Rebuking Rasmussen’s Geometric Argument

By R.N. Carmona

My purpose here is twofold: first and foremost, I want to clarify Rasmussen’s argument because though I can understand why word of mouth can lead to what is essentially a straw man of his argument, especially in light of the fact that his argument requires one to pay for an online article or his book Is God the Best Explanation of Things? which he coauthored with Felipe Leon, it is simply good practice to present an argument fairly. Secondly, I want to be stern about the fact that philosophy of religion cannot continue to rake these dead coals. Rasmussen’s argument is just another in a long, winding, and quite frankly, tired history of contingency arguments. In in any case, the following is the straw man I want my readers and anyone else who finds this post to stop citing. This is decidedly not Rasmussen’s argument:


Rasmussen has no argument called The Argument From Arbitrary Limits. Arbitrary limits actually feature in Leon’s chapter in where he expresses skepticism of Rasmussen’s Geometric Argument (Rasmussen Joshua and Leon, Felipe. Is God The Best Explanation For Things. Switzerland: Palgrave Macmillan. 53-68. Print.). Also, Rasmussen has a Theistic conception of God (omnipresent, wholly good, etc.) that is analogous to what Plantinga means by maximal greatness, but Rasmussen does not refer to God using that term. Perhaps there is confusion with his use of the word maximal conceivable. While given Rasmussen’s beliefs, he implies God with what he calls a maximal foundation, “a foundation complete with respect to its fundamental (basic, uncaused) features” (Ibid., 140). He makes it clear throughout the book that he is open to such a foundation that is not synonymous with God. In any case, his maximal conceivable is not a being possessing maximal greatness; at least, not exactly, since it appears he means something more elementary given his descriptions of basic and uncaused, as these clearly do not refer to omnipresence, perfect goodness, and so on. There may also be some confusion with his later argument, which he calls “The Maximal Mind Argument” (Ibid. 112-113), which fails because it is relies heavily on nonphysicalism, a series of negative theories in philosophy of mind that do not come close to offering alternative explanations for an array of phenomena thoroughly explained by physicalism (see here). In any case, Rasmussen has no argument resembling the graphic above. His arguments rest on a number of dubious assumptions, the nexus of which is his Geometric Argument:

JR1 Geometry is a geometric state.

JR2 Every geometric state is dependent.

JR3 Therefore, Geometry is dependent.

JR4 Geometry cannot depend on any state featuring only things that have a geometry.

JR5 Geometry cannot depend on any state featuring only non-concrete (non-causal) things.

JRC Therefore, Geometry depends on a state featuring at lest one geometry-less concrete thing (3-5) (Ibid., 42).

Like Leon, I take issue with JR2. Leon does not really elaborate on why JR2 is questionable saying only that “the most basic entities with geometry (if such there be) have their geometrics of factual or metaphysical necessity” and that therefore, “it’s not true that every geometric state is dependent” (Ibid., 67). He is correct, of course, but elaboration could have helped here because this is a potential defeater. Factual and metaphysical necessity are inhered in physical necessity. The universe is such that the fact that every triangle containing a 90-degree angle is a right triangle is reducible to physical constraints within our universe. This fact of geometry is unlike Rasmussen’s examples, namely chair and iPhone shapes. He states: “The instantiation of [a chair’s shape] depends upon prior conditions. Chair shapes never instantiate on their own, without any prior conditions. Instead, chair-instantiations depend on something” (Ibid., 41). This overt Platonism is questionable in and of itself, but Leon’s statement is forceful in this case: the shape of the chair is not dependent because it has its shape of factual or metaphysical necessity that stem from physical necessity. Chairs, first and foremost, are shaped the way they are because of our shape when we sit down; furthermore, chairs take the shapes they do because of physical constraints like human weight, gravity, friction against a floor, etc. For a chair not to collapse under the force of gravity and the weight of an individual, it has to be engineered in some way to withstand these forces acting on it; the chair’s shape is so because of physical necessity and this explains its metaphysical necessity. There is therefore, no form of a chair in some ethereal realm; an idea like this is thoroughly retrograde and not worth considering.

In any case, the real issue is that chair and iPhone shapes are not the sort of shapes that occur naturally in the universe. Those shapes, namely spheres, ellipses, triangles, and so on, also emerge from physical necessity. It is simply the case that a suspender on a bridge forms the hypothenuse of a right triangle. Like a chair, bridge suspenders take this shape because of physical necessity. The same applies to the ubiquity of spherical and elliptical shapes in the universe. To further disabuse anyone of Platonic ideas, globular shapes are also quite ubiquitous in the universe and are more prominent the closer we get to the Big Bang. There are shapes inherent in our universe that cannot be neatly called geometrical and even still, these shapes are physically and therefore, metaphysically necessitated. If JR2 is unsound, then the argument falls apart. On another front, this addresses Rasmussen’s assertion that God explains why there is less chaos in our universe. Setting aside that the qualification of this statement is entirely relative, the relative order we see in the universe is entirely probabilistic, especially given that entropy guarantees a trend toward disorder as the universe grows older and colder.

