Maverick Philosopher

Van Til on Divine Simplicity and the One and the Many

(Edits added 2/10/19)

Cornelius Van Til rightly distinguishes in God between the unity of singularity and the unity of simplicity.  The first refers to God's numerical oneness. "There is and can be only one God." (The Defense of the Faith, 4th ed., p. 31) The second refers to God's absolute simplicity or lack of compositeness: ". . . God is in no sense composed of parts or aspects that existed prior to himself." (ibid.)  Van Til apparently thinks that divine simplicity is a Biblical doctrine inasmuch as he refers us to Jer. 10:10 and 1 John 1:5.  But I find no support for simplicity in these passages whatsoever.  I don't consider that a problem, but I am surprised that anyone would think that a doctrine so Platonic and Plotinian could be found in Scripture.  What surprises me more, however, is the following:

The importance of this doctrine [simplicity] for apologetics may be seen from the fact that the whole problem of philosophy may be summed up in the question of the relation of unity to diversity; the so-called problem of the one and the many receives a definite answer from the doctrine of the simplicity of God." (ibid.)

That's an amazing claim!  First of all, there is no one problem of the One and the Many: many problems come under this rubric. The problem itself is not one one but many!  Here is a partial list of one-many problems:

1) The problem of the thing and it attributes.

A lump of sugar, for example, is one thing with many properties. It is white, sweet, hard, water-soluble, and so on. The thing is not identical to any one of its properties, nor is it identical to each of them, nor to all of them taken together.  For example, the lump is not identical to the set of its properties, and this for a number  of reasons. Sets are abstract entities; a lump of sugar is concrete. The latter is water-soluble, but no set is water-soluble. In addition, the lump is a unity of its properties and not a mere collection of them.  When we try to understand the peculiar unity of a concrete particular, which is not the unity of a set or a mereological sum or any sort of collection, we get into trouble right away.  The tendency is to separate the unifying factor from  the properties needing unification and to reify this unifying factor. Some feel driven to posit a bare particular or bare substratum that supports and unifies the various properties of the thing. The dialectic that leads to such a posit is compelling for some, but anathema to others. The battle goes on and no theory has won the day.

2) The problem of the set and its members.

In an important article, Max Black writes:

Beginners are taught that a set having three members is a single thing, wholly constituted by its members but distinct from them. After this, the theological doctrine of the Trinity as "three in one" should be child's play. ("The Elusiveness of Sets," Review of Metaphysics, June 1971, p. 615)

A set in the mathematical (as opposed to commonsense) sense is a single item 'over and above' its members. If the six shoes in my closet form a mathematical set, and it is not obvious that they do, then that set is a one-over-many: it is one single item despite its having six distinct members each of which is distinct from the set, and all of which, taken collectively, are distinct from the set.   A set with two or more members is not identical to one of its members, or to each of its members, or to its members taken together, and so the set  is distinct from its members taken together, though not wholly distinct from them: it is after all composed of them and its very identity and existence depends on them.

In the above quotation, Black is suggesting that mathematical sets are contradictory entities: they are both one and many.  A set is one in that it is a single item 'over and above' its members or elements as I have just explained.  It is many in that it is "wholly constituted" by its members. (We leave out of consideration the null set and singleton sets which present problems of their own.)  The sense in which sets are "wholly constituted" by their members can be explained in terms of the Axiom of Extensionality: two sets are numerically the same iff they have the same members and numerically different otherwise. Obviously, nothing can be both one and many at the same time and in the same respect.  So it seems there is a genuine puzzle here.  How remove it?  See here for more.

3. The problem of the unity of the sentence/proposition. 

The problem is to provide a satisfying answer to the following question: In virtue of what do some strings of words attract a truth-value? A truth-valued declarative sentence is more than a list of its constituent words, and (obviously) more than each item on the list. A list of words is neither true nor false. But an assertively uttered declarative sentence is either true or false.   For example,

Tom is tired

when assertively uttered or otherwise appropriately tokened is either true or false. But the list 

Tom, is, tired

is not either true or false. And yet we have the same words in the sentence and in the list in the same order. There is more to the sentence than its words whether these are taken distributively or collectively.  How shall we account for this 'more'?  

