The Library of Babel

Men usually infer from this mirror that the Library is not infinite (if it were, why this illusory duplication?); I prefer to dream that its polished surfaces represent and promise the infinite . . . Light is provided by some spherical fruit which bear the name of lamps. There are two, transversally placed, in each hexagon. The light they emit is insufficient, incessant.

Jorge Luis Borges, The Library of Babel.

Word-making isn't World-making

Properties don't stand in one-to-one correspondence with predicates, and predicates don't stand in one-to-one correspondence with properties.

Arguing in the first direction, there are probably properties for which human language has no terms. So, there are probably properties that don't stand in one-to-one correspondence with predicates.

And even if there aren't any properties for which human language has no terms, rocks, cabbages, trees and things had properties before man and would have had he never risen from the ooze at all.

Infinities and Infinities and Infinities

Arguing in the second direction, by following accepted predicate formation rules, predicates can be gratuitously generated from other predicates. They can, for example, be generated from disjunctive predicates like “—is red or yellow”, “—is red or shiny”, and “—is red or aquatic”, and negative predicates like “—is not yellow“, “—is not shiny”, and “—is not aquatic”. If predicates stand in one-to-one correspondence with properties, each of those predicates corresponds to a unique property. So, if predicates stand in one-to-one correspondence with properties, there is some indefinitely large number of properties in the world¹.

The one-to-one correspondence also leads to infinite regresses. For instance, “a is self-identical” would correspond to a property of self-identity. If, however, a has the property of being self-identical, it also has the property of being self-identical with itself-with-that-property-of-self-identity. And if a has the property of being self-identical with itself-with-the-first-self-identity-property, it also has the property of being self-identical with itself-with-the-self-identity-property-for-itself-being-self-identical-with-itself-with-the-first-self-identity-property. And so on, ad infinitum.

There is another regress. If predicates stand in one-to-one correspondence with properties, the truth of “a is red” necessitates that a has the property of being red. If, however, the truth of “a is red” necessitates that a has the property of being red, the truth of “a has the property of being red” necessitates that a has the second-order property of having the property of being red. And so on, ad infinitum.

There are more regresses. If predicates stand in one-to-one correspondence with properties, the previous argument applies to every property we can generate from a base predicate (e.g. red). So, if predicates stand in one-to-one correspondence with properties, there is an infinity of properties of having properties for every base predicate.

There are, however, probably not infinities of odious properties like the above. So, predicates probably don't stand in one-to-one correspondence with properties.

Contradiction

There are also paradoxical predicates like “—is a property to which no predicate corresponds”. So, predicates don't stand in one-to-one correspondence with properties, and we can abandon the disastrous conflation of predicates and properties, of language and reality, once and for all.

You will see why all this matters, if not now, in future posts.²


1. I take Ellis's word for it when he says that there is at least one infinite set corresponding to each generative operation.
2. Most of this post's arguments, as well as its title phrase, can be found in George Molnar's Powers.

Five Proofs Critique: The Aristotelian Proof

This next entry discusses Feser’s Aristotelian proof, the argument with which he opens the book, as well as a wider problem with Aristotelian accounts of agency and explanation. Central to this discussion is a certain account of free will mentioned in the last installment.

Tropes or God, II: Relata-specificity

This post assumes familiarity with Tropes or God, I.

Rejecting (1)

In Relata-specificity: A Response to Vallicella, Betti argues that we can resist (5) by rejecting (1).

Betti begins her argument by distinguishing relata-specific and relata-unspecific relations. A relation is relata-specific if and only if it's in its nature to relate specific relata; in contrast, it's relata-unspecific if and only if it isn't in its nature to relate specific relata. Relata-specific relations are unsaturated entities into which only specific objects fit; relata-unspecific relations aren't unsaturated entities into which only specific objects fit.

Betti then argues that if R in aRb can be construed as the relata-specific _a_R__b, aRb can be identified with the sum a + _a_R__b + b; R in aRb can be construed as the relata-specific _a_R__b; hence, aRb can be identified with the sum a + _a_R__b + b; hence, there isn't necessarily a real difference between aRb and the sum a + R + b. In other words, she argues that relata-specific relations can be used to reject (1).

