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A Conceptualist Argument for the Existence of God

Wednesday, January 9th, 2008

Over two decades ago Thomas Morris and Christopher Menzel published their widely influential paper “Absolute Creation,” provoking a brainstorm of thought among philosophers on the relationship between God and abstract objects.¹ Extending as far back as Plato (Sophist 246a-c), the topic overall is not by any means new. Nonetheless, fresh insights on the nature of abstracta have been breathed into the metaphysics of theism, providing new resources for the project of natural theology—in particular the so-called conceptualist argument for God’s existence. Alvin Plantinga foresees the argument’s barebones:

Suppose you find yourself convinced that (1) there are propositions, properties, and sets, (2) that the causal requirement is indeed true [i.e., a causal relationship between an external object of knowledge and the knower], and (3) that (due to excessive number or excessive complexity or excessive size) propositions, properties, and sets can’t be human thoughts, concepts, and collections. Then you have the materials for a theistic argument.²

Although Plantinga mentions this argument on a number of occasions, he unfortunately never elaborates much more than the above. I hope to sketch, in slightly more detail, a possible formulation of the conceptualist argument, or at least show in the endnotes that there are more than enough resources available in contemporary philosophy to furnish one. In so doing I also hope to show how the existence and nature of abstract objects bodes trouble for naturalism.

First and foremost, what are abstract objects and why bother arguing over their existence? Relevant literature on abstract objects can be divided into two categories: epistemological and metaphysical.³ By focusing only on a single object of thought and disregarding areas of peripheral awareness, the former category explores the notion of “abstract object” as merely an object of mental abstraction. The latter category, on the other hand, seeks to explore issues of ontological significance—do abstract objects exist? If so, what are they and what explains their existence? The two categories often overlap, but most of what follows will deal only with the metaphysical sense, focusing in particular on the ontological status of abstract objects.

Perhaps the best way to understand what an abstract object is is to provide examples rather than state necessary and sufficient conditions for their existence. Entities such as propositions, laws, relations, values, universals, logical and mathematical objects (numbers, sets, lines, shapes), fictional objects (characters, storylines, fantasy worlds), pieces of art, possible worlds, etc. are all commonly cited as abstracta. Abstract objects are typically contrasted with concrete objects, or substances, such as tables, trees, baseballs, and, if they exist, immaterial persons such as Angels and God. Gideon Rosen⁴ contrasts paradigmatic cases of each:

ABSTRACTA CONCRETA

Classes Stars

Propositions Protons

Concepts The electromagnetic field

The letter A Stanford University

Dante’s Inferno James Joyce’s Copy of Dante’s Inferno

… …

Even though clear examples of abstracta are not hard to come by, a good analytic definition of ‘abstract object’ is. Several criteria have been offered, but three stand out. First, abstracta are causally impotent. The number two, for example, cannot cause any effects. They are essentially acausal. This first criterion entails the second: abstract objects are unextended and immaterial. Philosopher Corey Washington captures this nicely when he asks, “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?”⁵ It is worth mentioning that this criterion doesn’t necessarily mean abstracta are non-spatiotemporal. For example, if the truth-value of tensed propositions are relative to when they’re uttered, this implies propositions are in some sense temporal. Or again, it is hard to make sense of a property (e.g. a universal) being exemplified by two different particulars without using spatial referents. But this suggests that properties are, at least in some sense, spatial. To avoid the bottomless issues relevant to linguistics and universals, I prefer to identify abstract objects simply as immaterial and unextended rather than non-spatiotemporal.

