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.

Nuestra Señora de Guadalupe, Ruega por Nosotros

Today we celebrate Our Lady of Guadalupe, the Patroness of Mexico and Latin America.

Official Catholic accounts state that on the morning of December 9, 1531, Juan Diego saw an apparition of a maiden at the Hill of Tepeyac, in what would become the town of Villa de Guadalupe in the suburbs of Mexico City. Speaking to him in the native Nahuatl language, the maiden asked that a church be built at that site in her honor; from her words, Juan Diego recognized the maiden as the Virgin Mary. Diego recounted the events to the Archbishop of Mexico City, Fray Juan de Zumárraga, who instructed him to return to Tepeyac Hill, and ask the “lady” for a miraculous sign to prove her identity. The first sign was the Virgin healing Juan’s uncle. The Virgin told Juan Diego to gather flowers from the top of Tepeyac Hill, where he found Castilian roses, not native to Mexico, blooming in December on the normally barren hilltop. The Virgin arranged the flowers in his tilma or cloak, and when Juan Diego opened his cloak before Bishop Zumárraga on December 12, the flowers fell to the floor, and on the fabric was the image of the Virgin of Guadalupe (Our Lady of Guadalupe, Wikipedia).

In honor of Our Lady, I thought I would share a reflection on the Holy Mother of the Church that occurred to me while I was researching for my post on Richard Carrier and γίνομαι.  According to Carrier, St. Paul never believed that Christ lived a human life on Earth.  Rather, Carrier claims that St. Paul worshiped a celestial Jesus.  Two passages often cited against this view are Romans 1:3 and Galatians 4:4, as both claim that Christ was of human birth rather than direct divine manufacture. Particularly relevant to the Blessed Virgin is the passage from Galatians, which says:

But when the fullness of the time came, God sent forth His Son, born of a woman, born under the Law… (Galatians 4:4, NASV).

Carrier counters that the woman in this passage must be taken allegorically, because Paul says:

Tell me, you who want to be under law, do you not listen to the law? For it is written that Abraham had two sons, one by the bondwoman and one by the free woman. But the son by the bondwoman was born according to the flesh, and the son by the free woman through the promise. This is allegorically speaking, for these women are two covenants: one proceeding from Mount Sinai bearing children who are to be slaves; she is Hagar. Now this Hagar is Mount Sinai in Arabia and corresponds to the present Jerusalem, for she is in slavery with her children. But the Jerusalem above is free; she is our mother (Galatians 4:21-26).

Carrier argues that the woman in Galatians 4:4 should be taken allegorically because the women in Galatians 4:24 (Hagar and Sarah) are taken allegorically to represent two covenants.  Rather, I think that St. Paul is drawing out an allegory from the literal and historical human birth of Christ to the Blessed Virgin.  Sarah is a typological pre-figuring of Mary.  Sarah’s miraculous conception and birth is the first fruits of God’s covenant with Abraham, a covenant that through the offspring of Isaac, all nations will be blessed (Genesis 22:15-18).  This covenant culminates in a second, greater, miraculous conception, which is the fulfillment of God’s covenant with Abraham to bless all nations of people.  However, if Christ is not truly an offspring of the line of Abraham, Isaac, and Jacob, St. Paul would not think that this covenant was truly fulfilled.  Thus, the woman in Galatians 4:4 should be understood to be a real flesh and blood mother, if Christ is to be the fulfillment of God’s promise to Abraham.  So, St.Paul takes a literal event, Christ’s birth to a woman, and ties it to Genesis 17, where he promises that Sarah will give birth to a child.

The beauty of the Catholic understanding of scripture is often “both…and” rather than “either…or”.  Carrier wants the woman in Galatians 4:4 to be allegorical rather than literal.  The Catholic response is not to say that she is literal rather than allegorical, but that she is both a literal mother and an allegorical mother.  Mary is, allegorically, the Mother of the New Covenant.  We see, particularly in the Gospel of Luke, to how Mary is likened to the Ark of the Covenant.  She is the Ark of the New Covenant.

On this day, we should remember that St. Paul tells us that the woman allegorically represents the covenant.  As the Son of God took on flesh and was born of a woman, we are adopted as sons and daughters of the same covenant (see Galatians 4:5).  This means that the woman adopts us, and we are her children, which is precisely the point St. Paul draws from the allegory:

So then, brethren, we are not children of a bondwoman, but of the free woman (Galatians 4:31, NASV).

As we are children of the free woman, she is our mother (see Galatians 4:26).  Thus, the Holy Catholic Church is quite correct to confer the title Mater Ecclesiae, Mother of the Church, upon the Blessed Virgin Mary.  For, she is the Mother of the Universal Church.  We see this in the scriptures amidst the most important event in all of human history.  During the crucifixion of Christ, He turns to the Beloved Apostle, John, and says:

…“Behold, your mother!” (John 19:27).