If Betti is right, we can resist (5) by rejecting (1).

Simple or Complex? Vallicella's Reply

In his review of Betti's Against Facts, Vallicella argues that, one, R can only be relata-specific if it's identical to aRb and incorporates its relata; two, if R is identical to aRb, it can't account for the unity of aRb; thus three, if R is relata-specific, it can't account for the unity of aRb; thus four, relata-specific relations can't be used to reject (1).

But why accept that R can only be relata-specific if it's identical to aRb? Construing relata-specific relations as unsaturated entities into which only specific objects fit provides a seemingly fine explanation for why they're relata-specific, and doesn't obviously make R into aRb.

We can go a step further than Betti herself does and bolster her explanation by turning Brentano on his head and making primitive directedness a mark of non-mental entities either instead of or as well as mental entities.

I wrote this article about a year ago and, at the time, I was keen to uphold something like Martin's naturalism. I no longer find naturalism convincing. I still, however, think that we must admit primitive directedness into our ontologies somewhere, and can find no real objection to admitting it in the non-mental world.

I would be interested if anyone can.

Further reading:

“Intentionality and the Non-Psychological”

The Mind in Nature

“Intentionality, Potentiality, and Dispositionality: Some Points of Analogy”

A Note on the Problem of Identity Through Change

The problem of identity through change asks how one individual can be both distinct from and identical with itself at different times. (The notion of identity through change looks like a contradiction in terms.) It can be solved by identifying enduring objects' natures with first-order bundles that are bundled with further tropes at different times.

There is a distinction between natures and accidents. A being a's nature is an instance of whatever every being of a's kind has that it can't gain or lose, and that makes it unique from beings of every other kind; its accidents are property-tropes that it might not have had. A young ass has the same nature as the lame old donkey it becomes; it, however, has different accidents.

There is also a distinction between first-order and second-order bundles. A first-order bundle is a system of dependent tropes combined into an independent substance; a second-order bundle is a system of dependent tropes combined with a first-order bundle into an independent substance. The system of dependent tropes combined into a donkey's nature is a first-order bundle; the system of dependent tropes combined with that nature into a donkey-with-all-its-accidents is a second-order bundle. I contend that all natures are first-order bundles and all natures-with-accidents second-order bundles.

These distinctions dissolve the problem of identity through change. The young ass, for instance, is a numerically distinct second-order bundle that has one and the same first-order nature as the old donkey it becomes. It and its counterpart are, in other words, the exact same (first-order) donkey with different accidents at different times.

Five Proofs Critique: The Rationalist Proof

To begin I wish to make a few remarks on what constitutes a satisfactory theistic argument. When assessing the value of a theistic argument it is vital not only to look at whether the argument itself succeeds or not, but also at the strength of the background metaphysics on which it depends. In many ways arguments for God’s existence are only as strong as their ontological backdrop. Consequently, an argument which requires a very specific metaphysical account, say a certain theory of dispositions or mental activity, will have less force than one which depends on a broader view, for instance: a cosmological argument that requires real powers and dispositions has high value, some powers theory being a strong contender for the only satisfactory account of causation—if on the other hand it requires a very specific powers account the argument loses force, since it is far more debatable which powers account is the correct one.

Similarly, if an argument commits one to an otherwise counterintuitive ontological thesis, then that is generally considered a point against it. For instance, were Anselm’s first ontological argument to commit one to Meinong’s theory of objects then many philosophers would take that as sufficient reason for rejecting that argument. Of course, one can argue the net gains and losses of primitives and counterintuitive theses must be weighed against the success of one’s broader metaphysics—a metaphysical account which explains the existence of contingent being at the cost of endorsing the theory of objects is probably preferable to one which provides no such explanation—but generally if similar conclusions can be reached without taking on the problem thesis then such alternate accounts are preferable.