Lastly, at least some abstract objects are necessarily existent. That is to say, some abstracta exist in all possible worlds. For example, propositions which are broadly logically necessary, such as “whatever has a shape has a size” seem to exist and be true in all possible worlds. Even propositions whose truth-values are subject to change seem necessary. For example, the proposition “there are human beings” could have been false, but it is hard to see how it could have been non-existent. Moreover, if propositions are necessary, then numbers can plausibly be taken as necessary also. Neil Tennant has persuasively argued that certain necessary propositions such as “There are n Fs” and “The number of Fs is n” incur ontological commitment to at least one number; namely, 0. If 0 exists, says Tennant, it must exist in all possible worlds.⁶ Why does Tennant think 0 must exist in all possible worlds? Briefly ponder the following proposition:

(P) There is no possible world such that there are no things that are not self-identical

It follows, according to Tennant, that (P) entails the existence of 0 as the number of things that are not self-identical. Indeed, the necessity of a whole host of abstract objects seems entailed by a similar concept; the impossibility of a null-world.⁷ To see why, Thomas Morris asks us to try to imagine a world in which nothing exists:

If there could be such a world, it would be a world, or state of affairs, in which the number of things that exist would be properly numbered by the number 0. The number 0 would be instantiated, or exemplified, precisely by the absence of anything else. But then it would have to exist to be exemplified, or to number the things that exist.⁸

Now if the number 0 exists in all possible worlds, then there is at least one number in all possible worlds, which implies the number 1 also exists in all possible worlds. In fact, that the number 1 exists necessarily seems to be true a priori of possible worlds, in that it will always designate the number corresponding to whichever world is possibly actual (i.e., the number 1 exists in the actual world because it refers to the number of worlds that are actual). But if that’s the case, there are at least two numbers in all possible worlds, 0 and 1, which implies there are three: 0, 1, and 2. And so on. So long as numbers necessarily exist, we can say properties and relations necessarily exist, too. For numbers have properties such as being even and stand in relations to other numbers, such as being more than. Morris summarizes:

The net result of such reasoning is that it is plausible to suppose that such abstract objects as numbers, properties, and propositions necessarily exist as a sort of formal framework of reality, providing necessary conditions for the possibility of any world.⁹

Why bother arguing over the existence of such entities? J. P. Moreland has pointed out that much more goes into the success of a worldview than mere logical consistency. He observes “it sometimes happens that some metaphysical commitment, though logically consistent in a strict sense with competing, broad world views is, nevertheless, more plausible and at home in one rival compared with the other.”¹⁰ Abstract objects, arguably, are a prime example of such a commitment. More to the point, abstract objects are more at home in a theistic weltanschauung than a naturalistic one.

But what sort of naturalism does abstracta supposedly rub against? There are of course varying degrees of naturalism, some strong and some modest. Stronger varieties, such as those committed to a hard-core materialism or only to objects existing within space and time are not just uncomfortable bedfellows of abstracta, they do not share the same bed at all. The vindication of one is the falsification of the other. Hence Howard Robinson’s remark that “materialist theories are incompatible with realist theories…the tie between nominalism and materialism is an ancient one.”¹¹ But more sophisticated versions of naturalism try to make room for abstracta. Take Graham Oppy’s, for example:

(N) a. There are no entities which are causally related to things hereabouts but which are not spatially related to things hereabouts (hence: no souls, no spooks, no entelechies, no gods), and b. there is no sufficiently good reason for believing in the kinds of entities which are denied to exist in a.¹²

There is no prima facie inconsistency between (N) and the existence of abstract objects. However, there are good reasons for thinking there is at least tension between the two—a burden theism doesn’t bear. In other words, even if one could draft a realist ontology of abstracta compatible with naturalism, a better, more-at-home account can be offered by theism. So what accounts are there to consider and into which worldview does the preferred account most comfortably fit?

According to W. V. O. Quine there have traditionally been three main positions regarding the ontological status of abstract objects: nominalism, platonism, and conceptualism.¹³ Each of these three positions can take different forms, but the trichotomy is sufficiently exhaustive and so should be beyond dispute. Nominalism, as previously mentioned, denies the existence of abstract objects, or at least eschews ontological commitment to them. On the other hand, platonism affirms their existence, though as independently existing realities. Abstract objects exist inexplicably a se; they’re just sort of “out there” as part of the necessary furniture of the universe. Conceptualism can be thought of as a middle ground between nominalism and platonism. A conceptualist would say that abstract objects indeed exist but are better understood as grounded in the mind of an agent. We can represent each view respectively in the premise

