Impossibility arguments

I’ve been reading The Cambridge Companion to Atheism (Cambridge 2007).

This volume is thinner than some other entries in the series, which means, in turn, that the essays are pretty thin as well.

This severely circumscribes the value of the work since many of the essays are just too cursory to prove or disprove anything. There is simply not enough space to mount a detailed argument and interact with the counterarguments.

One partial exception is Patrick Grim’s chapter (12, pp199-214) on “Impossibility Arguments.” By restricting himself to one narrow class of atheological arguments, he has less ground to cover. And that makes his actual performance all the more wanting.

There are some basic deficiencies in his treatment:

1.He acts as if any nuanced definition of omnipotence or omniscience is a purely evasive, ad hoc expedient which begins with a robust conception, then whittles in away in the face of criticism until we end up with a denial of the attributes in question.

Yet this is a very jaundiced view of the procedure. No doubt it’s possible for some definitions or redefinitions to be evasive or ad hoc expedients.

But to allege that all such definitions are fundamentally reactionary is, itself, fundamentally reactionary.

There’s a sense in which philosophical theology will always be underdetermined by revelation. The Bible doesn’t list the divine attributes, and it doesn’t define the divine attributes.

Rather, it describes God in a variety of ways, using colorful, concrete language. And these descriptions occur in a variety of topical circumstances.

This means that when we move from revelation philosophical theology, there are many speculative or specialized questions which the topicality and popular level of revelatory discourse are not designed to answer.

Since we don’t have ready-made definitions, we have to make up our own definitions. In terms of Protestant theological method, our definitions will attempt, at a minimum, to capture whatever the Bible affirms or denies respecting the nature of God.

Such definitions would only be evasive or ad hoc if they redefine God by scaling back on what the Bible affirms or denies respecting the nature of God.

Ever since Aristotle, Western thought has had a passion for classification. But it is very difficult to define anything.

The danger is that in attempting a general definition, you will overgeneralize. Any responsible definition will try to anticipate possible counterexamples.

And if the initial definition fails to anticipate possible counterexamples, then it may be necessary to refine the initial definition in light of various counterexamples which it did not take into account as originally formulated.

For Grim to insist that this process is an exercise in special pleading is, itself, an exercise in special pleading. For every serious philosopher is confronted with the same challenge.

Moreover, the objection is disingenuous. For the more technical the objection, the more technical the definition.

There’s a dialectical relationship between definitions and objections. In philosophy generally, and philosophical theology in particular, the definitions are revisable rather than infallible.

Revelation is infallible. But the move from revelation to philosophical theology is fallible.

Philosopher A proposes a definition. Philosopher B proposes an objection to his definition. Philosopher A refines his definition in light of the objection.

Now, there may come a point when it’s necessary to scrap the definition and return to the drawing board if the refinements are too radical or piecemeal. But to automatically allege that only the most unqualified definition of omnipotence or omniscience supplies the benchmark, such that any attempt to qualify these attributes is an evasive maneuver which entails a denial of said attributes, is a tendentious allegation which disregards the relationship between revelation and philosophical theology as well as philosophical method generally.

A philosophical theologian isn’t beginning with an unqualified definition of these attributes, as if that were a given, and then paring it down to size.

He isn’t beginning with any given definition at all, for the definition isn’t a given. Rather, he must come up with a definition.

Rather, the actual procedure is more like this:

i) A Protestant theologian will begin with Biblical descriptions of God.

ii) He will attempt to formulate a definition that captures the essential properties attributed to God in Scripture.

iii) He will also try to anticipate possible counterexamples to his definition.

These counterexamples may fall outside the scope of Scripture. Highly specialized questions or hypothetical scenarios.

iv) If he fails to anticipate certain counterexamples, he will then endeavor to refine his definition to make allowance for these counterexamples.

3.Let’s move on to the specifics:

Grim spends a lot of time on the stone paradox. I’ve discussed the stone paradox on several occasions. Here’s on example:

There are a couple of basic problems with the stone paradox:

i) It’s very anthropomorphic, as if God were a weightlifter, raising a cosmic boulder.

So it’s hard to know what the paradox literally amounts to. What does the atheist have in mind? If we strip away the picturesque imagery, is there anything left? Where does the metaphor begin and end?

ii) There is a physical upper limit on the size of rocks.

