Does the Cosmological Argument Prove That God Exists?
I will conclude that the cosmological argument does not prove that God exists
- Cosmological arguments are a posteriori arguments which aim to show that God exists by appealing to broad general facts about the world — that things have causes, or that things exist contingently — and arguing that these facts can only be fully explained by God - I will consider two versions: the Kalam cosmological argument, which argues from the fact that the universe began to exist, and Leibniz's cosmological argument from contingency, which argues from the principle of sufficient reason - Against each I will consider progressively more powerful objections: Hume's attack on the causal principle against the Kalam, the fallacy of composition against Leibniz, and — most crucially — the objection that both arguments commit special pleading by exempting God from their own explanatory demands, and that the only principled response to this charge requires a successful ontological argument, which neither cosmological argument can provide - I will conclude that the cosmological argument does not prove that God exists
Section 1: The Kalam Cosmological Argument and Hume's Attack on the Causal Principle
- Al-Ghazali's infinity paradoxes are defeated by modern mathematics — the traversal objection relies on a confused picture of infinity, and the Jupiter-Saturn paradox dissolves under transfinite arithmetic. These a priori defences of P1 fail - However Craig's Big Bang defence is significantly more resilient. It provides genuine empirical support that the universe had a beginning and is not vulnerable to the mathematical objections that defeat al-Ghazali. P1 survives - Hume's attack on P2 is powerful. The singularity point is particularly well-taken — modern physics gives us no reason to think the causal principle holds at the extreme conditions of the universe's origin. P2 cannot be established either a priori or a posteriori and the argument is seriously damaged - The Kalam therefore partially survives through Craig's empirical defence of P1, but P2 remains unjustified. The argument is significantly weakened but has not entirely collapsed
: The Kalam cosmological argument
- The Kalam cosmological argument was developed by the medieval Islamic philosopher al-Ghazali. It begins from the observation that the universe began to exist and argues that anything which begins to exist must have a creator. Formally: - P1. The universe began to exist - P2. Anything that begins to exist needs a creator - C. Therefore the universe has a creator — God - Al-Ghazali defends P1 using paradoxes about infinity. First, he argues that if the universe had existed forever, time would have to go back forever, meaning an infinite stretch of time would have had to be traversed to reach the present. If that were so, the present would never have been reached — yet it has. The past therefore cannot be infinite and the universe must have begun to exist - Second, he argues that if past time were infinite, Jupiter and Saturn would each have completed an infinite number of orbits. But since Jupiter orbits every 12 years and Saturn every 30, Jupiter must have orbited at least twice as many times as Saturn — meaning their orbit counts would be simultaneously greater than and equal to each other. This contradiction shows the past cannot be infinite - In defence of P2, al-Ghazali argues that we know by rational necessity that nothing originates in time by itself, and that therefore anything which begins to exist needs a creator. This is the causal principle — that every event which begins to exist must have a cause
: Attack on al-Ghazali's defence of P1
- Al-Ghazali's infinity paradoxes rest on confusions about infinity that modern mathematics dissolves. To say the universe has existed forever is not to say there is a beginning infinitely distant from the present — it is simply to say there is no beginning at all. The idea of an infinite stretch of time having to be traversed to reach the present is therefore confused: traversal implies a starting point, but an eternal universe has none - The Jupiter-Saturn paradox similarly dissolves under transfinite arithmetic. If both planets have orbited the sun an infinite number of times, their orbit counts are simply equal — this is a well-established property of infinite sets, not a contradiction. Al-Ghazali's argument assumes that infinite quantities behave like finite ones, which they do not
: Craig's Big Bang defence of P1
- William Lane Craig supplements al-Ghazali with a contemporary a posteriori defence. The Big Bang theory provides strong empirical evidence that the universe had a definite beginning approximately 13.8 billion years ago. Even if al-Ghazali's a priori arguments fail against modern mathematics, Craig argues that modern cosmology independently and empirically establishes P1. This defence is not vulnerable to the mathematical objections that defeat al-Ghazali
Hume: Hume's attack on P2
- P2 depends on the causal principle — that nothing originates in time by itself. Hume argues this cannot be established - First, it cannot be known a priori: there is nothing in the concept of an event which entails that it must have a cause. An uncaused event is not a logical contradiction in the way a four-sided triangle is — we can conceive of it without contradiction - Second, it cannot be established a posteriori: the range of events we have observed is far too limited to justify a universal causal principle extending to the origin of the universe itself. Physicists refer to the Big Bang as a singularity — a point at which our current physical theories break down entirely. The only relevant evidence for the universe having a cause would be observing the origins of multiple universes, which we have never done. We have no empirical basis for assuming that causal conditions which hold within the universe also hold at its ultimate origin
Section 2: Leibniz's Argument from Contingency and the Fallacy of Composition
- Copleston's response has genuine force. If PSR holds universally, then the series itself is a contingent fact demanding explanation, and Russell's mother analogy does not straightforwardly refute this — Leibniz is not simply committing an informal fallacy - However Russell's deeper point — that a series is a mental construction rather than a concrete thing — is difficult to dismiss. Copleston assumes the series is itself a well-formed object of explanation, but that is precisely what is at issue. The fallacy of composition objection is not conclusive but significantly damages the argument - The real vulnerability of Leibniz's argument is not the fallacy of composition but what happens at the conclusion — which is what Point 3 addresses
