Substack latest.
Do not comment unless you have carefully read the entire article.
Substack latest.
Do not comment unless you have carefully read the entire article.
A tip of the hat to Tony Flood for supplying me with the following important documents:
Bernard Lonergan, Religion: The Answer is the Question
R. C. Sproul and Greg Bahnsen Debate (full transcript)
I had asked Tony whether he had a copy of Lonergan's Method in Theology he was willing to part with. Here is his reply:
I don't think you asked, Bill, but the answer is yes. Since, however, he signed it when I visited him at a Jesuit infirmary in 1983 (you might enjoy my account of that meeting here), it is priceless. (You are free to test that claim. (:^D)) Should I sense that the end is near, I'll donate it to the Lonergan Institute as I did so much Lonergania a couple of years ago. The April 20, 1970 issue of Time covered what he was up to in theology; here's a link to the text. It will help contextualize him. (I know where I was that month.)
Trudy the Calvinist gave me a reading assignment. Herewith a first batch of comments for her and your delectation, discussion, and (presumably inevitable) disagreement.
In Chapter One, "The Case for God," Sproul distinguishes between four approaches in apologetics: fideism, evidentialism, presuppositionalism, and "the classical school" (4) He comes out against the first three and nails his colors to the mast of the fourth.
Fideists maintain that there are no rationally compelling arguments for the existence of God, and that we must therefore rely on faith alone. Sproul mentions Tertullian who opposed Athens (philosophy) to Jerusalem (Abrahamic religion) and famously asked what the latter has to do with the former. He held that Christianity is objectively absurd in the sense of logically contradictory, and that this absurdity was a sort of 'reason' to accept it: credo quia absurdum (I believe because it is absurd.)* Sproul rejects this extreme view on the ground that it amounts to "a serious slander against the character of God and the Holy Spirit, who is the Spirit of truth." (2) Sproul's point is solid. There cannot be self-contradictory truths. If so, how could the Source of all truth, the Spirit of truth, be self-contradictory?
Evidentialists defend the faith through appeals to biblical history. I am put in mind of what S. Kierkegaard calls "the infinite approximation process" (See Concluding Unscientific Postscript) a process which never arrives at a fixed and final result. According to Sproul, the most the evidentialist can attain is "a high degree of probability." (2) The probability is high enough, however, to prove the existence of God "beyond a reasonable doubt." Indeed, he thinks the probability sufficient to block every "moral escape hatch," except one: "You didn't prove it beyond the shadow of a doubt," i.e., the case has not been conclusively made. This is not good enough for Sproul: he thinks the case for the very specific God of the Christian Bible (presumably with all the Calvinist add-ons) must prove this God beyond even the shadow of a doubt.
Moreover, Sproul holds that one can establish the existence of the God in question beyond the shadow of a doubt. which is to say, in a rationally coercive, philosophically dispositive, entirely ineluctable, 'knock-down' way. Apologists of the classical school believe that the case for God can be made "conclusive and compelling." "It is actual proof that leaves people without any excuses whatsoever." (4) Sproul hereby alludes to Romans 1, as becomes clear at the end of the chapter. No excuses, no escape hatches. You are morally at fault for refusing to accept the God of the Christian Bible!
Presuppositionalists, led by Cornelius van Til, hold that the existence of the God of the Christian Bible can be conclusively established, but to do so, "one must start with the primary premise of the existence of God." (4) One can inescapably conclude that God exists only by presupposing his existence. Sproul's objection is the standard one levelled against the apologetics of the 'presuppers,' namely, that presuppositionalism enshrines (my word) the informal fallacy of petitio principii, or hysteron proteron if you prefer Greek. In plain English the fallacy is that of circular reasoning. To put it in my own way: every argument of the form p; therefore p is formally valid in that it is logically impossible for the premise to be true and the conclusion false. But no argument of this form could give anyone a reason to accept the conclusion. Circular arguments, though valid in point of logical form, are probatively worthless. Sproul goes on to tax Van Til & Co. with the fallacy of equivocation, but Sproul's discussion is rather less than pellucid, so I won't say any more about it; in any case, I agree with him that presuppositionalism is an apologetic non-starter, as I have argued over many an entry. (See my Van Til and Presuppositionalism category.)
Classical apologists such as Sproul and presuppositionalists both assert that without God there is and can be no rationality. The difference is that classicists insist that the existence of God cannot be merely presupposed, but must be proven in a non-circular or "linear" (Sproul) way. They also insist that it can be proven conclusively, and thus in such a way as to render the existence of God objectively certain. As I read Sproul, he is telling us that we can know with objective certainty, and thus without the possibility of mistake, that the God of the Christian Bible exists. In the later chapters of his book he lays out the proof.
Critique
So much for exposition. Where do I stand? I reject all four positions, as above formulated. My current position, tentatively and critically held, is however closer to fideism than to the other three. Call it moderate fideism to distinguish it from the Tertullianic and Kierkegaardian extremes. It is moderately fideistic in that it rejects the anti-fideism of the presuppositionalists and that of the classicists.
Readers of this weblog know that I have maintained time and again that one can both reasonably affirm and reasonably deny the existence of God. That is to say: there are no rationally coercive arguments either way. Nothing counts as a proof sensu stricto unless it is rationally coercive. So there are no proofs either way. An argument can be good without being rationally coercive, and there are good arguments on both sides. There are also bad arguments on both sides. The quinque viae of the doctor angelicus are good arguments for the existence of God, but in my view not rationally compelling, coercive, dispositive, ineluctable — pick your favorite word. They don't settle the matter, once and for all. But the same holds for some of the atheist arguments, some of the arguments from evil, for example. Galen Strawson is the polar opposite of Sproul on the God question. So to savor (bemoan?) the extremity of the worldview polarization, take a look at my critique of Strawson at Substack.
So am I taking the side of Tertullian and Kierkegaard? No way. They go to the opposite extreme to that of Sproul (although he is not as extreme as the 'presuppers'). I am a fair and balanced kind of guy.
