Cosmological Arguments – Maverick Philosopher

An Insufficient Argument against Sufficient Reason

This is an emended version of an entry that first saw the light of day on 21 May 2016. It is a set-up for a response to a question put to me by Tom Oberle. I'll try to answer Tom's question tomorrow.

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Explanatory rationalism is the view that there is a satisfactory answer to every explanation-seeking why question. Equivalently, it is the view that there are no propositions that are just true, i.e., true, contingently true, but without explanation of their being true. Are there some contingent truths that lack explanation? Consider the conjunction of all contingent truths. The conjunction of all contingent truths is itself a contingent truth. Could this contingent conjunctive truth have an explanation? Jonathan Bennett thinks not:

Let P be the great proposition stating the whole contingent truth about the actual world, down to its finest detail, in respect of all times. Then the question 'Why is it the case that P?' cannot be answered in a satisfying way. Any purported answer must have the form 'P is the case because Q is the case'; but if Q is only contingently the case then it is a conjunct in P, and the offered explanation doesn't explain; and if Q is necessarily the case then the explanation, if it is cogent, implies that P is necessary also. But if P is necessary then the universe had to be exactly as it is, down to the tiniest detail — i.e., this is the only possible world. (Jonathan Bennett, A Study of Spinoza's Ethics, Hackett 1984, p. 115)

A clever little argument, this. Either Q is contingent or Q is necessary. If Q is contingent, then it is a conjunct in P and no explanation of P is to be had. But if Q is necessary, then so is P. So explanatory rationalism fails: there is no explanation of P's contingent truth.

Bennett's point is that explanatory rationalism entails the collapse of modal distinctions. To put it another way, the principle of sufficient reason, call it PSR, according to which every truth has a sufficient reason for its being true, entails the extensional equivalence of the possible, the actual, and the necessary. These modal words would then differ at most in their sense but not in their reference. If we assume, as most of us will, the non-equivalence of the possible, the actual, and the necessary, then, by modus tollens, we will infer the falsity of explanatory rationalism/PSR.

This is relevant to the God question. If PSR is false, then cosmological arguments for the existence of God which rest on PSR will be all of them unsound.

Now let's look at Bennett's argument in detail.

The world-proposition P is a conjunction of truths all of which are contingent. So P is contingent. Now if explanatory rationalism is true, then P has an explanation of its being true. Bennett assumes that this explanation must be in terms of a proposition Q distinct from P such that Q entails P, and is thus a sufficient reason for P. Now Q is either necessary or contingent. If Q is necessary, and a proposition is explained by citing a distinct proposition that entails it, and Q explains P, then P is necessary, contrary to what we have assumed. On the other hand, if Q is contingent, then Q is a conjunct in P, and again no successful explanation has been arrived at. Therefore, either explanatory rationalism is false, or it is true only on pain of a collapse of modal distinctions. We take it for granted that said collapse would be a Bad Thing.

Preliminary Skirmishing

Bennett's is a cute little argument, a variant of which impresses the illustrious Peter van Inwagen as well, but I must report that I do not find the argument in either version compelling. Why is P true? We can say that P is true because each conjunct of P is true. We are not forced to say that P is true because of a distinct proposition Q which entails P.

I am not saying that P is true because P is true; I am saying that P is true because each conjunct of P is true, and that this adequately and non-circularly explains why P is true. Some wholes are adequately and non-circularly explained when their parts are explained. In a broad sense of 'whole' and 'part,' a conjunction of propositions is a whole the parts of which are its conjuncts. Suppose I want to explain why the conjunction Tom is broke & Tom is fat is true. It suffices to say that Tom is broke is true and that Tom is fat is true. Their being conjoined does not require a separate explanation since for any propositions their conjunction automatically exists. Nor does the truth of a conjunction need a separate explanation since the truth of a conjunction supervenes upon the truth of its conjuncts. It is an aletheiological free lunch.

Suppose three bums are hanging around the corner of Fifth and Vermouth. Why is this threesome there? The explanations of why each is there add up (automatically) to an explanation of why the three of them are there. Someone who understands why A is there, why B is there, and why C is there, does not need to understand some further fact in order to understand why the three of them are there. Similarly, it suffices to explain the truth of a conjunction to adduce the truth of its conjuncts. The conjunction is true because each conjunct is true. There is no need for an explanation of why a conjunctive proposition is true which is above and beyond the explanations of why its conjuncts are true.

Bennett falsely assumes that "Any purported answer must have the form 'P is the case because Q is the case'. . ." This ignores my suggestion that P is the case because each of its conjuncts is the case. So P does have an explanation; it is just that the explanation is not in terms of a proposition Q distinct from P which entails P.

Going Deeper

But we can and should go deeper. P is true because each of its conjuncts is true. But why are they each true? Each is true because its truth-maker makes it true. A strong case can be made that there are truth-makers and that truth-makers are concrete facts or states of affairs. (See D. M. Armstrong, et al.) A truth-making fact is not a proposition, but that which makes a contingently true proposition true. Contingent truths need ontological grounds. Armstrong finds the thought already in Aristotle. My being seated, for example, makes-true 'BV is seated.' The sentence (as well as the proposition it is used to express) cannot just be true: there must be something external to the sentence that makes it true, and this something cannot be another sentence or anyone's say-so. As for Bennett's "great proposition P," we can say that its truth-maker is the concrete universe. Why is P true? Because the concrete universe makes it true. 'Makes true' as used in truth-maker theory does not mean entails even though there is a loose sense of 'makes true' according to which a true proposition makes true any proposition it entails. Entailment is a relation defined over propositions: it connects propositions to propositions. It thus remains within the sphere of propositions. Truth-making, however, connects non-propositions to propositions. Therefore, truth-making is not entailment.

We are now outside the sphere of propositions and can easily evade Bennett's clever argument. It is simply not the case that any purported answer to the question why P is the case must invoke a proposition that entails it. A genuine explanation of why a contingent proposition is true cannot ultimately remain within the sphere of propositions. In the case of P it is the existence and character of the concrete universe that explains why P is true.