Some of my claims will be antipathetic to Feser’s preferred approach to Natural Theology. He has stated on a number of occasions, most recently in Scholastic Metaphysics, that proving the existence of God is easy providing one has the correct metaphysics beforehand. Whilst this is true, the ‘providing’ claim in question does restrict the value of his work. It remains a fact that many of the debates in the theory of powers, properties and accounts of universals depend not on knockdown arguments and refutations but on what primitives one is prepared to accept and how comfortable one is with a fulsome ontology (of course Feser might claim that the fact his preferred account leads to the existence of God and thus the resolution of a whole host of ethical and ontological problems is a reason why we should accept it—I have yet to read him argue in this way, though I’m somewhat sympathetic to it). In the project of Natural Theology then it would be preferable to steer a middle course between those, such as William Lane Craig, who only engage in ontology as far as it touches on theology, and the hyper-specific metaphysical requirements of those such as Feser.

In the following discussions my method will be to endeavour to ascertain how much one can prove from the premises of the argument itself and only then to discuss additional appeals to background ontology. This approach serves another purpose: when discussing theistic arguments it is often open to the atheist to claim that the argument in question appears to succeed but since it entails a conclusion i.e. God’s existence, that we have strong independent reason to think impossible, we ought to reject the argument even if we cannot detect where our reasoning went wrong. If, on the other hand, we do not appeal to external metaphysical concerns to determine that what the argument reaches is the God of classical theism, then the atheist has no a priori reason to reject it—in this latter case then both the theist and atheist can accept the minimal conclusion that the argument has established something and thus advanced the task of explanatory metaphysics.

In the following discussion I do not intend to discuss Feser’s arguments in chronological order. Instead I am going to approach them in a way that will prove more fruitful in raising pertinent philosophical issues which I’ll return to in discussion of later arguments.

The most important argument, and probably the only ‘knockdown’ argument for something approaching theism in the book, is what Feser calls the Leibnizian Argument. This argument, quite possibly the quintessential cosmological argument, appeals to that most venerable of metaphysical principles, the Principle of Sufficient Reason (henceforth PSR), and proposes that from this and the relatively uncontroversial premise that there exist contingent beings we can prove that there exists a necessary being. Of all arguments showcased in the book it is the one with the least metaphysical baggage.

It is fashionable to divide the PSR into a weak and strong variant: the former makes the modest claim that all existential fact have an explanation whilst the latter claims that all contingent facts have an explanation. Both of these suffice for a functional cosmological argument (as does the even weaker claim that for every existential fact it is possible that it has an explanation¹).  Feser gives three ‘Thomistic’ formulations of the principle, the first of these amounts to the weak version and the third, to the claim ‘there is a sufficient reason or adequate necessary objective explanation for the being of whatever is and for all attributes of any being’, to the strong version (assuming one is to take attributes in the wide sense including relational properties).

The second formulation, the claim ‘Everything is intelligible’, is more interesting as it suggests that the PSR might follow from the scholastic account of the transcendentals (truth being considered convertible, if not synonymous, with being). I do not know if it would be possible to give a deductive proof of the principle based on this—the transcendentals have received little to no attention in contemporary philosophy of religion and it is likely that the PSR is so basic that any proof for or even against it would end up tacitly appealing to it—but it represents an important area for further exploration.

As it stands Feser follows the well-trodden Leibnizian course and relies on abductive and retorsive argument to support the PSR. It is in the latter of those approaches that he makes what is undoubtably his most original contribution to the discussion. Against those who reject the PSR Feser argues that the nature of psychological justification itself implies the PSR—our acceptance of a claim as true, or at least rational, is itself a form of explanation (to put it another way: it is proposition Y’s appearing to be true because of factor X which explains why we accept Y). In other words if the PSR did not hold there would always be the risk that our seemingly true beliefs are held for no reason as opposed to some justificatory factor. In endorsing such an argument one need not deny the possibility of error—all the argument requires is that the beliefs in question have some justificatory factor even if it is a false one—or endorse Spinozistic epistemic determinism (more on this later). Such an argument must be spelt out in greater detail, say with distinctions between rational and psychological justification, before it can make headway, but as it stands it is an elegant fusion of the PSR and the argument from reason.

Of the weak and the strong formulation, the primary criticism people can muster against the former is that it is ad hoc. Feser takes the philosophically more interesting route and defends the latter. Two major problems present themselves on such an account².

