The Cerebrum View

Let’s say the cerebrum view is the thesis that you’re numerically identical to a cerebrum. Consider the following argument to that conclusion:

Suppose you’re the only human animal in your room and you’re reading this post. Then:

1. (∃x)(x is a cerebrum & x is in your room).
2. (∀x)((x is a cerebrum & x is in your room) → x is thinking).
3. (∀x)((x is thinking & x is in your room) → x = you).

Therefore,

4. (∃x)(x is a cerebrum & x = you).

(1) is plausible. There’s a cerebrum in your room whenever you’re in your room. (3) is plausible. If there’s only one human animal in your room, namely, the one with which you’re associated, and there’s a thinker in your room, then clearly you’re that thinker. Otherwise you’d be committed to saying there’s another thinker thinking your thoughts, which is one thinker too many. (2) is plausible if material objects can think. Let’s say that they can. Then the best candidate for the material thing that’s thinking is your cerebrum, for it is that in virtue of which you think and without which you cannot think. Moreover, if it were removed and connected to a machine that sustains it properly, thought would continue to be produced. But produced by what? The best material candidate is the cerebrum. So if it can think outside of the body, why not inside?

So…which premise is false?

Is Divine Foreknowledge Compatible with Human Freedom?

Let’s say that S is omniscient only if, for any proposition p, p is true only if S knows that p. There are propositions about what will happen in the future, e.g. “John will eat cheese at t.” So something is omniscient only if it knows the truth-value of these kinds of propositions. Let S(t) be the state of world at some time t in the distant past (say, one millions years ago). Let S(t*) be the state of affairs consisting in my deciding to read Descartes’s Meditations, now, at t*. Now God infallibly knows the future only if S(t) includes God’s knowing, at t, that I will decide to read the Meditations at t*. Then this is true:

1. ☐(S(t) → S(t*))

Since S(t) includes the state of affairs consisting in God’s knowing that I will decide to read the Meditations at t*, and since knowing that p entails that p is true, (1) is true. In no possible world is it the case that God knows that p and ~p.

Now consider the following Consequence-style argument for the incompatibility thesis: divine foreknowledge is not compatible with human freedom.

First, we have two inference rules, alpha and beta, where Np means “No matter what I now do, p”:

α: ☐p → Np

β: [(Np & N(p → q)) → Nq]

2. NS(t) [Premise]

3. N(S(t) → S(t*)) [from 1 and α]

4. NS(t) & N(S(t) → S(t*)) [from 2 and 3]

Therefore,

5. NS(t*) [from 4 and β]

The conclusion of the argument is: no matter what I do, S(t*) obtains. That is, no matter what I do, I decide to read the Meditations at t*. This entails that I am not free with respect to this action. But, if it is true that I am free with respect to this action, then something above must go. (2) looks airtight. There is nothing I can now do to change the past, especially the distant past. The only other premise is (1), which is entailed by foreknowledge. If we reject it, then we will be forced to maintain that God doesn’t know the future, which is something that some might want to avoid. If we accept the validity of α and β, then it looks like we are going to have to deny that we ever act freely, or we will have to deny that God enjoys infallible foreknowledge (and so isn’t omniscient in the sense described above).

Here’s an interesting implication of this argument. It is sound only if the following argument is sound:

6. I knew 3 seconds ago that I will press the enter button at some point in the next five minutes. 

7. There is nothing I can now do to change the fact that, 3 seconds ago, I knew that I will press the enter button at some point in the next five minutes. 

8. There is nothing I can now do to change the fact that, I knew 3 seconds ago that I will press the enter button at some point in the next five minutes only if I will press the enter button at some point in the next five minutes (knowing that p entails p). 

Therefore, by β

9. There is nothing I can now do to change the fact that I will press the enter button at some point in the next five minutes. 

This conclusion seems ridiculous. How does my knowing 3 seconds ago that I will do something make it the case that I didn’t act freely? My suspicion is that β is invalid, though it sure is seductive. [1]

[1] In fact, β is very controversial and there are interesting counterexamples in the literature. 

