Doxazo Theos

Here is an objection to Craig-style arguments against the existence of an actual infinite “in the real world”. It is often said that inverse operations on transfinite numbers are prohibited. But this is not entirely true. As Nowacki explains, “inverse operations are prohibited for transfinite numbers in cases where performing the operation would yield a result that is not actually infinite.” (Kalam Cosmological Argument for God, p. 281, n.12. My emphasis).  So where m = the number of books in an infinite library, n = the number of odd-numbered books, and o the number of books numbered 4 or higher, the following is permitted:

(i)            (m – n) = ℵ₀

while the following is not:

(ii)           (m – o) = 4

because (ii) yields a finite number. If inverse operations yielding finite numbers were permitted, then it would follow that we get inconsistent results by subtracting the same number from m since n = o (both n and o are infinite), and this of course is why operations like (ii) are prohibited. But this leads me to think the following.

Craig’s point is that while inverse operations yielding finite numbers may be prohibited on paper, nothing would prevent us from performing them in the real world (say, by checking out a book from the library). But is this right? What would performing such an operation “in the real world” really amount to? What (ii) makes clear is that one would have to check out an infinite number of books to get a finite difference, not just any finite number of books. But then does Craig’s point follow that “nothing would prevent us from performing them in the real world”? Here’s something that might prevent us: having to perform and infinite task (check out an infinite number of books).

I’m not convinced that this objection works, but I don’t know the answer to it.

When the theist says “God is good,” I take this to be saying something substantial about God himself; that is, goodness does not just describe the moral status of God’s thoughts, intentions, or actions, but the moral status of his very essence. Call the former sense of divine goodness “descriptive goodness” and the latter “essential goodness.” It should be clear that essential goodness entails descriptive goodness but not vice versa, and so essential goodness is greater than descriptive goodness. For this reason the anselmian theist will favor divine goodness as essential and not just descriptive. Moreover, it is essential goodness that is assumed in the standard response to the Euthyphro dilemma.

Descriptive accounts of divine goodness usually present goodness as a logical entailment or consequence of other divine attributes such as omniscience, omnipotence and freedom [E.g., Swinburne, The Coherence of Theism (Oxford, rev. ed. 1993), 184-216; Daniel Jill, Divinity and Maximal Greatness (Routledge, 2005), 226]. On such accounts goodness is not essential to God in the same way that omniscience and omnipotence are, which are in some sense more primitive attributes because they are not derived or logically entailed by other attributes. So where B is a being with the properties necessary and sufficient to logically entail descriptive goodness, or G, we have something like the following relation:

(1) (∀x) (Bx ⇒ Gx)

But (1) is not strong enough to capture essential goodness. Here’s an analogy: although light is logically entailed by a red giant star, light is analytically distinct from and not essential to the star itself. Again, anselmian theists are likely to think of goodness as having the same status as these other more primitive essential attributes, and so I don’t think they’ll be satisfied with accounts that analyze divine goodness in terms of (1). Perhaps logical equivalence is strong enough (speaking here of a relation between yet two distinct things, lest divine simplicity rear its ugly head). Now where B is any being which exemplifies anselmian divinity and G is essential goodness:

(2) (∀x) (Bx ⇔ Gx)

But even (2) is not likely to satisfy the anselmian theist unless the good that is essential to God is maximal. Rationality might be essential to man, but man is certainly not maximally rational. So (2) can be see as saying that any being which exemplifies anselmian divinity will be one that is essentially maximally good and any being which is essentially maximally good will be one which exemplifies anselmian divinity. “God” is not analytically distinct from “essential maximal goodness.” So the logical entailment runs in both directions. The same holds for the other essential divine attributes such as omnipotence and omniscience.

Now here is an interesting consequence of this idea. Assuming what I argue in “Theism and the Metaphysics of Meaning and Value” is correct, while a single agent can be good in the sense of (1), no single agent can be good in the sense captured by (2).  Just as three sides are essential to a triangle, at least two agents are essential to any being with essential goodness, and as I argued in the last post, perhaps exactly three agents are sufficient for maximal goodness. This means that a standard unitarian theist cannot say God is essentially good, and an anselmian theist must be a Trinitarian. This also means that if a theist wishes to avail himself of the standard response to the Euthyphro dilemma, his conception of God must be one in which there are at least two agents.