There is more to the sentence than the three words of which it is composed.  The sentence is a truth-bearer, but the words are not whether taken singly or collectively. On the other hand, the sentence is not a fourth thing over and above the three words of which it is composed. A contradiction is nigh:  The sentence is and is not the three words.

Some will say that the sentence is true or false in virtue of expressing a proposition that is true or false. On this account, the primary truth-bearer is not the (tokened) sentence, but the proposition it expresses.  Accordingly, the sentence is truth-valued because the proposition is truth-valued.  

But a similar problem arise with the proposition. It too is a complex, not of words, but of senses (on a roughly Fregean theory of propositions). If there is a problem about the unity of a sentence, then there will also be a problem about the unity of the proposition the sentence expresses on a given occasion of its use. What makes a proposition a truth-valued entity as opposed to a mere collection (set, mereological sum, whatever) of its constituents?

4) The problem of the unity of consciousness.

At Theaetetus 184 c,  Socrates puts the following question to Theaetetus: ". . . which is more correct — to say that we see or hear with the eyes and with the ears, or through the eyes and through the ears?" Theatetus obligingly responds with through rather than with. Socrates approves of this response:

Yes, my boy, for no one can suppose that in each of us, as in a sort of Trojan horse, there are perched a number of unconnected senses which do not all meet in some one nature, the mind, or whatever we please to call it, of which they are the instruments, and with which through them we perceive the objects of sense. (Emphasis added, tr. Benjamin Jowett)

The issue here is the unity of consciousness in the synthesis of a manifold of sensory data. Long before Kant, and long before Leibniz, the great Plato was well aware of the problem of the unity of consciousness. (It is not for nothing that Alfred North Whitehead described Western philosophy as a series of footnotes to Plato.)

Sitting before a fire, I see the flames, feel the heat, smell the smoke, and hear the crackling of the logs. The sensory data are unified in one consciousness of (genitivus objectivus) a self-same object. This unification does not take place in the eyes or in the ears or in the nostrils or in any other sense organ, and to say that it takes place in the brain is not a good answer. For the brain is a partite physical thing extended in space. If the unity of consciousness is identified with a portion of the brain, then the unity is destroyed. For no matter how small the portion of the brain, it has proper parts external to each other. Every portion of the brain, no matter how small, is a complex entity. But consciousness in the synthesis of a manifold is not just any old kind of unity -- it is not the unity of a collection, even if the members of the collection are immaterial items  -- but a simple unity. Hence the unity of consciousness cannot be understood along materialist lines.  It is a spiritual unity and therefore an apt model of the divine simplicity.

Back to Van Til

He is wrong to suggest that there is only problem of the One and the Many.  The One and the Many is itself both one and many. Whether he is right that it is "the whole problem of philosophy," it is certainly at the center of philosophy. But what could he mean when he claims  that the doctrine of divine simplicity solves the problem?  It is itself one form of the problem.  The problem is one that arises for the discursive intellect, and is perhaps rendered insoluble by the same intellect, namely, the problem of rendering intelligible the unities lately surveyed.

God is the Absolute and as such must be simple.  But divine simplicity is incomprehensible to the creaturely intellect which is discursive and can only think in opposites.  What is actual is possible, however, and what is possible might be such whether or not we can understand how it is possible. So the best I can do in trying to understand what Van Til is saying is as follows. He 'simply' assumes that the God of the Bible is simple and does not trouble himself with the question of how it is possible that he be simple.  Given this assumption,  there is no problem in reality of as to how God can be both one and many.  And if there is no problem in the supreme case of the One and the Many, then there are no problems in any of the lesser cases.

Two Senses of 'Presupposition' in Van Til and in General

Cornelius Van Til, The Defense of the Faith, 4th ed., p. 279: "Thus the truth of Christianity appears to be the immediately indispensable presupposition of the fruitful study of nature." My gloss:

The fruitful study of nature presupposes the truth of Christianity.  It is a fact that we study nature, and it is a fact that our natural-scientific procedures are successful in many ways and in many areas of inquiry.  Now what is factual is actual, and what is actual is possible. But how is it possible? What are the conditions of the possibility of our successful understanding of nature and (some of) her laws? We are being told by Van Til that an indispensable and thus necessary condition is the truth of Christianity.