(1) Abstract objects either a. do not exist, b. are independently existing realities, or c. exist as mental concepts

Given (1), we can begin to outline a conceptualist argument for theism with

(2) Abstract objects a. exist, and b. are not independently existing realities

Establishing (2) can be achieved by either offering positive arguments for it or by refuting its negations, nomonalism (1a) and platonism (1b). What follows is a brief sketch of some of the arguments and strategies one might using on behalf of (2). Taking their negations in turn, why think

(2a) Abstract objects exist

is true? The chief considerations here are indispensability arguments. Indispensability arguments attempt to show that abstract objects are indispensable to our experiential framework. Such arguments work as a sort of reductio strategy against nominalism, or (1a). Whether it be in mathematics, nomology, linguistics, or some other essential framework by which we experience and explain the world, the dispensing of abstract objects would have disastrous consequences.¹⁴ Consider propositions. According to truth-maker theory, truth obtains when some truth-bearer ‘captures’ or ‘corresponds to’ some state of affairs. For example, if Mary is watching television then what makes that true is some truth-maker (the state of affairs consisting in Mary watching television) to which some truth-bearer relates. Several candidates have been offered for appropriate truth-bearers, the most plausible being propositions (in this case the proposition “Mary is watching television”). The proposition“Mary is watching television” is true if and only if Mary is watching television. But if we dispense of propositions as real entities, as nominalism says we should, then we are left with nothing in which to ground truth. But this is absurd.¹⁴ It is up to the nominalist to find an escape route either by rejecting truth-maker theory or by offering an explanation of how to preserve truth despite this problem.

Numbers and other mathematical entities such as sets factor most heavily into indispensability arguments. It is on this point that Quine, who has been called “the leading advocate of a thoroughgoing form of naturalism,”¹⁶ abandoned his nominalist programme and embraced the existence of abstracta as indispensable to our best scientific theories. Quine, along with Hilary Putnam (who is himself no friend of realist commitments), later advanced what has become one of the most influential indispensability arguments.¹⁷ The idea of their argument is roughly the following:

(2a.1) We ought to have ontological commitment to entities that are indispensable to our experiential framework

(2a.2) Abstract entities are indispensable to our experiential framework

(2a.3) We ought to have ontological commitment to abstract entities

Though this argument has been influential, both of its premises have been called into question. Hartry Field, for example, argues that mathematical objects are ontologically dispensable, in a strict sense, but are nonetheless indispensable to our experiential framework as a consistent body of principles. Insistent on having it both ways, Field defends a version of nominalism called fictionalism, where abstract objects are more-or-less useful fictions.¹⁸ Propositions do not really have truth values, but are rather judged useful via consistency within a system or theory. If Field is right, then not only is (2a.1) false, but (2a) would be as well. Fictionalism may seem radical at first, but it should not be too quickly dismissed. For one thing, fictionalism arguably represents the most plausible form of nominalism to date. Moreover, fictionalism may actually prove to be an attractive option for theism in lieu of reconciling necessary abstracta with God’s aseity.¹⁹

These virtues considered, however, fictionalism is perhaps too radical. The most jarring problem is its renunciation of obviously true descriptive states of affairs the truth of which seem to be grounded in certain abstracta (“2 + 2 = 4” or “two entities x and y can have the same shape and size”). For according to fictionalism, such abstracta are merely useful fictions. Indeed, it will be hard to take seriously a view which maintains that propositions such as “4 is divisible by 2”, “Jones believes that [some proposition p]”, or “triangles have three sides” are not just false, but literally truth valueless! Consequently, the truth value of the proposition “something cannot both exist and not exist at the same time” is ontologically equivalent to the truth value of the proposition “2 + 2 = 5”. What are usually taken to be necessarily true propositions such as the former assume no privileged status over and above necessarily false ones such as the latter. So long as they operate consistently within their respective systems, even contradictory propositions could be said to accurately describe the way the world is.