In “Theism and the Metaphysics of Meaning and Value,” fundamental to the main argument against unitarian monotheism is the Endowment Thesis, or the claim that all meaning and value is endowed or bestowed by agents. Following Nozick, we can classify these and similar intentional verbs as ‘V verbs,’ for ‘valuing verbs,’ so as to speak generally about this endowing activity as a V-ing relationship between agents and that which they value. The argument is as follows: where P is meaning or value, the Endowmwnt Thesis formally states that for any x, x has meaning or value if and only if there is at least one agent y such that y V-s x:

(ET)	(∀x)Px ≡ (∃y) (Ay ∙ Vyx)

And where x is now some lonely object, or object with no wholly-distinct worldmates, (ET) entails that

(1)	◊(∃x)Px ⊃ (∃y)(Ay ∙ Vyx)

which is to be read as “if there possibly exists some lonely object x that has P, then there is at least one agent y such that y V-s x.” But exactly one agent, I argue, is not sufficient for x to have P:

(2)	◊(∃x)Px ⊃ ~(∃y){Ay ∙ Vyx ∙ (∀z) [(Az ∙ Vzx) ⊃ x = z]}

Therefore, for any world where x has P, at minimum two agents are necessary:

(3)	◊(∃x)Px ⊃ (∃y)(∃z)(Ay ∙ Az ∙ Vyx ∙ Vzx ∙ x ≠ z)

So if God possibly exists with no wholly-distinct worldmates and has meaning or value, then God must be at minimum two agents. The argument, if successful, shows that a necessary condition for God to have meaning or value is for God to be at least two agents. So we can summarize the main argument’s conclusion as simply

(A1)	If God possibly exists with no wholly-distinct worldmates  and has meaning or value, then God is at least two agents

As such, it only gets you to non-unitarian monotheism, not Trinitarian monotheism. However, other interesting considerations might be brought in to bear on the question of whether exactly two agents are sufficient for God to have the maximal degree of meaning and value possible. And I think there are good reasons to think exactly two agents are not sufficient for such, but exactly three are (a la Swinburne’s argument that three persons are necessary and sufficient for the most robust exemplification of love). So Swinburnian considerations could give us a second argument:

(A2)	If God has the maximal degree of meaning or value, then God is at least three agents

Combining these two arguments, I think, gives a powerful deductive argument for not just non-unitarian monotheism, but Trinitarian monotheism. So any theist who endorses the seemingly innocuous premise

(P1)	God possibly exists with no wholly-distinct worldmates and has the maximal degree of meaning or value

which would be most theists, should be ready to accept what (A1) and (A2) demonstrate that (P1) entails; namely,

(C)	Trinitarian monotheism is true

But what would “maximal value” or “maximal meaning” look like? Suppose we understand the relationship between meaning and value as follows. It is not implausible that meaning supervenes on value, or for value to supervene on appropriate states of affairs involving agents. Something might be meaningful because of its intrinsic value. Moreover, the degree to which something is meaningful is plausibly determined by the value of the object with which it bears a relation. For example, consider the following list of different kinds of beings with which we can have relationships: inanimate objects → plants → animals → persons → God. It seems clear that the meaningfulness of the relationship increases in tandem with the amount of value each being has. Furthermore, if we adopt some version. G. E. Moore’s Principle of Organic Unities, such as the one Robert Nozick develops in Philosophical Explanations, then the degree to which some thing is valuable depends on how intimately and harmoniously related it is with its parts, and its parts are with themselves.

Now apply these insights to a divine being in which there are multiple agents. Consider the value divine agents would have if in necessary and substantial relation. Being omniscient and omnipotent, there would be a maximally intimate union of knowledge and will, and so maximal value would be exemplified. And if the degree to which a relationship is meaningful is determined by the value of the beings that make it up, then the most meaningful relationship is one in which the members are maximally valuable. The agents would enjoy a maximally meaningful relationship, as each would stand in relation to a maximally valuable other. Thus, any meaning or value endowed would be of maximal quality such that no greater meaning or value would be possible.

