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A Modal Argument Against Naturalism from Transcendentals

For any argument against naturalism, we are going to have to specify the sort of naturalism we are discussing.  Here, my target is a rather broad notion of metaphysical naturalism.  Let’s define the notion in the following way: naturalism is the thesis that reality is exhausted by the natural.[1]  This is, admittedly not an informative definition (and somewhat circular), but it will do the job of being relatively broad for this argument, but not so vacuous as to be uninteresting.  Many contemporary naturalists would assent to the definition, and I, being Catholic, believe that naturalism, so defined, is false.

P1. Naturalism is true just in case “natural” is greater than and includes the combined extensions of terms that name each and every one of the categories into which being may be divided.[2]

P2. “Natural” is greater than and includes the combined extensions of terms that name each and every one of the categories into which being may be divided just in case “natural” is a transcendental that is convertible with “being”.

P3. All terms that are transcendental that are convertible with “being” are necessarily transcendentals that are convertible with “being”.

P4. If naturalism is true, naturalism is contingently true.

P5. If naturalism is contingently true, it is false that “natural” is necessarily a transcendental that is convertible with being.

C1. Therefore, naturalism is false.

The argument is a reductio, as the premises lead to an obvious contradiction if one assumes naturalism is true (i.e. “natural” is necessarily a transcendental that is convertible with “being” and it is false that “natural” is necessarily a transcendental that is convertible with “being”). Given the definition of “transcendental” and the plausibility of P3-P5, naturalism cannot be the case.

There are a few ways the naturalist may object (and why I think they are inadequate objections):

Objection 1: “Natural” is not a transcendental.

Reply to 1: If “natural” is not a transcendental, as defined extensionally, then it is not exhaustive of reality.  Let’s say that reality is composed of everything, all beings.  If “natural” doesn’t exhaust all beings, then there are beings that are not natural.  That, to me, is sufficient to falsify metaphysical naturalism.  So this is not a very good move to make, though it may be a knee-jerk move to make in response to the argument.

Objection 2: There are no transcendentals.  The idea that res, unum, aliquid, bonum, et verum or any other supposed transcendental like “beauty” is convertible with being is a quaint notion from an outmoded era of philosophy and theology when people drank in far too many Hellenistic notions.

Reply to 2: Fine, you dislike older ideas.  But the extensional definition of transcendentals are still on the table and there is no reason to think that we cannot categorize being, or devise a notion of a term that is universal.  After all, as I suggested in response to the first objection, to say that “natural” exhaust reality is to say something about the universality of “natural” and that its extension would be as broad as “being” or “reality”.  So, it sounds odd to object to there being transcendental terms when naturalism, so defined, depends on it.  Ah, but “naturalism” could be defined in other ways.  That’s true, but those sorts of “naturalisms” are not the target of this argument.  Moreover, I am not too sure that I am opposed to a form of metaphysical naturalism that is too timid to claim that “natural” exhausts “being”.

Objection 3: P3 is false.  There is no reason to think that if some term is convertible with “being”, then it is necessarily so.  It might be contingently convertible with being, especially if “transcendental” is only being defined extensionally.  That is, the transcendentals could merely happen to be convertible with “being”.

Reply to 3: It would seem, then, that we have two sorts of transcendentals: contingent transcendentals that happen to be convertible with “being” and necessary transcendentals that are necessarily convertible with “being”.  So, for instance, if God were actually to exist, there would be a sense in which res, unum, aliquid, bonum, et verum could be applied to God.  But, presumably, if God were to exist, “natural” could not apply to Him.  In other words, were there super-natural beings, “natural” would have a smaller extension than “being” and “natural” would cease to be a transcendental.  Yet, the other named transcendentals are not like this.  No matter what possibilia comes to be, the transcendentals would remain what they are.  It’s just that the actualization of the possibilia means that the actuality is res, unum, aliquid, bonum, et verum.  It seems, then, that the naturalist would be committed to the thesis that “natural” is convertible with “actual”, i.e. everything is actual if and only if it is natural.  But “actuality” is not a transcendental.  Rather, one can divide the various categories of being into act and potency.  In other words, actuality has a smaller extension than any given category and, a fortiori the combined extensions of all the categories of being.  Now the naturalist might quibble and say that any potential or possibility of the non-natural, or supernatural, is itself natural.  But this is not to address the question of whether “natural” is extensive with all potentials and possibilities, but just the actualities in which those potentials and possibilities obtain.

Another issue is that it is rather question-begging to demand that “natural” is one instance of a “contingent transcendental” convertible with being given what actually happens to exist.  Is there another such transcendental? Why are all the other transcendentals necessary and remain transcendentals no matter what happens to be in the world.

Objection 4: P4 is false.  Metaphysical worldviews, if true, are necessarily true.  Thus, if metaphysical naturalism is true, then it is somehow necessarily true.

Reply to 4: This is a rather strong position to take.  For it not only posits that supernatural entities, like souls, and gods, do not exist.  It posits that they cannot exist for metaphysical or broadly logical reasons.  It is not clear to me why this must be the case, and there seems to be good reason to think this is false.  1) Even if it is not supposed that the Anselmian God is metaphysically possible (from which, some would argue, His existence could be demonstrated), a less than maximally great or perfect divinity is plausibly metaphysically possible.  That is, a being that would sufficiently falsify naturalism, even if it is not morally perfect, omniscient, or omnipotent, could exist.  What’s more, if metaphysical naturalism is metaphysically necessary, then it would satisfy the Leibnizian question “why is there something rather than nothing” in much the way classical theists think God satisfies this question.  The classical theist says that God is metaphysically necessary, so not anything existing is impossible.  But the metaphysical naturalist doesn’t seem to make the same move.  Faced with the radical contingency of reality, the metaphysical naturalist usually doesn’t say that since metaphysical naturalism is metaphysical necessary, there must be at least one natural thing in existence.  If nothing were in existence, then nothing natural would exist.  Now a particularly impish naturalist might suggest that, were there nothing in existence, metaphysical naturalism would be true.  That is, one natural configuration of the world is “there not being anything”.  But if there were nothing, it wouldn’t be the case that “natural” exhausts reality.  “Natural” would not be predicated at all.  It would no more “exhaust” reality than “supernatural”.  So there not being anything is not compatible with metaphysical naturalism being true.  So if metaphysical naturalism is necessary, nothing is intrinsically impossible.  Yet, we have no reason to think that if naturalism is true, some natural thing or other must exist.