Christ adopts St. John the Evangelist as His brother in the last moments before His death.  And John took Mary into his household as his mother from that moment.  So we too should take Mary into our household as our mother. Today, we honor Mary the Mother of God, as it is through her offspring that all nations, including the nations indigenous to the Americas, were, and are, blessed.  The Covenant to God extends out from the tribes of Israel to all tribes and nations of the Earth.  And so she appeared to her children in Mexico in 1531.  When they saw her, they knew she was their mother.

Nuestra Señora de Guadalupe, ruega por nosotros.

A Response to the Argument from Material Causality

Ex-apologist presents an interesting argument against a form of classical theism that includes a classical view of creation: classical theismcvc (click here to read the original article). The argument is based on what he calls the principle of material causality, or PMC, which features in the first premise of his argument. The second premise states an implication of classical theismcvc and shows that one cannot hold to the PMC and to classical theismcvc at the same time, i.e. the two are inconsistent. Since one has good reason to hold to the PMC, classical theismcvc must be abandoned, so the argument goes.   Ex-apologists formulates it this way:

1. All concrete objects that have an originating or sustaining cause have a material cause of their existence.
2. If classical theismcvc is true, then the universe is a concrete object that has an originating or sustaining cause without a material cause of its existence.
3. Therefore, classical theismcvc is false. [1]

The argument is essentially valid, so the question of soundness comes down to the truth of the premises. In this critique, I will explore the notion of the principle of material causality, PMC, and show why, with a more precise notion of PMC in place, the argument cannot be successful. But first we must understand what ex-apologist means by a few of his terms.

Classical Theism: “…the view that there is a personal god who is omnipotent, omniscient, and morally perfect.”

The Classical View of Creation: “the view that consists in the following three theses: (i) God is wholly distinct from the natural world; (ii) God is the originating or sustaining cause of the natural world; and (iii) God created the natural world ex nihilo.

Originating cause: “…an efficient cause of the temporal beginning of a thing’s existence…”

Sustaining cause: “…an efficient cause of a thing’s continued existence.”

Matter cause: “…the things or stuff from which another thing is made…” [Note: Ex-apologist’s (1), his PMC, is restricted to concrete objects that have either a sustaining or originating cause. So no question is begged against God, since God is typically held to be uncaused. Also, though it is not explicitly stated, I take creation ex nihilo to be defined as the causation of something without pre-existing matter]

My Response:

First, something more should be said about what “universe” means, so as to avoid equivocation. With contemporary talk of multiverses, the word “universe” has been relegated to mean this particular spatio-temporal expanse. There may be parent universes that have generated our own universe along with countless sister universes. Of course, classical theismcvc claims that God has created and sustains the whole natural world, which would include the multiverse and any other natural thing beyond or outside of that. So the argument should avoid talk of the universe and instead just speak of the “natural world” as that which includes the totality of nature, whatever that was, is, or may be.

Ex-apologist uses a disjunction to say that God is the originating OR sustaining cause of the natural world. Now, some theists might object and say that God is both the originating AND the sustaining cause of the natural world. However, I think he is quite right to insist upon the disjunction. The idea of a “first cause” is not necessarily the same as an “originating cause”, which implies that the effect has a temporal beginning or begins to exist. When, for instance, Aquinas calls God the “first cause,” he does not mean to imply that God preceded the existence of the universe in time. In fact, as an Aristotelian, he thought that the best science of his day indicated that the universe could very well be past eternal (see SCG II.33 and SCG II.38).  Instead of thinking that God is temporally first in efficient causal priority, Aquinas thought God, who transcends time altogether, had priority or primacy as a causal explanation of everything, i.e. there is nothing beyond or beside God in the causal series out of which the universe is created. This is not to say that God can use secondary causes, but they are not “beside” God in the sense that they are uncaused and per se necessary. God is pure actuality, and He explains the actuality of all other things. I suspect that this is why ex-apologist is making use of the disjunction “originating or sustaining cause.” For, the universe need not be finite in the past for classical theismcvc to be true, and historically speaking, many proponents of classical theismcvc explicitly embraced the possibility that the natural world or cosmos lacked an originating cause.

Let us consider the principle of material causation more closely and whether it is genuinely inconsistent with creation ex nihilo. Now, as I have said, the doctrine of creation ex nihilo is the claim that God caused the natural world without using pre-existing matter. But this does not mean that the natural world lacks material causality at any moment when it exists. Suppose there were a possible world where God creates, ex nihilo, a singular bronze sphere. Would the principle of material causation hold for this sphere? Yes. The sphere is materially caused by the bronze from which it is composed. The Aristotelian would not say that the sphere lacks a material cause merely because it wasn’t created from pre-existing bronze, or pre-existing copper and tin. Rather, the Aristotelian would say that a material cause did not precede the effect in time. That is, God did not use bronze or the components of bronze that existed prior to His willing the brazen sphere’s existence. In fact, even if the sphere were eternal, we could say that God creates the brazen sphere from no pre-existing matter even though bronze is the matter that “sustains” the sphere in existence as a secondary cause. Thus the brazen sphere is created ex nihilo and has a material cause. Likewise, the natural world could have a material cause at any moment it exists while not coming to be from pre-existing matter.