Going Deeper Still

But we can and should go deeper still. Proposition P is true because the actual concrete universe U — which is not a proposition — makes it true. But what makes U exist and have the truth-making power? If propositional truth is grounded in ontic truth, the truth of things, what grounds ontic truth? Onto-theological truth?

Theists have a ready answer: the contingent concrete universe U exists because God freely created it ex nihilo. It exists because God created it; it exists contingently because God might not have created it or any concrete universe. The ultimate explanation of why P is true is that God created its truth-maker, U.

Now consider the proposition, God creates U. Call it G. Does a re-run of Bennett's argument cause trouble? G entails P. G is either necessary or contingent. If G is necessary, then so is P, and modal distinctions collapse. If G is contingent, however, it is included as a conjunct within P. Does the explanation in terms of divine free creation therefore fail?

Not at all. For it is not a proposition that explains P's being true but God's extra-propositional activity, which is not a proposition. God's extra-propositional activity makes true P including G and including the proposition, God's extra-propositional activity makes true P.

Conclusions

I conclude that Professor Bennett has given us an insufficient reason to reject the Principle of Sufficient Reason.

I apply a similar critique to Peter van Inwagen's version of the argument in my "On An Insufficient Argument Against Sufficient Reason," Ratio, vol. 10, no. 1 (April 1997), pp. 76-81.

Arguments to God a contingentia mundi that rely on PSR are not refuted by the Bennett argument.

Does Everything Contingent Have a Ground of its Existence?

What is it to be contingent? There are at least two nonequivalent definitions of 'contingency' at work in philosophical discussions. I will call them the modal definition and the dependency definition.

Modal Contingency. X is modally contingent =_df x exists in some but not all metaphysically (broadly logically) possible worlds.

Since possible worlds jargon is very confusing to many, I will also put the definition like this:

X is modally contingent =_df x is possibly nonexistent if existent and possibly existent if nonexistent.

For example, I am modally contingent because I might not have existed: my nonexistence is metaphysically possible. Unicorns, on the other hand, are also modally contingent items because they are possibly existent despite their actual nonexistence. It take it that this is what Aquinas meant when he said that the contingent is what is possible to be and possible not to be. If x is contingent, then (possibly x is and possibly x is not). Don't confuse this with the contradictory, possibly (x is and x is not).

Note that the contingent and the actual are not coextensive. Unicorns are contingent but not actual, and God and the number 9 are actual but not contingent. If you balk at the idea that unicorns are contingent, then I will ask you: Are they then necessary beings? Or impossible beings? Since they can't be either, then they must be contingent. Everything is either contingent or non-contingent, and everything non-contingent is either necessary or impossible.

Note also that because unicorns are modally contingent but nonexistent, one cannot validly argue from their modal contingency to their having a cause or ground of their existence. They don't exist; so of course they have no cause or ground of their existence.

Existential Dependency. Now for the dependency definition.

X is dependently contingent =_df there is some y such that (i) x is not identical to y; (ii) necessarily, if x exists, then y exists; (iii) y is in some sense the ground or source of x's existence.

We need something like the third clause in the definiens for the following reason. Any two distinct necessary beings will satisfy the first two clauses. Let x be the property of being prime and y the number 9. The two items are distinct and it is necessarily the case that if being prime exists, then 9 exists. But we don't want to say that the the property is contingently dependent upon the number.

The two definitions of 'contingency' are not equivalent. What is modally contingent may or may not be dependently contingent. Bertrand Russell and others have held that the universe exists as a matter of brute fact. (Cf. his famous BBC debate with Fr. Copleston.) Thus it exists and is modally contingent, but does not depend on anything for its existence, and so is not dependently contingent, contingent on something. It is not a contradiction, or at least not an obvious contradiction, to maintain that the universe is modally contingent but not depend on anything distinct from itself. 'Contingent' and 'contingent upon' must not be confused. On the other hand, Aquinas held that there are two sorts of necessary beings, those that have their necessity from another and those that have their necessity in themselves. God, and God alone, has his necessity in himself, whereas Platonica have their necessity from God. That is to say that they derive their esse from God; they depend for their existence on God despite their modal necessity. If, per impossibile, God were not to exist, then the denizens of the Platonic menagerie would not exist either. It follows that Platonica are dependently contingent even though modally necessary.

In sum, modal contingency does not straightaway entail existential dependence, and modal necessity does not straightaway entail existential independence.

So it is not the case that, as some maintain, "the contingent is always contingent on something else." Or at least that is not obviously the case: it needs arguing. One who maintains this absent the arguing ought to be suspected of confusing the two senses of 'contingency' and of making things far too easy on himself.

The following, therefore, is a bad argument as it stands: The universe is contingent; the contingent, by definition, is contingent on something else; ergo the universe is contingent on something else, and this all men call God. It is a bad argument even apart from the 'this all men call God' part because the existence of the universe might well be a brute fact in which case it would be modally contingent but not dependent on anything distinct from it for its existence.

What have I accomplished in this entry? Not much, but this much: I have disambiguated 'contingent' and I have shown that a certain cosmological argument fails. In my book, A Paradigm Theory of Existence, I present an onto-cosmological argument that fares somewhat better. Mirabile dictu, the book is now available in paperback for a reasonable price! The bums at Kluwer never told me!

Why Something rather than Nothing? The ‘Why not?’ Response

According to a presumably apocryphal story, Martin Heidegger asked G. E. Moore, "Why is there something rather than nothing?" Moore replied, "Why not?" A reader finds the 'Moorean' response cheap and unphilosophical. Let's think about this.

Suppose we ask a related but more tractable question: Why does the universe exist? and we get the response: Why not? Why shouldn't it exist? Charitably interpreted, the response amounts to the suggestion that the question is gratuitous or unmotivated or unnecessary in the sense of unneeded.

Some explanation-seeking why-questions are gratuitous. (It is worth noting that grammatically interrogative formulations such as 'Why does anything at all exist?' might be used merely as expressions of wonder that the, or a, universe exists, and not as requests for an explanation. Here we are concerned with ultimate explanations.)

Suppose it is 110 degrees Fahrenheit. I walk into your house where the temperature is a pleasant 80 degrees. If I were to ask why the air conditioning is on, you would be puzzled. "Why shouldn't it be on?"