Objection 5: Okay, metaphysical naturalism is only contingently true, but “natural” is necessarily a transcendental convertible with being anyways.  In other words, P5 is false.

Reply to 5: Well, if there is no possible world where “natural” fails to exhaust “being”, then metaphysical naturalism would be true in every possible world.  Metaphysical naturalism cannot be contingent while it be necessary the everything is natural.  That just is to claim that metaphysical naturalism is true in every possible world (a strong claim to make).

In Sum: If I were a naturalist, I think I would try to argue that some transcendentals are contingent. I don’t think the argument would be very convincing, for the reasons I mentioned.  After that, I think I would want to argue that metaphysical naturalism is necessary.  Remember, it is not enough to simply say that metaphysical naturalism could be necessary. If all of the other premises of my argument are correct, and one wants to maintain metaphysical naturalism as true, one would have to admit that the only way it could be true is if it is metaphysically necessary.  However, I don’t see any good reason to think metaphysical naturalism is metaphysically necessary for the reasons I’ve outlined above.  So, it seems to me that, since “natural” is not a transcendental of “being”, metaphysical naturalism is false.

[1] Papineau, David, “Naturalism”, The Stanford Encyclopedia of Philosophy (Spring 2009 Edition), Edward N. Zalta (ed.), URL = <>.

[2] This is based on an extensional definition of transcendentals offered by Jorge J.E. Gracia. See Jorge J.E. Gracia, 1992, “The Transcendentals in the Middle Ages: An Introduction,” Topoi 11(2): 113–120. Also Wouter Goris and Jan Aertsen, “Medieval Theories of Transcendentals”, The Stanford Encyclopedia of Philosophy (Summer 2013 Edition), Edward N. Zalta (ed.), URL = <>

Divine Propositions and Referential Opacity

The following thoughts occurred to me yesterday, and I wanted to jot some notes down before forgetting them, though I am far from endorsing them.  Just something to chew upon. Some philosophers reject Divine Simplicity and certain explications of the Doctrine of the Trinity because such doctrines seemingly involve contradictions. These contradictions arise when the attributes of God and/or Persons of the Trinity are related to one another by numerical identity. Here are some problematic Divine Propositions:

  1. God = the Triune Godhead
  2. The Son of God = God
  3. God = God’s Knowledge
  4. God = God’s Power

These are problematic, because (1) and (2) seem to suggest that the Son of God = the Triune Godhead, which no orthodox Christian wants to say. Likewise, it prima facie problematic to take (3) and (4) to mean that God’s Knowledge is identical to God’s Power. One solution to this latter problem is to appeal to the doctrine of analogy and say that God’s Knowledge and Power and not the same as the knowledge and power we commonly know about from our everyday experience, so they can be identical. This may be compelling for some, like myself, but for others, I suspect it comes off as appealing to mystery. That is, we don’t really know what we are saying when we say that God has power or knowledge. The former problem is more difficult to resolve. How can we say that the persons of the Trinity are identical to God, but not infer that they are identical to one another, or to the totality of the Godhead? A method to address this is to appeal to the Relative Theory of Identity, devised by Peter Geach. According to this theory, it is an incomplete expression to say that “x is the same as y”. Geach thinks we have to specify the sortal concept by which x and y are the same, that is “x is the same F as y”. This might help us to explain the “The Son of God is the same God as the Father” while also admitting “The Son of God is not the same Divine Person as the Father”.   The sortal terms prevent a direct contradiction. Of course, this may pose a problem for absolute simplicity, since it seems like a sortal is kind or type, and “The Son” or “The Father” are tokens of the type. Also, this solution does not seem to help with (1) and (2), since it seems that the same sortal term could be specified. That is “God is the same God (or Divine Substance) as the Triune Godhead” and “The Son of God is the same God (or Divine Substance) as God.” With the same sortals in place, it seems that Leibniz’s laws are in play again, and we should be able to substitute terms salve veritate. A recent discussion got me thinking of a possible solution to these puzzles. A person was arguing against the Identity of Indiscernibles by appealing to Max Black’s Spheres as possible counterexamples.  The other interlocutor noted that the issue really isn’t the Identity of Indiscenibles, but the Indiscernibility of Identicals. Just to be clear, the two principles are here:

  1. (∀x)(∀y)((x = y) ⊃ (∀φ)(φx ≡ φy)) [indiscernibility of identicals]
  2. (∀x)(∀y)((∀φ)(φx ≡ φy) ⊃ (x = y))[identity of indiscernibles]

The interlocutor seemed to be saying that while (6) may be controversial, it is irrelevant to his problem.  Rather, it is (5) which seems to imply that since the Son of God is numerically identical to God, and God is supposed to be Triune, the Son of God must be Triune, where “Triune” stands as some sort of property, attribute, predicate or description. This implies a transitivity among identicals, which I take to be the real underlying problem in these theological discussions. If the orthodox teachings of divine simplicity and the Trinity depend on a notion of numerical identity, and numerical identity is transitive, or admits of substitution, then certain untoward consequences and contradictions result. By transitivity, I mean the following formal expression:

  1. (∀x)(∀y)(∀z)(((x = y) & (y =z)) ⊃ (x = z)) [transitivity]

So my proposal is to consider whether there is a way to maintain the claim that all of God’s attributes and relations are strict identity claims (rather than relative identity claims, or mere predications) while avoiding untoward inferences. It occurs to me that the indiscernibility of identicals, identity substitution, and the transitivity of identity generally are disrupted in referentially opaque contexts.  So, for instance, consider the following:

  1. I believe that the Boston Strangler = Bobby Orr.
  2. The Boston Strangler = Albert DeSalvo.

We cannot infer from (8) and (9) that Bob Orr is Albert DeSalvo. Perhaps it is true that Albert DeSalvo has been living under a false identity of Bobby Orr, so “Bobby Orr” and  “Albert DeSalvo” refer to the same person. That’s possible, but it is not logically necessary, so truth would not be preserved. This is because “I believe” is a context that is referentially opaque. How does this help us in preserving orthodox theological claims? There are other referentially opaque contexts. One such context that Quine famously argued for is de re modality. In a de re modal claim, one asserts that a certain property, predication, or identity is necessarily predicated of an individual (or property). This is opposed to de dicto modal claims, in which propositions themselves are said to be necessary. So, for instance, a de re modal claim might be something like “Daniel is necessarily an animal” where as a de dicto claim might be something like “necessarily, Daniel is an animal.” Now it might not strike us immediately that de re and de dicto phrases are in any way different from one another, but consider something like this: “necessarily, a bachelor is an unmarried male” and “a bachelor is necessarily an unmarried male.” It seems clear that the de dicto expression is true, as it is positing a necessity between synonymous. The latter is clearly false, because many bachelors are not necessarily unmarried males, and many cease to be unmarried at some point in the future. Quine is suspicious of de re modality because of issues found in the above examples, but he makes his concern more explicit in the following:

  1. 9 = the number of planets.
  2. 9 is necessarily greater than 7.[1]

From (10) and (11) can we infer that the number of planets is necessarily greater than 7? It seems not, because the number of planets can change, and not just by scientific fiat (poor Pluto). A few planets could blow up, or fall out of orbit around the sun. There seems to be no logical or metaphysical necessity that the number of planets in our solar system is greater than 7. So Quine reasons that de re modality is referentially opaque. If this is so, then Divine Propositions expressed in contemporary logic, where modality is treated as an operator, may also be referentially opaque. Let’s stipulate that Divine Propositions are identity statements about God, the Persons of the Trinity, or the Divine attributes. So, I argue that they are not merely identity claims, but de re identity claims. Now some philosophers claim that de re necessity is not referentially opaque. David Wiggins, for instance, endorses the following argument, claiming that opacity is a problem that “no longer presses”:

  1. Hesperus is necessarily identical to Hesperus.
  2. Hesperus is identical to Phosphorus.


  1. Hesperus is necessarily identical to Phosphorus.[2]

I remain completely unconvinced that this argument is valid. While it might be the case that the object to which Hesperus and Phosphorus refer, the planet Venus, is necessarily self-identical, it doesn’t seem to me that there is any logical or metaphysical necessity that Hesperus and Phosphorus could not have been two distinct objects. So even though these are co-referring terms, it seems to me that de re identity is an intensional context, i.e. it is referring to the intension of the terms and relating them to one another by a necessity of identity. I find this tantamount to the following:

  1. I necessarily believe Hesperus is Hesperus.
  2. I believe Hesperus is Phosphorus.


  1. I necessarily believe Hesperus is Phosphorus.

Let’s say that (16) is true, that I am a consistent thinker. It seems odd though, that (17) should follow. Of course, those who think that de re contexts are not opaque will remain unconvinced. To me, this is one of the major shortcomings of contemporary modal logic, and is a primary motivator for seeking out a modal logic that avoids the opacity problem. In my estimation, Aristotelian modality has the advantage of making de re-like modal claims, but without being opaque. Aristotle achieves this by treating modality as a copula modifier rather than a predicate modifier, or movable operator. But this is a tangent that I will have to explore in later posts. Now let us re-examine Divine Propositions:

  1. God is necessarily identical to the Triune God.
  2. The Son of God is necessarily identical to God.

These are de re identity claims, and if these claims are referentially opaque, it unclear whether we can now infer from (18) and (19) the the Son of God is necessarily identical to the Triune God. So, if all identity relations said of God are de re identity claims, then substitution of identity cannot occur. This does not mean that certain substitutions will not happen to preserve truth, but that we simply cannot assume to make such substitutions.  That is, the identity relation in Divine Propositions will not guarantee the preservation of truth when terms are substituted.  This gives some philosophical reason to appeal to a certain mystery regarding God’s nature. That is, God’s nature cannot be fully comprehended, at least in part, because Divine Propositions are referentially opaque de re identity claims. Now one might object that if it is true that God is necessarily identical to the Triune God, then God is identical to the Triune God, and so we can reduce out the referential opacity so that the substitution problem arises. One response to this would be to say that it is simply false to assume that the reduction from de re modality is truth preserving for Divine Propositions. For if we assume that Divine Propositions are, at the very least, always based on identity, then a certain problem arises with Divine Identity itself.  That is:

  1. God’s identity to the Triune God is identical to God’s necessary identity to the Triune God.

If God’s identity to the Triune God is identical to necessary identity, then we must ask whether the identity relation that relates the two sorts of “God’s identities” is itself referentially opaque. If we grant that “identity” is not referentially opaque in (20), then by transitivity “God’s identity” on the left side is referentially opaque as it is on the right side. Alternatively, we might deny that such a transitive relation exists in (20), but that must be because it is an opaque context despite being explicitly de re.  And this is precisely what we are arguing.  So the conclusion seems unavoidable. Another objection one might make is that referential opacity disappears if the same intensional context is used throughout an argument. So, for instance:

  1. I believe that the Boston Strangler = Bobby Orr.
  2. I believe the Boston Strangler = Albert DeSalvo.

From this, it seems that I can validly infer that:

  1. I believe that Bobby Orr = Albert DeSalvo.

Is this true? Well, not if I am an inconsistent believer. We have to make certain doxastic assumptions about me, in addition to these premises, to reach that conclusion. What about in the case of de re modality?

  1. 9 is necessarily identical to the number of planets.
  2. 9 is necessarily greater than 7.

Does the following follow?