Second, fictionalism may itself fall victim to indispensability arguments. Take Tennant’s argument for the necessary existence of numbers (which can also serve as another argument for (2a)). Even fictionalist accounts cannot avoid quantifying over entities in their reductive analyses, which Tennet says commits them to the existence of numbers. Tennant writes:

Once the language of arithmetic has been adopted…one incurs commitments. These are, first, to the number zero, as the number of non-self-identical things; and, thereafter, to each natural number n in turn, as the number of numbers preceding n. In any world in which one uses a rich enough first-order language—with the identity predicate, the existential quantifier, negation and the numerical term-forming operator #—one has (on reflection) to acknowledge the existence of zero.²⁰

If Tennet’s argument passes, then fictionalism must be false. His argument can be outlined as follows:

(2a.4) There is no possible world such that there are no things that are not self-identical

(2a.5) 0 is the number of such things that are not self-identical

(2a.6) Therefore, 0 exists in all possible worlds

Does Tennet’s argument pass? (2a.4) is self-evidently true, so what support does Tennant give for (2a.5), the argument’s main premise? On the face of it, (2a.5) seems to beg the question against the nominalist by introducing the existence of a number into the premise. But what else could the number zero be replaced by? In Tennet’s words, “one cannot be thinking of ‘0’ as a term which might denote some person, or physical object.” He concludes

Why can one maintain [(2a.5)]? One can only consider the question whether 0 exists by framing the thought ∃x(x = 0) in a language one of whose sentences can be thus regimented. Moreover, one has to be thinking of 0 as a number, that is, thinking of “0″ as a term which, if it denotes anything at all, denotes a number.²¹

The insight behind Tennant’s argument can be formalized into an analytic proof.²² Many philosophers have pointed out that, contra Kant, existential statements are not always synthetic. An analytic proof for the existence of 0 would run thusly:

(2a.7) a exists ≡ (∃y) a=y
(2a.8) (number x) F(x)=0 ≡_df ¬(∃x)F(x)
(2a.9) F(x) is x≠x

Statements entailing the existence of analytic truths such as (2a.4) entail there is something ‘=’ to nothing. But obviously nothing does not exist. So what is there to be equal to? Well, the number 0 itself. Therefore,

(2a.10) (∃y) y=0

It is plausible to think, then, that the number 0 exists and is indispensable to our experiential framework. Even if partial fictionalism is granted (e.g., applicable only to mathematical entities), the fictionalist still bears the burden of extending his theory to incorporate other abstracta if realism is to be avoided. Indispensability arguments such as these prove to be a powerful force against nominalist theories.

What else can be said on behalf of (2a)? Perhaps a brief appeal to intuition favoring (2a) can be made. Upon considering the competing realist and nominalist theories, I get a feeling of unreality about the whole debate. The existence of abstracta is so obvious that realist theories often appear to be guilty of proving the obvious via the less obvious and the complex reductive analyses proffered by nominalist theories are so counterintuitive as to be rejected outright. I think it is the overwhelming consensus that abstract objects do exist, save only the few ever-present philosophers who voice their denials louder than their competitor’s arguments and the crowd’s intuitions. At any rate, (2a) appears to be on solid ground. But what about (2b)?

(2b) Abstract objects are not independently existing realities

A good argument for (2b) often overlooked is that it commits us to the existence of an actual infinite (ℵ₀). If abstract objects are independently existing realities, then each is a definite and discrete entity. But there are an infinite number of abstract objects. Just think of natural number series alone. Throw in sets and the number of propositions expressing possible states of affairs and we’re compiling infinitude on top of infinitude. The problem is that an actual infinite number of things generates absurdities. To simply illustrate, imagine we have a library with an actual infinite number of books. Wesley Morriston concisely summarizes the problem:

Let m = the number of books in our infinite library, n = the number of odd-numbered books, and o the number of books numbered 4 or higher…

(m – n) = infinity, whereas (m – o) = 4.

