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Anselm’s God to Plantinga’s God

Prefatory Remarks:

There is a slight difference in the way Anselm and Plantinga define God.  Anselm’s definition is that God is that than which none greater can be conceived.  Plantinga’s God is a maximally great being, i.e. a necessarily existing being that has omnipotence, omniscience, and morally perfection.  Anselm’s definition is negative, while Plantinga’s is positive.  Anselm’s definition fits with the apophatic tradition of a negative theology, i.e. God is not among those things of which a greater can be conceived.  It is because Anselm’s definition is negative that I contend that Thomas Aquinas is incorrect in his central critique of the ontological argument.  Anselm isn’t offering a positive account of God’s essential nature.  I agree with Aquinas that a positive account of God’s essential nature cannot be completely and univocally known to us, but I should also say that although Plantinga’s definition is positive, it is not claimed to be complete and it need not be interpreted as perfections of “power”, “knowledge”, and “goodness” as those terms are understood univocally.

There is still a strong relationship between the Anselmian definition of God and the Plantingan definition.  Namely, one can derive from the Anselmian definition various divine attributes like necessary existence, omnipotence, omniscience, and moral perfection, among other perfections.  So one can argue that if there is an Anselmian God, then there is a maximally great being, in the Plantingan sense.  Indeed, that impication necessarily holds, given that it analytically follows from the Anselmian definition.  As an aside, I would argue that the two definitions are not equivalent in that one cannot derive the Anselmian definition from the Plantingan definition.  So, the existence of a maximally great being would not necessarily imply the existence of Anselm’s God.

Another interesting aspect of Anselm’s definition is that, since it is negative, I think the case for its metaphysical possibility can be firmly established.  Now, I am not suggesting that Anselm makes a modal inference that the metaphysical possibility of God, as he defines it, entails his actual existence.  Still, it is often disputed that conceivability does not entail metaphysical possibility. However, in this particular case, the conceivability of the Anselmian God makes the following falsehood self-evident, viz. that it is somehow metaphysically necessary that for any object, there will always be something else one could conceive of which would be greater.

Given that Plantinga’s maximally great being is a necessarily existing omnipotent, omnicient, and morally perfect being, I think there may be a powerful way to combine the fact that we can understand the Anselmian God, and show the Anselmian God possible, and use that to demonstrate the existence of a being that is omnipotent, omniscient, and morally perfect.  In what follows, I exploit Anselm to vindicate Plantinga.

Informal Expression of the Argument:

P1) If I can understand the Anselmian definition of God, then it is not necessarily the case that, for any given thing, there will be something conceivably greater.
P2) If it is possible that there is something than which none greater can be conceived, then it is possible that there is an Anselmian God.
P3) The existence of the Anselmian God necessarily implies the existence of a maximally great being.
P4) I can understand the Anselmian definition of God.
P5) If it’s possible that something is maximally great, then it’s possible that there is a necessarily existing, omnipotent, omniscient, and morally perfect being.
C) There is an omnipotent, omniscient, and morally perfect being.

A Formal Expression of the Argument:

P1) If it is possible that the Anselmian God is in the understanding, then it is not necessary that, for all x, it is conceivable that there is y and y is greater than x.
P2) If it is possible that there is something, x, such that it is not conceivable that there is some y and y is greater than x, then it is possible that there is something, z, and z is the Anselmian God.
P3) Necessarily, if there is something that is the Anselmian God, then there is something that is maximally great.
P4) It is possible that the Anselmian God is in the understanding
P5) If it is possible that there is something that is maximally great, then it is possibly necessary that there is something that is omnipotent, omniscient, and morally perfect.
C) There is something that is omnipotent, omniscient, and morally perfect.