This illustrates one legitimate use of  'presupposition.' Presupposition in this sense relates an activity or procedure to a proposition.  To say that activity A presupposes proposition p is to say that A could not be undertaken with the hope of success  were p not true. 

For example, the procedures of natural science presuppose the intelligibility of nature.  We would not seek the laws of planetary motion, for example, if we did not antecedently believe that the motion of the planets was regular and law-like and understandable by us. But IS nature intrinsically intelligible, intelligible an sich? We have  good reason to think so given the success of our physics as shown by its technological implementation.

The presupposition of the intelligibility of nature is therefore well-grounded .

We can push our transcendental regress a step further by asking: what does the intelligibility of nature itself presuppose? What are the conditions of the possibility of nature's being understandable by us?  What would have to be the case for nature to be intelligible to us?  Here are some candidate answers:

A. The intelligibility of nature presupposes the truth of Christianity. (Van Til)

B. The intelligibility of nature presupposes the existence of God. (It is only because a supreme Intelligence created the world that it is intelligible.)

C. The intelligibility of nature presupposes the truth of Kant's transcendental idealism according to which "The understanding is the law-giver of nature." 

D. The intelligibility of nature presupposes an immanent order and teleology along the lines of Thomas Nagel's Mind and Cosmos. On Nagel's view, the rational order is self-explanatory, a necessary feature of anything that could count as a cosmos. Nagel views the intelligibility of the world as "itself part of the deepest explanation why things are as they are." (17).  Now part of the way things are is that they are understandable by us.  Given that the way things are is intelligible, it follows that the intelligibility of the world is self-explanatory or self-grounding. "The intelligibility of the world is no accident." (17)   "nature is such as to give rise to conscious beings with minds; and it is such as to be comprehensible to such beings." (17) See my Nagel category for much more on Nagel's book and other works of his.

I myself incline toward (B).  (A) entails (B), but I see no reason to accept (A).  The sort of bottom-up reasoning that can plausibly justify us in positing God cannot plausibly justify us in positing the God of orthodox Christian theism with all the Reformed add-ons.

The other sense of 'presuppose' is in play here: "I therefore presuppose the Reformed system of doctrine." (Van Til, p. 27) A presupposition in this sense is an assumption that is accepted unconditionally, uncritically, without question. 

Bottom-Up and Top-Down

The first sense of presupposition fits with a bottom-up approach. We start with various features of the world we experience and we then ask what makes them possible.  We attempt  a regress from the given to the hidden. We start with the world, not with God, and we aim to arrive at God.  But if we arrive at God in this way, then the properties we will be justified in attributing to God will  only be those needed for our explanatory purposes.   Those properties are in a certain sense tied to our starting points.  For example, one might reason along these lines: the universe is contingent, but its existence is not a brute fact; so it must have a cause external to it.  In this way we get to God as First Cause.  Or we start from the intelligibility of nature and arrive at God as the supremely intelligent source of the intelligibility we find here below.  Supposing we can get to the true God in this way, a God that needn't have caused anything, or sourced the intelligibility of anything distinct from himself,  it nonetheless remains the case that the properties of this God will reflect the facts we start with and our need to explain them. 

The second sense of presupposition fits with a top-down approach.  We start with God, or at least we try to start with God, and then, instead of regressing from the given to the hidden conditions of the possibility of the given, we progress from the hidden to the given.  This is possible if the God who is hidden to the natural man with his natural intellect has revealed himself.   I understand Van Til to be saying that we know the true God, the God of Abraham, Isaac, and Jacob only because he has revealed himself to us.  The revelation that Van Till accepts is the final truth, not only about God, but also about man, and the universe.  Since it the revelation of God, it cannot be questioned.   We can say that for Van Til, God and his revelation understood along Reformed lines constitute the Absolute Presupposition.