So what is going on here? How can some object be created ex nihilo and have a material cause? We need to make a parallel distinction to the one we find in efficient causality between originating and sustaining such that there can be an originating material cause for a thing and a sustaining material cause. We can define an originating material cause as the pre-existing matter out of which a concrete object begins to exist (e.g. the unformed bronze, or copper and tin). We can define a sustaining material cause as the matter that composes concrete object at all times that the concrete object continues to exist (e.g. the bronze currently in the sphere while it is existing). As the sphere and the bronze from which it is composed simultaneously exist as an effect of God’s will, the brazen sphere exists ex nihilo, from no pre-existing matter. Now, one might object by saying that this is not “creation” since creation must involve motion or change out of which something comes to be. This would be contrary, however, to what Aquinas argues in, for instance, the Summa Contra Gentiles II.17 where he specifically denies that creation involves motion or change.  For Aquinas, genuine creation is not merely changing one thing into another, but the very actualization of substance itself.  Creation is just what one calls the relationship between the first cause, God, and his effects, i.e. the creation of non-divine substance. Anything actualized by God, i.e. the being of pure actuality, is a created thing. So, for Aquinas, creation ex nihilo merely follows from the notion that God is the uncaused cause of all other things. It should also be noted that matter, the underlying stuff, is always a composite of act and potency. Consequently, on the Aristotelian-Thomistic metaphysical view, there simply cannot be uncaused or uncreated matter that co-exists with God from which other things are made. For such matter would have to receive its actuality from another, and so it must have a caused if it exists—a cause that will somehow trace back to the Being of Pure Actuality. Admittedly this is the Aristotelian-Thomistic notion of matter, and perhaps ex-apologist would like to distance himself from such an understanding of matter towards a more modern notion of matter as pure extended stuff. Perhaps pure extension can exist uncaused along with God. It is less clear whether standard particle theory, which seems to comport better with hylomorphism than early modern notions of matter, can be uncaused or self-actualizing. Either way, I think more needs to be said about what matter actually is.

Now consider ex-apologist’s argument and the disjunctions involved therein. Those disjunctions will prove important to this discussion. We may grant that a concrete object that has an originating OR sustaining [efficient] cause has a material cause, but for ex-apologist’s argument to work, there must always be an originating material cause. Otherwise, one might escape his argument through the following formulation, PCM’:

(4) All concrete objects that have an originating or sustaining efficient cause have an originating or sustaining material cause of their existence.

This reformulation will not force the falsity of classical theismcvc because it need not be the case that the universe has an originating material case. So:

(5) If classical theismcvc is true, then the natural world is a concrete object that has an originating or sustaining efficient cause and not an originating material cause of its existence.

(6) Therefore, if classical theismcvc is true, the natural world has a sustaining material cause of its existence.

Many classical theists will want to reject the notion that all of creation is material, but the thesis isn’t explicitly contrary to classical theismcvc, as ex-apologist defines it. So, the conclusion is consistent with classical theismcvc. To avoid this escape, ex-apologist will have to say that all concrete objects that have an originating or sustaining efficient cause, must have an originating material cause of their existence. This means that he must have an even stronger PMC’’ which states:

(7) All concrete objects that have an originating or sustaining efficient cause have an originating material cause of their existence.

From this, he can argue:

(8) If classical theismcvc is true, then the natural world is a concrete object that has an originating or sustaining efficient cause and not an originating material cause of its existence.

(9) Therefore, classical theismcvc is false.

Now PMC’’, as found in (7), seems a bit odd in that it maintains the disjunction with respect to efficient causality as though something could have an originating material cause (be composed from pre-existing unformed matter) simply because it has a sustaining efficient cause. Return to our possible world of the brazen sphere for a moment. Suppose God, or some other efficient cause, sustained the matter in the appropriate configuration for all eternity. Such a sphere would have a sustaining efficient cause but no originating material out of which the composite concrete object comes to be. This scenario has, at least, prima facie plausibility. So I see no good reason to suppose that a sufficient condition of having originating matter is for a concrete object to have a sustaining efficient cause. If something is eternal and sustained in existence (i.e. it has a sustaining efficient cause and no originating efficient cause), there is no good reason to think it came to be from pre-existing matter, and there is good reason to think that it would be incoherent to suppose it could have an originating material cause. Given that, (7) appears to be a false principle, and we should clarify our principle of material causality once again to PMC’’’:

10) All concrete objects that have an originating efficient cause have an originating material cause of their existence.

From here, one could argue:

11) If classical theismcvc is true, then the natural world is a concrete object that has an originating efficient cause and not an originating material cause of its existence.

(12) Therefore, classical theismcvc is false.

The problem, of course, is that (11) is too strong. Classical theism does not depend upon there being an originating efficient cause of the universe, just that there must be a first cause in order of explanation that could be either originating or sustaining. The universe need not have a temporal beginning at all. So it seems to me that ex-apologist needs argue, independently of whatever classical theismcvc may imply about the natural world, to say that it indeed has originating causes:

(13) All concrete objects that have an originating efficient cause have an originating material cause of their existence.