Formal Deductive Proof of the Argument:


Mx ≝ x is maximally great
Ox ≝ x is omnipotent, omniscient, and morally perfect
Ux ≝ x is in the understanding
Gxy ≝ x is greater than y
©… ≝ it is conceivable that…
g ≝ (ɿx)(~©(∃y)Gyx)
Theorem of K: ☐(p → q) → (♢p → ♢q)
Theorem of S5: ♢☐p → ☐p
Axiom M: ☐p → p

1. ♢Ug → ~☐(∀x)©(∃y)(Gyx) (premise)
2. ♢(∃x)~©(∃y)(Gyx) → ♢(∃z)(z = g) (premise)
3. ☐[(∃z)(z = g) → (∃x)Mx] (premise)
4. ♢Ug (premise)
5. ♢(∃x)Mx → ♢☐(∃y)Oy (premise)
6. ☐[(∃z)(z = g) → (∃x)Mx] → [♢(∃z)(z = g) → ♢(∃x)Mx] (Theorem of K)
7. ~☐(∀x)©(∃y)(Gyx) (1,4 MP)
8. ~~♢~(∀x)©(∃y)(Gyx)(7 ME)
9. ♢~(∀x)©(∃y)(Gyx)(8 DN)
10. ♢(∃x)~©(∃y)(Gyx)(9 QN)
11. ♢(∃z)(z = g) (2,10 MP)
12. ♢(∃z)(z = g) → ♢(∃x)Mx (3,6 MP)
13. ♢(∃x)Mx (11,12 MP)
14. ♢☐(∃y)Oy (5,13 MP)
15. ♢☐(∃y)Oy → ☐(∃y)Oy (Theorem of S5)
16. ☐(∃y)Oy (14,15 MP)
17. ☐(∃y)Oy → (∃y)Oy (Axiom M)
18. (∃y)Oy (16,17 MP)


Singleton Sets and Divine Simplicity

Plantinga argues against the doctrine of divine simplicity (DDS). Basically, if DDS is true God = God’s omnipotence. But this seems absurd to Plantinga since God is a person and not a property. Of course, we might also point out that DDS seems to imply that some properties are persons. But, I think the better route is to reject Plantinga’s property-based metaphysics in favor of substance metaphysics. This won’t help my friends who are less inclined towards Aristotelian-Thomistic metaphysics. So, in lieu of razing contemporary metaphysics to the ground and providing a cogent defense of A-T metaphysics, here is my attempt to construct a Quinean response to Plantinga’s Argument against Divine Simplicity:

xÎy – x has a membership relation to y
O – the set of beings that have omnipotence
g – God

1. (∀x)(∀y)(xÎy) ≝ [(x = y) ∨ x∈y)] (df “Δ )
2. (∀x)~(x∈x) (pr)
3. (∀x)(∀y)(x = {y}) → (∀z)[(zÎx ↔ (z∈x ∨ z=y)] (pr)1
4. O = {g} (pr)
5. (∀y)(O = {y}) → (∀z)[(zÎO ↔ (z∈O ∨ z=y))] (3 UI)
6. (O = {g}) → (∀z)[(zÎO ↔ (z∈O ∨ z=g))] (5 UI)
7. (∀z)[(zÎO ↔ (z∈O ∨ z=g))] (4,6 MP)
8. OÎO ↔ (O∈O ∨ O=g) (7 UI)
→9. OÎO (CP)
↑10. O∈O ∨ O=g (8,9 MP)
↑11. ~(O∈O) (2 UI)
←12. O = g (10,11 DS)
13. OÎO → (O = g) (9-12 CP)
14. (∀x)(x = x) (IR)
15. O = O (14 UI)
16. (O = O) ∨ O∈O (15 Add)
17. OÎO (1,16 df “Δ)

From this we can conclude that God is identical to the set of beings that have omnipotence:

18. O = g (13,17 MP)

And we can generalize this result, as we can also conclude that God is identical to {God}:

19. {g} = g (4,18 SI)

So divine simplicity could be argued if the following holds:

20. (∀x)[xÎg → (x = {g})] (pr)
21. (∀x)[xÎg → (x = g)] (19,20 SI)

So, if every divine property has a corresponding set, and that set has a membership relationship with God such that God is the only member, then God is identical with the set and each set identical with God is identical with one another. This may seem implausible to those who insist that sets are causally inert abstract objects, but as Vallicella suggests that we should not insist on a “non-constituent” ontology. A constituent ontology views properties not as causally effete abstracta, but as constitutive of a being’s ontology:

Constituent ontology allows for a sort of ‘coalescence’ of the concrete and the abstract, the particular and the universal. Indeed, such a coalescence is what we find in the simple God who is in some sense both concrete and abstract in that he is a nature that is his own suppositum.2

This may not solve all of the difficulties associated with DDS, but I do think it is a plausible response to Plantinga. Interestingly, the drive in set theory to avoid “a = {a}” was considered the drive to clarify an Aristotelian ambiguity. Instead, it begs the question towards some sort of Platonic extreme realism, which still pervades contemporary metaphysics.