Interim Conclusion

Van Til's bottom-up  transcendental argumentation appears to be a sham. Despite appearances, he is not trying to justify belief in the God of orthodox Christian theism by argumentation from given facts (the existence of nature, its order, beauty, and intelligibility) to that which must be presupposed if they are to be so much as possible; he is not trying to justify belief in the Christian God at all.  For he just assumes the existence of the Christian God as something that needs no justification and cannot be questioned since it is that without which there would be no questioning or proving or anything else.

With that absolute presupposition in place as his unquestionable starting point, he can then advance, but not justify, claims like (A) above: 

A. The intelligibility of nature presupposes the truth of Christianity.

What Van Til is doing in effect is simply presupposing the truth of (A)! What he ought to be doing, however, is giving us a reason to accept (A). It comes as no surprise, then, that Van Til claims that all reasoning is circular reasoning. (123) We will have to examine that claim and Oliphint's defense of it in a separate post.

Van Til just assumes the truth of his worldview and then in effect says: See! I can explain everything, including why there is no neutral ground for the assessment of worldviews, and why people who reject the particulars of my worldview reject them.  But this is of no help to someone who sees no reason to accept his worldview  in the first place.

Suppose I grant that that sin has noetic consequences. I grant the thesis.  But that leaves open the question as what exactly the noetic consequences are. Is it a noetic consequence of sin that I do not accept Van Til's worldview?  Or is rather a noetic consequence of sin that Van Til denies that there is a neutral ground for the assessment of worldviews?

Fascinating! More later. And thanks again to Dave Bagwill for inspiring me to get going on this.

Van Til on an Absolutely Certain Proof of Christianity

Cornelius Van Til, The Defense of the Faith, 4th ed., p. 381:

The best, the only, the absolutely certain proof of the truth of Christianity is that unless its truth be presupposed,there is no proof of anything.

Van Til's  claim, to employ some Kantian jargon, is that the truth of Christianity is a condition of the possibility of proving anything. That's quite a claim. Let's put it to the test.

One can prove that the null set is unique by reductio ad absurdum. We begin the reductio by assuming that the null set is not unique, that there are two or more null sets. By the Axiom of Extensionality, two sets differ numerically only if one has a member the other doesn't have, or vice versa. But the null set, by definition, has no members. So the assumption leads to a contradiction. Therefore there cannot be two or more null sets. Hence the null set is unique. 

The proof presupposes the Law of Non-Contradiction (LNC), and I am willing to grant that LNC and the other laws of logic can be argued to presuppose in their turn the existence of an omniscient necessary being. One argument to this conclusion is the Anderson-Welty argument which I critically examine here. I conclude that, while the argument is not rationally compelling, it does contribute to the rationality of belief in God.  In other words, the Anderson-Welty argument is a good reason to believe in the existence of God. It does not, however, establish the existence of God in a definitive manner. It does not show that the existence of God is absolutely certain.

At the very most, then, one can plausibly argue to, but not prove, the existence of an omniscient necessary being whose existence is a presupposition of our rational operations in accordance with the laws of logic.  But this is a far cry from what Van Til asserts above, namely, that the truth of Christianity with all its very specific claims is a condition of the possibility of proving anything. Trinity and Incarnation are among these specific claims. How are these doctrines supposed to bear upon the laws of logic?  Perhaps the Van Tilians have an answer to this. If they do, I would like to know what it is. But not only is Van Til's conception of God Christian, it is also Calvinist so that all the characteristic claims of Calvinism are also packed into the conception of a God that is supposed to be a condition of the possibility of all  proof.  How does predestination, for example, bear upon the laws of logic?

God, the Cosmos, Other Minds: In the Same Epistemological Boat?

Tony Flood has gone though many changes in his long search for truth. He seems to have finally settled down in Van Til's presuppositionalism.  Tony  writes,

God, the cosmos, and a plurality of minds other than one’s own are in the same epistemological boat. [. . .] To be skeptical about one but not the other two is arbitrary. Our innate predisposition to be realistic about all three is divinely written “software” that informs our cerebral “wetware.”

I wish I could accept this, but I don't, and I believe I have good reasons for my non-acceptance.