I say that the belief that God exists is a matter of faith. Faith is not knowledge, but it is not entirely opposed to it either, as it is for Tertullian and Kierkegaard who hold that belief in the God of the Christian Bible, God Incarnate, is logically absurd, and yet is to be maintained, for S. K. anyway, by infinite subjective passion. On the contrary, I say that one ought not believe anything that is demonstrably absurd (logically contradictory), and that to do so is a plain violation of the ethics of belief. (If you subscribe to an ethics of belief, then you must also be a limited doxastic voluntarist, and I am.) Faith does not and cannot contradict reason; it supplements it. Faith is on the way to knowledge and seeks its fulfillment in it. Faith is inferior to knowledge as a route to reality, as Aquinas would agree. Faith extends our grasp of reality — our contact with it — beyond what we can know, strictly speaking, except that there are and can be no internal assurances of veridicality here below: the verification, if it comes at all, will come after we have quit these bodies.
Faith is neither blind nor seeing. It is neither irrational nor rational, but suprarational. It goes beyond reason without going against reason. 1 Corinthians 13:12 may provide a clue: "For now we see through a glass, darkly; but then face to face: now I know in part; but then shall I know even as also I am known." (KJV) Paul is suggesting that we see all right; we are not blind. But the seeing is obscure at present and will culminate in luminosity. Cognitio fidei is not cognition strictly speaking, but it is not blind either. We could liken it to a dim and troubled sighting in the fog. Pace Kierkegaard, not a desperate leap, but a hopeful reaching out beyond the bounds of the certain.
Sproul thinks he can prove the existence of God by reason alone. In my next installment I will show that he fails in this endeavor.
_______________
*Nietzsche quipped that Tertullian should have said credo quia absurdus sum, "I believe because I am absurd."
I say Yes to the title question; Greg Bahnsen, glossing Cornelius Van Til, says No.
Yet it should be clear even to the atheist that if the Christian God exists, it is 'reasonable' to believe in him. (Greg L. Bahnsen, Van Til's Apologetic: Readings and Analysis, P & R Publishing, 1998, p. 124, fn. 108, emphasis added.)
This is the exact opposite of clear. Atheists believe that there in no God, and thus that the Christian God does not exist, and the philosophically sophisticated among them have argued against the reasonableness of believing that the Christian God exists using both 'logical' and 'probabilistic' arguments. So how could it be clear even to the atheist that if the Christian God exists, it is reasonable to believe that God exists? Bahnsen's claim makes no sense. It makes no sense to say to an atheist who sincerely thinks that he has either proven, or rendered probable, the nonexistence of God that it is nonetheless reasonable for him to believe that God exists even if in fact, and unbeknownst to the atheist, God does exist.
Bahnsen is missing something very important: although truth is absolute, reasonableness is relative. This is why an atheist can find it unreasonable to believe that the Christian God exists even if it is true that the Christian God exists. Let me explain.
I do not need to spend many words on the absoluteness of truth. I've made the case numerous times. Here for example. In any case, whatever presuppositionalists such as Bahnsen think of the details of my arguments, they will agree with my conclusion that truth is absolute. So that is no bone of contention between us.
Reasonableness or rational acceptability is something else again. It is not absolute but can vary from person to person, generation to generation, social class to social class, historical epoch to historical epoch, and in other ways. Let's quickly run through a few familiar examples.
1) Falling bodies. It 'stands to reason' that the heavier an object the faster it falls if dropped from a height. It's 'logical' using this word the way many ordinary folk often do. Wasn't Aristotle, who maintained as much in his Physics, a reasonable man? But we now know that the rate of free fall (in a vacuum) is the same in a given gravitational field regardless of the weight of the object in that field. So what was reasonable to Aristotle and his entire epoch was not reasonable to Galileo and later epochs. Rational acceptability is relative.
2) For the ancients, water was an element. For John Dalton (English chemist, early 19th cent.) it was a compound, HO. For us it is H2O. Has water changed over the centuries? No. Truth is non-relative. What it is reasonable to believe has changed. Rational acceptability is relative.
3) Additivity of velocities. It 'stands to reason' that if I am on a train moving in a straight line with velocity v1 and I throw a ball in the direction of the train's travel with velocity v2, then the velocity of the ball will be v1 + v2. It also 'stands to reason' that this holds across the board no matter the speed of the objects in question. But this belief, although reasonable pre-Einstein, is not reasonable post-Einstein. Once again we see that rational acceptability is relative.
4) Sets and their members. Suppose S is a set and T is one of S's proper subsets. Then every member of T is a member of S, but not every member of S is a member of T. Now suppose someone comes along and asserts that there are sets such that one is a proper subset of another and yet both have the same number of members. Many if not most people would find this assertion a highly unreasonable thing to say. They might exclaim that it makes no bloody sense at all. And yet those of us who have read Georg Cantor find it reasonable to maintain. If N is the set of natural numbers, and E is the set of even numbers, and O is the set of odd numbers, then E and O are disjoint (have no members in common), and yet each is a proper subset of N which the same cardinality (number of members) as N.
5) When I was a very young boy I thought that, since I am right-handed, my right hand and arm had to be weaker than my left hand and arm because I use my right hand and arm more. Was that reasonable for me to believe way back then? Yes! I had a reason to hold the empirically false belief. Of course, my little-boy reasoning was based on a false analogy. If you flex a piece of metal back and forth you weaken it. If you a flex a muscle back and forth you strengthen it. Use it and use it up? No, use it or lose it!
Examples are easily multiplied beyond all necessity. The point, I trust, is clear: while truth is absolute, rational acceptability is relative. What is true may or may not be reasonable, and what is reasonable may or not be true.
What Bahnsen and the boys appear to be assuming is that both truth and reasonableness (rational acceptability) are absolute. Well they are — but only for God, only from God's point of view. God is the IRS, the ideally rational subject. He knows every truth and he knows every truth without possibility of mistake. So for God every truth, being a known truth, is in accordance with divine reason, and everything in accordance with divine reason is true. But we do not occupy the divine point of view. To put it sarcastically, only a 'presupper' does.