: Leibniz's cosmological argument
- Leibniz’s cosmological argument begins from what he calls the principle of sufficient reason. This principle states that every fact has an explanation that provides a sufficient reason for why things are as they are and not otherwise, ie fully explains why it is the case. - The model of explanation that Leibniz has in mind here comes from mathematics, where the truth of each theorem is fully explained by the proof that mathematicians have given of it. - Leibniz believed that any necessary truth could be reduced through a finite process of logical analysis into ‘primitive truths of identity’, when the predicate is shown to be explicitly contained within the subject, eventually reaching an undeniable self-identity like 1+1=1+1. - The next key step in Leibniz’s argument, is to argue that contingent facts can never be fully explained in terms of other contingent facts. Every contingent fact needs some kind of explanation beyond itself- there is no contingent fact that is so obvious that it needs no further explanation. For Leibniz, the only facts that don’t need further explanation are necessary truths like 1 + 1 = 2. As every contingent fact needs explanation, we will never be able to fully explain contingent facts by just appealing to other contingent facts. - From this claim and the principle of sufficient reason, it follows that there must be some necessary fact or facts that explain all of the contingent facts about the world. Leibniz argues that the existence of God is the only necessary fact that can provide us with this explanation. The reason for this is that God is self-explanatory, and so needs no further explanation. But there is no other possible being which can explain its own existence in this way; so only God can provide us with a sufficient reason for all of the contingent facts about the world. - Formally: - P1. The principle of sufficient reason: every fact has an explanation that provides a sufficient reason for why things are as they are and not otherwise - P2. There are two kinds of facts: necessary and contingent - P3. The sufficient reason for necessary facts is found by a priori analysis: a finite process of analysis will resolve it into primitive truths of identity - P4. The sufficient reason of contingent facts cannot be found in other contingent facts, because these too will require a reason, and so on: no finite process of analysis will resolve them into primitive truths of identity - C1. Therefore, to provide a sufficient reason for any contingent fact, we must look outside the sequence of contingent facts - C2. Therefore, the sufficient reason for contingent facts must be a necessary substance that is a sufficient reason for all contingent facts - C3. This necessary substance is God - C4. Therefore, God exists - This argument is stronger than the Kalam: by beginning from an a priori principle of sufficient reason rather than from the observation of temporal causation, it appears to escape Hume's inductive attack entirely
: The fallacy of composition
- Russell argues that cosmological arguments commit the fallacy of composition — inferring that what is true of the parts of something must be true of the whole. An argument commits this fallacy when it assumes that because the parts of a thing have a certain property, the thing composed of those parts must have that property too - Russell's vivid example: just because every individual human being has a mother does not mean the human race as a whole has a mother. The inference from parts to whole fails - Applied to Leibniz: just because every contingent fact within the universe requires a sufficient explanation does not mean the totality of contingent facts — the universe as a whole — requires an explanation beyond itself. The universe may simply not have the same properties as its parts - Hume develops this further: imagine an infinite series of contingent beings, each explained by the one before it. Once every part of the series has been explained by its predecessor, the whole series is explained. There is no further unexplained 'whole' left over that requires its own separate explanation — the parts exhaust the explanatory task - This means we cannot simply point to the fact that each thing within the universe has an explanation and infer that the universe itself must have an external explanation. That inference is precisely what the fallacy of composition warns against
: Copleston's response
- Copleston argues that Leibniz's argument does not infer that the whole requires explanation because its parts do — it begins from an a priori principle of sufficient reason that every fact whatsoever requires explanation. The fallacy of composition objection therefore misunderstands the argument's structure entirely - A series of contingent beings — even an infinite one — is itself a contingent fact. No number of contingent beings can add up to a necessary being, just as no number of finite numbers adds up to infinity. The series as a whole therefore remains contingent and still requires an explanation that cannot be found within itself - Copleston adds that we can always ask, as Aristotle put it, why an infinite series exists at all. The existence of the series — including the causal power running through it — is itself a further fact demanding explanation. Simply pointing to the parts of the series does not answer this deeper question
Hume: Russell and Hume's reification counter
- Russell replies that Copleston's response commits what we might call a reification fallacy — treating an abstract concept, namely a series, as if it were a concrete thing requiring its own explanation. A series is not an entity over and above its parts; it is a mental construction we impose on a collection of things - Because a series is nothing over and above its parts, there is no additional fact of the series's existence requiring its own explanation. Once every member of the series is explained, there is simply nothing left to explain - Asking for the explanation of the series as a whole is therefore asking a question that may not be well-formed — it mistakes a mental abstraction for a genuine object of explanation - Furthermore, Russell points out that our concept of cause and explanation comes entirely from experience of individual things within the universe. Copleston illegitimately extends this concept to the universe or its totality, which is not something we have any experience of. There is no basis for assuming the concept applies there - Hume adds that in an infinite series, each contingent fact is fully explained by prior contingent facts. The explanatory demand is satisfied at every step. Demanding a further explanation of the whole is simply demanding an explanation that has already been given — distributed across the parts rather than concentrated in a single external source
