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Intelligibility, Information, and Beauty

What is information?  Information expresses something.  It is intentional and so not random, right?  A Youtube collaboration between VSauce and Veritasium presents an interesting argument that information is random, or rather, entropy:

But is that right?  Information is random?  If so, wouldn’t it be unintelligible?

When transmitting information, you can compress all that which is a pattern or predictable.  This means that whatever cannot be reduced or compressed is pure information.  At the same time, pure information without pattern and order is meaningless.  It is just white noise.  So it seems that intelligibility is not the same thing as information, at least when it is defined as entropy (as it is in this information theory).  Meaning emerges from patterns of information.  The random must be ordered and patterned in ways that we can decode and understand.  So intelligibility or meaning is the confluence of information and order.

The video makes the neat point that our scientific theories are really just attempts to compress the information we find in nature.  It is interesting to note that scientists often prefer theories and equations that are described as “elegant” or “beautiful”.  In certain sense, the idea that intelligibility, or meaning, emerges from patterns of random information can help us to understand why we find these compressions beautiful.

In an earlier post, I had defended the beauty of the Trinitarian God over unitarian gods on the grounds that the Trinity has both unity and distinction, i.e. a simple unified divine substance that is three distinct persons.  I argued that we can objectively define that which is beautiful as that which is unified, harmonious, and ordered while admitting distinctions.

If information is maxim entropy, it contains an irreducible unity.  That unity of information becomes intelligible when it is ordered into patterns and brought into harmony with other bits of information.  It becomes meaningful.  So whatever is intelligible is inherently beautiful.  Thus, there may be something metaphysical underlying the idea that a scientifically true formula or equation is objectively “elegant” or “beautiful”.  We find that it is “elegant” or “beautiful” because it is a simple unity, yet it has the power to explain a wide variety of our data by revealing patterns.  The more unified and simple an equation is, and the greater amount of distinct phenomena it captures, the more beautiful it is.  This also hints at the fundamental unity between objective truth and beauty, which I believe we find in nature as a reflection of what is fundamental to the Godhead.

How is this fundamental to the Godhead? If God is Being itself, or Being must truly, then God must be perfect, simple, and irreducible.  Whatever is perfect in Being must be truly Good, and indeed, the Father is Good. Goodness is opposed to ignorance, as ignorance is a source of evil, so if the Father is Good, he must know His own Nature, and so must be thought thinking itself.  Since the Divine Substance is absolutely simple, the Father cannot abstract a genus or species to comprehend His Nature propositionally.  Instead, He must comprehend or grasp the Divine Nature Itself in a concrete way, or else He grasps nothing.  And in doing this, conceives of the Divine Substance distinctly from the One who is conceiving.  If God’s knowledge is accurate, he must conceive of the same exact concrete Substance that He is.  So his eternal conception of the Divine Substance is the same substance that He is, it is the grasp of the Truth of God’s Goodness.  And we call this eternal conception, or this eternally begotten grasp of the Divine Substance, the Son, who is the Truth itself.  As the Father knows the Divine Substance, the Divine Substance is essentially intelligible to the Father.  There is a distinction between knower and known and a pattern of sameness that makes the Divine Substance knowable to itself.  Thus, Beauty is intrinsic to Divine Substance in its self-intelligibility.  Since Beauty is that which is desirable in itself, the Will of God is directed towards the Divine Substance.  So another relationship exists between God’s Will and the Divine Substance, which is desirable because of the intrinsic beauty of the Divine Substance as a Self-Intelligible unity.  So the Divine Substance, which is the object of the Divine Will, proceeds from the Father (as Knower) and the Son (as Known), and must be distinct from these Two.  We call the object of the Divine Will, which is God, the Holy Spirit.  The Holy Spirit is true Beauty.  And so there is a Trinity of Persons that is the Godhead.

If the Divine Substance is Being itself, it is also the representative of the transcendentals of Being: Goodness, Truth, and Beauty.  Interestingly, those three transcendentals are convertible with Being but remain distinct from one another.  So we find that the Persons of the Trinity are convertible with God, but are distinct from one another.  This is not to say that the Son is not Good or Beautiful, or that the Holy Spirit is not True or Good.  Rather, I am saying that the Persons of the Trinity relate to one another in terms of Goodness, Truth, and Beauty.  But they are far more than these transcendentals.  I think it is a helpful way of understanding the relationships among the Persons in the ontological structure of their relationships (unbeggotten, begotten, and proceeding). The relationship among the Persons of the Trinity and the Divine Substance is ultimately mysterious, but an analogy to the trinity of transcendentals is a helpful image to have in mind.

Of course, whenever I reflect on the Trinity, I fear that I might stumble into heresy.  Nonetheless, I am drawn to thinking about it, like a moth to the flame.  How could I not?  There is nothing more mysterious, more beautiful, and more true.  So, if my comments are in error, I humbly submit them as a mere reflection that is subject to revision.

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.

So,

  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.

So,

  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.

Divine Simplicity, Coconuts, and Hilbert Hotels

 

Gaunilo’s Lost Island?