But,

n = o (since both n and o are infinite)

It follows that we get inconsistent results subtracting the same number from m.²³

The conclusion is that we obviously couldn’t perform such operations in the actual world, so an actual infinite cannot exist. Ergo, platonism, or (1b), must be false. The argument could be outlined:

(2b.7) An actual infinite cannot exist

(2b.8) If (1b) is true, then there is an actual infinite number of abstracta

(2b.9) Therefore, (1b) is false

The great German mathematician Abraham Robinson reasoned similarly, confessing “I cannot imagine that I shall ever return to the creed of the true Platonist, who sees the world of the actual infinite spread out before him and believes that he can comprehend the incomprehensible.”²⁴

What else might be wrong with (1b)? No doubt the most frequent argument lodged against (1b) is known as the epistemological objection.²⁵ If abstracta are independently existing realities as (1b) holds and are also causally effete (as no philosopher to my knowledge denies), then it would be impossible for us to have knowledge of them. To have knowledge of something independent of us entails a relation of sorts; one where information about some object of knowledge can pass from it to us or vice versa. But how can this be if abstracta exist a se and unextended? (1b) therefore renders abstracta epistemologically inaccessible. Where O is some object of knowledge (say, an abstract object), the argument can be summarized:

(2b.1) If O is external to S, S can have knowledge of O only if there is some causal relation R between S and O

(2b.2) O is such that it cannot enter R

(2b.3) If (1b) is true, then O is external to S

(2b.4) Therefore if (1b) is true, then S cannot have knowledge of O

(2b.5) But S has knowledge of O

(2b.6) Therefore, (1b) is false

The best escape route for the platonist would be to refute (2b.1) by offering an account of how we can have knowledge of O that does not involve R. “After all,” the platonist might insist, “the very origin of the term ‘abstract object’ comes from their being ‘abstracted’ from our concepts.” Two replies can be made. First, so long as these “abstractions” remain derivatives of our concepts and do not somehow become independent, free-floating entities, the conceptualist will welcome this view as being similar to his own. Second, so reducing abstract objects to epistemic affairs only is a common nominalist strategy entirely inconsistent with plationism. So what could the platonist suggest as a non-causal relation between us and abstracta? Some form of intuition will be the most likely candidate here, serving to grant us access to abstracta in much the same way perception does concreta. Maybe our minds are such that we simply grasp or intuit the existence of abstracta in the appropriate circumstances. But this route fares no better. The chief difficulty for this approach, according to Alvin Goldman and Joel Pust, is that intuition doesn’t seem capable of delivering the information needed, and so can’t be the source of our knowledge of abstracta. They ask

Is there any reason to suppose that intuitions could be reliable indicators of a universal’s positive and negative instances (even under favorable circumstances)? The problem is the apparent “distance” and “remoteness” between intuitions, which are dated mental states, and a nonphysical, extra-mental, extra-temporal entity. How could the former be reliable indicators of the properties of the latter?²⁶

It will have to take more than intuition to cross the epistemological gap between us and abstracta. To make matters worse, no other candidates appear even remotely plausible. Thus Moreland’s comment that “[such] an attempt to account for knowledge of abstract objects will have to be given in terms of some mysterious, even mystical, aphysical ‘grasping connection,’” which is philosophically repugnant, especially for a contender for (N) (no souls, no spooks, no entelechies, no gods).²⁷ To this effect others have mentioned a sort of “argument from queerness” against platonism. Platonic entities are so foreign to and different from everything else in a naturalist ontology that special pleading against non-reductive theories threatens. In an oft-quoted passage, the late atheist J. L. Mackie wrote:

If there were [abstract objects], then they would be entities or qualities or relations of a very strange sort, utterly different from anything else in the universe. Correspondingly, if we were aware of them, it would have to be by some special faculty of … perception or intuition, utterly different from our ordinary ways of knowing everything else.²⁸

Platonist theories of free-floating immaterial objects knowable only via mystical experience prove adverse and excessive to (N).