By "in the same epistemological boat," Flood means that God, the physical universe, and other minds are all on a par in respect of dubitability. No one of them is more open to reasonable doubt than the other two, and none of them is open to reasonable doubt. Therefore, one can no more reasonably doubt the existence of God than one can doubt the existence of other minds.  Atheism is on a par with solipsism in point of plausibility.

And bear in mind that by 'God' here is meant something very specific, the triune God of Christian theism, the God of the Bible as understood by Van Til and Co.  It is one thing to argue -- and it can be done with some plausibility -- that the validity of all reasoning about any subject presupposes the existence of an omniscient necessary being. It is quite another to argue that the presuppositum must be the God of Christian theism as the latter is expounded by a Calvinist!

Now I concede that doubts about the external world and the the reality of other minds are hyperbolic, and if taken as genuine doubts, as opposed to thought experiments deployed in an epistemology seminar, unreasonable. No one really doubts the existence of rocks or other minds.  Not even Bishop Berkeley doubts, let alone denies, the existence of rocks, the tree in the quad, and suchlike.  This is why it is perfectly lame to think that Berkeley's idealism can be refuted by kicking a stone. (See Of Berkeley's Stones and the Eliminativist's Beliefs and Argumentum ad Lapidem?)

The hyperbolic skepticism of Descartes' dream argument and its latter-day brain-in-the-vat incarnations are methodological tools of the epistemologist who seeks to understand how we know what we know, and what it is to know what we know.   A philosopher who wonders how knowledge is possible may, but need not, and typically does not, deny or have any real doubt THAT knowledge is possible. For example, I may be firmly convinced of the existence of so-called abstract objects (numbers, sets, propositions, uninstantiated properties, etc.) but be puzzled about how knowledge of such entities is possible given that there is no causal interaction with them.  That puzzlement does not get  the length of doubt or denial. The same holds, mutatis mutandis, for knowledge of the past, knowledge of other minds, and knowledge of the external world.

My point, then, is that (i) practically no one has real doubts about the existence of the external world or the existence of other minds, and that (ii) it would not be reasonable to have such doubts.  But (iii) people do have real doubts about the existence of the God of Christian theism, and (iv) it is not unreasonable to have such doubts.  The various arguments from evil, and not just these, cast reasonable doubt on Christian theism.

One type of real doubt is an 'existential' doubt, one that grips a person who succumbs to it, and induces fear and perhaps horror.  There are those who lose their faith in God and suffer in consequence.  They experience a terrible sense of loss, or perhaps they fear that they have been duped by crafty priests who exploited their youthful innocence and gullibility to infect them with superstitious nonsense in order to keep the priestly hustle going.  One can lose one's faith in God, and many do.  No one loses his faith in the external world or in other minds. And this for the simple reason that there was no need for faith in the first place.

I believe I have said enough to cast serious doubt on, if not refute, the idea that God, the the cosmos, and other minds are are in the same epistemological boat. That's a boat that won't float.

Van Til and Romans 1:18-20

I tip my hat to David Bagwill for recommending that I read Cornelius Van Til. So I sprang for the fourth edition of The Defense of the Faith, with Oliphint's annotations, P & R Publishing, 2008. Van Til's presuppositionalism is intriguing even if in places preposterous. Having discussed Romans 1:18 a couple of time before in these pages, I looked to see what Van Til had to say about it. But first my take, one that Van Til & Co. might dismiss as 'Romanist' or worse.

Rather than quote the whole of the Pauline passage at Romans 1: 18-20, I'll summarize it. Men are godless and wicked and suppress the truth. What may be known about God is plain to them because God has made it plain to them. Human beings have no excuse for their unbelief. "For since the creation of the world, God's invisible qualities -- his eternal power and divine nature -- have been clearly seen, being understood from what has been made . . . ."

Paul's claim here is that the existence and nature of God are evident from creation and that unbelief is a result of a willful turning away from the truth.   There is no excuse for unbelief because it is a plain fact that the natural world is divine handiwork.  Now I am a theist and I am sympathetic to Christianity. But although I have one foot in Jerusalem, the other is  planted firmly in Athens. It therefore strikes me that to characterize the natural world as 'made' or 'created' begs the question in favor of theism. As begging the question, the Pauline claim about the evidentness of the world's being created offers no support for theism.  It is an analytic proposition that there is no creation without a creator. So if the heavens and the earth are a creation, then it follows straightaway that a creator exists.