(14) The natural world has an originating efficient cause.

(15) If classical theismcvc is true, then the natural world does not have an originating material cause of its existence.

(16) Therefore, classical theismcvc is false.

Now what could be said of this argument? One might object to (13). Ex-apologist anticipates a rejection of his PMC via quantum mechanics or libertarian free will. I am not certain that his discussion is successful with respect to libertarian freewill, since he suggests that since an agent’s free will is caused by energy from outside of the natural causal order, freely willed choice is not genuinely caused ex nihilo. According to ex-apologist, the story would be that energy from outside the natural causal order was part of the causal explanation of the will, and so the choice would not be genuinely ex nihilo. It’s not clear to me that such an event would not be ex nihilo because of some supernatural energy.  I am not sure what this energy would be, but it is not clear that it is equivalent to or convertible with matter in any sense of the term, or that a free will choice is somehow composed from this pre-existing supernatural energy.  And it seems to me that if this point is pushed too hard, determinism threatens.  For if this supernatural energy is the something like the “pre-existing matter” out of which an agent’s choices emerges, then even if our choices are inexplicable within the natural causal order (since it is not closed), it may be explicable and determined within the supernatural causal order and determined there within.  The libertarian must maintain that alternative choice is possible, and so whatever this supernatural energy is, it cannot be determining things in the way pre-existing matter/energy determines things within the natural causal order.  So it is a disanalogous energy.

I would think that a more straightforward defeater for (13) would be the creation of immaterial souls or intellects. There are plausible arguments for the immateriality of the soul or part of the soul, and those arguments would have to be addressed by ex-apologist if his argument is to have any merit. My personal favorite is James Ross’s argument for the immateriality of thought (which I have blogged about here), though there are many other such arguments. Ross says that physical and material process are indeterminate, and so do not perfectly align with truth-preserving determinate processes such as we find in the intellect’s formal and deductive rational processes. He concludes that these intellectual processes cannot be material processes. If so, these processes are concrete and also have originating efficient causes in the agent. Insofar as they are immaterial, they lack a material cause in their origination, and they are not sustained by matter. Rather, hylomorphicists, like me, argue that the originating causes are formal and efficient rather than material.

With respect to (14), ex-apologist will have to sustain an enormous burden of proof. For this is not merely the claim that the universe began to exist at some finite point in the past, but that the whole of nature, itself, is a concrete object that began to exist at some point, and so came from pre-existing matter. What’s more, if the totality of nature was composed from pre-existing matter, then that matter would have to be, by definition, beyond that which is within the scope of the natural world, and so would be supernatural. This is, of course, problematic for any sensible definition of “natural” since matter has always been taken to be a prime example of that which is natural. Of course we need to pin down what “natural” and “material” mean to consider whether it is even coherent to talk about supernatural matter. Moreover, natural material things would have to be ultimately composed out of whatever this supernatural matter is. And since other things begin to exist out of this matter, all concreta that begins to exist would have to be ultimately composed out of this supernatural stuff. Also, there would have to be a supernatural efficient cause of the universe, to maintain this argument—some sort of demiurge. This is a very untoward consequence of attempting to sustain (13) and (14), as it would be a defeater for naturalism as much as it would be a defeater for classical theismcvc. In other words, in using  (13)-(15) to defeat classical theismcvc, one is, in effect, arguing in favor of the sort of cosmogony one finds in Plato’s Timaeus. I doubt that ex-apologist wants to defend the notion that there is a demiurge who fashions the natural world out of supernatural matter.

Summary: many classical theists would reject (13) on the grounds that the soul or part of the soul begins to exist, but lacks a material cause. Those arguments should not be ignored. Furthermore, classical theismcvc is neutral with respect to (14), so it is a premise that ex-apologist would need to justify independently. The ultimate problem is that (13) and (14), taken together, would undercut naturalism as much as classical theismcvc and lead to the absurd conclusion that the natural world is made out of some spooky supernatural “stuff”. I doubt any naturalist would want to defend (14) on its own merits, and it would be unfair to saddle the classical theist with defending (14), though there are some theists who seem keen on the idea of a finite past (I’m looking at you, Dr. Craig). It is for these reasons that I do not think a successful argument against classical theism from material causality can be had.

Ultimately the PMC is not incompatible with creation ex nihilo. At best, creation ex nihilo is incompatible with the notion that all concreta which has an originating efficient cause has an originating material cause, but only if it is assumed that the natural world has an originating efficient cause. Does the natural world have an originating cause? I’m not sure we can know. If it does have one, I am not sure that it is so much better to posit that it came to be from a demiurge and supernatural matter than from God ex nihilo.

[1] All quotes taken from Ex-apologist (2014, December, 04) “Theism and Material Causality”. Retrieved from http://exapologist.blogspot.com.es/2014/12/theism-and-material-causality.html

Advent 2014

Just to get into the spirit of the season:

Circular Reasoning, the Bible, and Atheism

I had a discussion the other day in which my interlocutor cited “reading the Bible” as the cause of his atheism. This perplexed me. And he is not the only one who has said this.  Here is a common meme expressing the same sentiment:

So, here is my response, in meme form:

IMG_0973.JPG

If you are interested in how to approach scripture, I recommend reading Dei Verbum.

