What Is Metaphysical Demonstration?

Contemporary philosophers have attempted to reasonably affirm the existence of God through an abductive approach or “cumulative case” apologetic.¹ The idea is that there is certain data that is better explained by the hypothesis that God exists than its rival atheism. Depending on what philosopher is making the cumulative case, such data may include the universe having a beginning, or being fine-tuned, or that many near death experiences have occurred (and been highly resistant to physicalist explanation).²

Atheists also make cumulative cases, arguing that we would better expect – or be able to explain – the data we see on their metaphysical hypothesis (say, naturalism). They might include suffering, evolution, and religious pluralism as points in their favor. The contest then becomes one of trying to get a higher degree of probability for one metaphysical hypothesis over another, which requires a careful analysis of the evidence and then arguments for why this or that evidence is better explained (or expected) by theism or atheism. Either way, the cumulative case approach claims only to give probability, not certainty, that its hypothesis is true.

Contrast this approach with metaphysical demonstration, provided either by St. Thomas Aquinas or contemporary Thomists.³ The idea is that we can argue for God’s existence not with probability, but certainty, by setting up an argument that is deductive in its logical form and supported by premises that cannot without great difficulty (or even coherently, for that matter) be denied. In which case, the conclusion follows necessarily and inescapably. Hence the word “proof” being used.  (Example here.)

Further, metaphysical demonstrations for God should be distinguished from what are called propter quid (“why it is the case”) arguments, which is a form of reasoning familiar to science and average experience. Propter quid arguments proceed from a known cause to explain some observed effect. If someone notices a coffee ring on a table and they suggest somebody must have left their beverage there, they are offering an argument propter quid: They are appealing to a known cause to explain why the effect exists.

Conversely, some reasoning moves from effect to cause even if that cause is unknown. Recently, my dog (a St. Bernard) was having bowel issues – major ones, in fact – that prevented her from evacuating. My wife stipulated there must have been intestinal blockage (she has a habit of getting into the trash — my dog, that is.). Within a couple days, the blockage was evacuated: a clump of paper towels. The point is the effect would not have been intelligible unless there were some cause, even if we knew nothing more about the cause aside from it had the power to disrupt Lola’s digestive activity. The point to emphasize is we can demonstrate the existence of some cause from effects in the world without immediately knowing the nature of what that cause is, only that it must have the power to produce the effect under consideration: If there were no blockage (whatever that is), then Lola would be pooping normally. Lola is not pooping normally. So, there is blockage. This latter form of argumentation is known as demonstration quia (“that it is the case”).

Thus, metaphysical demonstrations are 1) deductive (vs inductive or abductive) and 2) quia (vs propter quid).

With an example of deductive argument being:

1)     All men are mortal

2)     Socrates is a man

3)     Therefore, Socrates is mortal.

Regarding deductive argumentation, if we were to draw Euler circles we could “see” the conclusion contained implicitly in the premises, since Socrates is contained in the class of man, and since the class of man is contained in the class of mortal, Socrates is himself contained in the class of mortal. Hence why the conclusion follows inevitably in a valid deductive syllogism given the truth of the premises.

It should be clear that if there is in fact a successful metaphysical demonstration for God, then cumulative case approaches against theism can do little to no work unless that metaphysical demonstration is shown to be unsound. The deductive nature of a metaphysical demonstration overpowers the abductive approach of cumulative case apologetics.

Here is an example of just such a metaphysical demonstration for God.

1)     Things change.

2)     Whatever is changed is changed by another.

3)     This causal series cannot proceed infinitely.

4)     Therefore, there is an unchanged changer.

The purpose of this article is not to defend this particular argument – a version of Aquinas’s 1st Way – but to highlight how metaphysical demonstration is supposed to work — and that will require at least some exposition. Still, it should be clear by this set up that if the premises are true we would derive the conclusion of an unchanged changer (which Aquinas, for various reasons, would take to be God).