Descartes’s Trademark Argument

Descartes’s Trademark Argument (TA) is an a priori argument from the existence of the idea of God, the perfect being, to His actual existence and, by extension, to the conclusion that we can trust our clear and distinct ideas (see his Third Meditation). First we must distinguish between “formal” and “objective” reality (of ideas). The former is to do with a being’s intrinsic reality, or the reality it has by virtue of its having a certain essence.[1] The latter is to do with representational content. So, for example, all ideas have the same formal reality because they have the same essence, but have different objective reality on the basis of their having different representational contents (e.g. the idea of a beach and the idea of a boat have the same formal reality but different objective reality). Here is the argument: I have an idea of God, a perfect being. Since something cannot arise out of nothing, this idea must have a cause. The cause must have at least as much formal reality as the idea has objective reality. Only a perfect being, or God, can be the cause of such an idea.[2] God can be the cause of this idea only if He exists. Therefore, God exists. Given that God exists, and that God is perfect, it is false that He is a deceiver, for no deceiver is perfect.[3] If God is the cause of our having the various mental faculties that we have, and God is not a deceiver, then we can trust our clear and distinct ideas (produced by those faculties). God is the cause of our mental faculties. Therefore, we can trust our clear and distinct ideas.

Descartes thinks the premises in his TA are known by virtue of the fact that they are clear and distinct to him. But, given the TA, he can trust his clear and distinct ideas only if he knows that God exists, which is a conclusion of his argument. So now comes the charge of circularity: Descartes can know that God exists only if he can trust his clear and distinct ideas and he can trust his clear and distinct ideas only if he can know that God exists. So, the objections goes, he must already presuppose his conclusion (that God exists and that we can trust our clear and distinct ideas) in order to accept the premises. Perhaps this means that if it is true that one must accept the conclusion in order to accept the premises, then anybody who doesn’t already accept the conclusion ought to accept any of the premises. It is in this sense that Descartes’ argument is said to be circular.

Another objection to this argument might be a similar line used against ontological arguments: parodies. One might go as follows. I have an idea of a supremely malevolent being (SMB) that is omnipotent and omniscient. Since something cannot come from nothing, this idea must have a cause. The cause must have at least as much formal reality as the idea has objective reality. Only a SMB that is omnipotent and omniscient can be the cause of such an idea. A SMB can be the cause of this idea only if it exists. Therefore, a SMB exists. The SMB is the cause of our mental faculties. If a SMB is the cause of our mental faculties, then we cannot trust our clear and distinct ideas. Therefore, we cannot trust our clear and distinct ideas. Since we can use the same form of argument to get to an obviously absurd conclusion (that a SMB exists and that we can’t know anything), the TA is good reason to accept its conclusions only if there is a premise in it that is more obviously true than a premise in this argument. Since, one might argue, the premises in this argument seem no less obvious than the ones in the TA, we can conclude that the TA, though valid, is not known to be sound, and so isn’t a good reason for us to accept its conclusion.

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[1] The essence being a mode of thought.

[2] This is true because only God, by definition, has as much formal reality as the representational content of my idea of God (perfection).

[3] This implies that the deceiver must deceive in order to will that something be the case, which is an imperfection.

Part I: Misconceptions About George Berkeley’s Metaphysics

I’m not a Berkeley scholar, so I may well get some of what follows wrong. Here I just want to begin a series on Berkeley’s immaterialism by doing away with some common misconceptions. Most of what I shall be writing about in this series is to be found in his Three Dialogues Between Hylas and Philonous, which I highly recommend to the reader.

In what follows I address what I consider to be three misconceptions about Berkeley’s metaphysics.

1. Berkeley doesn’t deny the existence of physical objects. 

That’s right. Berkeley thinks there are chairs, tables, brains, ants, etc. In Berkeley’s A Treatise Concerning the Principles of Human Knowledge (henceforth, the Treatise), Berkeley writes:

“The table I write on I say exists, that is, I see and feel it; and if I were out of my study I should say it existed—meaning thereby that if I was in my study I might perceive it, or that some other spirit actually does perceive it.”[1]

So Berkeley explicitly denies that he believes that ‘sensible things,’ or things that can be perceived by the senses, do not exist. Materialists who are not eliminativists believe that minds and mental states exist. What they believe, though, is that minds and mental states just are material substances or physical states. Theirs is a reductive account. Similarly, Berkeley doesn’t deny the existence of physical objects, which is evident by the fact that he wishes to give an account of what they are, which presupposes that they exist! Berkeley’s is a reductive account: there are no mind-independent substances, so the sensible objects that exist are mind-dependent; they’re ideas.

