Written by,
Aldrin Relador
Edited by,
Kang Sheng
Joshua Chua
Introduction
Descartes and Leibniz offer versions of an a priori argument for God’s existence. I classify their arguments as a priori because their arguments claim to proceed from some idea of God. For some argument to succeed, it should obtain the conclusion that God necessarily exists. An argument that obtains a conclusion as such is non-trivial. Something is non-trivial only if (and because) something is not obviously provable. In this paper, I argue that Leibniz offers a better argument than Descartes despite both their flaws. In §1, I explain Descartes’ a priori argument. I also give a central objection and a reply on his behalf. In §2, I explain Leibniz’s a priori argument. I also give a central objection. In §3, I discuss which argument is more philosophically interesting than the other – it’s Leibniz’s. This is because of the unorthodox reason that his argument is more aesthetically parsimonious than Descartes’ argument. In cases where both arguments fail to deliver their conclusions, the upshot here is that we may decide what to endorse on aesthetic grounds.
§1 Descartes’ A Priori Arguments for God’s Existence
Descartes offers an ontological argument for God’s existence in his Fifth Meditation. There are many versions of the ontological argument (Oppy, 2019) which take a general character. First, the argument begins with a concept or idea of God. Second, this concept or idea of God necessarily consists of existence. Third, the argument concludes that God necessarily exists from the concept or idea of God. Descartes (49:69)[1] makes his version clearest in this central passage:
[W]hatever kind of proof I use, the issue always comes down to this: that nothing convinces me fully but what I clearly and distinctly perceive. (…) But as far as God is concerned, certainly, if I were not overwhelmed by prejudices…I should recognize nothing sooner and more readily than him. For what is more obvious in itself than…that God, to whose essence alone existence belongs, exists?
The passage is central because it summarises the key considerations for Descartes’ ontological argument.
First, Descartes assumes that any clear and distinct idea is self-evidently true. Any clear and distinct idea is self-evidently true because it cannot be doubted without contradiction. Descartes (46:64) cites an example of the idea of a triangle. Descartes claims that an idea of a triangle being three-sided is clear and distinct. So, an idea of a triangle is self-evidently true. This is because a triangle that is not three-sided is a contradiction. The reason Descartes makes this claim follows from his next consideration.
Second, Descartes assumes that the essence of any self-evidently true idea is self-evident. Something is an essence if and only if something is a necessary property that makes something the thing it is. A reason for why any self-evidently true idea’s essence is self-evident (in the sense that you can intuit the idea) is that any self-evidently true idea is self-evidently true. The essence of the idea of a triangle is self-evident only because it’s self-evidently true that three-sidedness makes a triangle. So, there is a subtle distinction between whether something is self-evidently true and whether something is self-evident.
Thirdly, the essence of the idea of God is necessary existence. From the second consideration, the necessary property of necessary existence cannot be excluded from the idea of the essence God. These considerations are sufficient to reconstruct Descartes’ ontological argument.[2]
1. Any clear and distinct idea is self-evidently true. (first consideration)
2. Any self-evidently true idea’s essence is self-evident. (second consideration)
3. Some idea of God is clear and distinct. (47:66)
4. So, some idea of God is self-evidently true. (1, 3 modus ponens)
5. So, some idea of God has some self-evident essence. (2, 4 modus ponens)
6. The self-evidently true idea, in which God’s essence is necessary existence, is self-evident. (Descartes’ Intuition)
7. Therefore, God necessarily exists. (5, 6 Descartes special inference rule)
For brevity, I explain only the critical premises in Descartes’ argument that I have not yet explained. I also explain some ambiguities.
Premise 3. Descartes (47:66) claims that he has some clear and distinct idea of God in the same way as he has some clear and distinct idea of a “shape or number”.
Descartes’ Intuition. Descartes makes this claim on multiple occasions (47:66, 48:67, 49:69). The basis for this claim is that we can intuit the idea of God’s essence just as we can intuit an idea of a geometric shape such as a triangle. This is because Descartes (49:69) thinks we can intuit self-evidently true ideas. So, Descartes intuits the self-evidently true idea of God’s essence.
