Doxazo Theos

Aware of the many alleged prophecies in the Bible, many Christians eagerly point to them as evidence for Christianity without realizing certain constraints under which prophecy needs to be placed in order to have evidential value. When such constraints are in place, however, I think fulfilled prophecy could serve as powerful evidence. The great atheist J. L. Mackie agrees:

[It] is worth noting that successful prophecy could be regarded as a form of miracle for which there could in principle be good evidence. If someone is reliably recorded as having prophesied at t₁ an event at t₂ which could not be predicted at t₁ on any natural grounds, and the event occurs at t₂, then at any later time t₃ we can assess the evidence for the claims both that the prophecy was made at t₁ and that its accuracy cannot be explained either causally (for example, on the ground that it brought about its own fulfillment) or as accidental, and hence that it was probably miraculous.¹

Mackie therefore seems to have the following three conditions in mind that must be met for prophecy to be regarded as evidence:

(1)	The recording of the events must be historically reliable
(2)	The events cannot be artificially forged or coerced into being fulfilled
(3)	Fulfillment by coincidence or chance must be ruled out

Now that the proper restrictions are in place, the question can be asked, Does the Bible contain alleged fulfilled prophecy that meets conditions (1) through (3)? I think it does (if I can assert that without argument for the sake of brevity here). Another way alleged fulfilled prophecy could be used as evidence is by casting it into the form of a design argument. Consider prophecy in the context of Debmski’s so-called Generic Chance Elimination Argument²:

(1)	Some event e has occurred at t2
(2)	The occurrence of e at t2 was outside the control of human efforts
(3)	e was reliably predicted at t1 to occur at t2
(4)	The probability of the e occurring at t2 by chance is very small
(5)	The occurrence of e was only possible at t2
(6)	Given (5), the occurrence of e at t2 remains highly improbable
(7)	The probability of e occurring at t2 by chance is highly improbable
(8)	Contingent circumstances x are necessary for e to have occurred at t2
(9)	We can infer (3) from contingent circumstances x
(10)	One is warranted in inferring that the occurrence of e at t2 was not by chance

The main things to be worked out would be actually calculating the probability in (4) and elaborating on the contingent circumstances in (8). Regarding the former, the work of Peter Winebrenner Stoner and Robert C. Newman comes to mind, where they calculate the probability of individual and collective prophecies’ occurrence by chance.³ Regarding the latter, one would just need to spell out in detail what were the contingent states of affairs (people, places, events, etc.) necessary for the fulfillment of the prophecy.

By way of application, consider the triumphal entry of Jesus into Jerusalem. This event was allegedly prophesied in Zechariah 9.9 which, replete with Messianic language, says “Rejoice greatly, O daughter of Zion! Shout in triumph, O daughter of Jerusalem! Behold, your king is coming to you; He is just and endowed with salvation, Humble, and mounted on a donkey, Even on a colt, the foal of a donkey.” This prophecy is taken to be fulfilled by Jesus as he triumphantly rode into Jerusalem on a donkey, evoking bystanders to rejoice greatly, shouting in triumph, “‘Hosanna! BLESSED IS HE WHO COMES IN THE NAME OF THE LORD; Blessed is the coming kingdom of our father David; Hosanna in the highest!’” (Mark 11.1-11; see also Matt 21.1-11; Luke 19.28-38; John 12.12-16). Stoner and Newman estimate the probability of this prophecy occurring by chance to be 10⁶. The contingent states of affairs necessary for the fulfillment of this prophecy would include things like a messianic figure entering Jerusalem on a donkey accompanied by the scripture-alluding shouts of the bystanders.