Berkeley does deny this. He denies that there are any material substances, which he defines as physical objects that have ‘real absolute existence, distinct from, and having no relation to, their being perceived’ (see the first dialogue). So tables exist, alright, but they are not material substances in the sense that they enjoy mind-independent existence. This brings me to the next common misconception.

2. Esse est percipi.

If you’ve heard anything about Berkeley, you’ve probably heard his position reduced to this: esse est percipi, that is, to be, or to exist, is to be perceived. If this is all you’ve heard of Berkeley, then you’re unlikely to have been impressed. For obviously I exist even if I am not perceived by anyone, and if anyone should tell me otherwise I should think them a fool, or a solipsist, or else a sophist, whose only purpose is to be provocative. And if there is any doubt about my enjoying real, absolute existence, distinct from any mind’s perceiving me, then surely there is no question whatever as to whether or not God is so privileged. If God exists, surely he exists even if he isn’t being perceived; surely his existence, at least, does not consist in his being perceived. His being perceived isn’t that in virtue of which he exists, and the same is true of me (and, of course, you): being perceived by some other being isn’t that in virtue of which we exist, even if we are always and necessarily perceived by God.

So what does Berkeley actually say and mean?  Here’s what he says in the Treatise:

“For as to what is said of the absolute existence of unthinking things, without any relation to their being perceived, that is to me perfectly unintelligible. Their esse is percipi; nor is it possible that they should have any existence out of the minds or thinking things which perceive them.”[2]

What is Berkeley writing about here? He is writing about unthinking things, or sensible things such as mountains, chairs, and tables. Things that can be seen, heard, felt, etc. You’ll notice, then, that ‘esse is percipi,’ in context, does not at all entail the absurdities mentioned above. For he says their esse is percipi, and by ‘their’ he is clearly referring to what he calls unthinking things, or sensible things. “Nor is it possible that they should have any existence out of the minds…which perceive them.” So is it true that to exist is to be perceived? Not according to Berkeley, who thinks that there are some things, such as minds, whose existence doesn’t consist in their being perceived. What Berkeley maintains, then, is that the existence of sensible things consists in their being perceived. For them, esse is percipi.[3]

3. Physical objects don’t pop out of existence when we stop perceiving them.

Let’s say that the existence of sensible things consists in their being perceived. Suppose that, right now, nobody is in my house. I have the belief that, right now, in my closet there are shoes. But if the existence of sensible things consists in their being perceived, and there’s nobody perceiving my shoes, then it follows that I have at least one false belief, namely, the belief that there are shoes in my closet. Since it seems obvious that this is a member of the set of my true beliefs, it looks like there’s a problem for Berkeley’s view. My shoes exist even though I am not perceiving them. Certainly it is more plausible to suppose that when I am no longer looking at them, they continue to exist. For it is far simpler to suppose that they do continue to exist than to suppose that  they pop into and out of existence regularly.

This objection may seem compelling, but Berkeley has at least two replies. The first has already been mentioned: “The table I write on I say exists, that is, I see and feel it; and if I were out of my study I should say it existed—meaning thereby that if I was in my study I might perceive it.” According to this reply, then, when we say ‘my table exists in my study even though nobody is in my study,’ we really mean (or ought to mean?), “if I were in my study, then I would perceive my table.” But this doesn’t look like an adequate reply. When we say that the table exists in my study when we are no longer there, it seems pretty clear that we mean that it objectively exists there, not that, if I were there, then it would exist. But Berkeley has another, more interesting reply:

“To me it is evident, for the Reasons you allow of, that sensible Things cannot exist otherwise than in a Mind or Spirit. Whence I conclude, not that they have no real Existence, but that seeing they depend not on my Thought, and have an Existence distinct from being perceived by me, there must be some other Mind wherein they exist. As sure therefore as the sensible World really exists, so sure is there an infinite omnipresent Spirit who contains and supports it.”[4]

According to this reply, when you leave your study, your table continues to exist because there is some other spirit or mind who is perceiving it. The above objection works only if nobody is doing the perceiving when you aren’t in your study or closet. But Berkeley denies this, and produces an interesting argument for it. So far as I can see, it goes like this:

(P1) My table exists right now only if it is being perceived.

(P2) No finite mind is perceiving my table right now (I am not in my study, and neither is anybody else like me).

Therefore,

(C1) My table exists right now only if it is being perceived by an infinite mind. [from P1 and P2, because a mind is not finite only if it is infinite]

(P3) My table exists right now.