Problem of Induction

Inspired by my recent little debate: IMG_0937.JPG

A Debate on HEE and the Skeptical Argument against Rationality

Recently, I’ve had a little debate on Facebook that has prompted my interlocutor to take to his own blog in order to clarify his views and rebut my argument. Unfortunately, in the process, I believe my own position has been misrepresented, so I thought I would discuss some of the issues here and respond to some of his claims.

Essentially, my interlocutor fails to understand why Hume’s skeptical argument against rationalism is problematic for his particular epistemology.  In fact, he thinks the argument can be ignored precisely because it leads to untoward consequences.  And he thinks that I am guilty of special pleading because I do not think this problem affects my own epistemology. But before I respond to these issues, a little background on the debate is needed.
Read the rest of this entry

The Ontological Argument From Transcendence 2.0

I’ve presented my own version of Anselm’s ontological argument here and I’ve also argued for an ontological argument using “more transcendent” rather than “greater” here. Combining the two, and refining the argument, I got this:

1. Something is an Anselmian God if and only if it is conceivable, nothing can be conceived of which is more transcendent, and it necessarily exists (definition Θ).

2. There is something conceivable such that nothing can be conceived of which is more transcendent (premise).

3. For all x, if the possibility of failing to conceive of x implies the possibility that x doesn’t exist, x is mentally dependent (premise).

4. For all x, if x is mentally dependent, there is something conceivable that is more transcendent than x (premise). Therefore,

5. An Anselmian God exists.

Let

Cx – x is conceived
Mx – x is mentally dependent
Txy – x is more transcendent than y
Θx- x is an Anselmian God, that is: (∀x){Θx ≝ ([♢Cx & ~(∃y)(Tyx & ♢Cy)] & ☐(∃z)(z=x))} (Def Θ)

1. (∃x)[♢Cx & ~(∃y)(Tyx & ♢Cy)] (premise)
2. (∀x){[♢~Cx ⊃ ♢~(∃z)(z=x)] ⊃ Mx} (premise)
3. (∀x){Mx ⊃ [(∃y)(Tyx & ♢Cy)]} (premise)
4. (∀x){[♢Cx & ~(∃y)(Tyx & ♢Cy)] ⊃ [♢~Cx ⊃ ♢~(∃z)(z=x)]} (IP)
5. ♢Cu & ~(∃y)(Tyu & ♢Cy) (1 EI)
6. [♢~Cu ⊃ ♢~(∃z)(z=u)] ⊃ Mu (2 UI)
7. Mu ⊃ [(∃y)(Tyu & ♢Cy)] (3 UI)
8. [♢~Cu ⊃ ♢~(∃z)(z=u)] ⊃ [(∃y)(Tyu & ♢Cy)] (6,7 HS)
9. [♢Cu & ~(∃y)(Tyu & ♢Cy)] ⊃ [♢~Cu ⊃ ♢~(∃z)(z=u)] (4 UI)
10. ♢~Cu ⊃ ♢~(∃z)(z=u) (5,9 MP)
11. (∃y)(Tyu & ♢Cy) (8,10 MP)
12. Tvu & ♢Cv (11 EI)
13. ~(∃y)(Tyu & ♢Cy) (5 Simp)
14. (∀y)~(Tyu & ♢Cy) (13 QN)
15. ~(Tvu & ♢Cv) (14 UI)
16. (Tvu & ♢Cv) & ~(Tvu & ♢Cv) (12,15 Conj)
17. ~(∀x){[♢Cx & ~(∃y)(Tyx & ♢Cy)] ⊃ [♢~Cx ⊃ ♢~(∃z)(z=x)]} (4-16 IP)
18. (∃x)~{[♢Cx & ~(∃y)(Tyx & ♢Cy)] ⊃ [♢~Cx ⊃ ♢~(∃z)(z=x)]} (17 QN)
19. (∃x) ~{~[♢Cx & ~(∃y)(Tyx & ♢Cy)] ∨ [♢~Cx ⊃ ♢~(∃z)(z=x)]} (18 Impl)
20. (∃x){~~[♢Cx & ~(∃y)(Tyx & ♢Cy)] & ~[♢~Cx ⊃ ♢~(∃z)(z=x)]} (19 DeM)
21. (∃x){[♢Cx & ~(∃y)(Tyx & ♢Cy)] & ~[♢~Cx ⊃ ♢~(∃z)(z=x)]} (20 DN)
22. (∃x){[♢Cx & ~(∃y)(Tyx & ♢Cy)] & ~[~♢~Cx ∨ ♢~(∃z)(z=x)]} (21 Impl)
23. (∃x){[♢Cx & ~(∃y)(Tyx & ♢Cy)] & ~[☐Cx ∨ ♢~(∃z)(z=x)]} (22 ME)
24. (∃x){[♢Cx & ~(∃y)(Tyx & ♢Cy)] & [~☐Cx & ~♢~(∃z)(z=x)]} (23 DeM)
25. (∃x){[♢Cx & ~(∃y)(Tyx & ♢Cy)] & [~☐Cx & ☐(∃z)(z=x)]} (24 ME)
26. [♢Cu & ~(∃y)(Tyu & ♢Cy)] & [~☐Cu & ☐(∃z)(z=u)] (25 EI)
27. ~☐Cu & ☐(∃z)(z=u) (26 Simp)
28. ☐(∃z)(z=u) (27 Simp)
29. [♢Cu & ~(∃y)(Tyu & ♢Cy)] (26 Simp)
30. [♢Cu & ~(∃y)(Tyu & ♢Cy)] & ☐(∃z)(z=u) (28,29 Conj)
31. Θu (30 Def Θ)
32. (∃x)Θx (31 EG)