1This premise is based on H.A. Harris. 2011. God, Goodness and Philosophy. Burlington, VT: Ashgate Publishing (pg. 105). Harris argues against Quine, by saying that the membership-relation involves assimilation, which she takes to be asymmetrical. However, I think her complaint is misguided, since the issue isn’t whether the assimilation is symmetrical, but the asymmetrical assimilation entails something that is symmetrical itself. And in the case of the singleton, given that a set cannot belong to itself, symmetry is attained.

2W.F. Vallicella “Divine Simplicity”, The Stanford Encyclopedia of Philosophy (Fall 2010 Edition), Edward N. Zalta (ed.)

(For C’zar)

The Golden Rule and Physicalism

[Philosophical Musing Alert… the following is an idea that I have had, which I would like to expose to the light of day, feel free to find the flaws and point them out.]

In a previous post, I considered Plantinga’s modal argument for dualism.  The argument is essentially a refinement of the those put forward by Descartes, though perhaps a bit more rigorous in its appeal to the principle of the indiscernibility of identicals along with some modern notions of modality.  However, the whole argument really comes down to the intuition that if something is conceivable, then it is logically possible.  Some of my commentators countered Plantinga’s argument by saying that while it might be prima facie  conceivable that I inhabit another body, it may in fact be logically impossible for this to occur.  I countered with Chalmers‘ discussion of the conditions by which conceivability would entail logical possibility and that conceiving one could inhabit another body would fit those conditions.  Here I would like to offer a slightly different argument for the logical possibility of inhabiting a different body.  Basically, this is a reductio based upon one of the most universal moral intuitions there is: the Golden Rule.  Since the Golden Rule is accepted by almost every culture and religion, I would say that it is intuitively known to be an objective truth.  I think this insight goes far to dispel physicalism, but we have to consider what the Golden Rule entails.

The Golden Rule states something like, “one should love and treat one’s neighbor as oneself.”  It seems to me that the Golden Rule depends upon the conceivability of thinking that I could inhabit the position relative to my neighbor and/or that my neighbor could inhabit my position.  So, for instance, I determine that I ought not to steal my neighbor’s food, since I could conceive of myself as standing in my neighbor’s position and that his food is my food.  Since, I would not want my neighbor to steal my food, I can imagine that if I were him, I’d not want it to be stolen either.  So, the underlying empathy that the Golden Rule appeals to hinges on counterfactually conceiving oneself in another person’s position.  It is not enough to say “I don’t want my food to be stolen”.  That doesn’t get you far.  Nor can you say, “If I were my neighbor, I wouldn’t want my food to be stolen” because you don’t really know what your neighbor wants or desires.  The key to the Golden Rule is maintaining the “how you want to be treated” clause with a consideration for your neighbor’s situation.  You must bring yourself into his position not by imagining that you ARE him, but that you could be where he is.

But now consider this: ought I to cut my neighbor’s arm off?  If I apply the Golden Rule, I must be able to conceive of the possibility that I inhabit my neighbor’s body.  I certainly would not want the arm to be cut off were I to inhabit such a position, so I cannot cut his arm off. The issue then comes down to this point: when the Golden Rule is be applied to questions of the body, it seems that one must be able to conceive of the possibility of inhabiting one’s neighbor’s position, and in many cases this means his body.  This conception is certainly prima facie conceivable.  But if the conception is ultimately logically incoherent, then the application of the Golden Rule depends upon a logical impossibility.  This means that one cannot really conceive of what it would be like to be a neighbor’s body and so the empathy evoked is unjustified.  Thus, the appeal to how we want to be treated is improperly assumed to apply to our neighbor, since nothing really must be the case once an logical impossibility is admitted.