The triumphal entry is also a prime candidate for Mackie’s threefold criteria. (1) We have copies of the book of Zechariah predating the time of Christ by at least 100 years. Moreover, the triumphal entry recorded in Mark is very reliable, given Markan priority and the independent source of John’s account. (2) Many of the contingent states of affairs mentioned earlier were not within Jesus’ control (such as the crowd’s reaction) and so couldn’t have been forged. (3) The likelihood of this occurring by chance, as argued by Stoner and Newman, is obviously very low.
Read the rest of this entry »

The issue of intellectual responsibility, or epistemic duties, is at times a thorny one. It is a question at the heart of internalist views of justification, such as deontologism. For the sake of a point, let’s just breeze through whether a deotological view of justification is necessarily internalist. Let’s also suppose that knowledge is justified true belief, where a true belief’s degree of justification is considerably affected by deontic factors. Additionally, let’s suppose the project of reformed epistemology is largely correct and the belief that God exists is a candidate for bonafied knowledge. Now consider the following:

Judy is a 9-year old who has adopted the Christian faith of her parents as a result of being raised in a loving, Christ-centered household. Jay is a 21-year old college student who has adopted the Christian faith of his parents as a result of being raised in a loving, Christ-centered household.

Obviously Judy’s parents’ faith serves as sufficient justification for her belief that God exists, whereas Jay’s almost certainly does not. Although still a Christian at 21, Jay can no longer claim to know God exists because he failed to fulfill his epistemic duty of appropriating the source of justification as he became of age. Of course there is a lot of ambiguity here, such as why and when a source of justification becomes insufficient, but the point is this: I suspect there are many Judys and many Jays in the Church today. I bet there are even those younger than Judy who can rightly enjoy knowledge of God’s existence and others much older than Jay, perhaps having spent their whole life in a church setting, who can’t. Intellectual responsibility should therefore be of paramount importance to every Christian’s life.

I mentioned earlier that if God is essentially good (by “good” I just mean the attribute of omnibenevolence, a.k.a. all-loving, morally perfect, etc.), then he can plausibly be taken to be Trinitarian also. Could there be good reasons for thinking God essentially has the attribute of is goodness?

Oxford philosopher Richard Swinburne argues that “it is logically necessary that an omniscient and perfectly free being be perfectly good,” where a being is “morally perfectly good” just in case he always does the morally best action (Swinburne, The Coherence of Theism [Oxford, ed. 1993], p. 188; Ch 11 respectively). Unfortunately, Swinburne’s argument is less than clear. As best as I can gather from the text, Swinburne’s argument seems to be as follows:

(1)	An omniscient being knows all true propositions
(2)	A perfectly free being will always do an action if he judges that there is overriding reason for doing it rather than refraining from doing it
(3)	An action is morally good if, all things considered, it is better to do than not to do
(4)	There is overriding reason to do morally good actions than to refrain from doing them
(5)	A judgment about what is and is not a morally good action is either a true or false proposition
(6)	Therefore, an omniscient being will always make judgments about overriding reasons for doing actions which are true judgments
(7)	Therefore, an omniscient and perfectly free being will always do a morally good action

Though I am less than confident in my ability to structure it validly, I think this is a good argument at heart. One of the most attractive features of this argument is its independence of the notion of God as a greatest conceivable being, thus bypassing problems of whether perfect goodness is a great-making property.

As has been pointed out, contra Kant, existential statements are not always synthetic. For example, we can offer analytic proofs for the existence of numbers. Case in point, Neil Tennet’s argument for the existence of 0. John Baggaley also mentions this in his article on the ontological argument. Consider the following proof:

(1) a exists ≡ (∃y) a=y
(2) (number x) F(x)=0 ≡_df ¬(∃x)F(x)
(3) F(x) is x≠x

Statements entailing the existence of analytic truths, such as “There is no possible world such that there are no things that are not self-identical” 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,

(4) (∃y) y=0

But as I mentioned before, this may have profound theistic implications.

Consider the first premise:

(1) A perfect being would be omnibenevolent

An omnibenevolent being displays perfect love. It is a being that is “morally perfect” or “all-loving” or “all-good”. An omnibenevolent being is surely greater than a mere benevolent one, or one not essentially benevolent at all. Surprisingly, it is this premise which seems most susceptible to attack. But if it could be established, which seems reasonable to think it could, it seems the nature of omnibenevolence would lead to a trinitarian conclusion. Crucial to omnibenevolence is the perfect exemplification of love. It is love maximally exemplified.