Like Leon, I share his general concern about “any argument that moves from facts about apparent contingent particularity and an explicability principle to conclusions about the nature of fundamental reality” (Ibid., 67) or as I have been known to put it: one cannot draw ontological conclusions on the basis of logical considerations. Theistic philosophers of religion and unfortunately, philosophers in general, have a terrible habit of leaping from conceivability to possibility and then, all the way to actuality. Leon elaborates:

Indeed, the worry above seems to generalize to just about any account of ultimate reality. So, for example, won’t explicability arguments saddle Christian theism with the same concern, viz. why the deep structure of God’s nature should necessitate exactly three persons in the Godhead? In general, won’t explicability arguments equally support a required explanation for why a particular God exists rather than others, or rather than, say, an infinite hierarchy of gods? The heart of the criticism is that it seems any theory must stop somewhere and say that the fundamental character is either brute or necessary, and that if it’s necessary, the explanation of why it’s necessary (despite appearing contingent) is beyond our ability to grasp (Ibid., 67-68).

Of course, Leon is correct in his assessment. Why not Ahura Mazda, his hypostatic union to Spenta Mainyu, and his extension via the Amesha Spentas? If, for instance, the one-many problem requires the notion of a One that is also many, what exactly rules out Ahura Mazda? One starts to see how the prevailing version of Theism in philosophy of religion is just a sad force of habit. This is why it is necessary to move on from these arguments. Contingency arguments are notoriously outmoded because Mackie, Le Poidevin, and others have already provided general defeaters that can apply to any particular contingency argument. Also, how many contingency arguments do we need exactly? In other words, how many different ways can one continue to assert that all contingent things require at least one necessary explanation? Wildman guides us here:

Traditional natural theology investigates entailment relations from experienced reality to, say, a preferred metaphysics of ultimacy. But most arguments of this direct-entailment sort have fallen out of favor, mostly because they are undermined by the awareness of alternative metaphysical schemes that fit the empirical facts just as well as the preferred metaphysical scheme. By contrast with this direct-entailment approach, natural theology ought to compare numerous compelling accounts of ultimacy in as many different respects as are relevant. In this comparison-based way, we assemble the raw material for inference-to-the-best-explanation arguments on behalf of particular theories of ultimacy, and we make completely clear the criteria for preferring one view of ultimacy to another.

Wildman, Wesley J. Religious Philosophy as Multidisciplinary Comparative Inquiry: Envisioning a Future For The Philosophy of Religion. State University of New York Press. Albany, NY. 2010. 162. Print.

Setting aside that Rasmussen does not make clear why he prefers a Christian view of ultimacy as opposed to a Zoroastrian one or another one that may be proposed, I think Wildman is being quite generous when saying that “alternative metaphysical schemes fit the empirical facts just as well as the preferred metaphysical scheme” because the fact of the matter is that some alternatives fit the empirical facts better than metaphysical schemes like the ones Christian Theists resort to. Rasmussen’s preferred metaphysical scheme of a maximal foundation, which properly stated, is a disembodied, nonphysical mind who is omnipresent, wholly good, and so on rests on dubious assumptions that have not been made to cohere with the empirical facts. Nonphysicalism, as I have shown in the past, does not even attempt to explain brain-related phenomena. Physicalist theories have trounced the opposition in that department and it is not even close. What is more is that Christian Theists are especially notorious for not comparing their account to other accounts and that is because they are not doing philosophy, but rather apologetics. This is precisely why philosophy of religion must move on from Christian Theism. We can think of an intellectual corollary to forgiveness. In light of Christian Theism’s abject failure to prove God, how many more chances are we required to give this view? Philosophy of religion is, then, like an abused lover continuing to be moved by scraps of affection made to cover up heaps of trauma. The field should be past the point of forgiveness and giving Christian Theism yet another go to get things right; it has had literal centuries to get its story straight and present compelling arguments and yet here we are retreading ground that has been walked over again and again and again.