But of course neither we nor the presuppositionalists occupy the divine point of view. They only think they do. But that conceit is the whole essence of presuppositionalism, is it not?
Full disclosure: I am not a theologian. I am a philosopher of religion who, as part of his task, thinks about theologoumena which, on a broad interpretation of the term, are simply things said about God, a term which therefore includes not only official, dogmatic pronunciamenti of, say, the RCC's magisterium, but also includes conjectures, speculations, and opinions about God that are not officially promulgated.
………………………..
Anthony Flood writes,
The Christian worldview, expressed on the pages of the Bible, is a revelatory “package deal,” if you will, not a buffet of optional metaphysical theses. The organic connectedness (within the divine decree) of creation, trinity, and incarnation—even the so-called “contingencies of history,” e.g., Joshua’s impaling the King of Ai on a pole after slaughtering all of his subjects (Joshua 8)—await clarification in God’s good time, if He sees fit to provide it, but are put before us for our assent today.
Flood is a presuppositionalist who believes that "intelligible predication" presupposes the truth of the Christian worldview. Thus, "The Christian does not avail himself of his birthright (Christian theistic) worldview because it confers omniscience on him, but rather because (a) it saves intelligible predication and (b) no competing worldview does."
We are being told that the Christian worldview, as Flood understands it, offers the best and indeed the only explanation of the fact of intelligible predication. That intelligible predication is indeed a fact I do not question. But I do have some questions about Flood's explanation of the fact. One of them concerns what he includes in his explanation. It is clear that he includes more than the existence of God where 'God' refers to a purely spiritual being, of a personal nature, endowed with the standard omni-attributes, who exists of metaphysical necessity, and who created out of nothing everything distinct from himself, or at least everything concrete distinct from himself. One reason for this 'more' is because Flood's God is not just personal, but tri-personal: one God in three divine persons. This is not intended as tri-theism, of course, but as monotheism: one God in three divine persons.
Furthermore, in the Christian worldview as Flood understands it, the second person of the Trinity, variously known as the Logos, the Word, God the Son, became man in a particular man, Jesus of Nazareth, at a particular time in a particular place. One and the same person, the Son, without ceasing to be fully divine, became fully human, with a human body and a human soul, by being born of a virgin named 'Mary' in a stable in Bethlehem. So it seems that the 'package deal' must include, in addition to Trinity and Incarnation, some version of Mariology. Why must it? Because Jesus Christ, the God-Man, had to have gotten his human nature from somewhere. He inherited his human nature from his human mother.
Let's think about this. God the Son is not a creature. Is Jesus a creature? His earthly mother is a creature. Jesus had no heavenly mother, at least not until the Assumption of Mary, body and soul, into heaven. But that was long after the Incarnation event; I won't say anything more about the Assumption here. And Jesus had no earthly father. Joseph was his step-father, and a step-father is not a father in the earthly or biological sense of the term. The father of Jesus is a purely spiritual being. So Jesus Christ, the God-Man, at the moment of Incarnation, has a heavenly father but no earthly father, and an earthly mother but no heavenly mother.
Mary became pregnant. What was the nature of the inseminating seed? It had to be purely spiritual. Why? Because it came from God who is purely spiritual. What about the inseminated egg? It had to be physical. Why? Because it was the ovum of an earthly woman. It was a miraculous pregnancy by supernatural agency.
Now the God-Man had to be free of original sin to be able to do his redemptive work and restore right relations between man and God. So he could not have 'contracted' original sin from his earthly mother. Hence the logic of the soteriological narrative required that Mary be conceived without original sin. Hence the doctrine of the Immaculate Conception.
It therefore seems that Mariology must be part of Flood's 'package deal,' and indeed a Mariology that includes Immaculate Conception. So my first question to Flood is this:
Do you hold that the only possible explanation of intelligible predication must be in terms of a Christian worldview that includes not only Trinity and Incarnation but also Immaculate Conception?
This is not a rhetorical question. It is a genuine question raised so that I might understand what exactly Flood's position is. Tony is making a mistake if he thinks I am being polemical here. I am not. I honestly find presuppositionalism puzzling and I am trying to understand it.
My second question to Flood which I cannot develop and defend in this installment is this:
Given the well-known logical conundra that arise when we try to render intelligible to ourselves such doctrines as Trinity and Incarnation, conundra that seem to threaten the intelligibility of these doctrines, and therefore seem to threaten the intelligibility of any explanation of intelligible predication in terms of a worldview committed to them, how do you respond? Do you maintain that the supposed logical puzzles are easily solved and that Trinity and Incarnation in their orthodox formulations are logically and epistemically unobjectionable? If that is not the tack you take, what tack do you take?
On Romans 1: 18-20.
Substack latest.
Gordon Clark in Religion, Reason, and Revelation ( The Trinity Foundation, 1986, pp. 37-38) discusses and agrees with Karl Barth (Church Dogmatics II, 1, pp. 79 ff.). The following is my distillation of the Barthian argument to which Clark assents. Barth is attacking the Roman Catholic viewpoint as expressed at the Vatican Council of 24 April 1870.
1) The Christian God is triune.
2) The rationally demonstrable God is not triune.
Therefore
3) The Christian God is not the rationally demonstrable God.
Therefore
4) The Christian God is not the God of the philosophers.
Therefore
5) We cannot know God from nature, 'cosmologically,' by natural reason. (Natural theology is a non-starter.)
Therefore
6) We can know God only through God.
It is perhaps obvious why the presuppositionalist Clark would like this argument. Clark strikes me as the best theologian among the presuppositionalists. The book cited is extremely rich in provocative ideas.
Cornelius Van Til, The Defense of the Faith, 4th ed., P&R Publishing, 2008, p. 294: "To doubt God is to deny him."
I take that to mean that to doubt that God exists is to deny that God exists. The obvious objection to this is that doubt and denial are very different propositional attitudes. In most cases, one can doubt that p without denying that p. I can doubt that Biden will get a second term without denying that he will.