(2)	Omnibenevolence is possible only within a community of at least three persons

What about (2)? At first this seems just arbitrary, but it actually can enjoy some support by reflecting upon the nature of love. A relational display of love is clearly superior to that of a non-relational display. For example, love between two persons is more virtuous and rich than love only concentrated inward (in fact, we have a few contumelious words to describe the later sort of love). Maybe I would even go so far as to say that perfect love is necessarily relational, involving giving and receiving. When love is not relational it is defective and incomplete; we associate undesirable attitudes with it (pride, arrogance, narcissism, etc.). If perfect love is necessarily relational, then for it to be exemplified we need more than one person. Are two persons sufficient for perfect love? Oxford philosopher Richard Swinburne thinks not:

Love involves sharing, giving to the other what of one’s own is good for him and receiving from the other what of his is good for one; and love involves co-operating with another to benefit third parties. This latter is crucial for worthwhile love. There would be something deeply unsatisfactory (even if for inadequate humans sometimes unavoidable) about marriage in which the parties were concerned solely with each other and did not use their mutual love to bring forth good to others, for example by begetting, nourishing, and educating children, but possibly in other ways instead. Love must share and love must co-operate in sharing. The best love would share all that it had. (Richard Swinburne, The Christian God [Oxford, 1994], 177-178)

Perfect love, then, would seem to not only require reciprocracy, but community. Because the love between two persons could be greater (say, by inviting another to share in it), it seems then a community of three persons is sufficient for the exemplification of perfect love. Because three persons are sufficient, we needn’t posit any more. Swinburne concludes:

…perfection includes perfect love. There is something profoundly imperfect and therefore inadequately divine in a solitary divine individual. If such an individual is love, he must share, and sharing with finite beings such as humans is not sharing all of one’s nature and so is imperfect sharing. A divine individual’s love has to be manifested in a sharing with another divine individual…(Ibid, 190)

Which brings us to our conclusion

(3)	Therefore, a perfect being must be composed of at least three persons

Few trends in academia have astonished me more than atheistic moral realism (AMR), the view that moral principles are akin to abstract objects. Because abstract objects are plausibly taken to be necessary and universal, it would seem a comparative neoplatonic form of morality could sufficiently ground the objectivity of moral principles apart from God. This view is championed by atheist philosopher Michael Martin, and others have jumped on the bandwagon as well (Paul Kurtz, Louis Pojman, et. al.). Without detailing a critique, here are some reasons this view strikes me as immanently suspect.

First, if moral principles are treated as platonic abstract objects, then AMR faces the same difficulties Platonism does. Chiefly, the epistemological objection. If moral principles have the same properties as abstract objects (existence a se and causal inefficacy), then such a view would render moral principles unknowable. Knowledge of external objects entails a relation of sorts—one where information about that object can pass from it to us. But how can an unextended, causally effete abstract object enter a relation?

Similarly, abstract objects themselves aren’t exactly complimentary to a naturalistic worldview, much less moral ones (a further defense of these two points can be found here). The late atheist J. L. Mackie:

If there were objective values, 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. (Ethics: Inventing Right and Wrong [Penguin, 1977], 38)

Second, even if we could have knowledge of abstract moral principles somehow and they weren’t in tension with naturalism, such principles would nonetheless be unintelligible. Just what it means to say that moral principles such as justice and charitableness exist alone all by themselves is wholly unclear. I understand what these principles mean when associated with persons (the judge exacted justice; his charitableness is admirable), but to say there exists entities called justice and charitableness apart from persons, or at least states of affairs, is rather uninformative.

Third, even if we could have knowledge of abstract moral principles and they weren’t in tension with naturalism and they were intelligible to us, why should we feel obliged to obey them? Why should be duty-bound by them? They just are. Ethicist Richard Taylor points this out:

A duty is something that is owed…But something can be owed only to some person or persons. There can be no such thing as duty in isolation…Our obligations can … be understood as those that are imposed by God…But what if this higher-than-human lawgiver is no longer taken into account? Does the concept of moral obligation…still make sense?…the concept of moral obligation [is] unintelligible apart from the idea of God. The words remain but their meaning is gone. (Ethics, Faith and Reason [Prentice Hall, 1984], 83-84)

Nothing about a brute given conveys normativity. The problem would be even more pressing were such principles to conflict with my own self-interests.

