Some time ago I tackled the problem of abstract or non-physical objects and how an atheistic naturalism is philosophically incapable of either accounting for or justifying their use, by writing,
“What are non-physical realities? They are those things that we accept even though there is nothing physical about them. These realities appear to be simply arbitrary, merely brute facts, however they demonstrate an undeniable connection to the physical world, so much so that to deny their reality is to deny the physical reality that surrounds us.
One of the problems that I demonstrated is that these objects are imperceptible beyond our senses and our cognitive faculties unless they have been trained to not only detect them but to put them to use. One example that I used to demonstrate this fact is the number “2”, noting,
“…while it can be manifested in a manner that is physical, the meaning behind it is not. Meaning, semiotics, are not physical, they cannot be measured, handled, seen or tasted, but they will insist that these non-physical entities are real, because they need them to be to do the work of proving their reality.
The heart of the argument, not to get wrapped up in unnecessary jargon, is that in order for the concept of a number, like 2, to have any application to reality, the concept of “two-ness”—being a mental concept—must reside in a mind that possesses all knowledge in order to be coherent, much less applicable.
The Christian recognizes the fact that humans are limited beings. One example of such a limitation is found in perception. That is, visually and audibly, human perception is limited to a very narrow band of visible light and detectable sound. In order for someone to say, “There is a concept of two-ness that can be applied to the situation,” there must be an object to which they related either physically or conceptually by which all facts—both physical and conceptual—can be reconciled in order that the thought can be applied.
Now, there are some who believe that non-physical, abstract objects actually pose a problem for Christians, whose foundational presupposition was that there is something that is non-physical from which any and all facts proceed, which we call “God”. This way of thinking has been classified as “theistic activism”, and is described as, “the view that abstract objects depend on God in one way or another.”
I would have to agree, given that abstract objects are imperceptible without a referent. I would also accept that a similar premise is true: “If you deny the existence of God, then the most plausible alternative view for you to take is the view that the physical world is all there is.” Now, this problem is often sidestepped by admitting that, “most philosophers who accept the existence of abstract objects also think that they exist of metaphysical necessity — that is, they cannot fail to exist.” Well, it would seem that admitting that abstract objects are metaphysically necessary that must exist, poses a problem. The problem being that just because you believe something to be true doesn’t mean that it is true, because apart from possessing omniscience—which no philosopher has—there’s any way of justifying that belief in order to say that it is true. It is a belief for which—excluding the fact of the Christian God by which to justify it—there is simply no evidence.
To justify the claim that such is incoherent, the abstract of a paper by philosopher Matt Davidson is quoted. The abstract asserts that, “God can’t be the cause of abstract objects, for *being omnipotent* is both an abstract object and one of God’s essential properties.” The problem with this assertion immediately becomes clear just a few sentences later when Davidson writes, “…God can’t create and instantiate his own essential properties, for that would require him to be causally prior to himself…”
This demonstrates that in making the argument that there is either confusion about what is being said about God and the relationship to the reality of abstract objects or there is a deliberate equivocation going on. Davidson’s paper , while interesting seems to be consistent in conflating the physical property of an object with the conceptual, non-physical properties used to convey what is being described. This problem also exists in the post based upon Davidson’s work.
The question seems to be whether abstract objects are necessary in the same sense as the Christian believes that God is necessary. Much of the argumentation seems to derived on philosophical presuppositions of “possible worlds” rather than theological presuppositions of the actual world. Such is a demonstration of what happens when one allows their philosophy to determine their theology, rather than their theology to determine their philosophy. The question comes down to a matter of causation.
The issue seems to be Christian philosophers importing their ideas into the text, such as in passages like Colossians 1:16, which reads,
“For by him all things were created, in heaven and on earth, visible and invisible, whether thrones or dominions or rulers or authorities—all things were created through him and for him. (ESV)
Now, we have to ask what “things” in question are? Well, in the fuller context Paul is contrasting ruling powers, physical and spiritual in relation to and in contrast to Christ. That is what Paul is specifically speaking about, reinforcing the fact that Christ is the protokos, the firstborn or preeminent one, over the creation through whom and for whom all things were made. Now, this can be extended to physical creation, but it is contingent upon the person making the claim that abstracta are “caused” in the same way that physical objects are “caused” to exist and that they are “things” in the same way that a physical object is a “thing”. I’m going to argue that Paul would have looked confused by the question.
Most arguments seem to boil down to whether or not there is a possible world in which a mathematical statement like “2+2=4” could exist. I’m going to say that is the wrong question. The right question is, can a concept of “two-ness” exist in every possible world, since the statement hinges upon the truth of such really existing.
