Written By Thomas Perez. August 10, 2010 at 11:27pm. Copyright 2010.
Richard Dawkins often insists that the logic of the design argument immediately raises the question of who designed the designer. From The Blind Watchmaker:
To explain the origin of the [apparent design] by invoking a supernatural Designer is to explain precisely nothing, for it leaves unexplained the origin of the Designer. [p.141]
When I encounter a popular argument like this, I really try to give it the benefit of the doubt, considering that it must touch on some intuition many people share. Otherwise, popular arguments like this would never win the slogan status they do. But I have to confess – I have a truly hard time taking this argument seriously, especially when it’s presented by some sec-web goonie as a tour de force. The theist who even thinks about offering a rebuttal only demonstrates how hopelessly lost and confused he is in the aftermath of this end-all, knock-down argument akin to a modern-day Sherman’s march through theism. Alvin Plantinga similarly notes how this argument has gained momentum among the enlightened:
In Darwin’s Dangerous Idea, Daniel Dennett approvingly quotes this passage [The Blind Watchmaker, p. 141] from Dawkins and declares it an “unrebuttable refutation, as devastating today as when Philo used it to trounce Cleanthes in Hume’s Dialogues two centuries earlier.” Now here in The God Delusion Dawkins approvingly quotes Dennett approvingly quoting Dawkins, and adds that Dennett (i.e., Dawkins) is entirely correct.
Wow. “But the argument finds its origins in great philosophers, like David Hume!” you point out how Dennett pointed out. “So surely it must be some kind powerful weapon.” Point taken – a la Hume, let’s try to take the “who designed the designer?” argument seriously.
It is hard to see what exactly the argument is trying to achieve, much less how it goes about achieving it. Even if we assumed it completely and totally successful, it certainly doesn’t disprove theism or prove atheism. The only sense I can make out of what it wants to show is that we should not infer a designer based on the apparent design in the universe. But even if we concede this, it still does not follow that the universe is not designed or that the universe does not have a designer. All it would show is design arguments that utilize inference to the best explanation are mistaken. As such, the argument does nothing against design arguments the conclusions of which are arrived at deductively or probabilistically.
But does the argument show that we should not infer a designer based on the apparent design in the universe? I think not. Take a look at the assumption the argument rests on:
(1) A only explains B if A has an explanation of a similar kind
But this is just false. (1) can be broken into two parts: a. A only explains B if A itself has an explanation, and b. The explanation of A is of a similar kind. Consider them in turn.
(1a) A only explains B if A itself has an explanation
This is the insight behind the age old “who caused God?” question. There is no reason at all to assume this is true. Physical compounds are perfectly explainable in terms of the elements which compose them even if the elements themselves are not. Furthermore, if this assumption were true, then literally nothing would be explainable. Accordingly, for any explanation to be valid, it would have to have a valid explanation of its explanation, ad infinitum. Well, there goes the entire domain of natural science! The fact is that some things are perfectly explainable in terms of the explanation immediately prior to them. Theists like Richard Swinburne have rigorously argued that a regress of explanation almost always stops at the feet of an agent and his intentions, which leads us to (1b).
(1b) The explanation of A is of a similar kind
If we are to explain complexity in terms of design, so says Dawkins, the designer must himself be just as complex or even more so. To explain one phenomenon by appealing to a phenomenon of a similar kind does nothing to advance an explanation. But why should we think this? This seems more like rhetoric than argument. When an archaeologist unearths an ancient hand-tool of some sort and infers things about its designer (such as why it needed to make said hand-tool), his colleague doesn’t object to the inference because the designer itself must have been at least as complex as the hand-tool. Further, the principle “like begets like”, which no doubt is what Dawkins has in mind, seems to only be true of material causes (even that is debatable). But, of course, God is not a material entity. So applying such a principle in this case blatantly begs the question against the possibility of non-material causes.
In short, the explanans and the explanandum are not always similar. However, we can infer characteristics of the explanans based on the explanandum – and this is precisely why we’re justified in making an inference to intelligence based on the apparent design in the universe. This is also why we’re justified in dismissing the argument as remarkably sophomoric based on Richard Dawkins’ fondness of it. Plantinga, perhaps the world’s greatest living philosopher, thinks even the word sophomoric is an aggrandizement of Dawkins’ arguments:
…much of the philosophy he [Dawkins] purveys is at best jejune. You might say that some of his forays into philosophy are at best sophomoric, but that would be unfair to sophomores; the fact is (grade inflation aside), many of his arguments would receive a failing grade in a sophomore philosophy class.
So the “who designed the designer?” argument is an utter failure. For an entertaining read, see Plantinga’s review of The God Delusion, in which he also tries his best to take Dawkins the philosopher seriously.
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:
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.
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