  1. The number of planets is necessarily greater than 7.

Can we make this inference? I suspect not without making certain assumptions about the kinds of necessity at play. Even then, it is ambiguous as to which sort of “necessity” is found in the conclusion. So, I don’t think including the same opaque context throughout an argument transforms the premises into something transparent. For instance, it may be  that (24) is about metaphysical necessity, nomological necessity, physical necessity, or some other sort of necessity? Is the same sort of de re necessity used in (25)? I think most of us would see (25) as some sort of logical, or arithmetic necessity. What about in the case of Divine de re claims? Well, we would have to have a clear sense of the univocal way in which God’s attributes and persons are related to one another by de re identity. I suspect that our own understanding of the ways in which these relations are described will vary from logical necessity, to metaphysical necessity, to necessities that are contextualized by our understandings of specific attributes. For instance, there is a sense in which the Father is unbegotten and necessarily exists a se, and a sense in which the Son is begotten, but still necessarily existing in that the divine relation from the Father to the Son is a necessary because of the metaphysics of subsistent relations, or because of some necessity in the nature of perfect love and community. So the Son is necessary, but begotten of the Father, which doesn’t seem to be exactly the same sort of necessity.  Is there an overarching sense in which the Father and Son are both necessary, sure, but that sense may be beyond our immediate comprehension. Consequently, I find it dubious that we can settle on one opaque de re context in all of our discussions of God. And even if we could, it is not likely that opacity can be remedied by maintaining the same context throughout an argument. Therefore, I think we must conclude that Divine Propositions, i.e. propositions about God, the Persons of the Trinity, and Divine Attributes that are linked together by de re identity relations can be strict, opaque, and not admit of transitivity.  Thus, God’s nature can be described through the Divine Propositions, but God’s nature prevents inferences about specifics about His nature unsubstantiated by revelation, which preserves mystery.  This is not a fallacious appeal to mystery though, but one that has philosophical motivation.  If this is so, it represents one way that orthodoxy can be intellectually defended.

[1] See W.V.O. Quine. 1966. “Three Grades of Modal Involvement” in The Way of Paradox and other Essays. New York: Random House. pg. 161.

[2] See David Wiggins. 2001. Sameness and Substance Renewed. New York: Cambridge University Press. pp. 114-115.

An Argument from the Regularity of Nature to the Falsity of Metaphysical Naturalism

I find the following argument compelling:

P1. If it is both the case that something has an explanation and that explanation is natural, then it has an explanation that depends on the actuality of the regularity of nature.
P2. If something is contingent, it is not the case that it has an explanation that depends upon the actuality of itself.
P3. All things that are actual are possible.
P4. All things that are possible, and not necessary, are contingent.
P5. All things that are contingent have an explanation.
P6. The regularity of nature is actual.
P7. The regularity of nature is not necessary.
P8. If something has an explanation and it is not the case that the explanation is natural, then metaphysical naturalism is false.
C1. The regularity of nature is possible (from P3 and P6).
C2. The regularity of nature is contingent (from P4, P7, and C1).
C3. The regularity of nature has explanation (from P5 and C2).
C4. It is not the case that the regularity of nature has an explanation that depends upon the actuality of itself (from P2 and C2).
C5. It is not both the case that the regularity of nature has an explanation and that explanation is natural (from P1 and C4).
C6. It is not the case that the explanation of the regularity of nature is natural (from C3 and C5).
C7. Therefore, metaphysical naturalism is false (from P8, C3, and C6).

An Argument Against Naturalism from Abstract Objects

Some naturalists, like Quine, feel compelled to admit abstract objects, like numbers, sets, and propositions, into their ontology. But I’ve always had the sense that abstract objects are incompatible with naturalism. Here I will lay out some premises about abstract objects and naturalism that appear fairly intuitive to me. I will then represent those premises in logical notation, and demonstrate that they do, indeed, serve as a defeater for naturalism.

1. If a thing1 is natural then it is possibly not the case that there exists a thing2 where thing2 is natural and identical to thing1.

In other words, if a think is natural, then it possibly doesn’t exist.

2. There exists some proposition such that necessarily that proposition is true.

For example, the mathematical proposition ‘2 + 3 = 5’ is necessarily true and cannot be false.

3. For all propositions, necessarily, if a proposition is true, then there exists some thing1 such that thing1 is abstract and thing1 is identical to that proposition.

This is just to say that it is necessary that if a proposition is true, then it is an existing abstract object. After all, it would seem odd to predicate a truth-value to a proposition, but deny that said proposition doesn’t exist.

4. If there exists a proposition that is necessarily true, and everything is natural, then for all proposition, necessarily, if there exists a thing1 that is an abstract object identical to that proposition, then there exists a natural thing2 identical to that proposition.

I defend this premise on the grounds that, if a proposition is natural, then in every world where it obtains, it obtains as a natural proposition. That is, if ‘natural’ is predicated of a proposition, it is essentially predicated of it, which is to say that in every world where that proposition exists, it exists as a natural object.

From these four premise, we can conclude that naturalism, which I take to be the claim that everything is natural, is false.

The deduction is as follows:

Nx – x is natural
Tp – p is true
Ax – x is an abstract object

1. (∀x){Nx ⊃ ♢~(∃y)[Ny & (y=x)]} (premise)
2. (∃p)☐Tp (premise)
3. (∀p)☐[(Tp ⊃ (∃x)(Ax & (x=p))] (premise)
4. (∃p)(☐Tp & (∀x)Nx) ⊃ (∀p)☐{(∃x)[Ax & (x=p)] ⊃ (∃y)[Ny & (y=p)]} (premise)
5. (∀p)☐{(∃x)[Ax & (x=p)] ⊃ (∃y)[Ny & (y=p)]} (IP)
6. ☐Tu (2 EI)
7. ☐[(Tu ⊃ (∃x)(Ax & (x=u))] (3 UI)
8. ☐(∃x)(Ax & (x=u) (6,7 MMP)
9. ☐{(∃x)[Ax & (x=u)] ⊃ (∃y)[Ny & (y=u)]} (5, UI)
10. ☐(∃y)[Ny & (y=u)] (8,9 MMP)
11. (∃y)[Ny & (y=u)] (10 NE)
12. Nv & (v=u) (11 EI)
13. Nv ⊃ ♢~(∃y)[Ny & (y=v)] (1 UI)
14. Nv (12 Simp)
15. ♢~(∃y)[Ny & (y=v)] (13,14 MP)
16. (v=u) (12 Simp)
17. ♢~(∃y)[Ny & (y=u)] (15,16 ID)
18. ~☐(∃y)[Ny & (y=u)] (17 MN)
19. ☐(∃y)[Ny & (y=u)] & ~☐(∃y)[Ny & (y=u)] (10,18 Conj)
20. ~(∀p)☐{(∃x)[Ax & (x=p)] ⊃ (∃y)[Ny & (y=p)]} (IP 5-19)
21. ~(∃p)(☐Tp & (∀x)Nx) (4,20 MT)
22. (∀p)~(☐Tp & (∀x)Nx) (21, QN)
23. ☐Tu (2 EI)
24. ~(☐Tu & (∀x)Nx) (22 UI)
25. ~☐Tu ∨ ~(∀x)Nx (24 DeM)
26. ~~☐Tu (23 DN)
27. ~(∀x)Nx (25,26 DS)
28. (∃x)~Nx (27 QN)