The Christian platonist must insist that abstracta are they way they are because they, not God, are the very essence of uncreatable reality, and that they delimit all possible realities, even God’s nature. Hence, abstracta are explanatorily (if not causally) prior to God’s nature.

But the nature of certain abstracta clearly seem explanatorily posterior God’s nature. For example, necessarily true propositions the truths of which are determined by God’s nature—e.g., necessarily true moral propositions, such as it is wrong to torture babies for fun. The orthodox theist can explain why this is a necessarily true proposition—because moral goodness, as God’s very nature, delimits what necessary moral truths there are, it is wrong to torture babies for fun being one of them.

But here the Christian Platonist confronts a dilemma: he must either deny that the nature of all abstrcta is explanatorily prior to God’s nature, or he must reaffirm this but deny that the abstracta typically seen as explanatorily posterior God’s nature, such as necessarily true moral propositions, are so.

The former move seems very arbitrary and ad hoc. It has us believe that only certain abstracta are the way they are independently of God. But what calls for the difference? It is hard to see what, if anything. If one says “God’s nature,” then incoherence looms, for really this amounts to saying “God’s nature determines which abstracta are explanatorily posterior his nature.” Not only is this obviously circular, it faces the further question, “what about God’s nature determines which abstrcta are explanatorily posterior his nature?” Either way the first horn of this dilemma does not seem palatable.

The second horn states that all abstracta, even necessarily true moral propositions, are the way they are just because. They are the very essence of uncreatable reality, and they delimit all possible realities, including God’s nature as it were. But this horn immediately puts the Euthyphro dilemma back on the table, for it can no longer be said that certain things are good because God’s nature is such, but, quite literally, God’s nature is such because certain things are good. This would also remove any potential for the moral argument for God’s existence, as the explanation of any moral truth would not be in terms of God’s nature, but in terms of a general reality apart from God.

Because it is not a brute fact that God’s nature is good, the question of why God’s nature is good for the Christian Platonist becomes very difficult to answer. It just seems convenient that he is good. Moreover, strictly speaking, God’s nature cannot be good, for if it were, then no further account of goodness is needed. If the Christian Platonist maintains that God’s nature is good, then the further account of goodness in terms of abstracta is superfluous. But if the Christian Platonist maintains that goodness is not strictly God’s nature, then God’s goodness becomes a contingent matter.

Thus, like the attribute of aseity, goodness as a divine attribute also seems attenuated on a Christian platonist view. The second horn of the dilemma also seems unpalatable.

According to orthodox Christian theology, there are two kinds of reality: God and not God. The former is necessary, the latter is not (at least not necessary in the same way God is). This distinction gives rise to a further distinction, that between Creator and creature. It is then said that all things that are not God, therefore, are part of creation.

The Nicene Creed confesses God to be “Maker of heaven and earth, and of all things visible and invisible” and the Father as “by whom all things were made.” Here, the phrase “heaven and earth” harkens back to the Hebrew expression ha·sha·ma·yim ve·’et ha·’a·retz (Gen 1:1; Ex 20:11; Jer 51:48 et al) which is recognized by scholars as a collective reference to “absolutely everything” apart from God, because God is not made. Moreover, the repeated phrase “all things,” (Rom 11:36; Col 1:16; 1 Cor 8:6 et al) also plausibly refers to all things apart from God, because God is not made.

Therefore, the traditional doctrine of creation affirms that whatever is not God is created. Moreover, they are not just created—they are created ex nihilo. This creates a problem (pun intended) for the Christian platonist who thinks there are an infinite number of uncreated abstract objects that exist independently of God. Not only is this inconsistent with creation ex nihilo, but also the attribute of aseity, which names God as the only necessarily existent, self-sufficient being.  The Christian platonist could try to avoid this by tweaking the doctrine of creation from “all things not God”  to “all creatable things not God.” Given that abstract objects are not creatable, one could say they do not properly fall under the scope of creation. It seems to me that this tweaked notion of creation does not avoid the problems. In fact, it makes matters worse.