In almost all cases. But in every case? Suppose we replace 'p' with 'truth exists.' Can we doubt that truth exists without denying that truth exists. No! In the case of truth, the distinction between doubt and denial collapses.
To doubt that truth exists is to presuppose that truth exists. For if you doubt that truth exists, you are doubting whether it is true that truth exists. The same goes for denial. If you deny that truth exists, you affirm that it is true that truth does not exist.
Whether you doubt or deny that truth exists, you presuppose that truth exists. Truth is such that doubt and denial are the same. Truth cannot be doubted and it cannot be denied. The existence of truth is the ultimate transcendental condition of all our intellectual operations, doubt, denial, affirmation, predication, reasoning, and so on. So we may say:
To doubt truth is to deny her.
Of course, it remains that case that doubt and denial are different propositional attitudes. But in the case of truth, doubt becomes denial.
Therefore, if God is identical to truth, then Van Til is right: "To doubt God is to deny him." If God is identical to truth, then God is the ultimate transcendental condition of all our intellectual operations, including giving arguments for God's nonexistence! If so, then Van Til and his followers are not begging the question against atheists and agnostics by simply assuming what they need to prove; they are giving a noncircular transcendental argument for the existence of God.
But is God identical to truth? Is it true that God is identical to truth? These remain open questions. I grant that if God is identical to truth, then God exists as the necessary condition of all affirmation, denial, and argument, including atheistic argument. But how do we know that the antecedent of this conditional is true?
It may be that in reality apart from us, God and truth are the same. But from our point of view, the only POV available to us, God and truth are not the same. To see this, note that it is conceivable (thinkable without contradiction) that God not exist, but not conceivable that truth not exist. So it might be true that God exists and it might be true that God does not exist. The 'might' in the preceding sentence in both of its occurrences is epistemically modal. It is epistemically possible that God exist and epistemically possible that God not exist. For all we know, either could be the case. But it is epistemically necessary that truth exist: we cannot help presupposing it. Given that we know anything at all, truth must exist. So the argument could be put like this:
a) That truth exists is epistemically necessary: we cannot help presupposing that it exists.
b) That God exists is not epistemically necessary: we can conceive the nonexistence of God.
Therefore
c) God cannot be proven to exist by proving that truth exists.
Therefore
d) The Transcendental Argument for God fails as a proof.
As you may have noticed, I am none too impressed with Cornelius Van Til and his presuppositionalist followers. Intellectual honesty being one of my epistemic virtues, however, I need to be sure that I really understand what they are saying. Now James N. Anderson strikes me as the sharpest presuppositionalist among the professional philosophers. (Among the theologians, I give the palm to Gordon Clark.) So here is a list of Anderson's articles for your, and especially my, perusal.
I thank Anthony G. Flood for his The Transcendental Argument for the Existence of God Revisited: Toward a Response to Bill Vallicella. Herewith, a first installment by way of rejoinder. Convergence upon agreement is not to be expected, but clarification of differences is an attainable goal. In any case, philosophy is a joy to its true acolytes, and in dark times a great consolation as well. Now let's get to work.
Tony introduces the theme skillfully:
Preamble: if the God of the Bible, who created human beings in his image to know and love him and to know, value, and rule the rest of creation under him (hereafter, “God”), exists, then we know one way that the conditions of intelligible predication (IP) can be met. The preceding sentence includes key aspects of the Christian worldview (CW)—the Theos-anthropos-kosmos relationship—expressed on the pages of the Bible.
If no alternative explanation for IP is possible, then Biblical theism is necessarily true (which is what the CW predicts).
[. . .]
If no worldview other than the Christian (CW) can account for IP, if (as I now hold) an alternative to the CW when it comes to accounting for IP cannot even be conceived, then to hold out for an alternative, as though doing so were an expression of rational exigency (“demandingness”)—that to reserve judgment somehow accords with epistemic duty—models only dogmatic stubbornness, not tolerant liberality.
Given the actual fact of intelligible predication, which is not in dispute, and assuming, as we must, the modal axiom ab esse ad posse valet illatio, it follows that intelligible predication (IP) is possible. Necessarily, whatever is actual is possible. So we ask the transcendental question: under what conditions is IP possible? What condition or conditions would have to obtain for it to be possible that there be actual cases of intelligible predication? An example of an intelligible predication is any true or false statement, such as 'The Moon is presently uninhabited' which happens to be true, or its negation which happens to be false.
Now I agree with Flood that if the God of the Christian Bible (hereafter 'God') exists, then the condition or conditions of the possibility of IP are satisfied. The existence of God suffices for the possibility of intelligible predication. But here we need to remind ourselves of a couple or three simple points of logic.
The first is that if X is sufficient for Y, it does not follow that X is necessary for Y. So if the existence of God is not only a sufficient but also a necessary condition of IP, this will require further argumentation. The second point is that to assert a conditional is not to assert either its antecedent/protasis or its consequent/apodosis. To assert or affirm a conditional is to assert or affirm a connection between antecedent and consequent, the nature of the connection depending on the type of conditional it is, whether logical or nomological or whatever. The third point is that some conditionals are true despite having a false antecedent and a false consequent.
And although it is not self-evident, I also agree with Flood that there is and must be some condition or set of conditions that make IP possible. Let 'TC' stand for this transcendental condition or set of conditions. We agree then that the TC necessarily exists.
We seem to have found some common — dare I say 'neutral'? — ground: (a) there are actual cases of IP; (b) given that they are actual, they are possible; (c) it is legitimate to launch a regressive (transcendental) inquiry into the condition or conditions of the possibility of these actual cases; (d) there must be such a transcendental condition; (e) the existence of God suffices for the possibility of IP.
This leaves us with the question whether the God of the Christian Bible = TC. Is God's existence not only sufficient but also both necessary for the possibility of IP? Flood will answer with alacrity in the affirmative: yes, God and God alone is (numerically) identical to the ultimate transcendental condition of all intelligible predication. This of course implies that it is not possible that anything distinct from God be the TC. God necessarily exists, and is necessarily identical to the ultimate transcendental condition of intelligible predication.