Line 28 is our conclusion, namely that something exists that is not natural. I take this to be incompatible with naturalism. Therefore, I take the existence of abstract objects, like propositions, to be a defeater for naturalism. I suspect that the naturalist will take issue with one or more of the premises, but at a cost. Likely (4) will require the most defending. Again, (4) says that, given naturalism and the existence of necessary truths, it is necessarily the case that if a proposition exists as an abstract object, it will exist as a natural object. If one denies this, then it would seem possible that an abstract object be natural and possibly not natural. But then in what way is it the same sort of thing? It seems odd to me that a proposition is a natural thing in this world, but a non-natural thing in other possible worlds. For it seems to me that the property of being natural is an essential property. If something is natural, it is necessary that it is natural. Thus, if naturalism is true, then all abstract objects are natural and essentially natural. But our argument shows, by indirect proof, that it is possible for there to exist an abstract object that is not natural. Giving up on (4) entails that ‘natural’ is non-essential to some things, and I find that to be implausible.

(My thanks to Skepticism First on Twitter, who dialogued with me on this argument and pushed me in some new directions)

An Indispensability Argument for God’s Existence

An Indispensability Argument for God’s Existence:

1. Whatever is indispensable in generating some theoretically insightful thought experiments must be admitted into our ontology.
2. A perfect being, or God, is indispensable in the generation of many theoretically insightful thought experiments across multiple disciplines.
3. Therefore, a perfect being must be admitted into our ontology.

I don’t think this argument works because (1) is too strong a claim. There are indispensable entities in many thought experiments, which we don’t admit into our ontologies, like frictionless planes and ideal gases. Nonetheless, those ideas are useful in many thought experiments. But why should they be so useful? I think it is because they substantively entail certain facts were they to actually obtain.

A Modest Indispensability Argument for God’s Existence:

1. Whatever is indispensable in generating some theoretically insightful thought experiments is logically possible (premise).
2. A perfect being, or God, is indispensable in generating some theoretically insightful thought experiments (premise).
3. Therefore, a perfect being is logically possible (From 1,2).
4. If a perfect being is logically possible, then a perfect being exists (by S5, given that a perfect being has necessary existence).
5. Therefore, a perfect being exists (From 3,4).

It seems to me that this argument is sound. An atheist might reject (1), but if something is logically impossible, it is hard to see why it would be theoretically indispensable, since it would entail anything. Impossible entities are, therefore, dispensable, since they function trivially in the thought experiment, and any impossible entity would function in the same way. So one impossible entity is no more indispensable than any other. What’s more, while impossibilities entail anything, we would find ourselves like Buridan’s ass, not directed by the concept itself in any particular way when thinking through the thought experiment. Rather, the direction would be determined by some sort of misapprehension of what a perfect being is–a misapprehension that oddly happens to be shared by every person who grasps the thought experiment. But then it is the “misapprehension” of a perfect being that is functioning indispensably, and we would have to see why it is the case that we are dealing with a misapprehension rather than the concept of a perfect being.

I think the atheist might be more successful in denying (2), by arguing that the idea of a perfect being is not actually integral to many thought experiments. Of course, this places a huge burden on the atheist of wading through thought experiments that make use of a perfect being, so as to demonstrate dispensability. Absent such a demonstration, it seems to me that thought experiments that make use of God do so in a substantive and indispensable manner. For as Voltaire says, “Si Dieu n’existait pas, il faudrait l’inventer” (Epistle to the author of the book, The Three Impostors, 1768). Except, if it is necessary to invent God, then according to my reasoning, God is logically possible, and so actual.

A Modalized Moral Argument

The follow argument attempts to do a few things:

A) It tries to ground the intuition that only God could be the ontological ground of moral values. That is, if God exists, then the cause of facts in the world is identical to the cause of values, and so facts cannot be divorced from values, a la Hume.

B) It provides a straightforward account of value by which a thing can be said to have value if goodness is said of it in relation to something. A thing could be said to have subjective and extrinsic value to, say, me if it is a good in virtue of my being. I take intrinsic value, then, to be a modal property where a thing is good in virtue of itself in all possible worlds. This is because a defender of intrinsic moral values will say that something like a human being is necessarily good in virtue of itself in all possible worlds, even if humans don’t obtain in every possible world. Rather, should a human come into existence in said world, it would have intrinsic goodness.

Finally, C) the argument attempts to show that the mere logical possibility of intrinsic values is sufficient to prove God’s existence. This depends upon my use of the S5 axiom, and a corollary to the Barcan Formula. So while the atheist might object to the traditional non-modal version of the moral argument on the grounds that objective and intrinsic moral values don’t actually exist, this version of the argument forces the atheist into the position of saying that intrinsic moral values are plausibly logically incoherent, or metaphysically impossible. But I see no reason why it is incoherent or impossible to be necessarily good in virtue of itself, at least prima facie.

One might note that my defense of the need for God as the ontological foundation for values depends upon a few theological notions. The first is that God is the eminent cause of truth and goodness in the world. Thus, God is the supreme exemplar of truth and goodness. Furthermore, Hume’s so called fork is circumvented in classical theism through the doctrine of Divine Simplicity, wherein Goodness and Truth are merely transcendental modes that, while perspectively distinct to finite knowers like us, are identical to Being itself, and therefore, God.