However, it is plainly obvious that the Golden Rule can be applied in moral considerations considering the treatment of the human body.  And it would be absurd to think that a rule to which so many often appealed when justifying non-violence against another person’s body is,within its core assumptions, logically impossible. Therefore, it must be conceivable and also logical possibility.  But then, if I could be my neighbor’s body, then I am not my body.  This is because while it is possible that I could be me and in a different body at the same time, it is logically impossible that I could be me and also a different me at the same time.  Thus, the empathy that lies at the core of the Golden Rule requires a discernible difference between myself and my body.  Since physicalism posits that I am my body, it must be false.

There are a couple of objections that I could anticipate to this argument:

1.  The most obvious objection is that the empathy that lies at the heart of the Golden Rule needn’t depend upon the logical possibility of counterfactually conceiving oneself in another person’s position.  A physicalist might give an entirely naturalistic account of empathy which avoids such reasons.  For instance, a man stubs his toe and screams and moans.  Those sound waves evoke brain states in me whereby I  come to believe that I understand that there is a person other than myself experiencing pain and I feel bad about that belief.  No mystery, no ghosts in the machine, nothing “spooky” is going on at all in this account.  Furthermore, it seems that we have not applied counterfactual thinking to explain empathy.  And indeed, I would agree that we could explain empathy without appeal to counterfactuals.  But an explanation is very different from a justification.  If the Golden Rule can be explained, but not justified, then it is not an adequate ground for moral reasoning.  So often in debates between physicalists and non-physicalists the distinction between explanation and justification is missed.  The physicalist claims only to be able to give an account for something purely physically.  The non-physicalist demands not a physical explanation, but a physical justification for something like empathy or the Golden Rule.  At least to me, there can be no justification of the principle unless it is assumed that there are not just other bodies, but other minds and that it is at least possible to think of minds as separate from bodies so that a switching of positions is conceivable.  The Golden Rule requires a “bringing-together” of “how I want to be treated” with the other.

2. It could be objected that it is logically possible to imagine that I am my neighbor’s soul.  In other words, shouldn’t the Golden Rule apply to cases where I consider whether I ought to cause harm to the soul of my neighbor.  I’d have to be able to conceive that I am my neighbor’s soul, which would mean, by an analogous argument, that I am not identical to my soul.  So it seems that I must argue that the Golden Rule only prima facie  applies to cases where harm might be caused to a neighbors soul, but that it is really logically impossible to apply the Golden Rule in such cases.  I think this would mean that, ultimately, the Golden Rule could not be applied to cases where one might directly harm a neighbor’s soul.  Why might this be?  Perhaps it is because it is impossible for one  to harm another person’s soul directly–one can only harm one’s own soul and only another person’s soul indirectly.  But this does not mean that one cannot cause harm to another person’s soul in another sense.  For instance, suppose I were to tempt my neighbor into stealing an automobile.  We might suppose that becoming a  thief is damaging to a person’s self, or soul, rather than to his body.  But, am I really causing harm directly to my neighbor’s self or soul when I tempt him?  No.  What I am doing is making use of my neighbors ears, by whispering tempting words into them.  I am using words to alter my neighbor’s emotional states, or passions.  I am altering my neighbor’s body in an attempt to influence his will.  In such a case, I am responsible for affecting my neighbor’s body in a way that I would not want my own body to be affected, so I have done my neighbor wrong–but it is a wrong to his body.  Thus, if the Golden Rule applies to cases of harm to the soul, it is only insofar as one can do harm to a body, which affects the soul.  I cannot harm another person’s soul directly, but only through the other person’s cooperation.  So in the case of temptation, I only take the position of my neighbor’s body.  If I were also to take the place of his soul, then I am really not imagining the situation properly to derive reciprocity.  For if I were to imagine that I were his soul too, then I could not use any of my own intuitions about how I would want to be treated so as to apply those intuitions to his case.  Deriving reciprocity depends upon keeping some aspect of myself while counterfactually exchanging some non-essentials between neighbors.

