Church Voices

An argument which I think is begging for a more contemporary and public defense is the conceptualist argument for the existence of God.¹ You’d be hard pressed to find it given a fair treatment of more than a few sentences at best or a passive mention at worst in a typical introductory apologetics text (and unfortunately even thicker books as well). The argument isn’t totally neglected, however. Greg Bahnsen used a form of this argument as his devastating weapon of choice in his lively debate with Gordon Stein.² More recently, William Lane Craig sometimes uses it in his some of his debates.³ Interestingly enough, prominent atheist philosopher Quinten Smith has developed a version of the conceptualist argument that has become quite popular.⁴ The conceptualist argument is named for its relevance to the philosophical view known as conceptualism, which holds that abstract objects are metaphysically grounded in the mind of an agent. But, according to the argument, abstract objects aren’t metaphysically grounded in just any mind, but an ultimate (omniscient), divine mind. That being said, the main focus of the conceptualist argument is the (seemingly) peculiar existence of abstract entities.

Usually contrasted with concrete objects, abstract entities are things like numbers, sets (and other mathematical entities), propositions, properties (and universals), values, relations, laws, theories, etc. What all of these entities seem to have in common is the curious possession of positive ontic status without spatiotemporal extension. That is to say, an abstract object is a real entity that does not exist in space and time. Something exists in space (or time) if it has spatial (or temporal) duration or location.⁵ If something has spatiotemporal duration, that is to say it has a length, height, size, etc. If something has spatiotemporal location, it exists at a certain place during a certain time; we could ask or its whereabouts and when-abouts. But abstract objects seem to lack spatiotemporal duration and location. So if we take numbers as abstract entities, for example, it would be nonsensical inquire of the number 2’s dimensions or whereabouts. Or in the words of Corey Washington, “When’s the last time you bumped into the number one? When’s the last time you slipped on the concept of truth? Or saw a justice sitting by the side of the road?” In addition to being immaterial and timeless, abstract entities are generally understood as being utterly effete (the number two cannot cause anything) and metaphysically necessary (it exists in every possible world).

The conceptualist argument, in short, is that the best metaphysical grounding for the existence of abstract objects is an omniscient mind whose concepts they are.⁶ But unfortunately, the argument can get pretty intricate not only in its formulation, but also its defense. But to keep things clear, a tidy outline of it can be as follows:

1. Abstract objects either:

a. do not exist,
b. are independently existing realities, or
c. exist as mental concepts.

2. Abstract objects:

a. exist and
b. are not independently existing realities.

3. Therefore, abstract objects exist and are mental concepts.
4. If abstract objects exist and are mental concepts, they exist as mental concepts in the mind of an omniscient, metaphysically necessary being.
5. Therefore, an omniscient, metaphysically necessary being exists.

Premise (1) should be uncontroversial, for there has traditionally been three main schools of thought with respect to the ontological status of abstract objects: (1a) nominalism, (1b) Platonism, and (1c) conceptualism. Premise (2) would involve a refutation of the alternatives to conceptualism: (1a) nominalism and (1b) Platonism. With that in mind, lets take a brief look at each.

2a. Abstract objects exist.

As just said, to establish this, a refutation of (1a) is in order. (1a) implies the philosophical view known as nominalism. There are varying degrees of nominalism. Most forms of nominalism amount to trying to save a naturalistic ontology.⁷ If we take naturalism to be the worldview that the only thing that exists is the spatiotemporal universe and nothing more, then there is immediate problem with what to so with abstract objects. Either the naturalist denies their existence outright (extreme nominalism) or he reduces them to spatiotemporal entities and/or mere linguistic or categorical referents (nominalism and moderate nominalism) that don’t have objective meaning (fictionalsim). Arguments against nominalist views are numerous and complex, but I’ll only note a few that can generally be raised against them all. First, it is extremely hard to see how we can, in theory, reduce or eliminate the entire realm of abstract objects and not have our knowledge of the physical world severely depreciated if not precluded. Abstract objects seem truly indispensable. Second, most forms of nominalism run into major difficulty with the problem of property exemplification. It seems concrete objects do have properties like shape, color, size and so forth that are not identical to one other nor to the object itself, but are real, independent nonphysical properties had by the object. The realist (or conceptualist in this case) has a straightforward and powerful account for these features. The extreme nominalist has to give his reductive analysis to show this is not the case.