But if your house were a miserable 95 degrees and I asked why the air conditioning was not on, or why it was so bloody hot in there, you would give some such answer as: "My A.C. unit is on the fritz; the repairman should be here in a couple of hours."

My first question is gratuitous; my second question is not. Some things need explaining; other things don't need explaining.

Perhaps it is like that with the universe. Why should anyone think that it needs an explanation in terms of some item transcendent of it such as the One of Plotinus or the God of Aquinas?

I assume, quite reasonably, that the universe U is modally contingent. Thus it does not exist of metaphysical necessity, the way God exists if he exists; nor is U's existence metaphysically impossible. U exists, but it might not have: its nonexistence is possible. That is to say: U exists, but its nonexistence is not ruled out by the laws of logic or the laws of metaphysics. It exists, but its nonexistence is neither logically nor metaphysically impossible.

But if x is modally contingent, 'contingent' for short, it does not straightaway follow that x depends for its existence on something. It is a mistake to conflate modal contingency with contingency-on-something. That is an important conceptual/semantic point.

So it might be like this: U exists, and exists contingently, but it exists without cause or reason or explanation. If this is the case, then we say that the universe exists as a matter of brute fact. The factuality of the fact resides in its existence; the 'brutality' in (a) its contingency and (b) its lacking a ground, cause, reason, explanation.

I conclude that one cannot argue a contingentia mundi to a prima causa without a preliminary demonstration that our ultimate explanation-seeking why-question is not gratuitous. Before one can mount a cosmological argument from a contingent universe to a transcendent Cause, one must show or at least give a good reason to think that the universe needs an explanation.

In my published work on this topic I argue that contingent particulars, taken by themselves as "independent reals" are contradictory structures. But they patently exist, and nothing can exist that is self-contradictory. So there must be something transcending th realm of contingent particulars to remove the contradiction. Now I cannot go into the many details here and fill in the steps in the argument, but the main point I want to make, in answer to my reader's query, is that it is not unphilosophical to take seriously the 'Why not?' response.

One needs to be able to show that the question, Why does the universe exist? is not gratuitous.

Contingent Existence Without Cause? Not Possible Says Garrigou-Lagrange

A reader claims that "to affirm that there are contingent beings just is to affirm that they have that whereby they are, namely, a cause." This implies that one can straightaway infer 'x has a cause' from 'x is contingent.' My reader would agree with Reginald Garrigou-Lagrange who, taking the traditional Thomist position, maintains the following Principle of Causality (PC):

. . . every contingent thing, even if it should be ab aeterno, depends on a cause which exists of itself. (Reality: A Synthesis of Thomistic Thought, tr. Patrick Cummins, O. S. B., Ex Fontibus 2012, p. 62)

So even if the physical universe always existed, and therefore never came into existence, it would nonetheless require a cause of its existence simply in virtue of its being contingent. I find myself questioning both my reader and Garrigou-Lagrange. For it seems to me to be conceivable that an item be contingent but have no cause or ground of its existence. This is precisely what Garrigou-Lagrange denies: "contingent existence . . . can simply not be conceived without origin, without cause . . . ." (p. 63)

But it all depends on what we mean by 'conceivable' and 'contingent.' Here are my definitions:

D1. An individual or state of affairs x is conceivable =_df x is thinkable without formal-logical contradiction.

Examples. It is conceivable that there be a mountain of gold and a tire iron that floats in (pure or near-pure) water. It is conceivable that I jump straight out of my chair, turn a somersault in the air, and then return to my chair and finish this blog post. It is inconceivable that I light a cigar and not light a cigar at exactly the same time. As for formal-logical contradiction, here is an example: Some cats are not cats. But Some bachelors are married is not a formal-logical contradiction. Why not? Because its logical form has both true and false substitution instances.

D2. An individual or state of affairs x is contingent =_df x is possibly nonexistent/nonobtaining if it exists/obtains, and possibly existent/obtaining if it does not exist/obtain.

The contingent is that which has a certain modal status: it is neither necessary nor impossible. For example, me and my cigar are both contingent beings: neither is necessary and neither is impossible. My smoking the cigar now is an example of a contingent state of affairs: it is neither necessary nor impossible that I smoke a cigar now. The type of modality we are concerned with is broadly logical, not nomological.

Now is it conceivable that something exist contingently without a cause? It seems so! The nonexistence of the physical universe is thinkable without formal-logical contradiction. The physical universe is contingent: it exists, but not necessarily. Its nonexistence is possible. Do I encounter a formal-logical contradiction when I think of the universe as existing without a cause or explanation? No. An uncaused universe is nothing like a non-triangular triangle, or a round square, or a married bachelor, or an uncaused effect. Necessarily, if x is an effect, then x has a cause. It is an analytic truth that every effect has a cause. The negation of this proposition is: Some effects do not have causes. While this is not a formal-logical contradiction, it can be reduced to one by substituting synonyms for synonyms. Thus, Some caused events are not caused.

Contrary to what Garrigou-Lagrange maintains, it is conceivable that the universe exist uncaused, despite its contingency. If one could not conceive the uncaused existing of the universe, then one could not conceive of the universe's being a brute fact. And 'surely' one can conceive of the latter. That is not to say that it is possible. There is a logical gap between the conceivable and the possible. My point is merely that the 'brutality' of the universe's existence is conceivable in the sense of (D1). To put it another way, my point is that one cannot gain a a priori insight into the necessity of the universe's having a cause of its existence. And this is because the Principle of Causality, if true, is not analytically true but synthetically true.

Of course, if one defines 'contingency' in terms of 'existential dependence on a cause' then a thing's being contingent straightaway implies its being caused. But then one has packed causal dependency into the notion of contingency when contingency means only what (D2) says it means. That has all the benefits of theft over honest toil as Russell remarked in a different connection.

Garrigou-Lagrange thinks that one violates the Law of Non-Contradiction if one says of a contingent thing that it is both contingent and uncaused. He thinks this is equivalent to saying:

A thing may exist of itself and simultaneously not exist of itself. Existence of itself would belong to it, both necessarily and impossibly. Existence would be an inseparable predicate of a being which can be separated from existence. All this is absurd, unintelligible. (p. 65)

Suppose that a contingent existent is one that is caused to exist by a self-existent existent. If one then went on to say that such an existent is both contingent and uncaused, then one would embrace a logical contradiction. But this presupposes that contingency implies causal dependency.