In addition, to “lift” something implies a spatial frame of reference. Lift something relative to what?

For example, what would it mean for an earthling to lift a rock larger than the earth itself?

God can levitate a rock. But beyond a certain magnitude, the question is physically meaningless.

Continuing:

“A number of philosophers have taken it to be impossible to change the past, and have on that basis constructed definitions of omnipotence that do not require an omnipotent being to bring about a past state of affair. Such a move seems to concede that God is temporally bound as well as less than fully omnipotent” ibid. 202.

This criticism is equivocal. What would it mean to change the past?

i) Does this mean that God cannot undo the past in the sense of making something that happened not to have happened?

But if that’s the question, then this is not a question of power, but truth. If something happened, then it’s true that it happened. It’s always true that it happened.

God cannot cease to make it true, for that would be a logical impossibility (rather than a physical or metaphysical impossibility).

But a logical impossibility is a pseudotask. It doesn’t amount to a coherent proposition. So there’s nothing for God to do or not to do.

As Grim himself admits, “contradictory specifications fail to specify anything” (200).

ii) Or is this like one of those time travel scenarios in which a man travels back in time and changes something in his then-present which alters the course of the future?

Assuming that this is even a coherent proposition, the effect would be, not to change the past that was, but to add another past that overrides the preexisting segment. The agent undoes the past, not by unmaking the past, as if it never occurred, but by changing the initial conditions at some point in the past to yield a different outcome.

Whether or not God can do this depends on whether or not retrocausation is coherent:

a) Assuming it’s coherent, then, in principle, God could change the past.

b) But retrocausation is often thought to be incoherent. In a time travel scenario, it begins in the future. It takes the future as its point of departure. But the effect of changing the past is to change the future. Thus, retrocausation seems to be viciously circular. For there would be no future to hook into in order to get this scenario off the ground. There’s not point in the cycle where you can break into the cycle and recalibrate the cycle. Once set, it’s set for all time.

There’s a large literature on the paradoxes of time travel.

4.More to the point, this is obviously one of those conjectural questions which the Bible doesn’t pretend to address.

Suppose we could dream up some coherent task which God is unable to perform? That, of itself, doesn’t deny omnipotence in the way that Scripture describes omnipotence.

So, for this to have any bite, it would be necessary for Grim to show that something is at stake with respect to the revealed attributes of God.

Otherwise, he’s attacking a straw man. An artificial concept of God that has no bearing on the faith of Bible-believing Christians.

Moving from omnipotence to omniscience:

“If God is a being without a body, he cannot know how to juggle, how to balance on the parallel bars, or how to compensate for a strained muscle in the right calf” (205).

“If a God is without moral fault, he cannot know lust or envy, and thus cannot qualify as omniscient. If a God is without limitation, he cannot know fear, frustration, or despair” (205).

“An omniscient being would have no ignorance, and thus this is a felling no omniscient being could know” (205).

Several problems here:

i) There’s a running equivocation of terms. When he says “know,” he really means “feel.”

Can God “feel” what it’s like to do this or that? A physical feeling.

Can God experience a particular passion? An emotional feeling.

Grim is assuming, without benefit of argument, that a feeling is an object of knowledge rather than an incidental mode of knowledge.

To take his example of a strained muscle, his criterion would rule out sports medicine, for, by his yardstick, a physician couldn’t tell an injured athlete how to compensate for a strained muscle unless the physician had the very same experience.

Does Grim really want to make such a vulnerable claim?

To make good on his argument, Grim needs to demonstrate that a physical or emotional feeling is either an object of knowledge in its own right or else a necessary mode of knowledge. But he does neither. He assumes what he needs to prove.

ii) Even assuming, for the sake of argument, that this poses a limiting case for omniscience, what gives? The Biblical doctrine of God? Or a philosophical concept of God?

iii) Apropos (ii), to say that God cannot experience a sinful emotion is hardly an objection to the Biblical doctrine of God.

So how would that objection count as a “victory” for impossibility arguments? It’s a victory against a straw man.

iv) Notice too how his argument reduces to the tautology that an “unlimited” God cannot be subject to certain limitations.

Well, by definition, that’s true. And what’s the relevance of that tautology?

Is it a victory for impossibility arguments that God cannot be a fork or spoon or teapot?

In other words, God cannot be omnipotent unless God can cease to be God? Or cease to exist?