3.  A physicalist friend of mine has prompted me to consider a third possible objection.  Though perhaps practically infeasible, suppose a complete brain transplant were possible.  One might be able to imagine oneself as “conscious” in another person’s body if one were to imagine that one survives a brain transplant into a new body.  Thus, the counterfactual imaginings central to the Golden Rule need not be anti-physicalistic at all, if physicalists can meaningfully speak of a person being conscious at all.  I think this is an important objection because it gets at the heart of the physicalist problem for me.  Suppose I were to imagine that such a surgery took place–that my brain has been transferred into my neighbor’s body.  Is the result a switch of position?  Is my conscious-self in a new body?  I would say no.  The result is far from my possessing or inhabiting my neighbor’s body.  Rather, the result of the surgery seems to be some sort of chimerical Frankenstein’s monster, at least that is how the thought strikes me.  Thus, the result of such a thought experiment allows for no application of my intuitions as to how I want to be treated if I were in my neighbor’s position.  Instead, given the veridicality of physicalism and a successful brain transfer, two humans are destroyed and something new has been made.  The Golden Rule question is lost and instead one is mired in a sorties paradox of how much of you is necessary for you to remain yourself.  I don’t think there is a good answer to this question under physicalism, so the paradox cannot be resolved.  Rather than providing a good counter-example as to how a physicalist might counterfactually imagine him or herself in another person’s position, such thought experiments reveal only deeper metaphysical problems for the physicalist.  Rather than pumping our moral intuitions about how we ought to treat our neighbors, we are left scratching our heads without a good account of what makes a person self-same.  No, I don’t think a brain transfer thought experiment will help us to be able to appeal to the Golden Rule and also be physicalists.

To sum up, my argument would run something like this:

(1)  The Golden Rule is moral principle that can truly be applied to a case if and only if counterfactually conceiving myself in another person’s position is logically possible.

(2)  If the Golden Rule can truly be applied to cases of the human body, then conceiving myself in my neighbor’s body is logically possible.

(3)  If I am my body, then it is not logically possible to conceive myself in my neighbor’s body.

(4)  If physicalism is true, I am my body.

(5)  The Golden Rule can truly be applied to cases of the human body.

(6)  Conceiving myself in my neighbor’s body is logically possible. 3,5 MP

(7)  I am not my body.  3,6 MT

(8)  Physicalism is not true. 4,7 MT

It all comes down to the price you have to pay.  If you want to maintain physicalism, you have to deny the logical possibility of inhabiting a body other than your own.  This means that you cannot coherently apply the Golden Rule to cases of the human body.  Since nearly every ethical and religious moral theory appeals to the Golden Rule on some level, this is a very high price to pay.  I have to give up on physicalism so that I can continue to use a moral principle that has not only served me well, but I think lies at the core of any conception of morality.

Am I My Body?

Aside from the fact that Dr. Plantinga isn’t quite sure how many legs a beetle has–come on, eight, really?!?–I think he presents a really good argument against physicalism.

The argument runs something like this:

1.  If I am my Body, then anything possible with regard to me is also possible with regard to my body.

2.  It is possible that I exist when my body does not exist.

3.  It is not possible that my body exists when my body does not exist.

4.  Thus, “I exist without my body” is something possible with regard to me that is not possible with regard to my body.

5.  Therefore, I am not my body.

The argument demonstrates a discernible difference between the body and the self.  But does it matter that we are talking about mere possibilities here?  Plantinga’s point is that there is no possible world where a body exists without itself.  Yet, it does not seem logically impossible to imagine a possible world where the self exists without its body.  We take such stories to be supernatural, fantastical, or fictional, but not logically incoherent.  So, it seems reasonable to suppose the logical possibility of a disembodied self.

This means that proving an identity relationship between the self and the body requires a lot more than empirically proving a causal relationship between physical states and mental states.  One must also prove that it is logically incoherent to suppose that there are any possible worlds where the self is disembodied.  So it seems that while this burden is heavily placed upon the physicalist, the supernaturalist can merrily go along believing that she is her soul.  Right?