And therein lies the rub. That the universe is contingent I grant. But how does one get from contingency in the sense defined by (D2) supra to the universe's causal dependence on a causa prima? If one simply packs dependency into contingency then one begs the question. What is contingent needn't be contingent upon anything.

An Insufficient Argument Against Sufficient Reason

Let P be the great proposition stating the whole contingent truth about the actual world, down to its finest detail, in respect of all times. Then the question 'Why is it the case that P?' cannot be answered in a satisfying way. Any purported answer must have the form 'P is the case because Q is the case'; but if Q is only contingently the case then it is a conjunct in P, and the offered explanation doesn't explain; and if Q is necessarily the case then the explanation, if it is cogent, implies that P is necessary also. But if P is necessary then the universe had to be exactly as it is, down to the tiniest detail — i.e., this is the only possible world. (Jonathan Bennett, A Study of Spinoza's Ethics, Hackett 1984, p. 115)

This is relevant to the God question. If PSR is false, then cosmological arguments for the existence of God which rest on PSR will be all of them unsound.

Now let's look at Bennett's argument in detail.

The world-proposition P is a conjunction of truths all of which are contingent. So P is contingent. Now if explanatory rationalism is true, then P has an explanation of its being true. Bennett assumes that this explanation must be in terms of a proposition Q distinct from P such that Q entails P, and is thus a sufficient reason for P. Now Q is either necessary or contingent. If Q is necessary, and a proposition is explained by citing a distinct proposition that entails it, and Q explains P, then P is necessary, contrary to what we have assumed. On the other hand, if Q is contingent, then Q is a conjunct of P, and again no successful explanation has been arrived at. Therefore, either explanatory rationalism is false, or it is true only on pain of a collapse of modal distinctions. We take it for granted that said collapse would be a Bad Thing.

Preliminary Skirmishing

I am not saying that P is true because P is true; I am saying that P is true because each conjunct of P is true, and that this adequately and non-circularly explains why P is true. Some wholes are adequately and noncircularly explained when their parts are explained. In a broad sense of 'whole' and 'part,' a conjunction of propositions is a whole the parts of which are its conjuncts. Suppose I want to explain why the conjunction Tom is broke & Tom is fat is true. It suffices to say that Tom is broke is true and that Tom is fat is true. Their being conjoined does not require a separate explanation since for any propositions their conjunction automatically exists.

Going Deeper

But we can and should go deeper. P is true because each of its conjuncts is true. But why are they true? Each is true because its truth-maker makes it true. A strong case can be made that there are truth-makers and that truth-makers are concrete facts or states of affairs. (See D. M. Armstrong, et al.) A fact is not a proposition, but that which makes a contingently true proposition true. My being seated, for example, makes-true 'BV is seated.' The sentence (as well as the proposition it is used to express) cannot just be true: there must be something external to the sentence that makes it true, and this something cannot be another sentence or anyone's say-so. As for Bennett's "great proposition P," we can say that its truth-maker is the concrete universe. Why is P true? Because the concrete universe makes it true. 'Makes true' as used in truth-maker theory does not mean entails even though there is a loose sense of 'makes true' according to which a true proposition makes true any proposition it entails. Entailment is a relation defined over propositions: it connects propositions to propositions. It thus remains within the sphere of propositions. Truth-making, however, connects non-propositions to propositions. Therefore, truth-making is not entailment.

Going Deeper Still

Conclusions

I conclude that Professor Bennett has given us an insufficient reason to reject the Principle of Sufficient Reason.

I apply a similar critique to Peter van Inwagen's version of the argument in my "On An Insufficient Argument Against Sufficient Reason," Ratio, vol. 10, no. 1 (April 1997), pp. 76-81.

Arguments to God a contingentia mundi that rely on PSR are not refuted by the Bennett argument.

Two Senses of ‘Contingency’ and a Bad Cosmological Argument

Fr. Aidan Kimel asked me to comment on a couple of divine simplicity entries of his. When I began reading the first, however, I soon got bogged down in a preliminary matter concerning wonder at the existence of the world, its contingency, and whether its contingency leads us straightaway to a causa prima. So I will offer some comments on these topics and perhaps get around to divine simplicity later.

Fr. Kimel writes,

Why is it obvious to [David Bentley] Hart, when it is not obvious to so many modern theologians and philosophers, that a proper understanding of divinity entails divine simplicity? Earlier in his book Hart invites us to consider with wonder the very fact of existence. “How odd it is, and how unfathomable,” he muses, “that anything at all exists; how disconcerting that the world and one’s consciousness of it are simply there, joined in a single ineffable event. … Every encounter with the world has always been an encounter with an enigma that no merely physical explanation can resolve” (pp. 88-89). The universe poses the question “why?” and in so posing this question, it reveals to us its absolute contingency. The universe need not have been. [Emphasis added.]“Nothing within the cosmos contains the ground of its existence” (p. 92):

All things that do not possess the cause of their existence in themselves must be brought into existence by something outside themselves. Or, more tersely, the contingent is always contingent on something else. This is not a difficult or rationally problematic proposition. The complications lie in its application. Before all else, however, one must define what real contingency is. It is, first, simply the condition of being conditional: that is, the condition of depending upon anything external or prior or circumambient in order to exist and to persist in being. It is also mutability, the capacity to change over time, to move constantly from potential to actual states, and to abandon one actual state in favor of another. It is also the condition of being extended in both space and time, and thus of being incapable of perfect “self-possession” in some absolute here and now. It is the capacity and the tendency both to come into and pass out of being. It is the condition of being composite, made up of and dependent upon logically prior parts, and therefore capable of division and dissolution. It is also, in consequence, the state of possessing limits and boundaries, external and internal, and so of achieving identity through excluding—and thus inevitably, depending upon—other realities; it is, in short, finitude. (pp. 99-100)

And now some comments of mine.