Fourth, even if we could have knowledge of abstract moral principles and they weren’t in tension with naturalism and they were intelligible to us and we did feel obliged to obey them, why obey certain ones as opposed to others? For every moral value we deem good, surely there exists another which is bad. For example, opposing charitableness would be greed; justice, injustice, and so forth. Why choose to obey the former as opposed to the latter? Pain of arbitrariness seems unavoidable. This in turn lands us right back into the relativism AMR sought to avoid: how can we go about criticizing a person who chooses to obey difference abstract moral principles than the ones we have? To avoid this we can deny the existence of those moral values we see as bad and claim only ones like charitibleness exist (this seems to be the position of Martin and others). But this move itself is completely arbitrary. It seems awfully convenient that only those values we deem good happen to exist and that we have evolved in such a way as to incorporate them into daily living. As is often said, “It’s as if the moral realm knew we were coming!”

Fifth, even if we could have knowledge of abstract moral principles and they weren’t in tension with naturalism and they were intelligible to us and we did feel obliged to obey certain ones as opposed to others, why think they’re any more applicable to us humans than any other creature? If the moral realm just exists wholly apart from creatures, wouldn’t it be just as true and binding for one species as another? To say not would be guilty of speciesism.

Sixth, even if we could have knowledge of abstract moral principles and they weren’t in tension with naturalism and they were intelligible to us and we did feel obliged to obey certain ones as opposed to others and didn’t occasion speciesism, AMR is patently ad hoc. Traditionally, the atheist has agreed with the theist that if morality is objective, God is needed. Consequently, the atheist has bitten the bullet and defended moral relativism. Only recently, however, has AMR been seriously entertained. To me this shows that theism had the upper hand in the debate and that the unlivability of relativism is finally being recognized. Rather than stomach the moral relativism their own view logically leads to, atheists are now borrowing from a theistic metaphysic—sort of like having their philosophic cake and eating it, too.

Finally, even if we could have knowledge of abstract moral principles and they weren’t in tension with naturalism and they were intelligible to us and we did feel obliged to obey certain ones as opposed to others and this didn’t occasion speciesism and AMR wasn’t patently ad hoc, the theistic grounding of the objectivity of morality should be preferred. This is because objective morality fits better into a background theory of theism than atheism. Moreland notes this well:

If evolutionary theory is all there is to the development of the cosmos from the big bang to man, then any view which postulates the brute existence of morals would seem to do so in an ad hoc way. The general background theory would count against the veridicality of the claim to know that morals exist, even though it would still be logically possible for them to exist. If theism is true, one’s background theory explains the existence of human morality. But if one denies God and accepts evolution, then it would seem more reasonable to accept an evolutionary, subjectivist view of morality. The existence of objective values would still be possible, but it would be unlikely and ad hoc, given this background theory. The claim to intuitively perceive such values would have such a background theory as a defeater. The background theory of theism supports such claims and makes them prima facie justified because it removes the background theory (atheistic evolution as the only account for human life and morality) which is the defeater. (Scaling the Secular City [Baker, 1987], 125)

More could be said on this point, such as how theism’s account of objective morality is simpler and has more scope. In other words, Pr(OM|N) < Pr(OM|T), where (OM) is objective morality, (N) is naturalism, and (T), theism.

In conclusion, then, if we could have knowledge of abstract moral principles and they weren’t in tension with naturalism and they were intelligible to us and we did feel obliged to obey certain ones as opposed to others and this didn’t occasion speciesism and AMR wasn’t patently ad hoc and Pr(OM|N) ≥ Pr(OM|T), then I guess AMR isn’t that implausible, afterall.

I was recently asked an interesting question: What is the difference between brainwashing and preaching? At first I thought it a hard question, but as I reflected on it the answer became apparent.

In short, the autonomy of the subject. Brainwashing has as its aim the coercion of assent, whereas preaching respects the listener’s freedom to assent. This is why if a person were brainwashed to accept Jesus, the person’s belief would doubtlfully be salvific, even if it were true. This is a great example of why mere true belief is not sufficient for knowledge. In addition, what is needed is for true beliefs to be arrived at in an appropriate manner, conferring justification or warrant. Brainwashing precludes the possibility of knowledge whereas preaching does not.