Therefore,

(C2) It is being perceived by an infinite mind. [from C1 and P3]

The problem with the objection with which I began, then, is the idea that Berkeley must maintain that a sensible object’s existence consists in its being perceived by us. Berkeley denies this. He maintains only that they must be perceived, whether or not it is us doing the perceiving. If we are right that the sensible objects that we perceive continue to exist even after we stop perceiving them, then there must be some other mind perceiving them who is that in virtue of whom they continue to exist—this mind we would call God. So not only does Berkeley have an argument to the conclusion that there is some other mind perceiving your table, he has an argument to the conclusion that that mind is God. If you want to be a Berkeleyan, you’ll have to be a theist.

The only premise that looks objectionable is P1. Why think it true? I will turn to this question in subsequent posts.

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[1] See Pg. 16 here: https://scholarsbank.uoregon.edu/xmlui/bitstream/handle/1794/653/berkeley.pdf?sequence=1.

[2] Ibid.

[3] For this point, see John Roberts. A Metaphysics for the Mob. (Oxford University Press, 2007). Chapter 1.

[4] See the Second Dialogue, Pg. 44 here: http://www.cfh.ufsc.br/~conte/berkeley-dialogues.pdf

Mereological Constancy and Immaterialism

Here I shall argue that the doctrine of mereological constancy (MC), together with an innocuous premise, entails immaterialism, the thesis that each of us is numerically identical with an immaterial substance. What is MC?

(MC) It is impossible for a material object to gain or lose material parts.[1]

At first, MC seems palpably false. Surely if my body gains or loses an atom, it doesn’t cease to exist. Surely it continues to exist despite the fact that it gains or loses a part (this is, of course, compatible with its not being able to survive through significant change). But there is an excellent reason to think that MC is true, the denial of which requires one’s commitment to views that may seem to be more implausible.

I. The Paradox of Increase

Consider the paradox of increase.[2] Let A and B be any two material objects. When we attach B to A, have we made it such that B becomes a part of A? It seems not. It seems that we have created a new composite object, AB, and B does not become a part of A for A still exists as it was as part of the new composite substance. Similarly, we don’t make AB smaller when we remove from it B. AB is composed of both A and B, and removing B (perhaps by utterly destroying it) leaves us only with A. But it is palpably obvious that A is not identical to AB. Since destroying B leaves only A, and A ≠ AB, it follows that removing B causes AB to cease to exist. Since both of these arguments can be generalized, it follows that no material object can gain or lose material parts, that is, that MC is true.

We may also follow Olson and argue to MC as follows:

(1)  A acquires B as a part [assumption for reductio].

(2)  When A acquires B as a part, A comes to be composed of B and C.

Since we are supposing that A gains a new part, B, we are not saying that there is a new object distinct from A. We are saying that A just is the object that now has B as a part, and C is the rest of A. The following illustration might help:

(3)  C does not acquire B as a part [premise].

Of course, B doesn’t become a part of C, because both B and C exist, and both are distinct from A, which is the thing composed of both B and C.

(4)  C exists before B is attached [premise].

It seems obvious that attaching B didn’t cause a new object, C, to suddenly pop into existence.

(5)  C coincides materially with A before B is attached [premise].

C didn’t get any bigger or smaller when B was attached, and the things that composed A prior to B’s being attached now compose C, so it seems that C coincides with A prior to the attachment of B.

(6)  No two things can coincide materially at the same time [premise].

(7)  C = A [from 5 and 6].

(8)  A does not acquire B as a part [from 3 and 7].[3]

Since our assumption in (1) entails a contradiction, namely, that A does and does not acquire B as a part, it follows that (1) is false.

II. The Argument to Immaterialism

One thing is clear. Olson doesn’t think the above argument, even if sound, entails immaterialism.[4] It turns out that he is wrong. We know that our bodies and brains are constantly changing, because they gain and lose material parts all the time. Let O₁ be the organism/brain/body that I had at t₁, and O₂ the body I had at t₂. Let P₁ be me at t₁ and P₂ be me at t₂. If I were a material substance, then (9) and (10) would be true:

(9)  O₁ = P₁.

(10) O₂ = P₂.

It is obviously true that I persist through time. I am the same person that existed 10 years ago. So,

(11) P₁ = P₂.

It follows by transitivity that

(12) O₁ = O₂.