Moreover, if there are sufficiently strong arguments in favor of conceptualism, they could count as evidence against both (1a) and (1b). Unfortunately most philosophers see no arguments here strong enough to sufficiently eliminate an alternative view such as platonism. However, this point is not entirely lost for at least two reasons. First, it can be argued that conceptualism has more scope than (1a) and (1b), as it nicely accounts for precisely the desiderata they are at odds with (more on this later). Second, it is the testimony of some philosophers that conceptualism has more intuitive support than its alternatives, or at least enough to make it rationally acceptable in the absence of compelling pros and cons.²⁹ I’ve found this intuition shared by laypeople also. In my discussions about the ontological status of abstract objects with people wholly unfamiliar with philosophical parlance, I often receive the eager opinion that “they’re like, in your brain or mind” before I even mention conceptualism as an option. One instance was even with a Jr. High student! Plantinga gives a similar report: “It also seems plausible to think of numbers as dependent upon or even constituted by intellectual activity; indeed, students always seem to think of them as ‘ideas’ or ‘concepts’, as dependent, somehow, upon our intellectual activity.”³⁰ Admittedly, this doesn’t prove that conceptualism is true, but I certainly think it is a consideration in its favor and hence out of favor with (1a) and (1b).

Furthermore, in a situation like this we might be able to justify our inference (to conceptualism) by appealing to the Principle of Credulity expounded by Richard Swinburne: certain beliefs with which agents find themselves are—in the absence of counter evidence—probably true; the mere fact that you have a belief is grounds for believing it.³¹ These points notwithstanding, there just might be a positive argument for conceptualism after all. Recent thought on the nature of intentionality may provide us one. Intentionality is the property of being of or about something (of-ness or about-ness). Many abstracta seem to be characterized by intentionality. For example, thoughts, as propositions, are of and about things. Possible worlds and (and perhaps states of affairs) consist of and are about descriptions of reality. The curious thing about intentionality is that it is characteristic exclusively of mental phenomena, so much so that it has been dubbed ‘the mark of the mental.’³² The implication is obvious: if intentionality is characteristic exclusively of mental phenomena and some abstracta have intentionality, then by modus ponens abstracta are characteristic of mental phenomena. This argument has the potential to be developed in much more detail (and, to some extent, already has³³). What has been mentioned so far suffices to show how (2) could be met. From (1) and (2) it follows that

(3) Abstract objects exist and are mental concepts

So far any philosopher could accept our running argument regardless of whether God plays a role in their metaphysic. That is not to say, however, that (3) is metaphysically-neutral. Ardent naturalist David Armstrong, a main voice in the realism/anti-realism debate, is not dull to this point:

I suppose that if the principles involved [in analyzing and explaining reality] were completely different from the current principles of physics, in particular if they involved appeal to mental entities, such as purposes, we might then count the analysis as a falsification of Naturalism.³⁴

Atheist philosopher Kai Neilson agrees:

Naturalism denies that there are any spiritual or supernatural realities. There are, that is, no purely mental substances and there are no supernatural realities transcendent to the world; or at least we have no sound grounds for believing that there are such realities for perhaps even for believing that there could be such realities. It is the view that anything that exists is ultimately made up of physical components. … There are no purely mental realities in a naturalistic account of the world.³⁵

Armstrong’s and Neilson’s characterization of naturalism is clearly incompatible with (3). The defender of (N), on the other hand, can yet consistently maintain (3), though not without considerable tension (for reasons outlined above). But here the logical consistency between (N) and (3) ends by adding the explicitly theistic premise

(4) If abstract objects exist and are mental concepts, they must be concepts of a necessary, omniscient mind

What can we adduce for (4)? Why do we need a necessary, omniscient mind? The school of thought known for grounding abstracta in human minds is known as psychologism, traditionally associated with John Stuart Mill’s System of Logic. Psychologism, however, infamously stands as one of the most thoroughly refuted views in this field, beginning with the analyses of F. G. Frege and Edmund Husserl.³⁶ Among phychologism’s insufferable difficulties is its inability to account for the necessity and sheer volume of abstratca. It would do precious little to explain the necessity of one entity in terms of another entity that is itself not necessary. Human minds are wholly inadequate for the task. Say some abstract object O is the concept of some human mind at time t₁. Surely there must have been times t_i–t_n< t₁ such that there were no human minds that had O as a concept. It would be less congenial to say that at t₁ O came into existence than to say O must have existed as a concept of a necessary mind during t_i–t_n. This argument runs backwards as well: given their voluminous and complex nature, there must be abstract objects that have not yet nor will ever be concepts in human minds.