Conclusion. The critical move that Descartes makes is that from the idea of God’s essence he concludes that God necessarily exists. The move is critical because he makes an existential claim from an epistemic claim. We can capture the inference with the rule: if I can intuit a self-evidently true idea of God’s essence, then God necessarily exists. The question is whether the antecedent warrants the consequent. If it does, then Descartes’ argument would have succeeded. So, I take this to be Descartes’ argument’s central inference.
I disagree that the inference is valid. The inference relies on the premise 2. It is false that any self-evidently true idea’s essence is self-evident on the grounds that it is self-evidently true.
Case 1. Suppose something’s being an essence of something is an identity statement of the form A=B. So, a triangle’s essence = three-sidedness. The proposition <the idea of a triangle’s essence = three-sidedness> is self-evidently true. The proposition is self-evident (i.e. intuitable) only if we understand the concepts of a triangle or [3] three-sidedness. This is because the concepts are interchangeable.
Case 2. Consider the proposition <the idea of God’s essence = necessary existence>. I grant that the proposition is self-evidently true. If the proposition is self-evident, then I understand either the concepts of God’s essence or necessary existence. Suppose that I’m an atheist. I try to understand the concept of God. But it seems odd to me. So, I try to understand the concept of necessary existence. The concept could mean either: (1) something that is required to exist for anything to exist or (2) something that exists independently from any existing thing. From my intuition alone, it’s not self-evident that whether (1) or (2) is self-evidently true. I require independent arguments for why (1) or (2) are self-evidently true. So, from intuition alone, I cannot understand either the concepts of God’s essence or necessary existence. Therefore, the proposition <the idea of God’s essence = necessary existence> is not self-evident.
There is an asymmetry between the two cases. There is no successful analogy between the first case and the second case. If there is no analogy, then only some self-evidently true idea’s essence is self-evident. So, only some self-evidently true idea’s essence is self-evident as in the first case. Therefore, the argument does not warrant the conclusion.
Descartes (49:69) could reply that the atheist in the second case is “overwhelmed by prejudices”. This is the reason why the atheist cannot intuit that the proposition – the idea of God’s essence is necessary existence – is self-evident. I reply that Descartes’ is still insisting that there is a successful analogy between the first and second case. An idea of a triangle’s essence is not analogous to the idea of God’s essence unless Descartes’s conception of God is akin to that of a geometric object. Descartes’ does not have such a conception of God. Descartes’ conception of God is that of a creator (15:21). So, an idea of a triangle’s essence is not analogous to the idea of God’s essence. Therefore, the atheist is able to intuit the idea of a triangle’s essence but not the idea of God’s essence as self-evident.
§2 Leibniz’ A Priori Arguments for God’s Existence
Leibniz also offers an a priori argument for God’s existence. His argument is a version of an ontological argument. Leibniz’s ontological argument is similar to Descartes’ ontological argument because Leibniz’s argument begins from some idea of God. The difference in Leibniz’s argument is that Leibniz (6:38-39) explains his idea of God in terms of an idea of a necessary being. Here is a reconstruction of Leibniz’s argument.
1. If God is possible, then God necessarily exists. (PSR and PC)
2. God is possible. (PC)
3. So, God necessarily exists. (1, 2 modus ponens)
The argument is misleadingly simple. But it contains some critical premises and inferences.
Premise 1. Leibniz (7:45) claims “if he is possible, then he must exist”. I take ‘must’ to mean necessary. Leibniz (5:31-32) asserts premise 1 because of his commitment to two principles: Principle of Contradiction (PC) and Principle of Sufficient Reason (PSR).
PC says that something is impossible if and only if there is a contradiction between truths of reason (5:33). A truth of reason is a necessary truth such that for any necessary truth (a) its predicate is contained within the subject and (b) it is analysable into basic unanalysable truths (6:35). PSR says that there is always some non-final antecedent explanation for how things are until we arrive at a final antecedent explanation (5:32). For example, according to PSR, a final antecedent explanation for some mathematical truth is some unanalysable axiom.