The traditional view says that all possible creatable things are delimited by God’s nature, where abstracta are seen as somehow “part of” God’s nature (say, as God’s ideas or something like that). So abstraca are the way they are because they are part of God’s nature, and God’s nature, as the very essence of uncreatable reality, delimits possible creatable realities. In this sense, minimally, God’s nature is explanatorily (if not causally) prior to abstracta. But the Christian platonist must reverse this. He must insist that abstracta are they way they are because they, not God, are the very essence of uncreatable reality, and that they delimit all possible realities, even God’s nature. Here, abstracta are explanatorily (if not causally) prior to God’s nature. This attenuates God’s aseity even more than it first seems.

According to the traditional view, whatever God creates must be consistent with his own nature, and sans creation nothing exists apart from God. Hence, whatever is created is created ex nihilo. But this is not possible for Christian platonism, for it is not just false that nothing can exist apart from God, it is necessarily false. All things creatable by God are not delimited by God’s nature alone, as orthodoxy would have it, but also by abstracta. For example, God couldn’t create a world where 2+2=5 not because anything about God’s nature prevents such incoherence, but because it is a brute and inexplicable fact, even for God, that 2+2=4. Thus, God creates not strictly ex nihilo, but also according to abstracta. Thus, even the tweaked notion of creation gives us at best creation ex abstracta.

Therefore, it seems impossible to square either a robust conception of God’s aseity or the doctrine of creation ex nihilo with platonism. Furthermore, platonism may have further untoward consequences for the Christian philosopher. Such will be the subject of the next post.

Intuitions are roughly non-inferential seemings. But intuitions can be, and probably often are, conditioned by (not inferred from) occurrent or tacit beliefs.

It seems to me that part of the task of justifying an intuition over a conflicting one (or perhaps more accurately, defeating an opposing intuition) involves being able to plausibly explain the origin of the opposing intuition and why its origin is relevant to its defeasibility. Abstractly, take any two conflicting intuitions, i₁ and i₂. Say I want to justify i₁ over i₂. I engage as follows: The reason S has i₂ is because of reasons r₁, r₂, r₃, etc., where r₁, r₂, r₃, etc. are likely occurent beliefs S holds.  But reasons r₁, r₂, r₃, etc. should not properly give rise to i₂ either because one or more of them is false or unjustified, or because they properly give rise to something else (some other occurent belief implied them?) that does not at all conflict with i₁.

This leads me to wonder whether all intuitions are actually just occurrent beliefs that we can’t identify or haven’t identified plausible origins of, perhaps because of weak powers of introspection. Of course, this does not mean no intuition is ever justified. In the case of i₁, it is entirely possible that undiscovered reasons r₁, r₂, r₃ etc. do properly give rise to i₁.

And this means that in cases where our introspective powers are too weak to uncover the occurent beliefs relevant to either person’s opposing intuition, an argumentative (though not necessarily epistemic) stale-mate is reached. This also means that in cases like the one explained above where r₁, r₂, r₃ etc. are exposed as not properly giving rise to i₂, if the reasons giving rise to i₁ are unknown, then merely argumentative superiority is demonstrated, not epistemic. After all, the reasons giving rise to i₁ could also be bogus, in which case there would be an epistemic stalemate.

And this leads me to wonder whether there can ever be a genuine case of epistemic stalemate between two conflicting intuitions, each of which are properly the result justified and true occurent beliefs. Sure it is possible that each opposing intuition can be properly the result of justified false beliefs, but once truth is thrown into the mix, it is a matter of propositions being either consistent or contradictory.

As a Christian who often finds himself with a pessimistic disposition, I think the following is very insightful:

The same motive [lust for control] may lead us to curtail our hopes. We adjust our plans easily to pleasant surprises, but unpleasant surprises threaten our control. From the standpoint of control, therefore, pessimism seems a stronger position than optimism. I think this fact is the main source of the intellectual machismo that prides itself on a sort of “tough-mindedness” that refuses to hope for very much. The desire for control tempts us to believe that if we hope for too much we will make fools of ourselves, whereas if we turn out to have hoped for too little we will only have proved to be “stronger” than we needed to be. This machismo is no more rational than the wishful thinking of which the hopeful are often accused. And when there is talk of “wishful thinking,” we would do well to realize that if we have a nonrational motive for believing the best, most of us have a nonrational motive for believing the worst. Pessimism is not happier than optimism; hope is happier than despair. But it is quite possible to prefer control to happiness.