Moreover, it’s a bit too optimistic (even for the philosopher!) to think, as Abraham Robinson remarked, that we can “comprehend the incomprehensible,” such as the hierarchal order of sets or some immensely complex mathematical formula. The existence and truth of abstracta such as these is obviously independent of our cognizing them. Quentin Smith, for example, imagines an infinitely complex conjunct of all true propositions as itself a single proposition. Such a proposition, Smith argues, could only be the accusative of an omniscient mind. In addition to propositions, Plantinga suggests reasons for thinking the same is true of sets, numbers, and properties as well.³⁷ Alternatively, It is not hard to see how the theist’s version of conceptualism would be immune to the standard objections to psychologism. It is also not hard to see how the theist’s version of conceptualism would be a hand-in-glove fit with precisely the desiderata these other theories of abstracta are at odds with: knowability despite causal impotence, unextendedness, and necessity. But if (3) is true and other theories like psychologism that try to “drag everything down to earth out of heaven and the unseen” cannot bear the argument’s weight, then plausibly

(5) Therefore, a necessary, omniscient mind exists

which turn entails ~(N). But the theist shouldn’t be too hasty. It remains to be shown that the conclusion is coherent. If demonstrated that (4), for example, is in some way incoherent, the conceptualist argument would be unsound (here one thinks of Morris and Menzel’s theistic activism). No doubt the theist will also have to spell out in much more detail the version of conceptualism needed. For example, even if the theist establishes conceptualism, it still needs to be said how abstract objects become concepts in human hinds. One can predict the Christian’s appeal to the imago Dei within us, the blueprint of which includes knowledge of abstracta. Moreover, the inherent fallibility and error in our best efforts at reasoning with abstracta would not be surprising given the cognitive consequences of sin. Robert Adams entertains these possibilities:

If God of his very nature knows the necessary truths, and if he has created us, he could have constructed us in such a way that we would at least commonly recognize necessary truths as necessary. In this way there would be a causal connection between what is necessarily true about real objects and our believing it to be necessarily true about them. It would not be an incredible accident or an inexplicable mystery that our beliefs agreed with the objects in this.³⁸

Forthcoming efforts on these and similar issues are already underway.³⁹ At any rate, the existence and nature of abstract objects might prove to be either at odds or flatly inconsistence with naturalism whereas no such difficulties loom for theism. Indeed, abstract objects may provide the tools for a promising theistic argument. I therefore agree with eminent atheist philosopher Quentin Smith that “the conceptualist argument … may be interpreted as contributing to establishing the rational acceptability of theism.”⁴⁰

(more…)

Posted in Arguments for God's Existence, Philosophy | 30 Comments »

ABSTRACTA	CONCRETA

Classes	Stars
Propositions	Protons
Concepts	The electromagnetic field
The letter A	Stanford University
Dante’s Inferno	James Joyce’s Copy of Dante’s Inferno
…	…

(2a.1)	We ought to have ontological commitment to entities that are indispensable to our experiential framework
(2a.2)	Abstract entities are indispensable to our experiential framework
(2a.3)	We ought to have ontological commitment to abstract entities

(2a.4)	There is no possible world such that there are no things that are not self-identical
(2a.5)	0 is the number of such things that are not self-identical
(2a.6)	Therefore, 0 exists in all possible worlds

(2b.7)	An actual infinite cannot exist
(2b.8)	If (1b) is true, then there is an actual infinite number of abstracta
(2b.9)	Therefore, (1b) is false

(2b.1)	If O is external to S, S can have knowledge of O only if there is some causal relation R between S and O
(2b.2)	O is such that it cannot enter R
(2b.3)	If (1b) is true, then O is external to S
(2b.4)	Therefore if (1b) is true, then S cannot have knowledge of O
(2b.5)	But S has knowledge of O
(2b.6)	Therefore, (1b) is false

Archive for January, 2008

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