Here is an argument for Divine Simplicity inspired by this argument formulated by Alexander Pruss.  In my argument, I define God as a maximally great being.

1.  If God has parts, then either God has an actual infinity of parts or a finite amount of parts.
2.  God has an infinity of parts only if there can be an actual infinity of concreta.
3.  God has a finite amount of parts only if a finite amount of coconut trees on an island doesn’t prevent it from being a maximally great island.
4.  An actual infinity of concreta is impossible.
5.  An finite amount of coconut trees on an island prevents it from being a maximally great island.
6.  Therefore, God has no parts.

Defending (1)-(5):

1.  This premise is essentially trivially true.  It should be noted, though, that I take the claim that God has parts to be a real ontological claim about constituents that jointly compose the divine substance.  That is, the denier of divine simplicity cannot fall back onto an anti-realist position about parts (that the parts of God are just ways we conceive of God’s essence) as that would be indistinguishable from the doctrine of divine simplicity.

2.  Given that God is a concrete reality, the parts of God would be concrete realities. Hence an actual infinity of parts would be an actual infinity of concrete parts (not too controversial).

3.  A common objection to Gaunilo’s lost island, one that I think is quite right, is that an island cannot be maximally great since it must have an finite amount of some constituent parts, e.g. coconut trees or, say, island beauties.  But the addition of one more part would be greater, so finite parts are incompatible with maximal greatness.  One might insist that the parts of God are not like trees or beauties.  But why think that? Suppose you think, for instance, that God is three persons, but you deny that those persons are identical with God (as some theistic personalists are apt to do). Instead, you hold the view that the Father, Son, and Holy Spirit are parts of the Divine Substance.  Why wouldn’t you be inclined to think that one more person would be greater?  Perhaps you might have some argument about harmony to justify a particular finite set of person-parts, but it isn’t obvious that that sort of “aesthetic” judgment is objectively correct, or, if one is at all concerned with defending Christianity, that three persons achieves that harmony.  Or, consider omnipresence.  Does it entail that God is present in every spatial location?  Some argue that omnipresence is entailed by omniscience, that God is present in all locations in so far as intellect is cognizant of those locations. But those who want to attribute parts to God want to say that God’s Intellect is a different part than, say, God’s will, love, power, etc.  If so, it seems that only part of God is omnipresent, namely God’s intellect.  But is all of God’s intellect cognizant of a location or only part of God’s intellect?  Could more of God’s intellect be cognizant of a location?  Could more of God’s parts be present in a given location?  Could more locations add to the parts of God’s intellect?  If so, it would seem that more parts of the intellect, more intellects, more wills, more love between more persons of the God-head would increase God’s greatness.  But then a God with parts cannot be maximally great for the same reason an island, pizza, or human cannot be maximally great.  A person who rejects divine simplicity, but holds that God has a finite amount of parts, needs to show that no addition of parts could make God greater.  But prima facie, and absent any reason to think otherwise, I think it is reasonable to think that an addition to at least some of the finite sets of divine parts would make a non-simple god greater, which is to say that a maximally great non-simple God is impossible.

4.  There are many arguments against an actual infinity of concreta.  Consider, for example, Craig’s use of Hilbert’s Hotel and related paradoxes.

5.  As mentioned in my defense of (3), there doesn’t seem to be a finite amount of coconut trees (or island beauties) that would be consistent with an island being maximally great.  All else being equal, an island with 100 coconut trees seems to make an island greater than some island with 99 coconut trees.  We might suppose then that, all else being equal, an island with n coconut trees is less great than an island with (n+1) coconut trees.  Therefore, a maximally great island with finite parts is impossible.  Given that all islands are necessarily finite, a maximally great island is a logical absurdity, which is why I think most parodies of the ontological argument are ineffectual.  They depend upon substituting “God” with something that is implicitly a finite composite. Now, one might say that there are other reasons for why a maximally great island is impossible, e.g. such an island must be a contingent thing given its dependence on space and time. But surely the finitude of great-making island properties are among the reasons such an island cannot be.

I think (1)-(5) are defensible and true.  Therefore, I think God has no parts, i.e. God is simple.  QED

The Beauty of the Trinitarian God

One thing I ask of the LORD, this is what I seek: that I may dwell in the house of the LORD all the days of my life, to gaze upon the beauty of the LORD and to seek him in his temple (PS 27:14).

It seems that beauty is a kind of perfection.  So if God is a being that has all perfections, it follows that God is beautiful. Furthermore, beauty is found in the natural world. If God is the cause of the natural world, then God Himself must be beautiful, given the metaphysical principle that there cannot be more reality in the effect than in the cause. But what is beauty? Is something beautiful merely because it is deemed to be so by a mind?  Is it entirely subjective?