But MC entails that (12) is false and, indeed, necessarily false, because O₁ and O₂ are composed of different parts. Hence, it is false that I am a material substance. What this shows is that MC, together with the premise that I continue to exist through time and through changes in my body (I continue to exist when my body gains or loses an atom), entails immaterialism. Olson is therefore wrong: the paradox of increase is a good argument for immaterialism insofar as he is right when he argues that a rejection of any of the argument’s premises commits one to unsavory positions, such as sparse ontology (when one rejects 2), or constitution (when one rejects 6).

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[1] Or as Eric T. Olson puts it, ‘it is absolutely impossible for anything to have a certain part at one time and exist without that part at another time.’ See What Are We?. (Oxford University Press, 2007). Pg. 155.

[2] Ibid. Pg. 153.

[3] For this argument, see Ibid. Pg. 159.

[4] Ibid. Pg. 163.

Another Argument for the Possibility of the Existence of God

The second premise of Robert Maydole’s Modal Perfection Argument[1] is as follows.

(M) Perfections entail only perfections.[2]

For any properties J and K, if J is a perfection and J entails K, then K is a perfection.[3] Consider Maydole’s argument for (M):

“Suppose X is a perfection and X entails Y. Then it is better to have X than not, and having Y is a necessary condition for having X. But it is always better to have that which is a necessary condition for whatever it is better to have than not; for the absence of the necessary condition means the absence of the conditioned, and per assumption it is better to have the conditioned. Therefore, it is better to have Y than not. So Y is a perfection.”[4]

This argument has some prima facie plausibility. But what does Maydole mean by perfection here? This argument seems to presuppose the following:

(D) A property P is a perfection just in case P is better to have than lack.

Let us begin with (M). I shall stipulate that properties fall into and only these three categories with respect to their contributing to the greatness of the beings in which they inhere. Properties are either great-making, neutral, or lesser-making. I shall understand great-making in the way Maydole understands perfection: P is a great-making property (GMP) just in case P is necessarily better to have than lack (e.g. being good). I shall understand neutral as a property whose instantiation does not necessarily add or subtract to the greatness of the being in which it inheres; they are neither necessarily better to have than lack or lack than have. I shall understand lesser-making properties as properties that are necessarily better to lack than have (e.g. being evil). Now, there are in fact neutral properties. Every actual being has the property of being self-identical. But the property of being self-identical does not seem to be either great or lesser-making. So it is plausible to suppose that it is neutral. Given that there are neutral properties, consider Oppy’s counterexample to M. He writes:

“Consider the property of being supreme or else a mass murderer…it is quite clear that anything that has the property of supremity has this further property.  But it is quite unintuitive to suppose that being supreme or else a mass murderer is a perfection. This is particularly clear when we consider the intuitive gloss that Maydole puts upon perfections: it is plainly not so that the property of being supreme or else a mass murderer is a property that is better to have than not. It would have been far better than not had Stalin and Hitler lacked this property. End of story.”[5]

It seems to me that Oppy succeeds in refuting M. Although, pace Oppy, one can reasonably deny that being evil or else a mass murderer is a property that is better for Hitler to have lacked than have, it is extremely implausible to suppose that this property in any way added to his greatness. At best, we can say that it neither added nor subtracted from his greatness, that it is a neutral property. Its being a neutral property is sufficient to refute M, for it would then be true that perfections entail non-perfections. Hence, even if one might not be convinced that this property is better for Hitler to lack than have, Maydole would have to argue that he was greater in virtue of his having that property, and that seems a bit too implausible.

Consider an amended version of Maydole’s premise:

(M*) Perfections entail only GMPs or neutral properties.

The following is an argument from (M*) and a couple of other plausible premises to the conclusion that perfection is possibly instantiated.

Let PA = A is a perfection, GK = K is Great-Making, NK = K is neutral (with respect to greatness), A = the property of being perfect, and B = the property of being evil.

1. (J)(K)[PJ & ☐(x)(Jx -> Kx)] -> (GK v NK)].          [Premise]

Or, if J is a perfection and, necessarily, for all x, x has J only if x has K, then K is great-making or K is neutral.

2. (PA & ~GB).                                                           [Premise]

Being perfect is a perfection and it is false that being evil is great-making.

3. ~NB.                                                                       [Premise]

It is false that being evil is neutral.

4. ∴ ◊ (Ex) (Ax).