The first thing to note is the starting point, which is to say that things change. This seems obvious enough; certainly, it is one of the most basic aspects of experience. However, the “things changes” starting point is more secure than people may initially realize, since to deny change – as some philosophers have been wont to do – results in radical incoherence and ultimately self-defeat.⁴ For change must be a real feature of the world for somebody to work their way even logically through an (ultimately sophistical) argument for why they wind up denying the reality of change. Thus, to deny it is already to assume it. The point is that metaphysical demonstration, to constitute a proof, must start from some aspect of experience that is not just exceedingly general but undeniable apart from incoherence. Other starting points for metaphysical demonstration may be, “there is a cause,” or “contingent things exist,” or “some things are composite,” etc.   

The next step is to analyze (metaphysically) that starting point then deduce some causal principle from it. For our purposes, St. Thomas Aquinas follows Aristotle in arguing that change involves the actualization of potential. Which is to say, for something to change is for that something to have actualized an inherent latency within itself – some potential aspect. For example, I am currently drinking a hot cup of coffee; however, the water in my coffee was previously cold. How the water became hot – since at one point it was actually cold – must be explained by the water having a potential to become hot and that potential becoming actualized. If we fail to admit the distinction between actual being and potential being, we plunge into the absurdity of having to say something comes from nothing, which is unacceptable. The water becoming hot does not involve something coming from nothing but rather an inherent potential – a particular “being in dormancy” related to the very nature of water – becoming non-dormant, or actual.⁵

The question then is how this happens, and the response is that something already actual causes it. Why so? Because potential being – qua potential – cannot rise itself to being actual since it has no actual power to do so. For example, my only potentially writing this article does nothing to instruct anybody about metaphysical demonstration: only my actually having written this article does. Or, my only potentially lifting a barbell does nothing to increase my muscle strength; only actually lifting the barbell does. The other option, namely that nothing causes the potential to become actual, is equally absurd. There is just one alternative left: whatever is made actual must be made actual by something already actual. Hence why it was the flame (ultimately) that caused the water to heat up, which was actual in the relevant respect to actualize that inherent potential in water.

Importantly, we do not derive the cause principle that whatever is reduced from potency to act is so reduced by something already in act by just observing x-number of instances of it. Indeed, this causal principle is about as inductively supported as anything can get, but really it is derived deductively by evaluating the logically exhaustive alternatives and seeing that two of the three are impossible, forcing us to accept the third. Potential being cannot make potential being actual (remember: potential being, as potential, is not yet actual, so no actual causal power!) and neither can nothing, so it must be actual being that makes potential being actual, if potential being is made actual at all. Also, importantly, this does not mean that whatever is made actual is made actual by something formally identical. While this may sometimes be the case, it does not always have to be the case; all that is required is that whatever makes some potential being actual (call that being y) is that that something have an y-ness producing power. So, while something already hot can make other things hot (something of the form y causing something else to be of the form y), I can make a chair without myself being a chair. In virtue of being a rational animal I have a chair-producing power: given the right material and my rational powers (trained to an appropriate degree), I can actualize the potential in those materials to become a chair. Finally, note that even things which appear to be self-movers – such as animals – always have some controlling part (that is actual in some respect) that moves another part (that is potential in another respect); never do we have something that is both actual and potential in the same aspect – and nor could we, because that is a contradiction. Hence, whatever is moved from potential being to actual being is moved by something already actual.

The next step is to argue this chain cannot proceed infinitely, in which case, there must be something which is categorically different – call that, a “primary cause” – to ultimately explain the category of changing things – that is, things rising from potential being to actual being – otherwise we invite vicious circularity. But whatever is categorically different than changing things (= things made actual through another) must be unchanging (= actual through itself) – so, how do we get there?

The argument against this causal chain proceeding infinitely (perhaps other causal chains could proceed infinitely? We leave that open.) relates to the notion of actuality being derived from – or dependent upon – something beyond itself. My coffee did not have the actuality of heat in virtue of itself; rather, it had to have that actuality imparted to it. If what heated my coffee itself did not have the actuality of heat in virtue of itself – for example, the pot my coffee was heated in – then we keep looking. However, once we get to fire, we find something that, by its very nature, has that actuality inherently rather than derivatively. In this case, we have found the primary cause of heat and our search is terminated, at least with respect to the actuality of heat (we may want to ask what caused the fire, but that is seeking explanation in a different order). It was ultimately the fire that made the coffee hot, through the instrument of the pot.⁶