The first is just an expanded version of the Standard Objection to Free Will, which in its normal formulation appeals to causation. The dilemma goes like so: a so-called free action is either explained by a pre-existing factor in which case it can hardly be called free, or lacks an explanation, thus happening for no reason, in which case it can hardly be called an 'action', the deliberate choice of an agent. The proponent of the PSR is, the critic will say, committed to the first freedom-denying option of the disjunction.

The second, really the major criticism against the strong PSR, is that it leads to ‘Modal Collapse’, a scenario in which all contingent truths become necessary ones³. The most common formulation refers to the ‘Big Contingent Conjunctive Fact’. If every contingent fact has an explanation—if there is an explanation for why each contingent state-of-affairs holds—then there must also be an explanation for why the contingent fact which is the conjunction of all smaller contingent facts holds. This explanation cannot itself be a contingent fact, for no contingent fact can explain itself, and therefore must be a necessary one. Yet if it is a necessary fact that certain other facts hold then those facts too are necessary.

Although most analytical philosophers prefer the above formulation of the objection, the general problem in fact dates back to the question of whether God must choose the best of all possible worlds. This problem can be put as follows: God, as a supremely rational agent, must always choose the best; therefore God must have a sufficient reason for choosing to actualise this possible world as opposed to all the other seemingly possible options⁴. But if God (the being in which all possibilities are grounded as both Feser and Leibniz would agree) must actualise this possible world and thus cannot actualise any others, it follows that it is in fact the only possible world, and, once again, all seemingly contingent facts, facts about things which could have seemingly been otherwise, become necessary. If the theist tries to escape this conclusion by pointing out that there is no single ‘best possible world’, (that there are worlds containing distinct but comeasurable goods) then the critic will fling the PSR back in their face. If there is no sufficient reason to prefer one possible world over another then God cannot rationally act. The deity will be trapped, like some divine Buridan's Ass, eternally contemplating an infinitude of equally tempting alternatives yet never acting⁵.

Feser’s response to this problem is infuriatingly insubstantial. As in Scholastic Metaphysics he gestures to the fact that scholastics do not treat propositions as platonic entities existing apart from the mind’s entertaining them⁶. Whilst true this is irrelevant to the criticism, since it is concerned not with propositions in and of themselves but with the states-of-affairs (the ways reality is, e.g. X entity having Y property) which they represent; this is why the term ‘facts’ is used as a way of remaining neutral as to whether truths add another entity to one’s ontology above the beings involved. He also makes the case that not all explanations need be such that potential explanans entail their explanandum. Whilst I’m sympathetic to such a view—I suspect logical entailment in the strict sense belongs only to narrow logic and that our unwillingness to let go of lingering prejudices linking necessity with analyticity—the supposed counterexamples that Feser gives of statistical and scientific explanation are unconvincing: in each case they appear merely to be incomplete explanations which, if sufficiently fleshed out, would give the same appearance of entailment. Take his example of the sun’s gravitational influence explaining the elliptical orbits of the planets: accepting an account of the laws of nature on which such laws are metaphysically necessary, then if one has a complete description of a physical domain—that is all the substances that make it up and all the causal powers at work—then from that description the outcome necessarily follows. It does no good to say that it would be different if there were other factors at work because a description of the other-factored system would necessitate the different result just as much. What is needed is a paradigmatic example of a complete explanation which looks sufficiently different to those presenting the appearance of entailment.

Surprisingly, and perhaps tellingly, Feser does not discuss the most significant response to all of the above problems, one that has been lurking in the wings since Leibniz’s correspondence with Samuel Clarke. Richard Gale and Alexander Pruss have proposed that an elegant and brutal way to defuse all such problems is to hold that contingent facts stating an agent’s free choices are in fact self-explanatory (how one formulates this is still up for debate—of the options discussed by Pruss readers would probably prefer ‘X freely chose Y because impressed by reason Z’ as it leaves room for the Scholastic insight that every agent acts for a perceived good)⁷. This account fits well with our intuitions about free agents being neither random nor externally determined but self-determined—whilst one may grant that causa sui (in the sense of cyclical causation) is impossible one can still accept self-explanation. True there is something unsatisfactory about non-necessitating explanation, but the atheist libertarian will have to bite the same bullet; the mystery lies not with the theism but with the free will. One might press an analogy with abstract objects: the difference between agents and non-agents is as radical as the difference between abstracta and concreta—abstracta have their own account of explanation separate from most concreta so why should it surprise us if agents do as well? A free choice seems a good candidate for that ‘paradigmatic example of a complete explanation sufficiently different to those presenting the appearance of entailment’.