To reinforce my point, I am going to quote Mackie and Le Poidevin’s refutations of contingency arguments like Rasmussen’s. It should then become clear that we have to bury these kinds of arguments for good. Let them who are attached to these arguments mourn their loss, but I will attend no such wake. What remains of the body is an ancient skeleton, long dead. It is high time to give it a rest. Le Poidevin put one nail in the coffin of contingency arguments. Anyone offering new contingency arguments has simply failed to do their homework. It is typical of Christian Theists to indulge confirmation bias and avoid what their opponents have to say. The problem with that is that the case against contingency arguments has been made. Obstinacy does not change the fact. Le Poidevin clearly shows why necessary facts do not explain contingent ones:

Necessary facts, then, cannot explain contingent ones, and causal explanation, of any phenomenon, must link contingent facts. That is, both cause and effect must be contingent. Why is this? Because causes make a difference to their environment: they result in something that would not have happened if the cause had not been present. To say, for example, that the presence of a catalyst in a certain set of circumstances speeded up a reaction is to say that, had the catalyst not been present in those circumstances, the reaction would have proceeded at a slower rate. In general, if A caused B, then, if A had not occurred in the circumstances, B would not have occurred either. (A variant of this principle is that, if A caused B, then if A had not occurred in the circumstances, the probability of B’s occurrence would have been appreciably less than it was. It does not matter for our argument whether we accept the origin principle or this variant.) To make sense of this statement, ‘If A had not occurred in the circumstances, B would not have occurred’, we have to countenance the possibility of A’s not occurring and the possibility of B’s not occurring. If these are genuine possibilities, then both A and B are contingent. So one of the reasons why necessary facts cannot causally explain anything is that we cannot make sense of their not being the case, whereas causal explanations requires us to make sense of causally explanatory facts not being the case. Causal explanation involves the explanation of one contingent fact by appeal to another contingent fact.

Le Poidevin, Robin. Arguing for Atheism: An Introduction to the Philosophy of Religion. London: Routledge, 1996. 40-41. Print.

This is a way of substantiating that an effect is inhered in a cause or the principle, like effects from like causes. This has been precisely my criticism of the idea that a nonphysical cause created the physical universe. There is no theory of causation that permits the interaction of an ethereal entity’s dispositions and that of physical things. It is essentially a paraphrase of Elizabeth of Bohemia’s rebuttal to Cartesian dualism: how does mental substance interact with physical substance? This is why mind-body dualism remains in a state of incoherence, but I digress. Mackie puts yet another nail in the coffin:

The principle of sufficient reason, then, is more far-reaching than the principle that every occurrence has a preceding sufficient cause: the latter, but not the former, would be satisfied by a series of things or events running back infinitely in time, each determined by earlier ones, but with no further explanation of the series as a whole. Such a series would give us only what Leibniz called ‘physical’ or ‘hypothetical’ necessity, whereas the demand for a sufficient reason for the whole body of contingent things and events and laws calls for something with ‘absolute’ or ‘metaphysical’ necessity. But even the weaker, deterministic, principle is not an a priori truth, and indeed it may not be a truth at all; much less can this be claimed for the principle of sufficient reason. Perhaps it just expresses an arbitrary demand; it may be intellectually satisfying to believe there is, objectively, an explanation for everything together, even if we can only guess at what the explanation might be. But we have no right to assume that the universe will comply with our intellectual preferences. Alternatively, the supposed principle may be an unwarranted extension of the determinist one, which, in so far as it is supported, is supported only empirically, and can at most be accepted provisionally, not as an a priori truth. The form of the cosmological argument which relies on the principle of sufficient reason therefore fails completely as a demonstrative proof.

Mackie, J. L. The Miracle of Theism: Arguments for and against the Existence of God. Oxford: Clarendon, 1982. 86-87. Print.

Every contingency argument fails because it relies on the principle of sufficient reason and because necessity does not cohere with contingency as it concerns a so-called causal relation. Mackie, like Le Poidevin, also questions why God is a satisfactory termination of the regress. Why not something something else? (Ibid., 92). Contingency arguments amount to vicious special pleading and an outright refusal to entertain viable alternatives, even in cases where the alternatives are nonphysical and compatible with religious sentiments. In any case, it would appear that the principle of sufficient reason is not on stable ground. Neither is the notion that a necessary being is the ultimate explanation of the universe. Contingency arguments have been defeated and there really is no way to repeat these arguments in a way that does not fall on the horns of Le Poidevin and Mackie’s defeaters. Only the obdurate need to believe that God is the foundational explanation of the universe explains the redundancy of Christian Theists within the philosophy of religion. That is setting aside that apologetics is not philosophy and other complaints I have had. The Geometric Argument, despite using different language, just is a contingency argument. If the dead horse could speak, it would tell them all to lay down their batons once and for all, but alas.

Ultimately, contingency arguments are yet another example of how repetitive Christianized philosophy of religion has become. There is a sense in which Leon, Le Poidevin, and Mackie are paraphrasing one another because, and here is a bit of irony, like arguments result in like rebuttals. They cannot help but to sound like they each decided or even conspired to write on the same topic for a final paper. They are, after all, addressing the same argument no matter how many attempts have been made to word it differently. It is a vicious cycle, a large wheel that cannot keep on turning. It must be stopped in its tracks if progress in the philosophy of religion is to get any real traction.

One comment

  1. Pingback: Skeptical Theism and New Arguments For Atheism | The Philosophy Corner

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