Gxy – x is good in virtue of y; something has intrinsic value iff it is necessarily good in virtue of itself, or □Gxx

t – the eminent cause of truth in all things

g – the eminent cause of goodness in all things

θx – x is divine

1. (∀x) [(□Gxx) → □(t = g)] (premise)
2. (∀x) {□(t = g) ≡ [□(x = t) & □(x = g)]} (premise)
3. (∀x) {[□(x = t) & □(x = g)] → θx} (premise)
4. ◊(∃x)□Gxx (premise)
→5. ~(∃x)θx (assumption)
↑6. ~θu (5 EI)
↑7. [□(u = t) & □(u = g)] → θu (3 UI)
↑8. ~[□(u = t) & □(u = g)] (6,7 MT)
↑9. □(t = g) ≡ [□(u = t) & □(u = g)] (2, UI)
↑10. {□(t = g) → [□(u = t) & □(u = g)]} & {[□(u = t) & □(u = g)] → □(t = g)} (9 Equiv)
↑11. □(t = g) → [□(u = t) & □(u = g)] (10 Simp)
↑12. ~□(t = g) (8,11 MT)
↑13. □Guu → □(t = g) (1 UI)
↑14. ~□Guu (12,13 MT)
↑15. (∀x)~□Gxx (14 UG)
16. ~(∃x)θx → (∀x)~□Gxx (5-15 CP)
17. ~(∃x)θx → ~(∃x) □Gxx (16, QN)
18. ◊(∃x)□Gxx → (∃x)◊□Gxx (CBF)
19. (∃x)◊□Gxx (4,18 MP)
20. (∃x)◊□Gxx → (∃x)□Gxx (S5 axiom)
21. (∃x)□Gxx (19,20 MP)
22. ~~(∃x)□Gxx (21 DN)
23. ~~(∃x)θx (17,22 MT)
24. (∃x)θx (23 DN)

More needs to be argued by way of the premises, but I think this moral argument is more powerful than those traditionally offered in defense of theism.

Short Necessary Being Quiz

Skeptical of whether there is a concrete necessary being?  Take this quick quiz put together by Joshua Rasmussen to find out whether you are committed to such a belief  [H/T Czar Bernstein].

Don’t worry, you won’t be graded!

Oh, and let me know of your results via comments.  Did the quiz change your position?  If not, why not?

Start here: The Necessary Being Interactive Survey

A Meta Version of a Modal Ontological Argument

[Update again: Revised version of the argument is here]

[Update 7/19/2012: On further reflection on this argument, I’ve discovered that it does not succeed.  The second level of symmetry does permit identity between the two entities described in each argument.  I hope to continue to work on this argument in the future and develop a version that is immune.  For now, I cannot see how to get this argument off the ground]

It’s been quite a while since I last posted on this blog. My program has been keeping me busily preparing for my comprehensive exams.  But I wanted to air an argument that I am working on.  This is by no means a finished draft.  It’s just an argument that I’ve been thinking for some time.  I call it a “Meta Version of a Modal Ontological Argument”.

In the latter half of the twentieth century, the ontological argument enjoyed a remarkable revival.  This was due, primarily, to the work of Norman Malcolm, Charles Hartshorne, and Alvin Plantinga.  Perhaps the best known is Plantinga’s “A Victorious Modal Version” which Robert Maydole (2009, 573) succinctly reconstructs as:

P1 The property of being maximally great is exemplified in some possible world.

P2 The property of being maximally great is equivalent, by definition, to the property of being maximally excellent in every possible world.

P3 The property of being maximally excellent entails the properties of omniscience, omnipotence, and moral perfection.

P4 A universal property is one that is exemplified in every possible world or none.

P5 Any property that is equivalent to some property that holds in every possible world is a universal property.


P6 There exists a being that is essentially omniscient, omnipotent, and morally perfect (God).

Much ink has been spilled in defending an critiquing the soundness of this argument, and its sister versions developed by Malcolm and Hartshorne.  Maydole remarks,

And what should we think about the first premise of each of these arguments, which effectively says in each case that it is possible for God to exist? None of the authors of these respective arguments is particularly sanguine about proving this. Hartshorne merely suggests that we might “employ one or more of the other theistic proofs . . . to demonstrate that perfection must at least be conceivable” (1962, p. 52). Plantinga treats the possibility premise as a philosophical hypothesis, which he says it is rational to accept because otherwise “we should fi nd ourselves with a pretty slim and pretty dull philosophy” (1974, p. 221). (Hardly the highest standard for what counts as rational!) And Malcolm says that he does “not know how to demonstrate the concept of God . . . is not self-contradictory” (1967, p. 318). Yet he assumes that it is not self contradictory because it has “a place in the thinking and lives of human beings” (1967, p. 318).

In other words, the force of these arguments hangs and, unfortunately, falls on the key possibility premise that is difficult, if not impossible to defend.  At best, then, these modal ontological arguments demonstrate the reasonableness of believing in God, granting that God is at least possible.

There are further problems with these arguments, namely, that they are easily parodied.  Maydole (2009, 573-574) explains:

For example, one might easily validly argue contra Hartshorne that Anselm’s Principle, and the premise that it is possible that a supremely perfect being does not exist, jointly entail that a supremely perfect being does not exist. If we were merely to postulate that, possibly, a supremely perfect being exists, then we could also rightfully postulate that, possibly, a supremely perfect does not exist. But then the parody would refute Hartshorne’s argument because we should not be able to rightfully claim that the premises of the parody are less justifiable than those of Hartshorne’s argument.

In other words, one could run a symmetrical version of the ontological argument that seeks to prove God’s non-existence.  All that such an argument would require is a parallel possibility premise–one that suggests that, for instance:

P7 The property of being maximally great is not exemplified in some possible world.

But since being maximally great is defined as being maximally excellent in every possible world, it would follow from P7 and P4 that maximal greatness is a universal property only insofar as it holds in no possible world, thus refuting God’s existence or:

P8 There does not exist a being that is essentially omniscient, omnipotent, and morally perfect (God).

Trent Dougherty has offered some helpful insights into the problem of the possibility premise.  And much of his discussion will be crucial for understanding the meta argument that will be developed here.  However, I do not think Dougherty’s argument ultimately succeeds in rescuing modal arguments of the Malcolm-Hartshorne-Plantinga variety.