What Christianity promises may seem “too good to be true”; the emotional meaning of this is that Christianity promises more than we can hope for without giving up control. The supreme threat to our control, however, is God himself…Is the desire for control something that inhibits me from trusting God? …The feeling that it is stronger, more controlling, to expect evil than to expect good is a powerful enemy of faith.

From Robert Adams, “The Virtue of Faith” in The Virtue of Faith and Other Essays in Philosophical Theology (Oxford, 1987), 19-20

Some have claimed that the problem of evil for theism has, ironically, an evil twin brother for non-theism: the problem of goodness. If evil seems odd or out of place in a theistic universe, then goodness seems equally out of place in a Godless universe.

T and N are theism and naturalism, respectively. G is goodness, or anything the opposite of evil. Altruism, aesthetic and sense-based pleasures, love and other virtues, etc. are all broad instances of G. A naive probability application of our question is whether the expectation of G is greater on T than N, or Pr(T|G) > Pr(N|G). That we should expect G on T is not at all surprising. In The Existence of God, Swinburne quotes Mark Wynn as observing that nature is ‘uniformly beautiful whereas the products of human beings are rarely beautiful in the absence of artistic intent.” And this seems true. In a mindless universe, there is no beauty. The real question is whether we should expect G on N.

Barring the objectivity of G, any account of G on N will be a story involving G’s being a great-making property for an evolving organism. Physical, sense-based pleasures aren’t hard to account for, as an organism is likely to gravitate toward what feels ‘good’ and away from what doesn’t. But I have a hard time coming up with just-so stories accounting for aesthetic sensibilities and the desire for cultivation of genuine virtues as opposed to the mere appearance of virtues.

In his forthcoming article “Resurrecting the Logical Problem of Evil,” Nathan Hanna purports to “offer a version of the Logical Argument from Evil that is immune to the Free Will Defense.” This would be significant, as most judge the FWD to have decisively solved the logical problem of evil. Hanna argues as follows (forgive the lengthy quotations. I’m after a quick and dirty reply, not necessarily an elegant one). Where “E can be all moral evil or a particular instance of or type of moral evil” and “G is free will or whatever other important goods free will might be necessary to obtain”:

(1)	God exists and is omnipotent, omniscient and morally perfect
(2)	E exists
(3)	If God exists and E exists, God has not eliminated E while securing G (necessary truth)
(4)	So, God has not eliminated E while securing G (1, 2, 3)
(5)	If God has not eliminated E while securing G, God is not as morally praiseworthy as he would have been had he done so (premise)
(6)	So, God is not as morally praiseworthy as he would have been had he done so (4, 5)
(7)	There are possible worlds where this can be done and where God would do so
(8)	So, there are possible worlds where God is more morally praiseworthy than he in fact is (6, 7)
(9)	Being more morally praiseworthy than a morally perfect being is logically impossible (premise)
(10)	Contradiction (8, 9)

If 5, 7 and 9 are necessarily true, 1 and 2 are inconsistent. Since 2 is obviously true, it would follow that 1 – theism – is false.

The crucial premise, it seems to me, is (5). Hanna defends (5) as follows. Imagine the moral status of a hero, H, depending on which action he performs in Thomas Nagel’s rescue scenario:

“However jewel-like the good will may be in its own right, there is a morally significant difference between rescuing someone from a burning building and dropping him from a twelfth-storey window while trying to rescue him.” Hanna further quote Nagel as saying “What has been done, and what is morally judged is partly determined by external factors.” External factors are “beyond [H]’s control, factors like the choices of others.” Hanna writes:

“If [H] manages to rescue him, [H] will arguably be more morally praiseworthy than [H] would have been [H] she failed. [H] will have accomplished something that affects one’s moral standing significantly. But [H’s] prospects depend on something beyond [H’s] complete control: the other person’s choices.”