Not so fast, my friend Shaun Miller has pointed out to me that this argument, if anything, proves too much (Shaun was inspired by Shelly Kagan, ff about 43 min in for the appropriate part).  Kagan points out that we could imagine that the same body is possessed by different souls. His point is not that we are not our soul, but that our soul doesn’t seem sufficient to establish personal identity.  As far as I can tell, Shaun’s response to Plantinga is original, and quite difficult to overcome.  He points out that we could substitute just about anything in the argument, including the soul, and prove it to be non-identical with the self.  Does this mean that I am not my soul?!? My initial reaction to this was, “Well, it’s just not possible that I exist without my soul, since I am my soul.”  But now I’m guilty of special pleading.  This fallacious soul-ution is to stipulate that “soul” is simply defined as “self”.  But then we have just stipulated our way to victory, which is not very satisfying.  What would prevent the physicalist from stipulating “body” as “self”?  We’re back to square one.

Upon further reflection, I think the argument achieves something.  It proves that unless we have good reason to think that it’s not possible for X to exist when Y doesn’t exist, then we don’t have good reason to think X and Y are identical.   I have no good reason to think I am my body, because I think it is at least logically possible to be disembodied and survive.  But then I should be willing to bite the bullet and concede that I have no good reason to think I am my soul.  So be it.  I have no good reason to think I am my soul either.  As I said before, we could substitute just about anything for body–just about.  However, I cannot substitute “self”.  Whatever “self” is, it cannot both exist and not exist, at the same time, and in the same possible world!  So I do have good reason to think at least this…  I am myself.

But is this an adequate response?  Are there other problems with the argument that I am not mentioning here?

Plantinga’s Ontological Argument

Things have been pretty crazy lately and so I have been forced to slow my posting while I try to meet some deadlines. However, I thought I would start a series on the Ontological Argument as it is of interest to me.

Here is Plantinga’s version of the argument as laid out by R.E. Maydole (The Blackwell Companion to Natural Theology 2009, 590):

Ax =df x is maximally great
Bx =df x is maximally excellent
W(Y) =df Y is a universal property
Ox =df x is omniscient, omnipotent, and morally perfect


1. ◊(∃x)Ax                                      pr                           
2. □(x)(Ax ≡ □Bx)                               pr
3. □(x)(Bx ⊃ Ox)                                pr
4. (Y)[W(Y)≡(□(∃x)Yx ∨(□~(∃x)Yx)]              pr
5. (Y)[∃(Z)□(x)(Yx ≡ □Zx)⊃ W(Y)]               pr
6. (∃Z)□(x)(Ax ≡ □Zx)                          2,EG
7. [(∃Z)□(x)(Ax ≡ □Zx) ⊃ W(A)]                5,UI
8. W(A)≡(□(∃x)Ax ∨(□~(∃x)Ax)                 4,UI
9. W(A)                                         6,7 MP
10. W(A)⊃(□(∃x)Ax) ∨ (□~(∃x)Ax)               8,Equiv, Simp
11*. □(∃x)Ax ∨ □~(∃x)Ax                     9,10 MP
12. ~◊~~(∃x)Ax ∨ □(∃x)Ax                     11,Com, ME
13. ◊(∃x)Ax ⊃ □(∃x)Ax                         DN, Impl
14. □(∃x)Ax                                    1,13 MP
15. □(x)(Ax ≡ □Bx) ⊃ (□(∃x)Ax ⊃ □(∃x)□Bx)    theorem
16. □(∃x)□Bx                                   14,15 MP (twice)
17. □(x)(Bx ⊃ Ox) ⊃ (□(∃x)□Bx ⊃ □(∃x)□Ox)    theorem
18. □(∃x)□Ox                                   16,17 MP (twice)
19. (∃x)□Ox                                    18,NE

*Premise 11 seemed to contain an error. I added the disjunctive symbol as it was missing from Maydole’s account.

So, the argument is valid. The question is with the premises. Most take issue with premise 1, that it is possible that there exists something that is maximally great. One response that I have heard is that while the burden of proof is on the person making the positive assertion, in the cases of probability, the benefit of the doubt sides with the person supposing possibilities. In other words, one must provide me with good reasons to suppose some proposition could not obtain in any possible world. How would one do this in this case? Any thoughts?