But wait, there's more! Flood tells us that "an alternative to the CW [the Christian worldview] when it comes to accounting for IP cannot even be conceived." So it is not just impossible that anything other than God be identical to the TC; this is inconceivable as well.
Here is one of the places where Flood blunders: he confuses the epistemic modality inconceivability with the ontic modality impossibility. Conceivability and inconceivability are tied to the thinking powers of such finite and limited intellects as ours. By contrast, what is possible and impossible in reality are independent of what we frail reeds are able to think and unable to think. I will have more to say about this in subsequent posts since it appears to be a trademark mistake of presuppositionalists to conflate epistemic and ontic modality.
In any case, it is very easy to conceive of alternatives to Flood's candidate for TC status. Here is a partial catalog of candidates in which (B), (C), and (D) are alternatives to Flood's candidate, (A).
A. Intelligible predication presupposes the truth of the Christian worldview (Van Til & Co.) as the transcendental condition of IP's very possibility.
B. Intelligible predication presupposes the existence of God, but not the Christian worldview as the Calvinist Van Til and his followers calvinistically understand it, the essential commitments of which include such specifically Christian doctrines as Trinity, Incarnation, etc. as well as the specifically Calvinist TULIP doctrines. Some who call themselves Christians are unitarians and deniers of the divinity of Christ. Our friend Dale Tuggy is such a one. And those the presuppositionalists refer to as 'Romanists' who do accept Trinity and Incarnation don't accept the specifically Calvinist add-ons.
C. Intelligible predication presupposes the truth of Kant's transcendental idealism according to which "The understanding is the law-giver of nature," and space and time are a priori forms of our sensibility. For Kant the ultimate transcendental condition of the objective validity of every judgment, and thus of every intelligible predication, is located in the transcendental unity of apperception which is assuredly not God, whatever exactly it is.
D. Intelligible predication presupposes, not the God of the Christian Bible, but an immanent order and teleology in nature along the lines of Thomas Nagel's Mind and Cosmos (Oxford 2012). On Nagel's view, the rational order of nature 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) But neither is it due to theistic intervention or imposition. "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 overview of Nagel's book for details.
I am not endorsing any of the above-listed alternatives to (A). They all have their problems as does (A). My point is that they are conceivable alternatives to (A). This being the case, Flood's asseveration, "an alternative to the CW [the Christian worldview] when it comes to accounting for IP cannot even be conceived" is false.
It is quite clear that what Van Til & Co. want is a rationally compelling, 'knock-down,' argument for the existence of the God of the Christian Bible calvininstically interpreted. But they know (deep down even as they suppress the knowledge) that no circular argument is probative. So they essay the above transcendental argument.
What I have shown, however, is that the transcendental argument is not probative. It fails to establish that the God of the Christian Bible is both sufficient and necessary for the possibility of intelligible predication. At most, it renders rationally acceptable the conclusion that the God of the Christian Bible exists.
I am not denying that the God of the Christian Bible exists. Nor am I denying that if said God exists, then he flawlessly executes all the transcendental functions that need executing. How could he fail to? In particular, how could he fail to be the ultimate ungrounded transcendental-ontological ground of intelligible predication? My point is that the presuppositionalists have not proven, i.e., established with objective certainty, that God alone could play the transcendental role.
This is number 4 in the new series on presuppositionalism. Both the old series and the new are collected under the rubric Van Til and Presuppositionalism. The old series consists of five entries written between January 17th and February 9th, 2019.
Today's entry examines a passage from Cornelius Van Til's The Defense of the Faith, 4th ed., P & R Publishing, 2008, p. 294. I have intercalated numerals in brackets so that I can refer to the sentences seriatim for purposes of commentary and critique.
The main question I want to raise is whether Van Til and such of his followers as Greg L. Bahnsen conflate epistemic modality with real (ontic) modality. See the Internet Encyclopedia of Philosophy for an introduction to the distinction. Here is the Van Til passage for analysis:
[1] One’s conception of reality is one’s conception of the foundation of the laws of logic. [2] If men are 'neutral' in their methodology, they say in effect, that as far as the possibilities involved in their investigations are concerned, God may or may not exist. [3] The facts and the laws of this universe may or may not be sustained by God. [4] The law of contradiction does not necessarily have its foundation in God. [5] A may be A tomorrow or it may be not A tomorrow.
Ad [1] So far, so good.
Ad [2] It seems to me that Van Til is here confusing epistemic with real (ontic) possibility. We are told that for the neutralist, God may or may not exist. But "God may or may not exist" is susceptible of two very different readings, one epistemic, the other real, the first arguably true, the second arguably false.
Read in terms of epistemic possibility, the sentence says that both the existence of God and the nonexistence of God are consistent with what we know. It says that neither state of affairs is ruled out by what we know. For all we know, God might exist, but then again, he might not. By 'know,' I mean what we humans actually know 'here below,' in our present state, i.e., this side of the grave.
As I have made clear in earlier entries, my position is that both the existence of God and the nonexistence of God are epistemic possibilities. Both are possible for all we (can legitimately claim to) know. It follows that both theism and atheism are rationally acceptable. To whom? To us, not to God obviously. (If God exists, you can be sure that he is a theist!) There are rationally acceptable arguments on both sides of the God question, but on neither side are there rationally compelling arguments. It is reasonable to be a theist, but it is also reasonable to be an atheist. This is my 'signature thesis.' The thesis could also be put as follows: the existence of God is epistemically contingent, which implies that it is not epistemically necessary, and therefore not objectively certain, however subjectively certain it may appear to Van Til or anyone else.
My 'signature thesis' will be strenuously resisted both by dogmatic theists and by dogmatic atheists. These dogmatists think that they can prove, i.e., establish with objective certainty, that either God exists or that God does not exist. I take an anti-dogmatic line, a critical line.