[Update 11/9/204] I’ve noticed that some did not understand why if possibility that failing to conceive x implied that x possibly didn’t exist, then a greater could be conceived than x.  I’ve tried to make this more explicit by explaining this in terms of mental dependence.  Here, a concept is not an abstract object, but an object in the mind.

A Voltairean Argument for God’s Existence

This post is a variation on what I have called an indispensability argument.  My original formulation can be found here, and I have made some further comments here. In this post, I thought I would do a take on the argument using Voltaire’s famous dictum “Si Dieu n’existait pas, il faudrait l’inventer” as an explicit premise (Epistle to the author of the book, The Three Impostors, 1768).  As an aside, it is commonly supposed that, since Voltaire was critical of organized religion, he was an atheist.  Voltaire was a deist. In fact, in the poem where he says that if God does not exist, it would be necessary to invent him, Voltaire doesn’t merely refer to God as some generic super-being, but as the “supreme essence.”  So it seems that he has something like a perfect being, or the God of the philosophers, in mind, at least in this poem.  I find the following argument cogent, and I think historical reflection makes the premises plausible. Thoughts are always appreciated, of course, though I anticipate some objections below.

  1. If God does not actually exist, it is necessary to invent the concept of God. [Voltairean Premise]
  2. For all x, if it is necessary to invent the concept of x, the concept of x is logically coherent. [Premise]
  3. If the concept of God is logically coherent, God actually exists. [By S5 and the logical possibility of God as a perfect being is necessarily existent and essentially perfect]
  4. For all x, x does not actually exist, or x actually exists. [Law of the Excluded Middle]

Therefore, God actually exists. Proof:

  1. Either God actually exists, or it is necessary to invent the concept of God. [From 1 Material Implication]
  2. If it is necessary to invent the concept of God, the concept of God is logically coherent. [From 2 Universal Instantiation]
  3. If it is necessary to invent the concept of God, God actually exists. [From 3, 6 Hypothetical Syllogism]
  4. God does not actually exist, or God actually exists. [From 4 Universal Instantiation]
  5. If God actually exists, God actually exists. [From 8 Material Implication]
  6. Either God actually exist, or God actually exists. [From 5, 7, and 8 Constructive Dilemma]
  7. God actually exists. [From 9 Tautology]

In this argument, I want to grant the Voltairean Premise, though I suspect most atheists would attack it with a Laplacean counter that “I have no need for that hypothesis.” Indeed, Laplace did not have a need to invoke God to explain the motion of the planets, but I don’t think that was Voltaire’s point. Rather, he was talking about the need of the concept of God for social cohesion. But, I think the concept of God plays a larger role than merely grounding natural law for a social contract, or putting the fear of hellfire into the hearts of the criminally minded and depraved. There is a necessity of God in many aspects of philosophical speculation. It is out of the concept of God that various philosophical concepts found further development, such as the notions of free will, personhood, simplicity, and aseity. The concept of God has helped thinkers clarify concepts surrounding Being, substance, essence, the relationship between eternality and time, etc. I suspect that the concept of God, a perfect being, was necessary in the intellectual development of our civilization. Whether one thinks that God is currently necessary to ground human rights and dignity, natural law, it happened that way historically. So it is important to note that the concept of this God, the God of the philosophers, is one that is both maximally great and fecund.

If the concept of God, a perfect being, is incoherent then such a history would be surprising, since incoherent concepts are not really all that necessary for anything. I take a concept to be incoherent if the sense of the concept is implicitly contradictory. Such a concept would not be any more necessary for deriving other philosophically interesting concepts than any other incoherent concept. For, impossibilities trivially imply anything and everything. Nonetheless, real work and reflection has gone into inferring the attributes and implications of the God of the philosophers. It is true that theologians and philosophers have come to contrary conclusions from the concept of God, but the steps by which they reach those contrary conclusions are comprehensible and not merely based on an explicit use of the principle of explosion or by being arbitrary. Often times the dispute is based on one philosopher taking an attribute or the concept of perfection to have a different sense than what another philosopher thinks. They genuinely disagree. So, it is not the case that they are simply picking out contradictions—contradictions that they would bashfully agree are there within the concept of God all along— and reaching contrary conclusions. They are actually disagreeing on basic definitions of terms that they think are implied by perfection. That being said, there is some consensus that has grown around perfect being theology. For instance, God’s power does not imply the ability to do the logically impossible, and God cannot make free-agents always do what is morally right. There are still genuine disputes over the details of a maximally great being, or a perfect being, but few would dispute that such a being would be necessary, omnipotent, omniscient, and morally perfect. Some dispute whether God’s omniscience is propositional. For instance, if God is absolutely simple, there can be no composition in God’s knowledge, and so it cannot be based on the composition of subject terms and predicates in the mind of God. But these sorts of disputes are not willy-nilly where anything goes. The disputes are rigorous, and based on careful definitions. So, it seems to me that while the concept of God is not settled upon by all philosophers, there are definite rules around how to do natural theology, and limits upon what the God concept entails.