2b. Abstract objects are not independently existing realities.

Again, demonstrating (2b) would be to show (1b) false. (1b) implies the philosophical view known as Platonism. In contrast to nominalism, Platonism in its basic form has us believe that while abstract entities do in fact exist, their existence is nonetheless inexplicable; they exist naturally and necessarily a se. While there are several major arguments often leveled against Platonism, I’ll briefly mention just one.⁸ The first problem springs from the nature of abstract objects themselves—their causal inefficacy. If abstract objects are truly effete and exist independently from minds, then how is it we have knowledge of them? If Platonism were correct, then it seems reasoning would be impossible. For Platonism would preclude our having a working knowledge of abstract entities like numbers and the laws of logic, each of which are indispensable to our epistemic life.

So it seems neither (1a) or (1b) are plausible accounts for the metaphysical grounding of abstract objects. But that leaves us with (1c); or rather

3. Therefore, abstract objects exist and are mental concepts.

With Platonism, conceptualism affirms the necessary existence of abstract objects but maintains their existence is conceptual in nature; that is, they exist not inexplicably a se but as concepts to be had by minds. But the theist usually has a different kind of conceptualism in mind than what is typically inferred by the term. A basic doctrine of conceptualism holds that abstract objects are grounded in the minds of humans as perceiving agents, as developed by Kant. The theist takes it a step further and argues human minds are an inadequate basis on which to metaphysically ground abstract objects, and so argues further that only an omniscient mind has the capacity to ground such. For our purposes, the former can be called Kantian conceptualism and the latter theistic conceptualism. This distinction leads the theist into a defense of (4), which involves a refutation of the Kantian-type conceptualism:

4. If abstract objects exist and are mental concepts, they exist as mental concepts in the mind of an omniscient, metaphysically necessary being.

Why can’t abstract objects be metaphysically grounded in human minds? Alvin Plantinga provides us with at lest one reason:⁹

It seems plausible to think of numbers as dependent upon or even constituted by intellectual activity. But there are too many of them to arise as a result of human intellectual activity. We should therefore think of them as… the concepts of an unlimited mind: a divine mind.

The main point is that there are far too many abstract entities that have not yet been the object of human conception. There are multitudes of numbers, sets, properties, etc. not thought of—an infinite amount, even! But if abstract objects exist and are mental concepts, but are not mental concepts of humans, then they must conceptually reside within another kind of mind—a mind that has the capacity to host such (metaphysically necessary) infinitude. In short, if not humanly conceptual on account of our ignorance, abstract objects are most plausibly divinely conceptual on account of omniscience. And so we may now accept premise (4). And this of course brings us to our conclusion:

5. Therefore, an omniscient, metaphysically necessary being exists.

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1. The conceptualist argument is closely related to the transcendental argument for the existence of God.
2. This debate is freely available online in both audio and transcribed formatting here.
3. For example, see the Craig-Tooley debate and the Craig-Washington debate.
4. Quentin Smith, ‘The Conceptualist Argument for God’s Existence’, Faith and Philosophy, 11, 1 (January 1994), pp. 38-49. In fact, the whole chapter is available online here.
5. I have borrowed this wording from J. P. Moreland, Universals (McGill-Queen’s University Press: London, 2001), p. 17.
6. This definition is borrowed from J. P. Moreland and William Lane Craig, Philosophical Foundations for a Christian Worldview (IL: InterVarsity Press, 2003), p. 498.
7. For a good survey of the major arguments against the various forms of nominalism, see J. P. Moreland, Universals (McGill-Queen’s University Press: London, 2001), pp. 23-73. And for the problems naturalists face with abstract objects, namely, properties, see J. P. Moreland, “Naturalism and the Ontological Status of Properties,” in Naturalism: A Critical Analysis, ed. William Lane craig and J. P. Moreland, Routledge Studies in Twentieth-Century Philosophy 5 (London: Routledge, 2000), 67-109.
8. For a good survey of the major arguments against Platonism, see two articles by Paul Benacerraf, “What Numbers Could Not Be,” Philosophical Review 74 (1965): 47-73 and “Mathematical Truth,” Journal of Philosophy 70 (1973): 661-79.
9. Alvin Plantinga, “Two Dozen (or so) Theistic Arguments,” lecture presented at the 33rd Annual Philosophy Conference, Wheaton College, October 23-25, 1986.