Strictly speaking, the universe does not pose any questions; we pose, formulate, and try to answer questions. I share with Hart, Wittgenstein, et al. the sense of wonder that anything at all exists. But this sense of wonder is ours, not the universe's. We sometimes express this sense of wonder in a grammatically interrogative sentence, 'Why does/should anything at all exist?'
But please note that this expression of wonder, although grammatically interrogative, is not the same as the explanation-seeking why-question, Why does anything at all exist? And again, this is a question we ask; it is not one that the universe asks.
Nor does the universe reveal to us its absolute contingency by asking this question: it does not ask the question. We ask the explanation-seeking why-question, and in asking it we presuppose that the universe is contingent, that it "need not have been," that it is not necessary. For if the universe were necessary, it would make little or no sense to ask why it exists.
But is the universe contingent? Its contingency does not follow from the fact that we presuppose it to be contingent. But for the sake of this discussion I will just assume that the universe is contingent. It is, after all, a reasonable assumption.
But what is it to be contingent? There seems to be two nonequivalent definitions of 'contingency' at work above. I will call them the modal definition and the dependency definition.
X is modally contingent =df x exists in some but not all metaphysically (broadly logically) possible worlds. But since possible worlds jargon is very confusing to many, I will also put the definition like this: X is modally contingent =df x is possibly nonexistent if existent and possibly existent if nonexistent. For example, I am modally contingent because I might not have existed: my nonexistence is metaphysically possible. Unicorns, on the other hand, are also modally contingent items because they are possibly existent despite their actual nonexistence. This is what Aquinas meant when he said that the contingent is what is possible to be and possible not to be. Note that the contingent and the actual are not coextensive. Unicorns are contingent but not actual, and God and the number 9 are actual but not contingent. If you balk at the idea that unicorns are contingent, then I will ask you: Are they then necessary beings? Or impossible beings? Since they can't be either, then they must be contingent.
Now for the dependency definition. X is dependently contingent =df there is some y such that (i) x is not identical to y; (ii) necessarily, if x exists, then y exists; (iii) y is in some sense the ground or source of x's existence. We need something like the third clause in the definiens for the following reason. Any two distinct necessary beings will satisfy the first two clauses. Let x be the property of being prime and y the number 9. The two items are distinct and it is necessarily the case that if being prime exists, then 9 exists. But we don't want to say that the the property is contingently dependent upon the number.
The two definitions of 'contingency' are not equivalent. What is modally contingent may or may not be dependently contingent. Bertrand Russell and others have held that the universe exists as a matter of brute fact. (Cf. his famous BBC debate with Fr. Copleston.) Thus it exists and is modally contingent, but does not depend on anything for its existence, and so is not dependently contingent, contingent on something. It is not a contradiction, or at least not an obvious contradiction, to maintain that the universe is modally contingent but not depend on anything distinct from itself. 'Contingent' and 'contingent upon' must not be confused. On the other hand, Aquinas held that there are two sorts of necessary beings, those that have their necessity from another and those that have their necessity in themselves. God, and God alone, has his necessity in himself, whereas Platonica have their necessity from God. That is to say that they derive their esse from God; they depend for their existence of God despite their metaphysical necessity. If, per impossibile, God were not to exist, then the denizens of the Platonic menagerie would not exist either. It follows that Platonica are dependently contingent.
So I would urge that it is not the case that, as Hart says, "the contingent is always contingent on something else." Or at least that is not obviously the case: it needs arguing. Hart appears to be confusing the two senses of 'contingency' and making things far too easy on himself. The following is a bad argument: The universe is contingent; the contingent, by definition, is contingent on something else; ergo the universe is contingent on something else, and this all men call God. It is a bad argument because it either equivocates on 'contingency,' or else the second premise is false. I am not sure that Hart endorses this argument. I am sure, however, that it is a bad argument.

Did the Universe Have a Beginning in Time?

Some of you may remember the commenter 'spur' from the old Powerblogs incarnation of this weblog. His comments were the best of any I received in over ten years of blogging. I think it is now safe to 'out' him as Stephen Puryear of North Carolina State University. He recently sent me a copy of his Finitism and the Beginning of the Universe (Australasian Journal of Philosophy, 2014, vol. 92, no. 4, 619-629). He asked me to share the link with my readers, and I do so with pleasure. In this entry I will present the gist of Puryear's paper as I understand it. It is a difficult paper due to the extreme difficulty of the subject matter, but also due to the difficulty of commanding a clear view of the contours of Puryear's dialectic. He can tell me whether I have grasped the article's main thrust. Comments enabled.

The argument under his logical microscope is the following:

1. If the universe did not have a beginning, then the past would consist in an inﬁnite temporal sequence of events.
2. An inﬁnite temporal sequence of past events would be actually and not merely potentially inﬁnite.
3. It is impossible for a sequence formed by successive addition to be actually inﬁnite.
4. The temporal sequence of past events was formed by successive addition.
5. Therefore, the universe had a beginning.

Premise (3) is open to a seemingly powerful objection. Puryear seems to hold (p. 621) that (3) is equivalent to the claim that it is impossible to run through an actually infinite sequence in step-wise fashion. That is, (3) is equivalent to the claim that it is impossible to 'traverse' an actual infinite. But this happens all the time when anything moves from one point to another. Or so the objection goes. Between any two points there are continuum-many points. So when my hand reaches for the coffee cup, my hand traverses an actual infinity of points. But if my hand can traverse an actual infinity, then what is to stop a beginningless universe from having run through an actual infinity of events to be in its present state? Of course, an actual infinity of spatial points is not the same as an actual infinity of temporal moments or events at moments; but in both the spatial and the temporal case there is an actual infinity of items. If one can be traversed, so can the other.

The above argument, then, requires for its soundness the truth of (3). But (3) is equivalent to

3*. It is impossible to traverse an actual infinite.

(3*), however, is open to the objection that motion involves such traversal. Pace Zeno, motion is actual and therefore possible. It therefore appears that the argument fails at (3). To uphold (3) and its equivalent (3*) we need to find a way to defang the objection from the actuality of motion (translation). Can we accommodate continuous motion without commitment to actual infinities? Motion is presumably continuous, not discrete. (I am not sure, but I think that the claim that space and time are continuous is equivalent to the claim there are no space atoms and no time atoms.) Can we have continuity without actual infinities of points and moments?