Leibniz applies a parallel reasoning to the idea of God’s necessary existence. According to PSR, there is a final antecedent explanation for something’s existence. Leibniz thinks that the final antecedent explanation for something’s existence is God. This is because Leibniz’s (6:38) concept of ‘God’ means necessary being. A being is necessary because it does not have any limits (6:40). The property of non-necessary existence is an impossible limit on a necessary being. So, a necessary being necessarily exists. By making this move, Leibniz (7:44) claims that if a necessary being is possible, then a necessary being necessarily exists. The challenge is whether Leibniz successfully shows that a necessary being is possible in the relevant sense.
Premise 2. Leibniz claims that a necessary being consists of no negations (e.g. non-necessary existence) (7:45) and only eternal (i.e. necessary) truths (7:44). So, a necessary being does not contain any contradiction. Recall that PC says that something is impossible if and only if there is a contradiction between truths of reason (5:33). So, from PC, a necessary being is possible.
Conclusion. If Leibniz is right, then the conclusion is secured straightforwardly.
I object that Leibniz’s second premise begs the question. He would first need the additional claim that either God is possible or God is impossible. To infer that God is possible, Leibniz must show that it is not the case that God is impossible. He appeals to PC to justify this. Recall that in order to establish that God is possible Leibniz need only assume that there is no contradiction in the concept of “God”. But according to PC, the claim that God is possible is just true by definition. Given this fact, PC permits all sorts of necessary truths. An atheist may then reject this definition on grounds that PC proves too much. This is because PC is able to easily secure a modally strong claim about the necessity of God. Note that all true modally strong claims are true in all possible worlds. And so, they are extremely vulnerable to counterexample. Thus, the standard of justification for them is higher than other modal claims. But so far Leibniz has not offered any justification for the claim that God is possible other than PC. So, even if PC is true, it is insufficient to justify the claim. So, at most Leibniz has to accept the disjunction that either God is impossible or God is possible. This move blocks crucial his inference from his second premise to his conclusion.
§3 Evaluation
Overall, both arguments have their flaws. Descartes’ argument suffers from a confusion between the self-evident and self-evidently true distinction. Leibniz argument proves too much with too little. I do not accept either of their arguments for these reasons. However, even if the arguments did work I think that Leibniz’s argument is more philosophically interesting than Descartes’ argument because it is more aesthetically parsimonious. This is because the fact that Leibniz’s argument can prove too much with too little turns the argument into an artefact as if it represented the simplicity of God – to which both Leibniz and Descartes could agree. In this sense, any support for either argument is a matter of aesthetic preference in its faithful presentation of God’s simplicity in the same way a gothic-style cathedral might faithfully present God’s grandeur. This fact makes a difference and not their merely apparent soundness.
Conclusion
I conclude that Leibniz offers a better argument than Descartes on the grounds that Leibniz’s argument is more aesthetically parsimonious than Descartes’ argument. This is despite flaws in both their arguments. In cases where both arguments fail to deliver their conclusions, the upshot here is that we may decide what to endorse on aesthetic grounds.
References
Descartes, René. “Meditations on First Philosophy, trans. Michael Moriarty.” Oxford: Oxford University Press, pp. AT 1 (2008): 19.
Leibniz, Gottfried. “Monadology.” in the version by Jonathan Bennett presented at http://www.earlymoderntexts.com. Accessed on 29 April 2019.
Oppy, Graham, “Ontological Arguments”, The Stanford Encyclopedia of Philosophy (Spring 2019 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/spr2019/entries/ontological-arguments/>.
[1](a:b) is such that a refers to the text’s page number and b refers to the text’s section number.
[2] I reconstructed the argument so that it works with first-order logic inference rules to assess whether the argument is valid.
[3] Inclusive use of ‘or’
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