I think not.  Thomas Aquinas agrees:

Thomas maintains the objectivity of beauty, in the sense that beauty resides in the object. In other words, beauty is not a concept in the mind of the beholder imposed onto a given object. If beauty is objective, then there must be some criteria by which we discover whether something is in fact beautiful. 1

What might the criteria for beauty be?  Unfortunately, beauty is difficult to define. Indeed, if it is one of the transcendentals, it is impossible to give an essential definition for it. Nonetheless, there are some great pre-modern theories about the beautiful. The great theories of beauty generally agreed that it consists of unity, proportion, equality, harmony, and order. (Tatarkiewicz 1972, 168-9)2

I would distill the great theories of beauty down to this.  Beauty is a sort of harmony, equality, or order among those which are distinct in number but which are somehow formally unified.

How could God of classical theism be beautiful, or rather, most beautiful according to this theory? For, the God of classical theism is divinely simple.  And in being simple, he satisfies one of the necessary conditions for our theory of beauty.   But, there is no diversity in God, nor parts to be arranged in any sort of harmony, proportion, order, or equality.  So it seems that God cannot be beautiful.

If God is not beautiful, then either creation is in some way more perfect than the creator, or beauty is not really a perfection. But, even if beauty is not a perfection, or some sort of “divine” perfection, there is still the problem of how it could be caused by God. For to deny that beauty is caused by God is to deny God’s aseity.  And to say that God is the cause of beauty but not beautiful Himself undercuts our metaphysical principle that the cause must have at least as much reality as its effect.

If there is supreme beauty, it would be in that which is most unified and which nonetheless has genuine distinction. It seems to me that the Trinity offers us an example of a classical theistic God in whom there are a number of persons in perfect harmony, equality, order, and unity. If the Trinity is coherent, then it offers an answer to the question of divine beauty. We can maintain that beauty is a perfection, that God truly is beautiful, and is the cause of beauty in nature. Nature, in effect, is beautiful insofar as it reflects the unity and harmony of the Trinity. Aquinas would not say that the Trinity is a diversity within God, but he would agree that the persons are distinct and three in number. His hesitancy of saying that God is a unity with a diversity of persons is due to his strong emphasis on the doctrine of simplicity. Nonetheless, the distinctness, unity, harmony, equality, and order of the Trinity is a perfect expression of beauty.

One might go so far as to press this a a problem for those who conceive of God as a singular person. It seems to me that the unitarian has the following options:

A) Deny that God is beautiful, and offer a theodicy for why there is beauty in the world.
B) Grant that God is simple and beautiful, but that beauty does not involve harmony, equality, or order among distinct members.
C) Grant that God is beautiful, but not simple. And hold that there are distinct parts to God to which harmony and order can be predicated.

There are problems with all three of these positions. Consider option A form a moment. Perhaps beauty is a property of matter, and since God is not material, God doesn’t have such a property. But beauty is often ascribed to immaterial things like equations, abstract object, and theories.  So why can’t an immaterial god be beautiful? Perhaps beauty, then, is some sort of privation, like evil? Of what is it a privation, ugliness?  This seems to have things backwards and only introduces another question regarding the origin of beauty’s contrary. Or perhaps one might maintain aesthetic anti-realism. Beauty truly is in the eye of the beholder and not a fact about anything, including God. But while there may be some subjective aspects to aesthetic experience, it just seems wrong when someone thinks that this picture by Chris Jordan:

is more beautiful than that:

2014-03-16 14.50.44

I don’t think I could take someone to be serious if he were to insist that the picture of a decaying bird engorged with litter is more beautiful than the picture of blossoming almond trees.  I would simply take such a person to be a contrarian, akin to the moral relativist who blushes slightly when he bites the bullet and says that segregation wasn’t really wrong for the societies that endorsed it.  Bite the bullet all you want.  If you think the bird is more beautiful, there is something wrong with you.

Next, there is option B.  But it denies a theory of beauty that seems to make sense of much of our experience of the beautiful, i.e. that it is a harmony, proportion, or equality of sorts. So if it is to be preferable to the Trinitarian explanation, if should offer a theory of beauty that explains the data of our experience at least as well as the “great” theories of old.  Absent an alternative theory of beauty, it is not clear that this option will be superior.  And if the alternative theory is merely fitted to the idea that God is beautiful, but that there are no distinctions in God, then this option simply comes across as ad hoc.  On the other hand, trinitarianism and the great theories of beauty are independently motivated, yet nicely converge.

Option C leaves classical theism behind, and raises new questions about the nature of the divine.  Diversity is introduced into the divine substance, and it seems we must now explain why these diverse parts are unified as a substance.  We must also explain why this complex divine substance is ontologically necessary, and impossible to separate.  Additional explanations that try to regain the attributes of the God of classical theism will appear to be ad hoc unless there are independent reasons to accepting them.

If one holds to i) the doctrine of divine simplicity, ii) beauty as an objective fact and perfection, and iii) a theory of beauty the convergence of unity and harmony, then Christian Trinitarianism best explains those commitments.

1M. Spicher. “Medieval Theories of Aesthetics”. In The Internet Encyclopedia of Philosophy. Accessed on March, 18, 2014. http://www.iep.utm.edu/m-aesthe/
2 W. Tatarkiewicz. 1972. “The Great Theory of Beauty and Its Decline” In The Journal of Aesthetics and Art Criticism, vol. 31, no. 2. http://www.jstor.org/stable/429278

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:

Let:
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)

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