Some say yes. William Lane Craig is one. The trick is to think of a continuous whole, whether of points or of moments, as logically/ontologically prior to its parts, as opposed to composed of its parts and thus logically/ontologically posterior to them. Puryear takes this to entail that a temporal interval or duration is a whole that we divide into parts, a whole whose partition depends on our conceptual activities. (This entailment is plausible, but not perfectly evident to me.) If so, then the infinity of parts in a continuous whole can only be a potential infinity. Thus a line segment is infinitely divisible but not infinitely divided. It is actually divided only when we divide it, and the number of actual divisions will always be finite. But one can always add another 'cut.' In this sense the number of cuts is potentially infinite. Similarly for a temporal duration. In this way we get continuity without actual infinity.

If this is right, then motion needn't involve the traversal of an actual infinity of points, and the above objection brought against (3) fails. The possibility of traversal of an actual infinite cannot be shown by motion since motion, though continuous, does not involve motion through an actual infinity of points for the reason that there is no actual infinity of points: the infinity is potential merely.

We now come to Puryear's thesis. In a nutshell, his thesis is that Craig's defence of premise (3) undermines the overall argument. How? To turn aside the objection to (3), it is necessary to view spatial and temporal wholes, not as composed of their parts, but as (logically, not temporally) prior to their parts, with the parts introduced by our conceptual activities. But then the same should hold for the entire history of the universe up to the present moment. For if the interval during which my hand is in motion from the keyboard to the coffee cup is a whole whose parts are due to our divisive activities, then the same goes for the metrically infinite interval that culminates in the present moment. This entails that the divisions within the history of the universe up to the present are potentially infinite only.

But then how can (1) or (2) or (4) be true? Consider (2). It states that an infinite temporal sequence of past events would be actually and not merely potentially infinite. Think of an event as a total state of the universe at a time. Now if temporal divisions are introduced by us into logically prior temporal wholes such that the number of these actual divisions can only be finite, then the same will be true of events: we carve the history of the universe into events. Since the number of carvings, though potentially infinite is always only actually finite, it follows that (2) is false.

The defense of (3) undercuts (2).

So that's the gist of it, as best as I can make out. I have no objection, but then the subject matter is very difficult and I am not sure I understand all the ins and outs.

McCann, God, and the Platonic Menagerie

I am reviewing Hugh J. McCann's Creation and the Sovereignty of God (Indiana University Press, 2012) for American Catholic Philosophical Quarterly. What follows is an attempt to come to grips with Chapter Ten, "Creation and the Conceptual Order." I will set out the problem as I see it, sketch McCann's solution, and then offer some criticisms of his solution.

I. The Problem

How does God stand to what has been called the Platonic menagerie? All classical theists will agree that divine creative activity is responsible for the existence of concreta. But what about abstracta: properties, propositions, mathematical sets, and such? These are entities insulated from the flux and shove of the real order of space, time, and causation. They belong to an order apart. McCann calls it the conceptual order. Does God create the denizens of the conceptual order? Or are the inhabitants of this order independent of God, forming a framework of entities and truths that he must accept as given, a framework that predelineates both the possibilities of, and the constraints upon, God's creative activity? For example, it is a necessary truth that the area of a circle is equal to pi times its radius squared (my example). Is God constrained by this truth so that he logically cannot create a circle not satisfying it? This question obviously bears upon the sovereignty issue. If God is absolutely sovereign, then neither his will nor his intellect can be constrained by anything at all, and certainly not by a bunch of causally inert abstracta and the necessary truths associated with them. (My slangy way of putting it, not McCann's.)

II. Three Types of Approach to the Problem

As I see it, there are three main positions. But first a preliminary observation. Most abstracta are necessary beings: their nonexistence is broadly logically impossible. Not all: Socrates' singleton, though an abstract object, is as contingent as he is. But I will ignore contingent abstracta since they are not relevant to our problem. By 'abstracta' in this post I mean 'necessary abstracta.'

A. The first view is that God must simply accept abstracta as I must. They form a logically and theologically antecedent framework that predelineates his and my possibilities while constraining his and my actions. He does not create abstracta in any sense. They do not depend on God for either their existence or their nature. Their existence and nature are independent of all minds, including God's. McCann and I both reject this view.

B. The second view is that abstracta depend on God for their existence but not for their essence. The property felinity, for example, though a necessary being, depends for its existence on God in this sense: if, per impossibile, God did not exist, then felinity would not exist. (I see no difficulty with a necessary being depending for its existence on another necessary being. See here and here.) I incline to a view like this. Abstracta are divine thought-accusatives, merely intentional objects of the divine intellect. They have an extramental existence relative to us but not relative to God. They cannot not exist, but their exstence is (identically) their being-objects of the divine intellect. This places a constraint on God's creative activity: he cannot create a cat that is not a mammal, for example, or a triangle that is not three-sided. But this constraint on the divine will does not come from 'outside' God as on (A). For it does not come from a being whose existence is independent of God's existence.

On the second view, God is the ultimate explanation of why the universal felinity exists and why it is exemplified. Felinity exists because it is a merely intentional object of the divine intellect. You could say that God excogitates it. Felinity is exemplified because God willed that there be cats. On the second view, however, God is not the explanation of why this nature has the essence or content it has. The essence necessarily has the content it has independently of the divine will, and it can exist unexemplified independently of the divine will. Thus on (B) the divine will is constrained by the truth that cats are mammals such that God could not create a cat that was not a mammal. The proposition and its constitutive essences (*felinity,* *mammality*) depend for their existence on the divine intellect, but they limit God's power. You could say that the objects of the divine intellect limit the divine will. Accordingly, God is not sovereign over the natures of things or over the conceptual truths grounded in these natures, let alone over the necessary truths of logic and mathematics. Triangularity, for example, necessarily has the content it has and God is 'stuck' with it. Moreover, the being (existence ) of triangularity is not exhausted by its being exemplified — which implies that God has no power over the nature in itself. He controls only whether the nature is or is not exemplified.