But is the world a divine creation? This is the question, and the answer is not obvious. That the natural world is a divine artifact is not evident to the senses, or to the heart, or to reason. Of course, one can argue for the existence of God from the existence and order of the natural world. I have done it myself. But those who reject theistic arguments, and construct anti-theistic arguments, have their reasons too, and it cannot fairly be said that what animates the best of them is a stubborn and prideful refusal to submit to a truth that is evident.  It is simply not objectively evident to the senses or the intellect or the heart that the natural world is a divine artifact. If it were objectively evident, then there would be no explanation of the existence of so many intellectually penetrating, morally upright, and sincere atheists.  Even if the atheisms of Nietzsche, Russell, Sartre, and Hitchens could be dismissed as originating  in pride, stubborness, and a willful refusal to recognize any power or authority beyond oneself, or beyond the human, as may well be the case with the foregoing luminaries, it does not follow that the atheism of all has this origin.

I am moved to marvel at "the starry skies above me."  This was one of two things that filled Kant with wonder, the other being "the moral law within me."  But  seeing as is not seeing.  If you see the starry skies as divine handiwork, then this is an interpretation from within a theistic framework.  But the datum seen can just as easily be given a non-theistic interpretation.

It is all-too-human to suspect in our opponents moral depravity when we cannot convince them. The Pauline passage smacks of that all-too-humanity. There are sincere and decent atheists, and they have plenty of excuse for their unbelief.  The fact of evil being perhaps the best excuse. The best of them, if wrong in the end, are excusably wrong.

Or so I tend to think. But I am open to a change of view and a change of heart (metanoia).

I suppose I will be told that I am falsely assuming that there are some neutral data that we can access via reason unaided by revelation, data that will supply premises for arguments to the existence of God, arguments that would constitute a philosophically neutral, theologically uncommitted preambulum fidei in Thomas's sense, when such a neutral method can only in the end issue in the conclusion that Christian theism is not true. The correct method, I will be told, is to start with and adhere to the presupposition that Christianity is true, lock, stock, and barrel, and to see everything in its light:

Roman Catholics and Arminians, appealing to the 'reason' of the natural man as the natural man himself interprets his reason, namely as autonomous, are bound to use the direct method of approach to the natural man, the method that assumes the essential correctness of a non-Christian and nontheistic conception of reality. The Reformed apologist, on the other hand, appealing to that knowledge of the true God in the natural man which the natural man suppresses by means of his assumption of ultimacy, will also appeal to the knowledge of the true method which the natural man knows but suppresses. The natural man at bottom knows that he is the creature of God. He knows also that he is responsible to God. He knows that  he should live to the glory of God. He knows that in all that he does he should stress that the field of reality which he investigates has the stamp of God's ownership upon it. But he suppresses his knowledge of himself as he truly is. (123-124)

At this point in the text comes a footnote referencing Romans 1: 18 ff.

Above I suggested that Paul begs the question. Now to beg a question is to assume what one needs to prove.  But there is no need to prove what one presupposes.  So one who presupposes the truth of Christian theism cannot be accused of begging the question. There just is no question that can be neutrally engaged by the reason of the natural man if the truth of Christian theism is presupposed.

The ultimate principle of all proof is the Law of Non-Contradiction. It therefore cannot be proved, but only presupposed.  One who affirms it cannot therefore be reasonably accused of begging the question: there simply is no question here that can reasonably be disputed.

But this leaves unanswered the question why we ought to presuppose the truth of Christian theism. For the latter, with all of its very specific claims about Trinity, Incarnation, etc. is rather unlike the logical law just mentioned -- to put it in the form of an understatement.  Why not presuppose atheism as many today do? They too can and do make claims about what we 'know' and what we 'suppress.'  We all know deep down that we are nothing but clever land mammals slated for extinction, with no higher origin or higher destiny, but we suppress this ugly truth because we are unwilling to face the dreadful facts.

If a gratuitous assertion can be met with a gratuitous counter assertion, the same goes for a gratuitous presupposition.

More later.