John Haldane summarizes the argument well, “Here we need to distinguish between a series of items the members of which are, merely as it happens, causally related to one another, and a series whose members are intrinsically ordered as cause and effect. To adopt Aquinas’s scholastic terminology, the first is a causal series per accidents (coincidentally), the second a causal series per se (as such). We can perhaps imagine objects, marked off by points in the number line and receding to infinity, among which there are causal relations; but this is not an intrinsic causal series. Contrast this with the situation in which each object is an effect of its predecessor and a cause of its successor: but for object -2, object -2 would not be, and but for object -3, object -2 would not be, etc. Here it is essential to any item’s being a cause that it also be an effect; but it is not necessary that they be temporally ordered, for in this case the terms ‘predecessor’ and ‘successor’ are not being used in an essentially temporal way. This is what it means to speak of a per se causal series’. Since the existence qua cause of any item is derived from the causality of a predecessor there has to be a source of causal power from outwith the series of dependent causes – an ultimate and non-dependent cause.”⁷

In short, if some entity in a causal series does not possess the actuality through itself — including and especially the actuality of their very existence — but through another, we must trace back to that which possess the actuality or the ability to produce the actuality through its intrinsic principles, otherwise that actuality would not be in the causal series to begin with.[1] And if we are considering a causal series where the actuality under consideration is actual being itself, we must get to that which has actual being through itself and not through another – i.e., that which can impart actual being to all things which were previously potential in some respect without having to have actual being imparted to it. The argument is metaphysical (as opposed to physical) because it is concerned with not any particular instance of change but what change is essentially, namely the actualization of potential being to actual being. So, what we are looking for in the argument from change is not something which can just make something (say) hot but that which can impart being to the entire class of changing things without having to have being imparted to it.⁸

A potential loophole: Previously I said something did not have to be formally identical to the actuality it produces in other things, only that it had to have the power to produce that actuality (a kingmaker need not be a king, for example). What then is to stop someone from saying that perhaps the ultimate cause of the actual being of things is not actual being through itself but something which just has the power to produce actual being in other things? Here the exception cannot be granted, because if it were not actual being through itself, then it would need to have actual being imparted to it, and we are sent back into the causal regress. In this case whatever ultimately imparts being to everything which needs being imparted to it must be formally identical to actual being itself. There is no other way to halt the regress.

Again, why? Because at each level of being, the potential existence at a higher level is actualized by the existence of something actual at a lower level (water is actualized by the particular configuration of elements, which have the potential to be configured differently, themselves actualized by the particular configuration of particles, which have the potential to be configured differently, etc) and because this cannot proceed infinitely it must terminate in that whose existence need not be actualized by anything else — namely, by that which just is pure actuality itself.⁹

Or, as Gaven Kerr puts it, “The upshot of interpreting the first way as a metaphysical argument is that what is at stake in Aquinas’s consideration of motion is the actuality of things that themselves are dependent for their actuality. So if we recall that in defending the motion principle, Aquinas is concerned with showing that the actualisation of some potency requires a distinct principle by which that actualisation takes place, e.g. fire in heating the wood. Now, Aquinas gives no indication in the first way here that such actualisation is limited to the three species of motion, i.e. alteration, increase and decrease, and locomotion; rather he simply speaks in terms of actualisation of some potency. Hence, what is at stake in the first way is the actualisation of any potency. That being the case, Aquinas is concerned with explaining the actuality that things have; and if we may anticipate a little, when he gets to the conclusion that there is a primary mover that is moved in no respect, what this means is that there is a primary moved that is not actualised in any respect, i.e. that has no potency that is actualised. But if it is not actualised in any respect, it is pure actuality, and so all things that are actual are dependent on it, in which case all actuality flows from it.”¹⁰

The whole argument is essentially this, “No unchanged changer (= unactualized actualizer), no change. Change, therefore unchanged changer.” Aquinas gives arguments throughout his work for why the unchanging changer must be God; arguments we will not entertain now, because (once again) the purpose of this article is not to defend Aquinas’s 1st Way, but to highlight how metaphysical demonstration is supposed to provide a deductive approach to God. In that respect, I hope enough has been shown how that metaphysical demonstration proceeds from a decidedly secure starting point to some purely actual cause of every contingent reality – i.e. God.