5. ~◊ (Ex) (Ax).                                  [ASM RAA]

6. ☐~(Ex) (Ax).                                 [5, MN]

7. ☐(x) ~(Ax).                                    [6, QN

Since, necessarily, A is not exemplified by anything, then trivially,

8. ☐(x) (Ax -> Bx).

9. PA                                                             [2, &E]

10. [PA & ☐(x) (Ax -> Bx)].                             [9, 8 Conj.]

11. (GB v NB).                                               [1, 10, MP]

12. GB.                                                          [3, 11, DS]

13. ~GB.                                                        [2, &E]

4. ∴ ◊ (Ex) (Ax).                                                [6-13, RAA]

The conclusion of this argument is that it is possible that there is at least one x such that x is perfect. Of course, anything that is perfect is God. So it is possible that God exists.

How might we defend M*? Suppose it is possible for a perfection P to entail a lesser-making property, or imperfection L. Then L is a necessary condition of the instantiation of P. L is a necessary condition of the instantiation of P only if P’s instantiation is sufficient for the imperfection of any being in which it inheres. For any being that has P also has L and L is lesser-making. So any being that has P is imperfect, and a sufficient reason of its being imperfect is that it has P. But clearly this is a feature only of lesser-making properties. Perfections add to, but do not subtract from, the greatness of the beings in which they inhere. Hence, it cannot be the case that the instantiation of L is a necessary condition of the instantiation of P. We can generalize and conclude that it cannot be the case that perfections entail imperfections. Since perfections do entail GMPs (e.g. omnipotence entails the property being powerful) and neutral properties (e.g. omnipotence entails being omnipotent or crunchy), and since these are the only three categories of properties, it follows that M* is true. If this is right then it follows that it is possible that there is at least x such that x is perfect. Since God is the perfect being, it is possible that God exists.

For an Ontological Argument that profits from this argument, see here.

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[1] Maydole, Robert. “The Modal Perfection Argument for the Existence of a Supreme Being.” Philo 6, no. 2 (2003).

[2] Ibid. Pg. 299.

[3] A property P entails a property Q just in case it is necessarily the case that, for all x, x has P only if x has Q.

[4] Ibid. Pg. 302.

[5] Oppy, Graham. “Maydole’s 2QS5 Argument .” Philo 7, no. 2 (2004).

Gaunilo’s Parody

I argued here that it is possible that a perfect being exists. The argument is as follows (for a defense of the argument, see the above link):

(1) It is false that being perfect entails being evil.

Assume for reductio that

(2) Being perfect is necessarily uninstantiated.

Since a necessarily uninstantiated property trivially entails any property,

(3) Then being perfect entails being evil.

Since (1) and (3) are incompossible, we must reject our assumption. Hence,

(4) Therefore, it is false that being perfect is necessarily uninstantiated.

Gaunilo famously rejected St. Anselm’s ontological argument on the basis of his island parody. Perhaps he might have similarly argued against the above argument. Let us say that an island-perfection (IP) is one whose instantiation adds to, but does not subtract from, the greatness of any island in which it inheres, and let us say that being a perfect island just is the conjunction of all IPs. The parody is as follows.

(1*) It is false that being a perfect island entails P, where P is an island-imperfection.

Assume, for reductio, that

(2*) Being a perfect island is necessarily uninstantiated.

Then

(3*) Being a perfect island entails P.

(1*) and (3*) are incompossible, so we must reject our assumption. Hence,

(4*) It is false that being a perfect island is necessarily uninstantiated.

Does this parody successfully refute the argument for the possibility of the existence of a perfect being? It seems to me that it does not. Perhaps it is possible that a perfect island exists. Possibility claims are very usually innocuous, so it seems to me that one can reasonably admit that both arguments are sound.  A problem arises only when the person who advances the parody attempts to argue from (4*) to

(5*) A perfect island exists.

But the inference from (4*) to (5*) is valid only if

(6*) Being a perfect island entails being necessarily existent 

is a necessary truth. But I see no good reason whatever to grant (6*) and very good reason to grant (7*):

(7*) Being an island entails being contingent. 

Several reasons can be given to prefer (7*) over (6*) that do not at all apply to perfect beings, which, if right, entails that the parody fails, for we have reasons to reject it that do not apply to the parodied argument. First, following Plantinga, let us say that a state of affairs S includes a state of affairs S* just in case it is impossible that S obtain and S* fail to obtain. Now, being an island entails being a material being. This strongly suggests that (7*) is true, for it is certainly possible that nothing material exists, in which case there is at least one possible world in which there are no islands, which is enough to falsify (6*). Interestingly, there is good scientific evidence to suppose that space and time began to exist. Since the existence of space and time are necessary conditions of the existence of material things, including islands, this entails that there is a possible state of affair that does not include the state of affair consisting in the existence of an island, or anything material. So there is a world W in which no islands exist.

