This is what Rand essentially meant by “measurement-omission.”) One of the measurements omitted in forming them is temporal measurement. The concept ‘man’ for instance does not stipulate that its units have to exist during some specific date range. On the contrary, it includes all men regardless of when they might exist. Thus the timelessness of the laws of logic is concurrent with their conceptual nature: they apply regardless of when the units informing an argument’s terms might exist.
The objectivity of the laws of logic is a corollary of their dependence on the primacy of existence metaphysics, i.e., the recognition that the objects of consciousness exist independent of consciousness. An apple is what it is, for instance, regardless of whether or not we like how they taste or believe they grow only in Antarctica or are ripe only on Tuesdays, etc. Similarly for the laws of logic: the law of identity is explicitly partnered with the primacy of existence because it states that a thing is itself independent of consciousness. This is the first law of logic, and its objectivity is explicitly involved in what it affirms.
But the problem with supposing that the laws of logic, given their timelessness (or eternality) and their objectivity, entails the existence of a “universal, necessary mental mind,” is that the issue of metaphysical primacy has been overlooked and the distinction between subject and object effectively blurred. This “universal, necessary mental mind” (e.g., the Christian god) is also said to be supernatural, omnipotent, omniscient, infallible, and able to create the objects of its own awareness. Such descriptions reverse the proper relationship between a consciousness and its objects, thus affirming the opposite of the primacy of existence, and in the case of logic essentially announces that it would be a mind which could have no use for logic (given its omniscience and infallibility). Where the original point was purportedly to account for the objectivity of the laws of logic, the apologist was lead by his faulty premises to a conclusion which denies any objectivity whatsoever.
Consider the role of objectivity when it is applied to human cognition. When we make statements (a conscious action), we make statements about things (i.e., objects of consciousness). Now it should be easy to see that in order to make statements about objects, those objects would have to exist already, before we could make those statements. (The same principle applies in the case of statements about things we imagine, without implying that the imaginary is real, for even in such cases we would have to imagine the things we make statements about before we could make any statements about them.) So on an objective account, the objects would have to exist independent of any statements made about them. So why wouldn’t we apply this principle consistently, and recognize that the objects of our consciousness would have to exist independent of our consciousness of them in order to make statements about them? We see this in the case of the Socrates syllogism: Socrates and the class of men to which the argument says he belongs, exist independent of the individual apprehending the truth of the argument’s premises and conclusion. If the truth of such premises derive their truth from the objects which their terms subsume (which is a conceptual operation), then a conclusion wholly opposite to the one which Tennant sought to draw is consistently implied: no eternal, universal mind is needed for these truths to obtain, since it is not any specific mind which gives them their truth status, but the objects which are subsumed by their terms and the process by which those terms are formed. This is consistent with the primacy of existence metaphysics – i.e., the primacy of the object in the subject-object relationship, and it is wholly suited to man’s specific type of consciousness, a consciousness capable of the conceptual level of cognition.
In sum, the laws of logic are conceptual in nature, and this very fact, for the many reasons which I have presented here, indicates on several levels that their basis could not be the god which Christians describe in their religious beliefs.
by Dawson Bethrick