That is not to say the argument is successful. There are, of course, objections we have not considered — plus, some important steps have been inadequately treated — but that is better left to articles dedicated to defending that particular metaphysical demonstration.¹¹ With the sketch of Aquinas’s 1st Way in place — which, whether successful or not, at least gives the idea of how metaphysical demonstration is supposed to work — I want to note how this approach differs from the cumulative case mentioned at the beginning of the article.

For one thing, it should be obvious that if — if, if, if! — a metaphysical demonstration goes through, then God’s existence has been established, which means other evidential considerations should be interpreted through the perspective of theism. For example, if someone thought that evil counted as evidence against God other things equal… well, if there is a successful metaphysical argument for God, that person should think God must not only be compatible with the evil and suffering we experience in the world but must have some good reason – even if we cannot see what that reason is – for allowing it.¹² Why? Because metaphysical demonstration also claims to tell us something about the nature of God (including that God is perfectly wise and good) which brings me to my next point.¹³

Metaphysical demonstration is able to extract the divine attributes in a way that cumulative case apologetics cannot. In abductive approaches to God, philosophers argue for God being all-powerful and all-knowing (largely) probabilistically, or suggestively. It is often remarked (for example) that if God is the cause of the universe, and if the universe is finely-tuned for the emergence of intelligent life, then it seems like God must have 1) enormous power to produce such a thing as a physical universe and 2) enormous intelligence to explain its extraordinarily exquisite set up.¹⁴ But being enormously powerful and enormously intelligent =/= being omnipotent or omniscient. I am not saying these arguments are without force, nor that other independent moves couldn’t be made to bridge the gap from enormously power to omnipotent. However, I am suggesting they are less forceful for establishing classical theism than metaphysical demonstration, which upon concluding that there is some unactualized actualizer, it cannot not be the case that this entity is omnipotent, omniscience, and perfectly good.

Space does not permit a full defense of these claims – especially since further metaphysical theses are required – but a few of them can be teased out. For example, that which is actual through itself (the unactualized actualizer) must be that which imparts actuality to anything which is actual through another (all potential realities). But that means it is the ultimate cause of everything distinct from itself. Further, if there can be only one unactualized actualizer – which Aquinas argues must be the case, particularly in his De Ente et Essentia – then that means the unactualized actualizer is the uncaused cause of everything else that exists or could exist, which is textbook omnipotence. But our world contains beings with substantial forms – which is to say, specific intelligible configurations of being – and whatever causes something must have the power to produce it (trivially but analytically true) – which is to say whatever is in the effect must IN SOME SENSE be in its total cause (principle of proportionate causality). God, however, cannot be materially identical to any of the forms God creates, otherwise God would just be those things, and it would be impossible for him to be all of them, or even any one of them, and still be God. This entails that God must contain the forms not as matter contains form but as form contains form, which is to say in an intellectual way (= as “ideas”, loosely speaking, in the mind of God). This shows God has (something like) intellect, and given God is the cause of all things distinct from himself, he cannot be ignorant about any such states of affairs, because his knowledge is executive: God knows everything that occurs in the world because God is the cause of it. This gives us omniscience. Further, if upon metaphysical analysis evil is ultimately a privation of some due good (or actuality) of being – i.e., being which has gone missing, for some reason or other, like blindness, or a hole in a sock – then that which is purely and fully actual cannot be in any sense evil – rather it must be fully and perfectly good.¹⁵ This absolves God from being the creator of evil because under the privation theory evil is not something created but something absent. What remains is the question — which is no doubt important — of why God created (or permitted) a world with absences. But that sketch should be sufficient to get the point across of how robust our conception of God is through metaphysical demonstration compared to cumulative case apologetics.

Metaphysical demonstration claims not to give us probable reason to believe God exists, but certainty, and not indications about what God is like, but knowledge. Granted, that knowledge is reached apophatically and analogically, and so there remains infinitely more mystery about God than clarity, but nevertheless we can confidently say – upon the success of metaphysical demonstration – that God is omnipotent, omniscient, perfectly good, eternal, immutable, and necessary.