Armed with such an account one can avoid modal collapse and liberate God from His divine indecision. This would not imply the extreme voluntarist position Feser has elsewhere called ‘liberty of indifference’, for one need not deny that an agent that does not make ‘evil’ choices is better, or even more ‘free’, than one that does (although, as Quentin Smith has pointed out, if one accepts the restriction of the principle of alternate possibilities to only good choices, the standard Free Will response to the Logical Problem of Evil appears to fail⁸). The observations do not concern a choice between a bad and a good option but between choices, of which there are likely an infinite number, where one alternative is no better or worse than another. Charges of doxastic voluntarism can be rebutted on the same grounds.

A bigger concern might be that in taking contingent facts regarding free choices as self-explanatory one risks vitiating the PSR’s role in the Cosmological Argument. I suspect that the worry here is that every explanatory chain might terminate in the free choice of a contingent agent: although the vast majority of existential facts do not appear to involve free acts on the part of contingent beings, might not the sceptic postulate a deceitful angel responsible for each fact? Multiple formulations of the argument do not suffer from this problem however: for instance those that ask ‘why does the set of contingent beings have the members that it does?’ (Rowe), ‘why do these contingent beings exist as opposed to others?’ (Pruss) or ‘why are there contingent beings at all?’ (Feser) (of course one can ask the same questions about the subset of contingent beings, contingent agents). Feser’s specifically Scholastic variant, ‘why do contingent beings remain in existence?’ is also unaffected. Finally, all that one needs to conclude from the existence of contingent beings to a necessary being is that a world without contingent free agents is possible, a premise that seems uncontroversial and can be supported with subtraction arguments.

It may be wondered why so much time has been spent on an argument Feser does not even mention; this will become apparent later on when I return to some of the points raised in discussion of the other proofs. For now let us take it that Feser’s PSR argument has worked and it has been granted that a necessary being exists.

Next, what attributes might the necessary being of the PSR Cosmological Argument have? In a sense this is one of the most existentially important questions in philosophy, for it is far easier—infinitely easier in fact if one wishes to remain rational—for the atheist to accept PSR reasoning from contingent beings to a necessary being but deny said being is anything like the God of classical theism. If one accepts the free will lemma, of course one gets agency. Feser appeals to a number of considerations from his Thomist metaphysics to derive the classical Divine Attributes; in keeping with our project, though, let us examine what one can derive solely from the argument itself.

The argument itself leads swiftly to the conclusion that the necessary being in question is omnipotent, for if all contingent states-of-affairs depend upon said entity then it follows that it has the power to actualise said states-of-affairs whether directly or through an intermediary. William Rowe objected to this course of argument claiming that all one is entitled to conclude is that the being is ‘very powerful’⁹, but not omnipotent—we know it can bring about all contingent states-of-affairs that actually are the case but what reason do we have to think it can bring about all others? An easy response comes to mind: being of its nature necessary, the being revealed in the PSR must exist in all possible worlds; if that is the case then—the notion of a contingent fact being the case for no reason at all having already been ruled out—the being could ultimately explain the existence of any contingent fact in every world in which it exists. Since it exists in all possible worlds, though, it exists alongside all possible contingent facts (thus all possible beings) and thus would have the power to actualise them.

An objection: might not it be the case that instead of the totality of contingent entities having its explanation in one necessary entity, the various subsets of that totality are explained by different necessary beings? Let us take two necessary beings, Scarlet and Azure. Scarlet has the power to actualise all contingent states-of-affairs related to material beings and Azure those relating to immaterial beings. What justification is there for belief in one omnipotent being as opposed to Scarlett and Azure or any number of specialised necessary beings? From the argument itself one can only appeal to the Principle of Parsimony—true, we have no a priori way of knowing that there is only the one necessary being, but if we can get away with only affirming one our theory will be in better shape.