One might also argue that, though the concept of God, the God of the philosophers, is incoherent, various aspects of the concept are coherent, and it is those aspects that have been fecund in the history of philosophy.  This doesn’t seem to be the case, however.  Rather, it is typically the confluence of various divine attributes that have generated so many ideas.  Perhaps even more to the point, if classical theism and absolute divine simplicity are granted, then these philosophers are not really considering a confluence of God’s attributes, but one essence that reveals itself to us an a variety of ways.  That thought itself has produced some of the most penetrating theology in Judaism, Christianity, and Islam.  The entire Summa Theologiae is built upon this foundation, brick by syllogistic brick.  Perhaps that brick was all straw, but the Summa itself has produced entire schools of philosophy and theology. I think the concept of God was a historical necessity and philosophical necessity, one born out of a reflection on the divine, the perfect, and the infinite. That this concept is both necessary and incoherent would be surprising since, as I have said, any incoherent concept could do the job of generating random inferences.  I don’t think that is what the concept of God has been doing in our history.  I don’t think it is there as an incoherency from which surprising and profound thoughts emerge.  The concept of God gives us traction in a way that a round-square does not.  Round-squares or squared-circles might in some sense be “meaningful” concepts, but they are not necessary to invent.  In fact, it is not entirely clear that they are concepts, at least in the sense that they can be conceived in the mind.  It seems more the case that one is conceiving of roundness and squareness and noting that they cannot be predicated of the same Euclidean plane figure.  They are more an oddity, a conceptual contradiction.  Their use is merely as a stand-in for any obvious instance of an impossibility.

As for premises (3) and (4), they are relatively uncontroversial rules of logic, and I will not go into defending them here. I know some people lament S5, but the issue is not whether the axiom is true, but rather, whether we genuinely know whether something is logically possible rather than, say, merely epistemically possible. I think my defense of (2) makes it clear that I am not merely saying that the God concept is conceivable, but that it contains no incoherency in it. So, I think that if Voltaire’s dictum is right, and the necessity of a concept implies its coherence, we have good reason to think God actually does exist.

An Argument from Transcendence

In a previous post, I attempted a version of the ontological argument that makes use of a comparative relation other than “greater than.” In the argument, I used “more actual.” Of course, I meant “actual” in a sort of Aristotelian-Thomistic sense, and so it depends upon understanding that particular set of metaphysical jargon. It occurs to me that one might make use of other comparatives to similar effect. This post can be considered a “Part 2,” as I attempt a similar argument with “more transcendent” as the comparative (though I have made a few modifications to the original version that I think strengthen it). Of course, there will still be some metaphysical unpacking to do. As I have said, it is impossible to avoid metaphysics when considering arguments for God’s existence. First, we must consider what it means to “transcend” and why it might be appropriate to define God this way. For, if an ontological argument is to be successful, the definition must at least implicitly contain the traditional divine attributes.  So we must consider if “transcendence” entails those other attributes.  I think it does.

That which transcends goes beyond some limit, whether it is the physical laws, space, time, or any of the fundamental categories of existence. God is often defined as transcendent, but not in the sense that He is completely detached from us and in no way relates. For, in a sense, to say that God lacks immanence is to say that God cannot transcend those limits back into our finite existence. So I don’t see transcendence and immanence as true opposites, but as two perspectives by which one can refer to the omnipresence of God. The concept of transcendence can also help us understand other divine attributes. God is said to be omniscient, transcending anything that would limit knowledge. Likewise God is omnipotent, transcending, for instance, the physical laws that limit the amount of power finite creatures possess. God is also morally perfect, transcending anything that might limit His ability to perfectly express his being good and loving towards others.  So a if we conceive of God as that than which none more transcendent can be conceived, it seems that we will arrive at a being that exists infinitely perfect and a se (self-existent and not limited to depending on other things to exist). Such a being would be omnipotent, omniscient and morally perfect (so personal), and transcending time and space.  Now one might consider whether it is conceivable that God transcends existence itself.  Some theological traditions flirt with this idea, but I strongly suspect that the idea that something transcends existence is logically incoherent.  That is, it would be something not limited by being something.  I have no idea what that would mean, but if it means that God is something or someone who doesn’t exist, then it is incoherent.  It may just be that “transcending existence” is just meaningless.