He’s attacking a definition of God which no reasonable believer ever affirmed in the first place.

v) And observe the equivocation of terms. What does he mean to say that God can (or cannot) become something that he is not?

If he could, then who would be the subject of the action, and who would be the object of the action? Is God the agent? And is this action self-referential?

That assumes the identity of the agent. But the action denies the identity of the agent. So the task is logically impossible, which renders it a pseudotask.

vi) One of the problems with this whole line of argument is that it plays grammatical games with negations, as if linguistic negations were the same thing as physical or metaphysical entities.

Let’s take a couple of examples:

a) By definition, a unicorn cannot have more (or less) than one horn. Is this a limiting-condition on what a unicorn can be? In a sense.

But since a unicorn is an imaginary creature to begin with, what it would mean for a unicorn to be limited is not self-explanatory. There’s a lot more in play than a linguistic negation.

b) Take an unbeatable chess player. There are different ways of expressing this property:

We could say (α) he’s unbeatable because no one can beat him at chess.

In this formulation, the limitation is on the second party or rival chess player, not on the chess player himself.

Or we can say (β) he’s unbeatable because he cannot lose.

In that formulation, the limitation is on the chess player himself.

These are two different ways of making the same point, yet they are not interchangeable formulations.

So is his unbeatability an ability or an inability? You could say, if you care to, that he’s a terribly limited chess player because he can never lose. He can only do one thing, which is to win every time.

By contrast, a mediocre chess player is a more able player because he has the ability both to win and lose. The mediocre player can do two things, whereas our unbeatable player labors under the handicap of winning every time.

I think it should be apparent at this point that we’re manipulating words rather than concepts. While it makes linguistic sense to say that a mediocre player has more ability than an unbeatable player, it makes no conceptual sense to say so. Yet this is the level at which Grim is operating.

The best example is his own example: God cannot be omniscient, for if he were omniscient, he couldn’t be ignorant, in which event he couldn’t know what it’s like to be ignorant.

Once again, this is just a shell game with grammatical negations:

i) If God is omniscient, then he can’t know what it’s like to know nothing;

ii) Since he can’t know what it’s like to know nothing, he is not omniscient.

The equivocation here is to treat ignorance as if it were an object of knowledge. That may generate a cute little paradox, but we’re manipulating words rather than concepts.

To say I don’t know what it’s like to know nothing treats nothing (not knowing) as if it were actually something that I don’t know.

It should be obvious that this is merely a negative way of expressing a positive concept, where not to know nothing (ignorance) is equivalent to knowing everything. The negation is equivalent to an affirmation. It’s just a question of alternative wording.

It tells you something that a high profile philosophy prof. is taken in by such featherweight sophistries.

Needless to say, the awareness of ignorance presupposes knowledge. It’s only because of what I do know that I can also know what I don’t know. “What” I don’t know in the sense “that” I know I don’t know it. Even then I have to know a little something about it to know “that” I don’t know it.

Strictly speaking, to say I don’t know something is self-refuting. But in terms of the speaker’s intent, it is not truly self-refuting. Rather, it’s simply a hyperbolic idiom.

Continuing:

“We would have to add at least that I also know that I am Patrick Grim, or that I know that he is me…Because of the role of the essential indexical, what I know when I know that I am making a mess is something that no other being can know” (206-07).

Grim acts as if this is a limitation on omniscience. But, once again, he’s tied himself in knots over linguistic conventions.

God cannot know that he is Patrick Grim since God is not Patrick Grim. Does this mean there is something to be known that God doesn’t know? Hardly.

A necessary, if insufficient, condition of knowledge is true belief. God knows all truths. Since God is not Patrick Grim, it isn’t true that God is Patrick Grim, in which case to say he doesn’t know he’s Patrick Grim is simply a negative of saying that he knows he isn’t Patrick Grim. He cannot identify with Grim’s first-person perspective because he isn’t identical with Grim.

He can’t know something that isn’t true, not because it’s an object of knowledge which he himself cannot know, but because it isn’t an object of knowledge with reference to him—since it isn’t true of him.

A high-profile philosophy prof. ought to be able to sort this out. It says something about atheism, even at the academic level, that this passes for serious reasoning.

Next, he introduces a set-theoretical objection to divine omniscience based on the Cartesian product. But there are several problems with this line of attack:

i) There is, to my knowledge, a point of tension in set theory between the actual infinite, Cartesian product, and absolute infinite.