Dougherty explains that the possibility premise has its origins in Leibniz, who argued that there was a gap in Anselm’s original formulation of the argument.  That is, God’s existence could not be inferred, unless it is established that God could at least possibly exist.  But Leibniz also notes that possibility can be safely assumed unless there is proof to the contrary.  Dougherty sums this doctrine up as the benefit of the doubt or BOD, and contrasts it with actuality claims which bear a burden of proof (Dougherty n.d. 4-5). In effect, I am permitted to assume the logical possibility of God, broadly construed, unless and until it can be shown that the concept of God is logically impossible.  But the benefit of the doubt is a benefit short lived for those who are hopeful for a sound modal ontological argument, for if BOD is granted to the possibility of God, or a maximally great being, then fair is fair and BOD must also be granted to the possibility of ~God, or there not being a maximally great being.  Dougherty (n.d. 6) refers to this as the symmetry problem.  To break the deadlock, he suggests an asymmetry that gives the possibility of God a certain kind of edge over the possibility of there not being a God.  What is this advantage?  Dougherty invokes a conceivability principle.  According to this principle (ibid.):

P9 For any sentence S and agent A, if A can conceive ~S, then A can conceive S.

Dougherty holds that supposing ◊~G, where G is God–the key premise to the atheologian’s parody, requires via P9, that ◊G has prima facie support.  And if ◊G has prima facie support, we can infer via the ontological argument that □G, or ~◊~G, which serves as a defeater for ◊~G.

I find Dougherty’s asymmetry argument to be rather weak in that it is not apparent to me why the atheologian might restore symmetry by offering a parody of the conceivability principle that:

P10 For any sentence S and agent A, if A conceive S, then A can conceive ~S.

Thus, if the theologian supposes ◊G, then by P10 ◊~G has prima facie support.  With symmetry restored, it seems there is no reason to prefer the ontological argument to the atheologian’s parody version.

What I would like to offer is a version of a modal ontological argument that is immune to parody by generously granting possibilities, come what may.  What we will see, is that even if parody is attempted, possibility granted, and the balance of symmetry achieved, the conclusion that God exists cannot be avoided.  It is in embracing the perceived shortcomings of previous versions of the ontological argument, that I hope to produce a truly victorious version.  To achieve this end, my possibility premise will be drawn from the arch-critic of ontological arguments, Graham Oppy.  Summarizing some of the primary objections to ontological arguments Oppy (2011) then goes on to say:

Even if the forgoing analyses are correct, it is important to note that no argument has been given for the conclusion that no ontological argument can be successful. Even if all of the kinds of arguments produced to date are pretty clearly unsuccessful—i.e., not such as ought to give non-theists reason to accept the conclusion that God exists—it remains an open question whether there is some other kind of hitherto undiscovered ontological argument which does succeed.

This stunning admission has led me to generate the following meta version of a modal ontological argument:

P11 Possibly, a sound version of the ontological argument is discoverable that is impervious to parody.

P12 If possibly a sound version of the ontological argument is discoverable that is impervious to parody, then possibly there is a true concluding proposition to an argument such that necessarily there is some being x that is omnipotent, omniscient, and morally perfect.

The plausibility of P12 is in the very fact that premises imply their conclusions.  So if there is a sound ontological argument, it certainly would establish the necessary existence of the being it purports to prove.

P13 If possibly there is a true concluding proposition such that necessarily, there is some being x that is omnipotent, omniscient, and morally perfect, then it is possibly necessary that there is some being x that is omnipotent, omniscient, and morally perfect.

P14 It is possibly necessary that there is some being x that is omnipotent, omniscient, and morally perfect (From P11-13)

P15 Necessarily there is some being x that is omnipotent, omniscient, and morally perfect (P14, S5 axiom).

P16 There is a being x that is omnipotent, omniscient, and morally perfect (P15, NE).

Note that the possibility premise of this argument is with regard to an argument, rather than God.  Thus, we are able to grant the possibility of the symmetrical proposition,

P17 Possibly, there is not a sound version of the ontological argument is discoverable and is impervious to parody.

Of course P17 is perfectly compatible with P16, for God’s necessary or actual existence does not necessitate there being a sound ontological argument that cannot be parodied.  Perhaps, for instance, God’s existence simply cannot be demonstrated a priori.  Or maybe God’s existence could be demonstrated a priori, but there are possible worlds where no such argument is ever discovered.  Or perhaps any sound ontological argument, will nonetheless always be subject to parody.  Of course one possibility is that God, in fact, does not exist.  But so long as these other possibilities remain, P17 remains compatible with the rest of the argument.  So the symmetry of P17 with P11 does not generate a parody.  But couldn’t there be a deeper symmetry by which a parody would be generated?  I have my doubts that another level of symmetry would generate a parody.  But, let us take this up in form of an argument.  Let us suppose, for a moment the following argument:

P18 Possibly, a sound version of an anti-ontological argument is discoverable that is impervious to parody.

P19 If possibly a sound version of the anti-ontological argument is discoverable is impervious to parody, then possibly there is a true concluding proposition to an argument such that necessarily there is not some being y that is omnipotent, omniscient, and morally perfect.

P20 If possibly there is a true concluding proposition such that necessarily, there is not some being y that is omnipotent, omniscient, and morally perfect, then it is possibly necessary that there is not some being y that is omnipotent, omniscient, and morally perfect.

P21 It is possibly necessary that there is not some being y that is omnipotent, omniscient, and morally perfect (P18-20).

P22 Necessarily there is not some being y that is omnipotent, omniscient, and morally  perfect (P21, S5 axiom).

P23  There is not a being y that is omnipotent, omniscient, and morally perfect (P22, NE).

Incidentally, we would also grant that that there is a symmetrical possibility premise:

P24 Possibly, there is not a sound version of an anti-ontological argument is  discoverable that cannot be parodied.

Likewise, there are a wide variety of disjunctive possibilities that might account for the compatibility of P23 and P24, i.e. that no such argument is possible, that there are possible worlds where no such arguments might be discovered, etc.  The pressing question is whether P16 and P23 are contradictory.  If they are, then this symmetry would result in a parody that would once again push off our discovery of a sound ontological argument, since there would be no good reason to prefer one contradictory over the other.  But P16 and P23 are not contradictory, at least not explicitly.  For the atheologian to succeed in parody, she would have to prove,

P25 x = y

That is, she would have to prove that whatever being is proved to exist in P11-16 is identical with the being proved not to exist in P18-23.  But what arguments might the atheologian provide to prove this identity relationship?