The question of whether or not 2+2=4 depends upon the conceptual reality of “two-ness” being true. Essentially, this is merely a reframing of the Euthyphro dilemma in mathematical terms. Is “two-ness” merely arbitrary, something God makes up, or does God have to appeal to it, making it external to God? Indeed, the philosophical theist, who places his philosophy first is in a pickle, caught between the horns of a dilemma: go one way, and the reality and applicability of numbers is undermined. Go the other and there is something external to God.
The splitting point, to the theological Christian is that God knows himself and that those concepts can only be anchored in God’s knowledge of himself and his creation. That the only reason that one can say that 2+2=4 is a true statement is because there is one God, who exists in Three Persons: Unity in Trinity, and Trinity in Unity. Human concepts can only be meaningful and true if there is an all-knowing, self-sufficient God who holds things—both physical and conceptual—together, and who has made sufficient revelation.
The concept of two-ness that undergirds the mathematical statement in question is dependent on God’s self-knowledge of the distinction between being and person. The concept of “omnipotence” only has meaning if there is a God whose power makes it coherent in his sovereignty over all things. The problem comes when these are confused.
Such confusion is seen in statements such as,
“…God’s causal activity is necessarily dependent on the prior existence of at least some abstract objects (e.g., the property of being omnipotent)…
The question is, what is the “abstract object” in question? Well, it’s the word “omnipotent”. Did God need the English language to exist and construct the word “omnipotent” to exist before exercising his power to create? Of course not. That’s absurd. It’s conflating cognitive recognition with the power to act, and they’re not the same thing. In fact, the abstraction known as “omnipotent” doesn’t have any causal power in itself, it is merely a linguistic label used to convey a recognized reality.
Abstract objects are necessary for thinking beings who need to communicate indirectly. I am typing words, composed of letters, arranged to follow the rules of grammar, all of which have no physical existence. You are reading the words that I have typed out, and while the letters that compose the words may have physical representation, the meaning and value they possess do not—in and of themselves—exist. In fact, they do not do anything. They have no causal power. So, if someone argues that they exist necessarily, then they are arguing absurdity because the letters do not exist, and neither do the words.
The real issue seems to be a question of “property”: can God be omnipotent if there is no one to conceive of omnipotence as a property? Such a question is nonsensical and I will use the following example to demonstrate it.
If diamonds existed prior to the existence of human beings, then diamonds possessed all of their inherent physical properties before there was a human to articulate them in language.
Did the physical properties of diamonds somehow change by the coming about of human beings who needed and used language and the abstractions present in language? Of course not.
If omnipotence is a necessary and inherent property of God then the linguistic abstraction “property of omnipotence” is only necessary—in a linguistically contingent since—for creatures that use language to communicate. And it, like the concept of two-ness that underlies the mathematical statement of 2+2=4 can only be coherent (ie intelligible) if there is a God who has a corresponding concept due to full knowledge of both himself and his creation.
In reality, such questions ultimately display a desire for sinful man to believe that if he can explain a feature of reality, then he has somehow dismissed God. In reality, it displays the sinful impulse to suppress the knowledge of God that every human being possesses through what has been made. The writer of Ecclesiastes is correct when he says, and I am paraphrasing, that men seek out man seeks out many devices in his rebellion.
What such philosophical exercises generally prove is that strict, atheistic materialism is false, proven by the recognition and dependence upon universal, abstract concepts. The atheist in these discussions desires to subject God to external powers and if he can, then he proves that God is not what he is purported to be. The Christian theist must recognize is that there are no facts that exist outside of God’s mind or purpose and that he alone is the only means to reconcile abstractions with human experience.
“If it is true that “in him we live and move and have our being,” we cannot start arguing any “fact” as though it might have its being apart from God. It is impossible to separate the that from the what, or denotation from connotation. If the theistic position is true, the that or existence of any finite “fact” depends upon the what or connotation. God has given that fact. If theism is true, connotation and denotation are identical in the case of the personality of God. The what of God is the that of God. It is this that furnishes the foundation for and is the ground of the necessity of analogical reasoning. The only exhaustive alternative to this position is to say that in the case of any finite “fact” its that and its what are independent and need no reference to God at all. To say that the that of a “fact” is independent of the existence of God but that the what of a “fact” cannot be understood unless reference is made to God, is to try to reason both univocally and analogically at once, and therefore to reason independently of God and his Word.
-Cornelius Van Til. Survey of Christian Epistemology. Chapter 10