C. McCann takes a step beyond (B). On his radical view God is absolutely sovereign. God creates all abstracta and all associated conceptual truths, including all logical and mathematical truths. But it is not as if he first creates the abstracta and then the contingent beings according to the constraints and opportunities the abstracta provide. Creation is not a "two-stage process." (201) God does not plan, then produce. Creation is a single timeless act in which natures and associated necessary truths are "created in their exemplifications." (201) Creating cats, God creates felinity by the same stroke. The creation of cats is not the causing of a previously existing unexemplified nature, felinity, to become exemplified. It is the creation in one and the same act of both the abstractum and the concreta that exemplify it. Another way God can create felinity and triangularity is by creating cat-thoughts and triangle-thoughts. Although my thinking about a triangle is not triangular, my thinking and its object share a common nature, triangularity. This common nature exists in my thinking in a different way than it does in the triangle. More on this in a moment. But for now, the main point is that God does not create according to specifications pre-inscribed in Plato's heaven, specifications that God must take heed of: there are no pre-existing unexemplified essences or unactualized possibilities upon which God operates when he creates. God does not create out of pre-existing possibilities, nor is his creation an actualization of anything pre-existent. The essences themselves are created either by being made to exist in nature or in minds.

III. Some Questions About McCann's Approach and His Use of Thomistic Common Natures

I now turn to critique.

It would seem to follow from McCann's position that before there were cats, there was no felinity, and in catless possible worlds there is no felinity either. It would also seem to follow that before cats existed there was no such proposition as *Cats are mammals* and no such truth as that cats are mammals. (A truth is a true proposition, so without propositions there are no truths.) Or consider triangles. It is true at all times and in all worlds that triangles are three-sided. How then can the essence triangle and the geometrical truths about triangles depend on the contingent existence of triangular things or triangle-thoughts? Surely it was true before there were any triangles in nature and any triangle-thoughts that right triangles are such that the square on the hypotenuse is equal to the sum of the squares on the remaining sides.

McCann attempts to deal with these fairly obvious objections by reverting to the old Thomistic doctrine of common natures. McCann does not use the phrase 'common nature,' nor does he mention Aquinas in precisely this connection; but what he says is very close to the Thomistic doctrine.

It is surely counterintuitive to say that felinity began to exist with the first cats, lasts as long as there are cats, and ceases to exist when — horribile dictu — cats become extinct. To avoid being committed to such an absurdity, McCann takes the line that felinity in itself has no being or existence at all. It has being only in its instantiations (203) whether in a mind, as when I think about or want or fear a cat, or in extramental reality in actual cats. "Felinity is in itself is not a being but an essence, and to think of it as such is to set aside all that pertains either to actual or to mental existence." (204) Actual existence is what Thomists call esse naturale or esse reale. Mental existence is what they call esse intentionale. Felinity in itself, however, has no esse at all. Now if felinity in itself has no mode of being or existence, then it cannot be said to begin to exist, to continue to exist, to cease to exist, or to exist only at those times at which cats exist. Nor can felinity be said to exist at all times. It is eternal, not sempiternal (everlasting, omnitemporal), says McCann. Substantial universals such as felinity and accidental universals such as whiteness are "timelessly eternal." (203) The eternal is that which is "excluded from the category of the particular." (204)

The objection was this: If God creates felinity by creating cats, then felinity comes into existence with the first cats. But it is absurd that felinity should come into existence or pass out of existence. Ergo, it is not the case that God creates felinity by creating cats.

McCann's response to the objection, in effect, is to deny the major by invoking the Thomistic doctrine of common natures. Felinity in itself neither comes into existence nor passes out of existence nor always exists. So the major is false and the objection fails.

The trouble with this response to the objection is that the doctrine of common natures is exceedingly murky, so murky in fact, that it causes McCann to fall into self-contradiction. I just quoted McCann to the effect that felinity in itself has no being. Now felinity, according to McCann, is a universal. (204). It follows that universals have no being.

But McCann, fearing nominalism, fails to draw this conclusion when he says that "universals do have being . . . ." (204) Now which is it? Do universals have being or not? If they have being then the above objection goes through. But if they do not have being, then they are nothing, which is just as bad. McCann fudges the question by saying that universals have being in their instantiations. This is a fudge because when felinity is instantiated in the real order in cats, felinity is particular, not universal.

Fudging the matter in this way, McCann fails to see that he is contradicting himself. To avoid nominalism, he must say that universals have being or existence. To avoid the above objection, he must say that they lack being or existence. He thinks he can avoid contradiction by saying that felinity has being in its instances. But felinity in its material instances is not universal, but particular, not one, but many. The Thomistic doctrine, derived from Avicenna, is more consistent: common natures such as felinity are, in themselves, neither universal nor particular, neither one nor many. McCann would have done better to take the classical Thomistic tack which accords to common natures a status much like Meinong's Aussersein. McCann does not go this route because he thinks that if universals have no type of being whatsoever, then ". . . we would grasp nothing in thinking of uninstantiated natures like unicornality." (204)

Trouble Even If 'Common Natures' Doctrine is Tenable: Collapse of Modal Distinctions?

I don't believe that the 'common natures' doctrine is tenable, either in McCann's version or in the strict Thomistic version. Suppose I am wrong. The doctrine — which is needed to evade the above objection — still presents problems for absolute divine sovereignty. Even if common natures have no being whatsoever, they nevertheless have or rather are definite natures. Felinity is necessarily felinity and logically could not be, say, caninity. So God is constrained after all: not by an existing nature but by a nonexisting one. He is constrained by the nature of this nature. He has no control over its being what it is. It is, in itself, necessarily what it is, and God is 'stuck' with the fact.

So a further step must be taken to uphold divine sovereignty in its absoluteness. It must be maintained that there are no broadly logical possibilities, impossibilities and necessities that are ontologically prior to divine creation. Prior to God's creation of triangles, there is no triangularity as an existing unexemplified essence or as a nonexisting unexemplified essence, and no possibilities regarding it such as the possibility that it have a different nature than it has, or the necessity that it have the nature it has, or the possibility that it be exemplified or the possiblity that it not be exemplified. (211). The idea is that triangularity and the like are not only beyond being but also beyond modality: it is neither the case that triangularity is necessarily what it is nor that it is not necessarily what it is. The modal framework pertaining to common natures is not ontologically prior to them or to God's will: it is created when they are created, and they are created when things having those natures are created. As McCann puts it, " . . . It is only in what God does as creator that the very possibilities themselves find their reality." (212)

In this way, God is made out to be absolutely sovereign: there is nothing at all that is not freely created and thus subject to the divine will. My worry is that this scheme entails the collapse of modal distinctions. Notionally, of course, there remain distinctions among the senses of 'possible, 'actual,' necessary,' and other modal terms. But if in reality nothing is possible except what is actual, i.e., what God creates, then the three terms mentioned have the same extension: the possible = the actual = the necessary.