Section 3: Special Pleading and the Smuggled Ontological Argument
- The special pleading objection is internally defeating in the strongest sense — it turns the arguments' own explanatory demands back on themselves. The theist response is genuinely philosophically serious and cannot simply be dismissed, which is what makes Kant's counter so powerful: it does not deny the distinction between necessity and contingency, but shows that establishing the relevant kind of necessity requires philosophical work that no cosmological argument can do - This objection applies to both arguments simultaneously for the same reason: both need their terminating entity to be logically necessary, and neither can establish this a posteriori. The Kalam cannot establish that its creator is logically necessary through empirical observation; Leibniz cannot establish it through PSR alone - It is worth being precise about what this does not show: it does not prove that God does not exist, or that a necessary being is impossible. It shows that the cosmological arguments fail to prove God exists because they cannot establish the logical necessity their own structure requires
: The special pleading objection
- Both the Kalam and Leibniz's argument are driven by a universal explanatory demand: the Kalam insists that everything which begins to exist must have a cause; Leibniz insists that every contingent fact must have a sufficient reason. Both arguments apply these principles universally to reach their conclusion — a first cause or necessary being - But both arguments then immediately exempt their concluding entity from the very demand that drove the argument. The Kalam concludes that God is an uncaused cause — a being that begins nothing and requires no creator. Leibniz concludes that God is a self-explanatory necessary being that requires no sufficient reason beyond himself - This is special pleading — sometimes called the taxicab objection: the arguments ride their explanatory principle as far as needed to reach God, then arbitrarily dismiss it the moment it would point toward God requiring his own explanation. The causal principle and PSR are either universal or they are not. If they have exceptions, the arguments never got started
: The theist response
- Theists argue that this charge of special pleading fundamentally misunderstands the metaphysical distinction at play. God is not arbitrarily exempt from the explanatory demand — he is principally exempt because he is a genuinely different kind of being - A necessary being, by definition, contains the sufficient reason for its own existence within its own nature. Unlike contingent things — which could have failed to exist and whose existence therefore demands explanation — a necessary being's non-existence would be a contradiction. Its existence is self-explanatory in a way that no contingent thing could be - This is not special pleading but a principled metaphysical distinction between necessity and contingency. Contingent beings require external explanations; necessary beings do not. God falls into the latter category, and exempting him from the explanatory demand is therefore not arbitrary but follows from what it means to be a necessary being
Kant: Kant's decisive counter — the smuggled ontological argument
- But this theist response reveals a fatal problem rather than solving one. To exempt God from the explanatory demand on the grounds that he is a necessary being — one whose non-existence would be a contradiction — is to claim that God exists with logical necessity. And establishing that something exists with logical necessity is precisely what the ontological argument attempts to do - Both cosmological arguments, at the very moment they try to complete their proof, silently depend on a successful ontological argument. Without it, the special pleading charge stands unanswered - As Hick's analysis of the ontological argument makes precise, there are two importantly different kinds of necessity. Logical necessity means something whose non-existence would be a logical contradiction — as impossible as a four-sided triangle. Ontological necessity — what Hick calls aseity — means something that is eternal, self-explanatory, and non-contingent, but whose non-existence is not logically impossible - What both cosmological arguments actually establish, at best, is ontological necessity: that God, if he exists, would be eternal and self-explanatory. But this falls critically short of what the theist response requires. A world without God — without a first cause or necessary being — would be a brute unexplained fact. Uncomfortable, perhaps. But not a logical contradiction. The special pleading charge therefore stands: God is not logically exempt from the explanatory demand, merely asserted to be so
- The Kalam's infinity paradoxes fail against modern mathematics, and Hume's attack on the causal principle seriously undermines P2 — the singularity point shows that physics cannot extend the causal principle to the universe's origin. Craig's Big Bang defence gives P1 genuine empirical support, but the argument cannot establish that the universe's beginning requires a cause in the relevant sense - Leibniz's argument from contingency is more sophisticated and partially escapes Hume's inductive attack, but the fallacy of composition exposes a real weakness — Russell's point that a series is a mental construction rather than a concrete thing requiring its own explanation is difficult to dismiss - Most crucially, both arguments commit special pleading: they apply their explanatory principles universally to reach God, then exempt God from those same principles. The only principled response is that God exists necessarily — but establishing logical necessity is precisely what the ontological argument attempts and fails to do. At best both arguments establish ontological necessity: that God, if he exists, would be eternal and self-explanatory. But a universe without God would be a brute unexplained fact, not a logical contradiction. The special pleading charge stands - The cosmological argument therefore fails to prove that God exists