John 8.32:

And Jesus said to them…”You will know the truth, and the truth will set you free.” (my italics)

I will assume for the sake of brevity that the Biblical data does in fact enunciate Trinitarian doctrine, and by that I mean we can proof-text the following from scripture:

(1)	There is but one God
(2)	There are three persons, denominated the Father, the Son, and the Holy Spirit, who deserve to be called God

There have been a number of positions which attempted to orthodoxly capture (1) and (2) developed, defended, and refuted. There is also no shortage of fallacious analogies accompanying each. Most did, however, agree that in whatever way the Trinity is to be explicated, it need be in terms of three persons in one substance. Other than that, what has become orthodox in discussions about the Trinity, it seems, is the renunciation of the very possibility of stating or defending the doctrine coherently. Saying the doctrine of the Trinity is “incomprehensible”, “beyond reason”, or “suprarational” (as opposed to irrational or arational) flows with as much ease as the traditional conciliar creeds themselves. One of the most exciting things I’ve discovered in my reading is that contemporary Christian philosophers of first rank have challenged this presupposition. There are now several philosophically-coherent statements of the doctrine of the Trinity on offer.¹ Without detailing each, I want to sketch briefly the model I’ve found to be most defensible and in line with orthodoxy.

Eager to affirm that all three of persons of the trinity are God, most Christians pay no attention to the logic involved. For example, to say “Jesus is God” or “the Father is God” is to assert an identity statement of sorts. In predicate logic, there are at least two types of identity statements that come from asserting the verb ‘is’.² Consider the two statements

(3) George Bush is President
(4) H₂O is Water

We can distinguish here between the ‘is’ of predication and the ‘is’ of identity; the former being instanced by (3) and the latter by (4). The ‘is’ of predication is used to ascribe a property (such as an attribute, role, position, etc.) to the objects denoted by the subject, whereas the ‘is’ of identity is used to state the relation of sameness, or strict identity. It is by equivocating these two uses of ‘is’ that many Christians unknowingly commit themselves to a rather unorthodox position. For if we affirm (1) along with the following

(5) The Father is God
(6) Jesus is God
(7) The Holy Spirit is God
(8) The Trinity is God

using the ‘is’ of identity, we end up with four distinct instances of divinity, or God. But this is obviously an unwelcome conclusion for orthodoxy. So how can we affirm the truth of (1) along with (5)-(8) without committing ourselves to a Quaternity? Oxford philosopher Brian Leftow succinctly outlines the options before us³:

We should immediately follow the right side of the dilemma, and, I suggest, follow the path that ends with what Leftow calls “Plantingian Arianism.” This is because I think it’s clear that denying the divinity of the Trinity is just as unbliblical as denying the divinity of each person of the Godhead. So what is “Plantingian Arianism”? Plantingian Arianism is just one view which holds there are two ways to be divine, so we need not concern ourselves with its details. So far as I can tell, then, “Plantingian Arianism” can be erased from the outline. So the question now is, What’s wrong with there being two ways of being divine? Nothing, I guess. Consider the following example:

One way of being feline is to exemplify the nature of a cat. But there are other ways to be feline as well. A cat’s DNA or skeleton is feline, even if neither is a cat. Nor is this a sort of downgraded or attenuated felinity: a cat’s skeleton is fully and unambiguously feline. Indeed, a cat just is a feline animal, as a cat’s skeleton is a feline skeleton. Now if a cat is feline in virtue of being an instance of the cat nature, in virtue of what is a cat’s DNA or skeleton feline? One plausible answer is that they are parts of a cat. This suggests that we could think of the persons of the Trinity as divine because they are parts of the Trinity, that is, parts of God. Now obviously, the persons are not parts of God in the sense in which a skeleton is part of a cat; but given that the Father, for example, is not the whole Godhead, it seems undeniable that there is some sort of part/whole relation obtaining between the persons of the Trinity and the entire Godhead.⁴

Therefore, we can we affirm the truth of (1) along with (5)-(8) only by qualifying the ‘is’ in each. The picture just sketched is coherent only if the ‘is’ in (8) is that of identity and the ‘is’ of (5)-(7), predication. So while we can affirm the truth of both

each proposition nonetheless mean very different things, for the former is the ‘is’ predication, the latter, identity. And so we can use the title “God” when referring to each individual member of the Trinity by way of predication, though only the Trinity as a whole is aptly deemed such in terms of identity. The church father Hilary had it right when he said “Each divine person is in the [Trinity], yet no person is the one God.”