Moreover, if (6*) is true and being a perfect island is possibly instantiated, then it follows that, in the actual world, a perfect island exists in a timeless state. For its having the property being necessary entails that it is impossible that it fail to exist and, given that time began to exist, the island would have to exist sans time. But clearly this is impossible. So the conclusion is that (6*) is false and that (7*) is true.

It seems to me, therefore, that this parody fails. The reasons for supposing that the parody is unsound do not at all apply to perfect beings.

*Thanks to the blogger at Vexing Questions for his helpful suggestions. You can find his blog here. I also wish to thank someone whose name shall remain anonymous for bringing this parody to my attention.

The Principle of Alternate Possibilities and Divine Hiddenness

J. L. Schellenberg, in his book Divine Hiddenness and Human Reason, advances what we might call the logical problem of divine hiddenness. His argument runs as follows:

(1)  If there is a God, he is perfectly loving.

(2)  If a perfectly loving God exists, reasonable nonbelief does not occur.

(3)  Reasonable nonbelief occurs.

(4)  Therefore, no perfectly loving God exists. [from 3 and 2]

(5)  Therefore, there is no God. [from 4 and 1][1]

Given premise (2), what Schellenberg is really committed to is that

(6)  A perfectly loving God exists

is logically incompossible with

(7)  Reasonable nonbelief occurs.

If (6) and (7) are compossible, then (2) is false and, therefore, his argument is unsound. Now, in order for this to be an argument against classical theism, it must also entail that it is impossible that God exists, because most theists take

(8)  God exists only if he necessarily exists

to be true. That reasonable nonbelief exists entails that God does not exist and could not have existed. This entails that God’s existence is incompossible with

(9)  Possibly, reasonable nonbelief occurs.

One way of showing how (6) and (7) are compossible is by identifying some proposition P that is compossible with (6) and that entails (7). Consider the following candidate for P.

(10 ) Morally responsible saintly and pious agents exist.

Now, an agent P is saintly in a world W just in case P never goes wrong with respect to any of the actions she performs in W. P is pious in a world W just in case P believes and has faith in God in W. Let W be any logically possible world in which both (6) and (10) hold. It is true in W that God exists and it is true that morally responsible saintly agents exist, all of whom believe in God. This entails that reasonable nonbelief does not occur in W, for everyone believes in God. So far as Shellenberg’s argument goes, (6) is compossible with (10). The conjunction of (6) and (10) entails that reasonable nonbelief does not occur, and so there is no problem: the conjunction does not entail a contradiction, and so is not logically incompossible.

Moreover, the agents that exist in W are morally responsible. Now consider the Principle of Alternate Possibilities:

(PAP) P is responsible for what she does only if she could have done otherwise.

I shall assume that PAP is true throughout the blog post. Thus, the people in W are morally responsible for what they do only if they could have done otherwise. Let us take one of these morally responsible saintly and pious agents, Jane. Jane decides to believe in God at some time t. Moreover, let us assume that the following counterfactual is true:

(11) If Jane had decided to not believe in God, then an instance of reasonable nonbelief would have obtained.

So there is a state of affairs S that obtains in W that (a) includes Jane’s being faced with a decision to believe or to not believe in God at t, (b) does not include Jane’s deciding to believe in God at t, and (c) includes (11)’s being true. Given PAP, Jane is morally responsible for this decision only if she could have done otherwise. I take it that she could have done otherwise only if it was possible for her to have done otherwise. That is, there is some possible world W* in which a state of affairs S* obtains such that S* (e) includes S,[2] (f) is identical to W in every way possible up to t, and (g) includes Jane’s deciding against believing in God at t. This entails that, in W*, there is an instance of reasonable nonbelief that obtains.

Since (6) and (10) are compossible, God’s existence is compossible with W. But this is true only if God’s existence is compossible with the possibility of there being reasonable nonbelief. That is, true only if (9) is false. But since (8) is true and God exists only if He necessarily exists, it follows that (6) and (7) are incompossible only if (6) and (9) are incompossible. Since we know that they are not, if follows that (6) and (7) are compossible. This, of course, entails that (2) is false. Schellenberg’s argument is unsound.