So Hanna sets up a scenario that places God in the same situation with respect to the rescue of his free creatures from evil. He writes:

What acts God manages to perform – whether he eliminates evil, say – depends partly on his creatures’ free choices. In this respect, God bears important relations to us that we bear to one another. The acts we manage to perform depend on factors beyond our control, among them others’ free choices. Our moral standing depends partly on the acts we perform. Our moral standing therefore depends partly on what others do. This is a kind of moral luck. If moral luck is real and God stands in the appropriate relations to his free creatures, his moral standing depends partly on what those creatures freely do. But then evil’s existence threatens theism in a way that has been overlooked. How so? … God could succeed in eliminating evil and securing the relevant goods with sufficient cooperation from his free creatures. Succeeding at this endeavor would be a significant moral accomplishment. But whether God does this is not entirely within his control. It depends on his creatures’ free choices. Success at such cooperative endeavors affects the moral standing of those involved. This is an example of moral luck.

Whether … H can rescue someone from a burning building and whether God can…rescue his free creatures from evil depends on factors beyond their control. Among these factors are the choices of others. Whether H can rescue someone depends partly on whether the person helps or hinders her.

God bears relevantly similar relations to us that H bears to the person she tries to rescue. So, similar things can be said about God and H depending on their success or failure. Being morally perfect, God would want to rescue us and he would try to do so. Moreover, he must succeed. If God succeeds, he will accomplish something amazing, something that, like H’s successful rescue, bears the marks of an action that significantly affects one’s moral standing. If he fails, however, then, just like H would be if she failed at her rescue attempt, he will not be as morally praiseworthy as he would have been had he succeeded – even if he is nevertheless very morally praiseworthy. So (5) seems true. … To rescue us is to eliminate evil while securing great goods. If evil exists, God has not done this.

The crux of the matter is the middle paragraph. It seems to me that Hanna’s argument stands or falls on the notion of “control.” Unfortunately Hanna doesn’t say much about this. A free will defender might be a molinist, in which case there is a relevant sense in which the actions of free agents are within God’s complete control: God chose to create a world in which agents act freely in the circumstances God knew they would. Moreover, the actual world could be a world, perhaps the only world, where the securing of G would have optimal consequences: say, a world in which God’s divinely inspired message is freely dispersed and, as a result, as most as possible are saved and as few as possible are lost. Therefore, if molinism is true, it is false that God is not as morally praiseworthy as he would have been had he not eliminated E while securing G.

Therefore, it remains safe to point out the tomb in which the corpse of the logical argument of evil has been finally placed—The Nature of Necessity.

Many important starting points and conclusions in philosophy rest on simple intuitions—non-inferential, non-sense-experiential seemings. Not every case of intuition has evidential value, but the great majority of philosophers are prepared to defend the claim that intuition provides prima facie evidence regarding the natures of real things in the world and not merely our concepts. So it is especially interesting when one finds oneself with conflicting intuitions. For example, I have a strong intuition that

(1)	Human persons, considered individually, seem to be more than just physical organisms

which implies a kind of dualism. But I don’t have the intuition that

(2)	Human persons, considered individually, seem to be (or have) immaterial substances

which may just be peculiar to me. Anyway, something like (1) and (2) is a very common and, I think, strong intuition. Human persons, considered qua individuals (or even in small or personal groups), impresses upon my mind that there is something about them more fundamental than matter. But I also find myself with the intuition that

(3)	Human persons, considered collectively, seem to be just physical organisms

and, even more accurately,

(4)	Human persons, considered collectively, do not seem to be more than just physical organisms

I don’t know if there’s as significant a difference between (3) and (4) as there is between (1) and (2), but (4) does seem more intuitively true to me than (3). When I survey large crowds of people, such as in sporting events or other mass public gatherings, it is not just easy for me to see them as just a collection of physical organisms, like insect gatherings, but they also seem to be no more than such. The intuition is even stronger upon viewing crowds in disaster situations, where many of them are squashed and/or are at the mercy of forces larger than they (also like insects). Maybe the intuition underlying (4) is the same as the one that suggests that any view that implies insects and lower life forms have souls doesn’t seem right. But then maybe what I am really intuiting in (1) is that human persons are fundamentally not like insects (surprise!), despite the perspectival similarities I can make between swarms of people and swarms of insects, which could be the source of the intuition behind (3) and (4).