This reveals an interesting limitation of the PSR argument taken on its own; namely that it proves there exists a necessary being but does not on its own furnish any further account of that being’s necessity¹⁰. This is not to the argument’s detriment (Clarke admits this limitation early on); after all, many philosophers, both atheist and theist, accept the existence of Platonic abstracta, for the necessity of which no account is given. By their very nature necessary facts are not brute facts, yet when weighing theoretical virtues it is considered good form to try to make necessity claims as transparent as possible. Let us look at the ‘necessity-making’ principles the PSR arguer might appeal to:

1. A form of Ontological Argument. This is the authentically Leibnizian option and the reason Kant claimed the Cosmological Argument depends upon the Ontological Argument to establish God’s existence. A perfect being is a necessary being and if a necessary being is possible then it is actual. We know from our PSR reasoning that a necessary being is actual, therefore we know that the ontological argument goes through, therefore our necessary being is a perfect being. The problem with this is that it gives no way of knowing whether the necessary beings in question are one and the same. At the back of the Leibnizian’s mind is the assumption that the only way one could account for the necessity of a concrete being is through its perfection, a claim modern philosophers might find too strong. A better way would be to claim that from Ontological Argument concerns we know that at least one necessary being is an omnipotent being, but that the existence of an omnipotent being is incompatible with almost omnipotent beings like Scarlet and Azure. If we have a priori reason to think omnipotence is metaphysically possible (the PSR argument certainly gives us reason to believe that) then we have additional reason to prefer that over merely epistemically possible limited necessary beings.

2. Divine Simplicity. Feser appeals to this option though he runs it into the next two options. A simple being, much like a perfect being, is such that if it is even possible then it actually exists. The challenge is then to derive some of the divine attributes from simplicity (Feser makes an interesting case for such in his Neo-Platonic proof) and argue in a similar way to the above.

3. Act and Potency. This the classic scholastic account, which will be looked at in greater detail during discussion of the Aristotelian Proof.

4. The identicality of Essence and Existence. This is the infamous Thomist account which holds that a necessary being (in the relevant sense) is a being in which essence and existence are one. Of all the accounts of necessity given this is probably the clearest. It requires commitment to an inflationary account of existence—one which treats existence as a really distinct property of things. Although Thomas derives this view from the Act/Potency distinction it is an open question whether one could hold it without that piece of Aristotelian metaphysics.

A few closing observations: none of these ways of accounting for necessity exclude the others; indeed, most of them follow from the others, e.g. in the case of 3 entailing 2 and 1. This gives the theist an impressive cumulative argument. One might worry that asking for an account of the being reached through the PSR cosmological argument is moving the goal posts; after all, it is only contingent being which requires an explanation and, unless the theist can give a very clear explanation of what elucidating necessity-maker principles actually means, all they have is a weak appeal to theoretical virtue. At any rate, in order for the theist to prove that the necessary being established in the course of PSR reasoning is God they must either show that the argument plus one’s background ontology means the being in question has all of the Divine Attributes, or that it is the only coherent (concrete) necessary being (in which case other attribute proofs pertaining to a necessary being in fact refer to this necessary being). Until such time theists must learn to live with the epistemic possibility of limited necessary beings.

Next up: the Aristotelian Argument

NOTES:

¹. This refers to the Cosmological Argument devised by Richard Gale and Alexander Pruss. The original paper can be read online here or with additional context in Gale’s God and Metaphysics. For an in-depth account of the Pruss-Gale Argument and some of the criticisms it has faced the reader should consult pages 51 to 97 of Emanuel Rutten’s A Critical Assessment of Contemporary Cosmological Arguments: Towards a Renewed Case for Theism.

². Other criticisms of the PSR usually take the form of denying the principle itself or claiming that we cannot, for Russelian reasons, coherently speak of a totality of contingent facts. Since none of them appear that plausible I do not discuss them here. There exists a further ingenious criticism mentioned by Rowe and further developed by Bede Rundle to the effect that instead of requiring a necessary being the existence of contingent being could equally be explained by a hypothetical principle: ‘necessarily there exists some contingent being’. Although a clear advance on criticisms which simply seek to deny the PSR I do not think this a serious contender to the necessary being option. For one thing the nature of this principle is left extremely unclear. For another it fails to satisfy variants of the PSR that cover all contingent facts or even all contingent existential facts: if it is necessarily the case that there exists a contingent being why is it the case that contingent being Y exists as opposed to contingent being X? This account provides no explanation as to why this possible world is the actual world.