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[1] Divine Hiddenness and Human Reason. (Cornell University Press, 1993). Pg. 83.

[2] Where a state of affairs S includes a state of affairs S* if it is impossible for S to obtain and S* to fail to obtain.

Is Omnipotence a Perfection?

Suppose we say that being omnipotent just is the ability to do anything that is metaphysically possible. So a being is omnipotent just in case it can do anything that is metaphysically possible. This seems to be the classic view of omnipotence (though more will have to be added, especially about free will). But is this omnipotence a perfection?

Before we answer this question it will be helpful to say what it is that makes a property a perfection. Consider the following:

(PER) A property is a perfection just in case it adds to, but does not subtract from, the greatness of the beings in which it inheres.

So the question I will be asking and answering is, is the omnipotence discussed above a perfection in that sense? My answer will be no. Now there are clearly metaphysically possible evil states of affairs. Hence, any being that has omnipotence will have the power to bring about all of these evil states of affairs. Keeping this in mind, consider the following argument:

Omnipotence is sufficient for the imperfection of any being in which it inheres in virtue of its entailing that that being has the ability to bring about evil states of affairs. Hence, the property subtracts from the greatness of any being in which it inheres. By PER, omnipotence is not a perfection. We can think of it like this: Suppose B is omnipotent in a world W. Further suppose that , in W, B does not bring about any evil state of affairs. But because B is omnipotent, he could have done so. That just is to say that there is a possible world W* in which B does bring about an evil state of affair. But that means that omnipotence entails the property possibly being evil, which is an imperfection. So omnipotence subtracts from the greatness of the beings in which it inheres, for any being that has it will also have these imperfections. Hence, omnipotence isn’t a perfection.

So that omnipotence won’t do. But a better view of omnipotence as a perfection might run as follows:

(O) S is omnipotent just in case S can bring about only all metaphysically possible good or neutral states of affairs.

Obviously more will have to be added to (O), such as conditions about the free actions of others, but I think the point is clear. We need to appeal to the omnipotence discussed previously. An omnipotence that does not entail the ability to do evil seems to me to be obviously better than one that does. So when we say that God is omnipotent, what we ought to mean is that He is omnipotent insofar as he can do all good and neutral things, not that He can do just anything. This also means that omnipotence and moral perfection are compossible. [1]

[1] I am indebted to my friend Marcus for this post.

An Argument for the Possibility of the Existence of God

I thought of this argument last night. First, a few definitions.

(PER) A property P is a perfection just in case, necessarily, P adds to but does not subtract from the greatness of the beings in which in inheres.

Let the property being perfect be the conjunction of all perfections. The argument is as follows.

The property being evil is an imperfection, as it subtracts from the greatness of any being in which it inheres. Is the property of essentially having not being evil a perfection? It is true of this property that it adds to but does not subtract from the greatness of any being in which it inheres. By (PER), therefore, this property is a perfection. We can generalize. For any object x, x has some property P only if it is false that x has P’s complement, P* , where P*  is the property of not having P. Moreover, for any object x, x has P essentially only if it is false that it is possible that it have P* ; that is, x lacks P* essentially.  Now, all of the complements of all imperfections that are essentially had are perfections. So for any property I, I is an imperfection only if essentially having I*  is a perfection. Hence, all of the complements of all imperfections are members of the set of all perfections.

Since being perfect is the conjunction of all perfections, and all of the complements of all imperfections are perfections, it follows that being perfect entails all of the complements of all imperfections. Hence, (1) is true:

(1)  It is false that being perfect entails an imperfection.

So here is the proof, stated informally.

(2)  Being evil is an imperfection.

Assume, for reductio, that

(3)  Being perfect is necessarily uninstantiated.

Since a necessarily uninstantiated property trivially entails any property,

(4)  Then being perfect entails being evil.

(5)  Therefore, being perfect entails an imperfection (from 2, 4).

Contradiction (5 & 1 are incompossible)! We must reject our assumption. Hence:

(6)  It is false that being perfect is necessarily uninstantiated.

(7)  Therefore, being perfect is possibly instantiated.

Of course, anything that has the property being perfect, that is, anything that has all perfections, is God. Such a being would have omnipotence, omniscience, moral perfection, etc. So, possibly, God exists.