Anselm defined God as that than which none greater can be conceived, and I think we can understand “greatness” in terms of “transcendence.” As I mentioned in a previous blog, “greatness” can be difficult for some people to grasp. Is it supposed to be defined subjectively? For Anselm, “greatness” was conceived in terms of the Great Chain of Being, and so was an objective evaluation of existing things. But today, most people think of “greatness” as something that is in the eye of the beholder–and opinion with no factual basis whatsoever. When I have presented Anselm’s argument in the classroom, a few of my students inevitably ask, “Why must anyone agree that it is greater to exist in reality than in the mind alone?” Responding with neo-platonic metaphysics might help the student to understand what Anselm was thinking, but it makes the argument seem irrelevant, antiquated, and weak. Transcendence, though, is more clearly an objective feature. One may simply observe whether some being goes beyond a certain limit.

Now one might say that it makes no sense to say that there is a limit if something transcends the limit. But we speak of things moving beyond limits all the time. Voyager I has recently transcended the limits of our solar system. When you drive too fast, you transcend the legal limit at which you can drive (though you might not use such a grandiose term as “transcend” when the cop pulls you over for speeding). So the existence of something surpassing a limit is not inconsistent with there being limits. The physical laws of nature are physical limits on the way natural objects can behave. If naturalism is true, there is nothing that transcends those limits. Whether something transcends those limits is an objective question, not a question dependent upon one’s opinions, desires, or tastes.

So perhaps we can modify Anselm’s definition and say that God is that than which none more transcendent can be conceived. Just as Anselm initially invites us to consider, we may ask ourselves if such a God could merely exist in the mind, as some idea, imaginary thought, or mental construct. Surely ideas, imaginary thoughts, and mental constructs are limited by the mind in which they inhabit. They are limited not only by the mental capacity of the mind conceiving of them, but also insofar as their existence depends upon and so are limited by the very existence of minds.

An argument from transcendence would look like this:

  1. God is that than which none more transcendent can be conceived. [Definition]
  2. If God exist only as an idea in the mind, something can be conceived more transcendent than God. [Premise]
  3. If it is not the case that something exists only as an idea in the mind, then it exists as an extra-mental reality. [Premise]
  4. If something can be conceived more transcendent than God, something can be conceived more transcendent than God. [Tautology]
  5. If something can be conceived more transcendent than God, something can be conceived more transcendent than that which none more transcendent can be conceived. [From 1, 4 Definition]
  6. If something can be conceived more transcendent than that than which none more transcendent can be conceived, then that than which none more transcendent can be conceived is not that than which none more transcendent can be conceived. [Premise]
  7. It is not the case that that than which none more transcendent can be conceived is not that than which none more transcendent can be conceived. [Law of Non-Contradiction]
  8. It is not the case that something can be conceived more transcendent than that which none more transcendent can be conceived. [From 6, 7 Modus Tollens]
  9. It is not the case that something can be conceived more transcendent than God. [From 5, 8 Modus Tollens]
  10. It is not the case that God exists only as an idea in the mind. [From 2, 9 Modus Tollens]

Therefore,

  1. God exists as an extra-mental reality. [From 3, 10 Modus Ponens]

Is this argument subject to parody? I think not, and much for the same reason I did not think an ontological argument using the comparative “more actual” is susceptible to parody. Consider, for instance, Gaunilo’s perfect island. It seems incoherent to define an island as “that island than which none more transcendent can be conceived.” The very nature of an island is such that it does not transcend the limits of water on all of its sides. Otherwise, it would cease to be an island! “Very well,” you might think, “let’s say that it does not transcend watery limitations, but it does transcend all other limits.” Well, which ones must such an island transcend? Must it transcend all limits as to the amount of sand it has on its beach? Would it have an actual infinity of sand on the beach? Perhaps there is some physical restriction you would want to place on the amount of sand, otherwise the gravitation would be so great that it would be more like a super-massive black hole than an island resort. Ah, but it transcends all physical limitations, and so it would not be bound to obey gravity or other physical laws. But now it is sounding less and less like an island, which seems to at least be bound by physical laws to do with water and land. Would it be limited such that it could not be conscious? Would it be limited in power? If you grant that it would, so that it could remain island-like, then it becomes more and more ad hoc that you should insist that one of the ways in which the island than which none more transcendent is transcendent is insofar as it must exist beyond the mental. If you insist that it would be conscious, even all knowing, and all powerful to boot, then it sounds less and less like you are really talking about an island, and more and more like you are really talking about God. Perhaps you are really just saying that God could choose to manifest himself as a physical island. And perhaps this is true. But then the island isn’t so much a parody as it is a reiteration of the actual proof, while insisting that we consider God in this odd manifested form. So, if we strictly hold to the concept of “island” it is not clear that the concept of an “island than which none more transcendent can be conceived” is coherent, or physically possible. If we ditch the idea that it really is an island, as islands are traditionally conceived, the parody crumbles apart and just becomes a reiteration of the proof.

There are, of course, other objections to ontological arguments. Perhaps you could mention your objections to the argument in the comments below.

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