So how is the Trinity to be explicated? Substance dualism may provide some insight. A substance is that which can have capacities or properties. Substance dualists hold that the soul is a substance which has various capacities and properties, one of which distinguishes persons from other substances—ratio, or rationality. A person can be defined as a single immaterial substance (soul) with a set of rational faculties. The Trinity, then, can be nicely put as being a single immaterial substance (soul) with three sets of rational faculties. On this model we have a single substance sufficient for securing tri-personhood.⁵
Read the rest of this entry »

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 isn’t 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 is more than enough resources available in contemporary philosophy to furnish one. In so doing I also hope to also show how the existence and nature of abstract objects prove troublesome to 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, seeking to answer the question, What is 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 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 aspect, 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 and perhaps more controversially, 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. Tennant further argues that we can deduce the entire natural number series granted only the existence of the number 0. If 0 exists, says Tennant, it must exist in all possible worlds.⁶ Hence, the entire series of natural numbers must exist in all possible worlds. Why does Tennant think 0 must exist in all possible worlds? Consider the proposition

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

It follows simply that 0 is the number of such things that are not self-identical. Therefore, 0 (sequentially, each natural number) exists in all possible worlds. More on this below.

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.”⁷ 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.”⁸ But more sophisticated versions of naturalism try to make room for abstracta. Consider Graham Oppy’s:

(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.9

There is no prima facie inconsistency between (N) and the existence of abstract objects, but 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.¹⁰ 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 consider using on the 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.¹¹ 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”). 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.¹² 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,”¹³ abandoned his nominalist programme and embraced the existence of abstracta as indispensable to our best scientific theories. Quine, along with Hilary Putnam (who himself is no friend of realist commitments), later advanced what has become one of the most influential indispensability arguments.¹⁴ 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.¹⁵ Propositions do not really have truth values, but are rather judged useful via consistency. If Field is right, then not only is (2a.1) false, but so is (2a). 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.¹⁶

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 like “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 x]”, or “triangles have three sides” are not just false, but literally truth valueless. Second, fictionalism may itself fall victim to indispensability arguments. Tennant’s argument for the necessary existence of numbers mentioned above is just such an indispensability argument, which can also serve as another argument for (2a). Even fictionalist accounts cannot avoid quantifying over entities in their reductive analyses, which Tennet argues 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.¹⁷

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.¹⁸

Therefore, the number zero 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 the 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 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:

(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. “Afterall,” 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. Fist, so long as these “abstractions” remain derivatives of our concepts and don’t 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? Certainly 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?²²

It will have to take more than intuition to cross the epistemological gap between us and abstracta. To make matters worse, no other candidates seem 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).²³ 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. 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.²⁴

Hence, even 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’re 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.²⁵ I’ve found this intuition shared by laypeople also. I’ve discussed the ontological status of abstract objects with many people wholly unfamiliar with philosophical parlance. As I describe the peculiar existence of abstract objects to them, I often receive the eager opinion that “they’re like, in your brain/mind” before I even mention conceptualism as an option. One instance was even with a Jr. High student! 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.²⁶ These considerations notwithstanding, what has been mentioned so far suffices to show how (2) can be met. From (1) and (2) we therefore conclude

(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.²⁷

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.²⁸

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 suggested 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 philosophies, beginning with the analyses of F. G. Frege and Edmund Husserl.²⁹ 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. For consider some abstract object O as the concept of some human mind at time t₁. Now there must have been times t_i–t_j prior to t₁ such that there were no human minds that had O as a concept. Surely there are some abstract objects that have never been and will never be concepts in human minds. 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_j.

Moreover, it’s a bit too optimistic (even for the philosopher!) to think, as Abraham Robinson remarked, “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. For example, Quentin Smith 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 well³⁰ 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

(5) Therefore, a necessary, omniscient mind exists

which turn proves ~(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. 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.³¹

I eagerly anticipate forthcoming efforts on these and similar issues, some of which are already underway.³² At any rate, the existence and nature of abstract objects prove to be either at odds with or flatly inconsistence with naturalism. Alternatively, no such difficulties loom for theism. In fact, abstract objects 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.”³³ Read the rest of this entry »

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.