³. This criticism is commonly associated with Peter Van Inwagen’s presentation of it in his 1983 volume An Essay on Free Will, although William Rowe had in fact raised a similar objection in his survey of the Cosmological Argument 8 years before. The most detailed presentation of modal collapse objections in contemporary literature can be found on pages 214 to 233 of J.H. Sobel’s dense and idiosyncratically written Logic and Theism. A dishonourable mention goes pages 119 to 123 of Graham Oppy’s Arguing About Gods.

⁴. The astute reader will have noticed that the much vaunted ‘Problem of Evil’ in fact boils down to the question of what worlds a morally good rational being can have a sufficient reason to actualise.

⁵. William Rowe sets out the various problems relating to Divine choice in his excellent study Can God be Free? though of course the question was first raised explicitly in relation to the PSR in Leibniz's correspondence with Samuel Clarke.

⁶. Here we come to a tricky question about priorities. Feser can hardly accept that truth is dependent on a contingent mind, that without thinking beings a certain fact e.g. ‘Snow is white’ is neither true nor false, since his denial of this forms a premise in his Augustinian Argument. Both he and the ‘Platonic’ atheist are committed to propositions being independent of contingent knowers. See pages 73 to 75 of Rutten for a good case as to why the PSR arguer can remain agnostic about the ontological status of propositions or even assay them in a nominalist manner should he or she wish to.

⁷. See page 240 of Gale’s On the Nature and Existence of God and pages 128 to 168 of Pruss’ The Principle of Sufficient Reason: A Reassessment.

⁸. See pages 148 to 157 of Smith’s Ethical and Religious Thought in Analytical Philosophy of Language for his ‘Divine Perfect Freedom’ objection to the Free Will Defense.

⁹. See pages 243 to 245 of Rowe’s The Cosmological Argument.

¹⁰. For reasons best known to themselves a number of people find this distinction confusing. For an explanation of how the Cosmological Argument establishes the existence of a logically necessary being without providing or needing to provide an account of that being’s necessity one is recommended to see Chapter 5 of Rowe’s study.

Bibliography:

Feser, Edward (2014). Scholastic Metaphysics: A Contemporary Introduction. Ignatius Press.
Feser, Edward (2017). Five Proofs of the Existence of God. Ignatius Press.
Gale, Richard (2004). God and Metaphysics. Prometheus Book
Gale, Richard (1999). On the Nature and Existence of God. Cambridge University Press
Oppy, Graham (2006). Arguing about Gods. Cambridge University Press.
Pruss, Alexander (2006). The Principle of Sufficient Reason: A Reassessment. Cambridge University Press.
Rowe, William (1975). The Cosmological Argument. Princeton University Press.
Rowe, William (2004). Can God Be Free?. Oxford University Press.
Rutten, Emanuel (2012). A Critical Assessment of Contemporary Cosmological Arguments:
Towards a Renewed Case for Theism. Academisch Proefschrift. Full text available here.
Smith, Quentin (2004). Ethical and Religious Thought in Analytical Philosophy of Language. Yale University Press.
Sobel, Jordan Howard (2004). Logic and Theism. Cambridge University Press.
van Inwagen, Peter (1983). An Essay on Free Will. Oxford University Press.

Critique of Edward Feser's Five Proofs

Over the course of the oncoming weeks I am going to undertake a critique of some of the arguments presented by Edward Feser in his new book, Five Proofs of the Existence of God. Although the tone of these articles will be primarily critical the intent will be to further the project of Natural Theology by flagging up areas where further work is required. I also hope, in later entries, to give some indication of how a non-theist who is not beholden to contemporary ‘scientistic’ naturalism might reply.

First under discussion will be Feser's account of the PSR Cosmological Argument, or, as he terms it, the Rationalist Proof.