For one thing, the atheologian might try to establish the identity between x and y through their shared properties, i.e. omniscience, omnipotence, and moral perfection.  Of course neither argument argued that such properties were exhaustive of the essential, or even accidental, natures of the entities established in each. So the atheologian could not make use of the identity of indiscernibles to establish the identity claim.

Might the atheologian establish identity because symmetry simply demands it?  I counter that such a demand is question-begging.  Furthermore, if P11 is granted by the benefit of doubt, then it is granted that it is possible that there is a sound ontological argument that is not parodied.  This is granted to the symmetrical claim in P18 that there is a sound anti-ontological argument that is also parody proof.  Therefore, whatever possible argument is invoked in P11-16, it is not going to be related to the argument invoked in P18-23 by way of parody.  So, if the same entity that is established to exist in P16 is identical to the being established not to exist in P23, then the fact that these two propositions are contradictories could not be relied upon by invoking the possibility that there are parallel premises and deductive steps in the possible ontological/anti-ontological arguments.  In other words, an identity between x and y would require two entirely independent sound ontological arguments reaching contradictory conclusions.  This is far more than a coincidence!  It is to affirm the existence of the grossest kinds of contradiction actually do obtain.

So while I have been overly generous in granting the possibilities of symmetrical premises for the atheologian, I will not grant an identity between x and y without an adequate argument.  And I have provided two reasons to think the atheologian will not succeed in this task.  If my argument is indeed successful, then it would be actually be the kind of argument that is supposed possible by the argument.  That is, the argument appears to be valid, with true premises.  And despite attempts at symmetrical parody refutations, it has shown to be impervious.  Of course this is not to say that the existence of this argument can serve as evidence in support of P11, as that would be question-begging.  Nonetheless, I think the existence of God, or a being with God-like attributes, can be demonstrated.


Dougherty, T.  N.D. “Conceivability, Defeasibility, and Possibility: A Defense of the Modal Ontological Argument” URL =<>

Maydole, R. 2009. “The Ontological Argument” in The Blackwell Companion to Natural Theology. Ed. J.P. Morland & W.L. Craig. Malden, MA: Wiley-Blackwell.

Oppy, G. 2011. “Ontological Arguments” in The Stanford Encyclopedia of Philosophy (Fall 2011 Edition), Edward N. Zalta (ed.), URL =< arguments/>.

Why A Posteriori Arguments Against God’s Existence Fail, pt. 2

A few weeks ago I posted my argument against any and all a posteriori arguments. I thought I would revisit the argument again today and try to spell it out more clearly and concisely.

By a posteriori argument, I merely mean any argument that seeks to disprove God’s existence on the basis of some fact of the world, be it evil, evolution, “divine hiddenness”, the success of the natural sciences, or the failure of mind/body dualism. These arguments essentially boil down to something like:

1. If God exists, we would expect to observe X.

2. X is not the case.

3. Therefore, God does not exist.

The argument is in the form of a modus tollens deduction, which is a perfectly valid form of argumentation. My response is a kind of dilemma that puts the atheist in the awkward position of defending the soundness of the argument. I contend that any successful defense of the soundness of such arguments requires one to commit an informal fallacy of begging the question.

But first I think it is important to unpack my concept of God. I believe God is the greatest conceivable being, a definition common to classical theism. Here, Dr. William Lane Craig discusses this concept of God, and its implications. I would agree with what he says:

Dr. Craig points that since God is conceived of as a necessary being, if God possibly exists, then God actually exists. Now my argument is much more humble than this, as I do not even suppose that God’s existence is logically possible. What I offer is the following dilemma:

1. If the a posteriori argument is to be sound, then the truth of the conditional premise must be based on appeals to possibility or impossibility.

2. If the truth of the conditional premise is supported on the grounds of possibility, then there must be a possible world where the antecedent and consequent obtain, be it a fact of the actual world or counterfactually.

3. If God’s existence possibly obtains, then God actually exists.

4. If God actually exists, then either the first or second premise of the a posteriori argument must be false and the argument unsound.

5. If the truth of the conditional premise is supported on the ground of impossibility, then there is no possible world where the antecedent obtains and this counterpossible conditional is trivially true.

6. If the conditional premise is true because it is a counterpossible conditional, then the support for the first premise is nothing more than the assumption of the conclusion, which is to beg the question.

7. Therefore, either the a posteriori argument is unsound or question-begging.

Now one might challenge my argument by saying that the atheist need not assume that God is possible or impossible at the outset. However, if the argument is to be any good, the atheist must provide reasons that compel her interlocutor to think there is epistemic warrant for accepting the truth of the premises. After all, the conditional premise might be false. If the atheist draws out implications from the concept of God, then we must ask how it could be that the concept of God supplies those implications. The atheist is limited here. She cannot admit that the implications are drawn from a coherent conceptual analysis of God, since this would suggest that in at least one possible world where God exists and such implications follow. That would mean that God is logically possible, and so actual. Thus, the only alternative is that the implication is drawn out of an incoherent or impossible concept. But then anything could be said to be implied by the impossible, so the implication is merely a trivial one. The atheist would have to admit that “If God exists, gratuitous evil would not exist” is just as true as “If God exists, light bulbs wouldn’t exist”. If that is all the atheist is saying, then the argument is no more interesting than its theistic cousin “Either God exists, or 2+2 is 5, and since 2+2 is not 5, God exists.” More to the point, if the conditional premise is trivially true because it is counterpossible, then the atheist’s argument is simply fallacious. Clearly the atheist intends to disprove God on a posteriori concerns, but she ends up appealing to the impossibility of God, a priori, as epistemic warrant for the truth of the conditional premise. Since no argument is given for the impossibility of God, and it is just smuggled into the first premise, this is textbook question-begging.

Let’s suppose that the atheist admits this much, but then claims that she will back up her a priori assumption that God is impossible by way of an argument. But then she is arguing about God’s existence purely on a priori concerns, and that is not the original argument offered at all. So, I think this adequately demonstrates that the atheist is limited to presenting a priori arguments in favor of that position and that a posteriori arguments are useless in disproving God’s existence.