1. Richard Swinburne would be one contemporary theistic philosopher who makes a cumulative probabilistic case. See his book The Existence of God: https://www.amazon.com/Existence-God-Richard-Swinburne/dp/0199271682  On the atheist side an example would be Paul Draper and his evidential arguments from evil. See https://philpapers.org/rec/DRAEAT-4

2. I offer a cumulative case apologetic for Catholicism, here: https://www.amazon.com/Metaphysics-Good-Evil-David-Oderberg-ebook/dp/B07V8K565G/ref=sr_1_3?dchild=1&keywords=metaphysics+good+and+evil&qid=1629140809&sr=8-3

3. Aquinas’s 5 Ways would be examples of metaphysical demonstration, though in summary form. See: https://aquinas.cc/la/en/~ST.I.Q2 . On the contemporary side, Edward Feser’s book 5 Proofs of the Existence of God (which are not Aquinas’s 5 Ways) claims to offer metaphysical demonstrations of God, as well. See: https://www.amazon.com/Five-Proofs-Existence-Edward-Feser/dp/1621641333

4. Parmenides seemed to want to deny change by implying that it would involve something coming from nothing, which is absurd. The response is to deny that change involves something coming from nothing (we agree that is absurd) and insist that upon deeper analysis we discover change involves potential being becoming actual being. See: https://en.wikisource.org/wiki/Fragments_of_Parmenides

5. Potentials are restricted by the essences, or natures. Water, for example, has a potential to become hot, but not a potential to speak German, given the sort of thing that it is.

6. Related to motion specifically, we can borrow Aquinas’s example of a hand, which moves a stick, which moves a stone. The stone acquires the actuality (or causal property) of movement (which it does not have inherently) because of the stick, which acquires the actuality because of the hand… but the hand itself only has that actuality derivatively. It is in virtue of the mental agent, acting as primarily cause – namely, that which has the causal property in virtue of itself – that the actuality of motion is introduced to the causal series at all, and without which there would be no such actuality. No mental agent, no movement to the hand, no movement to the stick, no movement to the stone. No primary cause, no casual property.

7. Theism and Atheism pg. 123.

8. An example of the first: Fire possesses the actuality of heat in virtue of what it is. An example of the second: a box of matches plus somebody with the ability to strike one – those entities working in tandem – possess the ability to produce heat in virtue of what they are, though they are not already hot.

9. For more justification on why the actualization of any changing things potential for existence must ultimately be actualized by an unactualized actualizer (for at any moment it exists) see Ed Feser’s Aristotelian Proofs in 5 Proofs:

10. Forthcoming in our book on Aquinas’s 5 Ways.

11. See Ed Feser’s Aquinas: A Beginner’s Guide, for example. David Oderberg’s Reappraisal of the 1st Way, as well: https://drive.google.com/file/d/0B7SKlRTfkUieN3dGVkhNTi1SQUU/view?resourcekey=0-rsz17QbtVgw3Ir7AkkZjgw

12. [8] I do not accept that evil counts as evidence against God. In fact, I arguing for the opposite conclusion here: https://www.catholic.com/magazine/online-edition/how-evil-proves-gods-existence

13. Same with evolution or religious pluralism. If God wanted to bring life about gradually and given that God exists, then that is God’s prerogative. As for diversity of religious beliefs (and non-belief), perhaps God just wants people to find their unique independent path to moral formation? In fact, that is just what religious pluralists who believe in God frequently contend. I personally don’t believe that — and Christian’s certainly have their own resources for handling pluralism and non-belief — but we needn’t settle that issue now. In fact, aside from infusing these data points with particular evils, it is hard to see how either evolution or religious pluralism could be counted even superficially as data points inconsistent with theism. Still, with metaphysical demonstration in place there is epistemic privileging, in which case someone should favor a theistic interpretation of these datum than an atheistic one.

14. Philosopher Stephen Meyer takes this approach in his recent volume Return of the God Hypothesis. https://www.amazon.com/Return-God-Hypothesis-Scientific-Discoveries/dp/B08DRSBYRJ/ref=sr_1_1?dchild=1&keywords=return+of+the+God+hypothesis&qid=1629132739&s=books&sr=1-1

15. For an extended defense of the privation theory, see David Oderberg’s The Metaphysics of Good and Evil: https://www.amazon.com/Metaphysics-Good-Evil-David-Oderberg-ebook/dp/B07V8K565G/ref=sr_1_3?dchild=1&keywords=metaphysics+good+and+evil&qid=1629140809&sr=8-3