For the Cartesian product evokes the specter of a transfinite regress. If, however, you have a regress, then you end up with a potential rather than actual infinite.

This is even more problematic when dealing with abstract objects. There is no potential with respect to abstract objects, as if they were increasing over time.

So even if we were to model omniscience on set theory, Grim is exploiting one side of the tension at the expense of the other.

We should also keep in mind that there are many different versions of set theory.

ii) But, as he also notes, a number of philosophers have also challenged the set-theoretical model of omniscience.

With respect to one version, he says: “It can be shown, however, that this move is futile” (209), and he then refers the reader to a footnote.

But when we turn to the footnote, we find him admitting that “the importance of this particular objection is significantly reduced in Simmons’s published paper…Also, see Alvin Plantinga…Gary Mar…Howard Sobel…” (231, n.26).

So is this move “futile” or not?

Respecting another move, he says: “What they all attempt to deny is the step that follows: that there will then be some truth about them,” which he opposes on the grounds that “it would have to be maintained that there is a specific group of things—that there really are these things—but tht there is no truth about them, not even that there are these things or that they are the things they are” (209).

Without my commenting on this particular formulation, I don’t see why a truth about all truths commits us to an infinite (or transfinite) regress.

That would only ensue if we treat the truth about all truths as something over and above the other truths about which it’s true.

But why cast this in hierarchical terms. Why operate with an implicitly foundationalist model rather than a conherentist model—moving in a virtuous circle of mutual truths rather than vicious regress of n-ordered truths?

What, exactly, is meant by the truth of all truths? Is it the tautology that any and all truths are true? How does that generate a regress?

No doubt it’s a truth about all truths in the sense that it’s a true statement or true proposition or true belief (take your pick) that any and all truths are true. Once again, how do we go from that tautology to the iterations of the power set?

Grim tries to raise unanswerable questions for the Christian, but his own objections raise more questions than they answer.

In his final section, he discusses the alleged impossibility of combined attributes:

“Since an omniscient God would know in advance (and from all eternity) all actions it would take, there can be no point at which such a God could make a genuine choice. Omniscience and freedom appear to be incompatible” (210).

i) This depends on how we ground his knowledge of his choices. A question of logical priorities. Is knowledge prior to choice, or choice prior to knowledge?

Clearly God’s knowledge of his choices cannot be logically antecedent to his choices, for his choices supply the object of knowledge. Rather, his choices are logically antecedent to his knowledge of them. So how would his knowledge inhibit his choices?

ii) Grim’s attempt to create a contradiction trades on temporal ambiguities, as if God knows what he’s going to do or going to choose, in which case his decision or action lies in the future while his knowledge lies in the past.

This makes it easier to claim that God cannot do otherwise or choose otherwise since his knowledge is literally foreknowledge. But if we construe divine eternality in timeless terms, the sequence collapses.

“Leibniz’s problem was that God’s moral perfection would entail that he must of necessity create the best of all possible worlds, and thus it could not be maintained that he was free to create any inferior world” (210).

This “problem” hinges on two or three assumptions:

i) There is a best possible world. But, on the face of it, there may be no best possible world, for different possible worlds may exemplify alternative and/or incommensurable goods.

ii) Even if there is a best possible world, why does God’s goodness entail that he instantiate the best?

While his goodness would entail that he will not instantiate an evil world, there’s a difference between good and evil, on the one hand, and lesser or greater goods, on the other.

On the face of it, there’s no compelling reason why God cannot instantiate a lesser good. It’s not as if he’s wronging anyone in the process, for they wouldn’t otherwise exist—and a good existence, even if a lesser good, is preferable to nonexistence. There are better men than me, but I’m glad that I exist. I can’t, in all good conscience, fault God for failing to create the best if I don’t make the cut.

iii) Is there only one actual world? Hard to answer.

Keep in mind that the first two objections pivot on fine points of philosophical theology. Do they expose any contradictions between a pair or set of revealed attributes? Or do they turn on philosophical definitions which outpace the range of revelation?

“Both [Peter Geach and Nelson Pike] admit an inconsistency in the idea that any being is both omnipotent and impeccable, or unable to do wrong” (210-211).

This is only inconsistent if you treat omnipotence as a self-referential attribute. But omnipotence is a creative attribute. It doesn’t take God as its own object.