My anti-dogmatism, however, does not make me a skeptic about the existence of God. I neither doubt nor deny the existence of God. I doubt that the existence of God can be proven, just as I doubt that the nonexistence of God can be proven. It must remain an open question on the theoretical plane in this life. My stance is critical and thus neither dogmatic nor skeptical. It could be called zetetic to avoid the unfortunate connotations of 'skeptical.' My critical stance, while zetetic, is consistent with taking a position on the God question: it is consistent with affirming the existence of God. It is just that this affirmation is pistic (by faith) rather than epistemic (by knowledge). I am not a Pyrrhonian skeptic who suspends belief, retreats to the quotidian, forgets about God and the Last Things, and lives the life of the practical atheist. I live the life, or try to live the life, of the practical theist: I live on the assumption that God exists, but without the conceit that I can prove that God exists, thereby resolving the issue on the theoretical plane. But a question that cannot be resolved impersonally on the theoretical plane can be decided personally on the practical plane.
Read in terms of real (non-epistemic or ontic) possibility, "God may or may not exist" says that God is a contingent being. It is however false that God is a contingent being as I am sure Van Til would agree: nothing could count as God that either merely happens to exist in the manner of a brute fact, or is caused to exist by another.
One who fails to make the distinction between epistemic and real possibility might think that the falsity of the second reading entails the falsity of the first. But that would be a mistake. I suspect that it is precisely this mistake that Van Til is making. He incorrectly thinks that because the existence of God is not ontically contingent, but is ontically necessary, the existence of God is epistemically necessary, i.e., ruled in by what we know and thus objectively certain.
But surely the existence of God is not ruled in, or entailed, by anything we can legitimately claim to know. If Van Til or his acolytes were to respond: "But we do know that God exists because his existence is attested by the Word of God, the Bible," then he or they would be arguing in a circle. But as I took pains to show in earlier posts, no circular argument is probative. A tenable presuppositionalism must somehow avoid circular reasoning. "Presuppers" are, I take it, aware of this requirement which is presumably why they present their position in transcendental form.
A transcendental argument is one that starts from some actual fact and then regresses to the necessary condition or conditions of the possibility of our knowledge of that fact. Such an argument does not move in a circle. To keep with the geometrical metaphor, a transcendental argument moves linearly and 'vertically' if you will from the plane of the actual to a dimension orthogonal to that plane, the 'transcendental dimension' wherein are to be found the necessary epistemic conditions of the possibility of our knowledge of the the items on the plane of the actual. The problem, of course, is to prove and not merely presuppose that God inhabits that dimension. The problem is to show that God and only God could be the ultimate transcendental condition of possibility. And please bear in mind that the God in question is the God of the Christian Bible interpreted along Calvinistic lines.
Ad [3] Van Til thinks that if God may or may not exist, then "The facts and the laws of this universe may or may not be sustained by God." Here again is the same epistemic-ontic confusion. What Van Til says is true only if God is ontically contingent. For if God is ontically contingent, then it will be possible for the facts and laws to exist and be what they are if not sustained by God. But if God is ontically necessary, as both Van Til and I believe, then, given that God is the creator and sustainer of everything distinct from himself, it will not be possible that there be uncreated and unsustained facts and laws.
Epistemically, however, it is possible both that the facts and laws are sustained by God and also that the facts and the laws need no divine sustenance. For example, David Armstrong's naturalistic but non-regularity theory of laws as relations between immanent universals is epistemically possible but has no need for God as sustainer of laws. (See D. M. Armstrong, What is a Law of Nature? Cambridge UP, 1983) Of course, if God exists, then he is the sustainer of natural laws. But whether God exists is precisely the question. (It is an elementary point of logic that when one affirms a conditional proposition such as the one two sentences up, one is not affirming the antecedent of the conditional.)
In sum, Van Til is on solid ground in holding that God is an ontically necessary being. But this gives him no good reason to think that God is epistemically necessary. By my lights, Van Til is conflating ontic and epistemic modality.
Ad [4]. Here we are being told that on a neutral approach, "The law of contradiction [LC] does not necessarily have its foundation in God." But here again we find the epistemic-ontic confusion. On a neutral approach, it is epistemically possible that LC, a necessary truth, be grounded in God, a necessary being, such that if God were not to exist, LC would not exist or be true. But it is also epistemically possible that LC, a necessary truth, subsist as a proposition and be true even if there is no God. Neither epistemic possibility can be ruled out by what we can legitimately claim to know. It is therefore epistemically contingent whether LC has a divine ground. This is why it is a question whether LC requires a divine ground, an open question not to be begged. If a Van Tilian replies that we do know that God exists because the Bible says so, then he moves in a circle of embarrassingly short diameter. Obviously, one cannot prove a proposition by presupposing it. If, on the other hand, one argues along the lines of the Anderson-Welty argument from the laws of logic to the existence of God, one will at most succeed in showing that the existence of God is rationally acceptable, but will not succeed in proving the existence of God, and this for the reason that one or more of the premises may be reasonably doubted as I point out in the linked article. It is because one cannot compellingly or coercively demonstrate the existence of God by either a circular argument or a non-transcendental argument such as the Anderson-Welty argument that the presuppositionalist tries for a transcendental argument. My point, however, is that such an argument may conduct us to a transcendental condition of intelligible predication, but cannot demonstrate that God and God alone is (identically) that transcendental condition.
Ad [5]. We are here being told that on the neutrality approach, "A may be A tomorrow or it may be not A tomorrow." I take it that 'A' names a proposition. The claim seems to be that the very identity of a proposition cannot be secured unless the laws of logic have a divine foundation. But why? Let 'A' name the Law of Contradiction (as Van Til calls it.) The law in question is necessarily true and necessarily existent. This is the case whether or not God exists. If it could be proven that LC could only exist as a divine thought-content, then it would be proven that the laws of logic must have a divine foundation.
But how prove that? I have shown that circular arguments and transcendental arguments and non-transcendental arguments such as the Anderson-Welty argument are all unavailing.