The violates our normal understanding of modality according to which the possible 'outruns' the actual, and the actual 'outruns' the necessary. We normally think that there are in reality, and not just epistemically, possbilities that are not actual, and actualities thatare not necessary. We suppose, for example, that there are merely possible state of affairs (including those maximal states of affairs called 'worlds') that God could have actualized, and actual states of affairs that he might have refrained from actualizing. On this sort of scheme, creation is actualization. But on McCann's it is clearly not.

So I am wondering whether McCann's absolute sovereignty scheme entails the collapse of modal distinctions. Might God not have created cats (or a world in which cats evolve)? No. He created what he created and that is all we can say. We can of course conceive of a world other than the world God created, but on McCann's scheme it is not really possible. It is not really possible because there is no modal framework that predelineates what God can and cannot do. Such a framework is inconsistent with absolute sovereignty. God does what he does and that is all we can say. Real modal distinctions collapse. God's creation of the world is neither necessary nor contingent.

I think this collapse of modal distinctions causes trouble for McCann's project. For the project begins in his first chapter with a cosmological argument for a self-existent creator. Such an argument, however, requires as one its premises the proposition that the world of our experience be contingent in reality. (If it is not contingent, then its existence does not require explanation.) I don't see how this proposition is logically consistent with the last sentence of Chapter Ten: "'Could have' has nothing to do with what goes on in creation." (212)

The problem in a nutshell is this: McCann argues a contingentia mundi to a creator whose absolutely sovereign nature is such as to rule out the reality of the very modal framework needed to get the argument to this creator off the ground in the first place. To put it another way, if McCann's God exists, then the world of our experience is not really contingent, and his cosmological argument proceeds from a false premise.

Perhaps Professor McCann can straighten me out on this point.

Could a Universe of Contingent Beings be Necessary?

If everything in the universe is contingent, does it follow that the universe is contingent? No it doesn't, and to think otherwise would be to commit the fallacy of composition. If the parts of a whole have a certain property, it does not follow that the whole has that property. But it is a simple point of logic that a proposition's not following from another is consistent with the proposition's being true.

And so while one cannot straightaway infer the contingency of the universe from the contingency of its parts, it is nevertheless true that the universe is contingent. Or so I shall argue.

The folowing tripartition is mutually exclusive and mutually exhaustive: necessary, impossible, contingent. A necessary (impossible, contingent) being is one that exists in all (none, some but not all) possible worlds. I will assume an understanding of possible worlds talk. See my Modal Matters category for details.

Our question is whether the universe U, all of whose members are contingent, is itself contingent. I say it is, and argue as follows.

1. Necessarily, if U has no members, then U does not exist. (This is because U is just the totality of its members: it is not something in addition to them. If U has three members, a, b, and c, then U is just those three members taken collectively: it is not a fourth thing distinct from each of the members. U depends for its existence on the existence of its members.)

2. There is a possible world w in which there are no concrete contingent beings. (One can support this premise with a subtraction argument. If a world having n members is possible, then surely a world having n-1 members is possible. For example, take the actual world, which is one of the possible worlds, and substract me from it. Surely the result, though sadly impoverished, is a possible world. Subtract London Ed from the result. That too is a possible world. Iterate the subtraction procedure until you arrive at a world with n minus n ( = 0) concrete contingent members. One could also support the premise with a conceivability argument. It is surely conceivable that there be no concrete contingent beings. This does not entail, but is arguably evidence for, the proposition that it is possible that there be no concrete contingent beings.)

Therefore

3. W is a world in which U has no members. (This follows from (2) given that U is the totality of concrete contingent beings.)

Therefore

4. W is a world in which U does not exist. (From (1) and (3))

Therefore

5. U is a contingent being. (This follows from (4) and the definition of 'contingent being.')

Therefore

6. The totality of contingent beings is itself contingent, hence not necessary.

What is the relevance of this to cosmological arguments? If the universe is necessary, then one cannot sensibly ask why it exists. What must exist has the ground of its existence in itself. So, by showing that the universe is not necessary, one removes an obstacle to cosmological argumentation.

Now since my metaphilosophy holds that nothing of real importance can be strictly proven in philosophy, the above argument – which deals with a matter of real importance — does not strictly prove its conclusion. But it renders the conclusion rationally acceptable, which is all that we can hope for, and is enough.

Do Physicists Bullshit?

To be precise, my question is whether or not there are any written specimens of bullshit produced by physicists. I submit that there are such examples. Herewith, one example. First a simple point of logic: To show that there are Fs, it suffices to adduce one F. And note: a person who produces a specimen of bullshit is not thereby a bullshitter. (A person who gets drunk a few times in his life is not a drunkard.)

The logically prior question of what bullshit is was treated in an earlier post. Briefly: a bullshitter is not a liar, although both are engaged in the enterprise of misrepresentation. The bullshitter's intention is not to misrepresent the way things are in the manner of the liar; his aim is to misrepresent himself as knowing what he does not know or more than he actually knows for some such purpose as impressing others, hearing himself talk, or turning a buck by scribbling.

Continue reading “Do Physicists Bullshit?”

On the Very Idea of a Cause of Existence: Schopenhauer on the Cosmological Argument

Cosmological arguments for the existence of God rest on several ontological assumptions none of them quite obvious, and all of them reasonable candidates for philosophical examination. Among them, (i) existence is a ‘property’ of contingent individuals; (ii) the existence of individuals is not a brute fact but is susceptible of explanation; (iii) it is coherent to suppose that this explanation is causal: that contingent individuals could have a cause of their existence. It is the third item on this list that I propose to examine here.

Continue reading “On the Very Idea of a Cause of Existence: Schopenhauer on the Cosmological Argument”