Tropes or God, I: Bradley's Regress

In Relations, Monism, and the Vindication of Bradley's Regress and Bradley's Regress and Relation-Instances, Vallicella argues:

(1) There is a real difference between the sum a + R + b and fact aRb.

(2) This difference isn't brute¹. That is, it must have an ontological ground.

(3) This ground is in (i) constituents a, R, or b; (ii) one or more additional constituents in aRb; (iii) aRb itself; or (iv) something outside aRb.

(4) The ground isn't in (i), (ii), or (iii).

(5) From (1) – (4), something outside aRb grounds its difference from a + R + b.

His argument implies that without God the world would fall apart.²

I begin my attempt to exorcise Bradley's ghost by supporting Vallicella's premises.

Premises (1), (2), and (3)

Vallicella starts by distinguishing the sum a + R + b from the fact aRb. The sum exists as long as a, R, and b exist; in contrast, the fact only exists if a, R, and b are unified or “together”. The sum of John, a tea cup, and the two feet from relation exists as long as John, the tea cup, and the relation exist; the fact of those constituents only exists if John is two feet from the tea cup. In short, since John + the tea cup + the two feet from relation can exist without its corresponding fact existing, sums are different from facts.

Vallicella argues that this difference has an ontological ground. He argues that, one, if the difference between a + R + b and aRb is brute, they're both composed of nothing more than a, R, and b; two, if a + R + b and aRb are both composed of nothing more than a, R, and b, they're identical; three, since aRb is the unity of a + R + b's constituents, a + R + b isn't identical to aRb; thus four, if the difference between a + R + b and aRb is brute, a + R + b both is and isn't identical to aRb; thus five, the difference between a + R + b and aRb has an ontological ground. It follows from the last two paragraphs that the difference between sums and facts has an ontological ground.

The foregoing and some analysis entail that the difference between a + R + b and aRb is grounded in (i) the constituents a, R, or b, (ii) one or more additional constituents in aRb, (iii) aRb itself, or (iv) something outside aRb.

Premise (4)

Vallicella argues that this difference isn't grounded in (i), (ii), or (iii). First, he argues that a + R + b and aRb are both composed of a, R, and b; if a + R + b and aRb are both composed of a, R, and b, they're identical in respect of a, R, and b, and neither a, R, nor b can ground their difference; thus, neither a, R, nor b can ground the difference between a + R + b and aRb. In other words, he argues that assumptions behind the sum-fact distinction rule out (i).

Second, Vallicella argues that aRb can only ground its own unity if it exists logically prior to its existing; it therefore can't ground its own unity; the difference between the sum and its fact is that the sum isn't relevantly unified and the fact is; therefore, since aRb can't ground its own unity, it also can't ground the difference between a + R + b and itself. In brief, he argues that (ii) is incoherently circular.

Third, Vallicella argues that if one adds a constituent (C) to aRb to try grounding aRb's unity, this results in a further fact (aRCb) that needs its unity grounded. And if one adds another constituent (C*) to that fact, this results in another fact that needs its unity grounded, and so on with each new constituent ultimately failing to ground its corresponding fact's unity. In fewer words, he argues that (iii) leads to a vicious, infinite regress. It follows from the last three arguments that the difference between a + R + b and aRb isn't grounded in (i), (ii), or (iii).

If the foregoing arguments are right, (5) follows. In future posts, I shall argue that some of them are wrong, and build an ontology that grounds the unity of facts in particularized relations.

1. I use brute, here, to mean "lacking an ontological ground".

2. Or, if you're truly brave, you can accept fact infinitism. I won't be developing the inference from external unifier to God in this post, though I think it right.

Bibliography

Betti, Arianna. Against Facts. The MIT Press, 2015.
Betti, Arianna, and Jan Willem Wieland. “Relata-specificity: A Response to Vallicella”. Dialectica, vol. 62 no. 4, 2008, pp. 509-524.

Vallicella, William F. A Paradigm Theory of Existence: Onto-Theology Vindicated. Kluwer Academic  Publishers, 2002.

---. “Bradley's Regress and Relation-Instances”. The Modern Schoolman, LXXXI, 2004.

---. “Relations, Monism, and the Vindication of Bradley's Regress”. Dialectica, vol. 56 no. 1, 2002, pp. 3-35.