This is the third in a new series on presuppositionalism. The first installment is here, and the second here.
I've been re-reading large chunks of Cornelius Van Til, The Defense of the Faith, P & R Publishing, 2008. This fourth edition, edited by K. Scott Oliphint, includes the complete text of the original 1955 edition and useful footnote commentary by Oliphint.
You will recall my claim that with respect to the existence of God there are rationally acceptable arguments for and rationally acceptable arguments against, but no rationally compelling arguments on either side. So I was pleased to find an attempt by Van Til to respond to this sort of objection. (DF 126) He formulates the objection as follows:
"While a Christian can prove that his Christian position is fully as reasonable as the opponent's view, there is no such thing as an absolutely compelling proof that God exists, or that the Bible is the Word of God, just as little as anyone can prove its opposite."
Van Til then responds:
In this way of putting the matter there is a confusion between what is objectively valid and what is subjectively acceptable to the natural man.
[. . .]
It is precisely the Reformed Faith which, among other things, teaches the total depravity of the natural man, which is most loathsome to that natural man.
Turning to p. 352, we learn that the natural man is "spiritually dead." "The natural man does not know God." Or rather, he knows God in an implicit way, but suppresses "the knowledge of God given man by virtue of creation in God's image." On p. 255 we learn that having been made in the image of God we have an "ineradicable sense of deity" within us. This of course is Calvin's sensus divinitatis. Van Til makes bold to say, further, that men's "own consciousness is inherently and exclusively revelational of God to themselves," and that "No man can help knowing God, for in knowing himself, he knows God."
I'll conclude the quoting with a Van Tilian slam against the 'Romanists' as he often refers to them:
It is the weakness of the Roman Catholic and Arminian methods that they virtually identify objective validity with subjective acceptability to the natural man. Distinguishing carefully between these two, the Reformed apologist maintains that there is an absolutely valid argument for the existence of God and the truth of Christian theism. (126)
Respondeo
'Virtually' is one of those weasel words that good writers either avoid or define. But let that pass. Speaking for myself and not for the 'Romanists,' I will say that what Van Til is doing above is simply adding a layer of psychologizing to his question-begging. He is engaging in the opposite kind of pure metaphysical bluster as I accused Galen Strawson of engaging in. Strawson:
We can, for example, know with certainty that the Christian God does not exist as standardly defined: a being who is omniscient, omnipotent, and wholly benevolent. The proof lies in the world, which is full of extraordinary suffering. If someone claims to have a sensus divinitatis that picks up a Christian God, they are deluded. It may be added that genuine belief in such a God, however rare, is profoundly immoral: it shows contempt for the reality of human suffering, or indeed any intense suffering.
What we have here are two opposite forms of pure bluster. Neither Van Til nor Strawson can prove what they claim to be certain of, and both psychologize their opponents, the one by appeal to a supposed "total depravity," the other by appeal to insanity.
There is nothing to choose between these two opposite forms of bluster. And so, dear reader, does not my position strike you as the only sane and reasonable one?
The day before yesterday, re: presuppositionalism, I wrote:
We need to bear in mind that arguments have premises and that no argument can prove its own premises. An argument of the form p therefore p is an argument valid in point of logical form in which premise and conclusion are identical, but no one will take an argument of this form as proving that p. Every circular argument of the above form is valid, and some are sound; but none are probative. By that I mean that no such argument constitutes a proof. That ought to be perfectly obvious.
'Circularity' in respect of arguments is of course a metaphor: no argument is literally a geometrical circle. But it is a useful metaphor and I propose we extend it by speaking of the 'diameter' of a circular argument. The logical form italicized above — p therefore p — has a 'diameter' than which no shorter can be conceived. Its 'diameter' is zero. If a geometrical circle has a diameter of zero, then it is not a circle but a point. The diameter of a circular argument of the above form is also a 'point,' figuratively speaking, the point being the one proposition that serves as both premise and conclusion.
A circular argument of zero diameter is said to be 'vicious.' Are there then 'virtuous' or if not positively virtuous then 'non-vicious' circular arguments? Can one argue in a way that is circular but logically acceptable? Brian Bosse brought up this issue over lunch Sunday as we were discussing my longish entry on presuppositionalism. He may have had John M. Frame in mind.
Presuppositionalists such as Frame take the Word of God as set forth in the Protestant Christian Bible as their "ultimate presupposition." (Five Views on Apologetics, Zondervan 2000, 209) It is their "ultimate criterion of truth." (209) This commitment of theirs is faith-based:
. . . for Christians, faith governs reasoning just as it governs all other human activities. Reasoning is not in some realm that is neutral between faith and unbelief. There is no such realm, since God's standards apply to all of life. (209)
What causes faith? ". . . God causes faith by his own free grace." (209) What is the rational basis of faith? ". . . the answer is that faith is based on reality, on truth. It is in accord with all the facts of God's universe and all the laws of thought that God has ordained. . . . The faith he gives us agrees with God's own perfect rationality." (209-210)
We want to know what rationally justifies faith in God and in his Word as found in the Bible. We are told that this faith is justified because it is true, agreeing as it does with all of the laws of thought that God has ordained. God himself, as the ultimate source of all things, including rationality, is the ultimate rational justification of our faith in him and his Word. The reasoning here is plainly circular as Frame admits:
There is a kind of circularity here, but the circularity is not vicious. It sounds circular to say that faith governs reasoning and also that it is based on rationality. It is therefore important to remember that the rationality that serves as the rational basis for faith is God's own rationality. The sequence is: God's rationality –>human faith –>human reasoning. The arrows may be read "is the rational basis for." That sequence is linear, not circular. (210)
Frame's fancy footwork here is unavailing, an exercise in sophistry. He is obviously reasoning in a circle by presupposing the very thing whose existence he wants to prove. But he is loathe to admit that this is what he is doing. So he introduces a bogus distinction between vicious circles and linear circles. But just as 'linear circle' in geometry is a contradictio in adjecto , so too is 'linear circle' in logic.
You are either arguing in a circle or you are not. You are either presupposing what you are trying to prove or you are not. You are either begging the question or you are not. You are either committing the formal fallacy of petitio principii (hysteron proteron) or you are not. That is the long and the short of it. One or the other and no weaseling out via some bogus distinction between vicious and non-vicious circular arguments.
What Frame wants is a 'knock-down' (rationally compelling or rationally coercive) argument for the existence of the God of the Protestant Christian Bible interpreted along Calvinist lines. He thinks he can get what wants by way of a transcendental argument, one that issues in God "not merely as the conclusion of an argument, but as the one who makes argument possible." (220) He wants God to play a transcendental role as the ultimate and unconditioned condition of the possibility of all our intellectual operations including reasoning, whether valid or invalid, sound or unsound. (If his God does play the transcendental role, then Frame can say that the arguments of atheists, just insofar as they are arguments, prove the existence of God!)
Now it must be granted, as I granted to Brian over lunch, that if Frame's God exists, then he does play the transcendental role. The question, however, is whether it can be proven that nothing other than Frame's God could play the transcendental role. It can be proven that there is a transcendental condition of all our intellectual operations. (See my earlier entry.) Where Frame goes wrong is in thinking that from the fact that there is a rationally compelling argument for the existence of a transcendental condition of the possibility of all our intellectual operations (forming concepts, defining terms, making judgments, giving arguments, replying to objections offering hypotheses, etc.) it follows immediately that his God exists beyond the shadow of a rational doubt. How does he know that his God alone could play the transcendental role? Frame may be taxed with giving the following invalid argument:
a) If the God of the Protestant Christian Bible exists, then he plays the transcendental role;
b) It is objectively certain that something plays the transcendental role;
ergo
c) It is objectively certain that the God of the Protestant Christian Bible plays the transcendental role.
The premises are true, but the conclusion does not follow from them. For it is not objectively certain that nothing other than the God of the Christian Bible could play the transcendental role. This is because no non-transcendental argument — Frame mentions the "causal argument" — for the existence of God is rationally compelling. Hence no non-transcendental God argument can assure us that the existence of God is objectively certain.
Here is another way to see the matter. It is rationally demonstrable that there is a total and unique way things are. (For if you assert that there is no way things are, then you are asserting that the way things are is that there is no way things are.) Now if Frame's God exists, then he is the concrete and personal metaphysical ground of the way things are. But how do we know that Frame's God exists? We cannot simply assume that the transcendental proof of the existence of the way things are is also a proof of Frame's God. So non-transcendental arguments must be brought into to take us to Frame's God, Frame's "causal argument" for example. But these arguments are none of them rationally compelling. They do not generate objective certainty. So how do we know that something else is not the metaphysical ground of the way things are?
The presuppositionalism of Cornelius van Til, Greg L. Bahnsen, John M. Frame and others sets me a challenge given some long-held views of mine. I will here explain one of these views and then explain why it is incompatible with presuppositionalism. After that, I will begin to explain my reasons for rejecting presuppositionalism. This third task will require additional posts.
I have maintained that both theism and atheism are rationally acceptable by beings like us in our present state. Theism is the view that there is a supreme transcendent being of a personal nature who created ex nihilo everything other than himself. Atheism, then, is the view that there is no such being. Because the competing views thus defined are logical contradictories, they cannot both be true and they cannot both be false. Not everyone will accept the above definitions of 'theism' and 'atheism,' but if I am not mistaken presuppositionalists do accept them.
So on my accounting theism and atheism are both rationally acceptable. To appreciate my thesis you must understand that truth and rational acceptability are not the same. Some propositions are true but not rationally acceptable. It is also easily shown that some propositions are rationally acceptable but not true. This is because truth is absolute whereas rational acceptability is relative to various indices. Rational acceptability can vary with time and place and other factors; truth cannot. That there are four elements, air, earth, fire, and water was rationally acceptable to the ancient Greeks. It is not rationally acceptable to us. If one were to identify the true with the rationally acceptable, one would have to say that the number and nature of the elements has changed over time.
To claim that both theism and atheism are rationally acceptable is to claim that good arguments can be given for both. A good argument, as I use 'good argument,' is one that has plausible premises and commits no formal or informal fallacy. A good argument, then, is not the same as a rationally compelling or rationally coercive argument. Every rationally compelling argument is of course good, but not every good argument is rationally compelling. A well-reasoned case for a proposition needn't be a rationally compelling case. If it is well-reasoned, then I call it 'good.' Here are the details. (The reader may want to skip the next section (in Georgia 12-pt) the better to catch the drift of this entry, and then come back to it.)
Excursus
. . . it will be easily seen that the absence of such disagreement must remain an indispensable negative condition of the [objective] certainty of our beliefs. For if I find any of my judgments, intuitive or inferential, in direct conflict with the judgment of some other mind, there must some error somewhere: and if I have no more reason to suspect error in the other mind than in my own, reflective comparison between the two judgments necessarily reduces me temporarily to a state of neutrality. (342, emphasis added)
. . . our [apologetic] argument should be transcendental. That is, it should present the biblical God, not merely as the conclusion to an argument, but as one who makes argument possible. We should present him as the source of all meaningful communication, since he is the author of all order, truth, beauty, goodness, logical validity, and empirical fact. (Five Views of Apologetics, Zondervan 2000, p. 220)
1) We finite cognizers in pursuit of our cognitional goals must presuppose the existence of truths
2) We finite cognizers in pursuit of our cognitional goals must presuppose the existence of the biblical God.
We can reach this transcendental conclusion by many kinds of specific arguments, including many of the traditional ones. The traditional cosmological argument, for example, argues that God must exist as the First Cause of all the causes in the world. That conclusion is biblical and true, and if it can be drawn from true premises and valid logic, it may contribute to the goal of a transcendental conclusion. Certainly if God is the author of all meaning, he is the author of causality. And if God is the author of causality, the cause of all causes, he is the cause of all meaning. Therefore, the causal argument yields a transcendental conclusion. (pp. 220-221)
(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.