Written by,
Joshua Chua (Editor 19/20′)
In this essay, I examine specific lines of arguments for God proposed by Spinoza and Leibniz from the Principle of Sufficient Reason (PSR) and argue that Spinoza’s argument is more compelling. In the first section, I explicate Spinoza’s argument for God, followed by Leibniz’s argument for God. In the second section, I focus on their accounts of contingence and how contingence results in their differing definitions of God. Then, I argue that Spinoza’s argument is more compelling while demonstrating a logical flaw in Leibniz’s argument.
Section 1: Arguments for God/Substance
Spinoza’s defines God/substance as an “absolutely infinite” being (Id6). One way to understand this is that substance has no limits and is infinite in every possible way. Spinoza contrasts this to a being that is “infinite in its own kind”, which he refers to as an entity which is only infinite in a particular way (Id6 Exp). An example of an entity that is “infinite in its own kind” could be the totality of space. This entity would be infinite in the ‘way’ of space – that is, there is no space outside of the totality of space. One might object that there is a finite amount of space and that it follows that the totality of space is finite, but this is absurd according to Spinoza’s conception of infinity. Spinoza holds that something that is finite in its own kind is something that is limited by another of the same nature (Id2). What one means when one objects that the totality of space is finite is that the totality of space is theoretically measurable. However, this does not make the totality of space finite in the ‘way’ of space. Because the totality of space contains all space, there is nothing outside it that is finite in its own kind to limit it in the ‘way’ of space. (i.e. There is no space outside of the totality of space to limit it.) This means that the totality of space cannot be finite in the “way” of space. To Spinoza, to be infinite is to be without limits. Now, Spinoza’s God is defined as an entity that is infinite in all (infinite) ways – that is, it has absolutely no limits. It follows that Spinoza’s God is all of existence – because there cannot exist anything outside of God to limit it.
Spinoza also defines substance as “what is in itself and is conceived through itself” (Id3). Spinoza means that substance is absolutely individuated. Substance exists in-itself (does not depend on anything) and is self-explanatory in-itself (contains in-itself a complete explanation for itself and does not have anything outside of itself to explain it). This definition follows naturally after analysis of substance as absolutely infinite. Because, if there exists nothing outside of God/substance, there does not seem to be anything outside of God/substance that God/substance is ontologically dependent on/is required to explain God/substance.
After defining substance, Spinoza explicates his arguments that substance necessarily exists. In comprehending Spinoza’s definition of substance, it is apparent that “it pertains to the nature of a substance to exist” (Ip7). One way to interpret this is that it is deducible from the definition of substance – that all that exists, exists. However, this proof is seemingly uninteresting, as it merely points out a tautology. Furthermore, Spinoza wants to prove a stronger point, not just that substance exists but that substance necessarily exists. The definitional proof here does not strongly motivate this necessity, which Spinoza provides a stronger argument for. Spinoza argues that it is impossible for substance to not exist. He assumes the PSR in his argument: “For each thing there must be an assigned cause, or reason, both for its existence and for its nonexistence” (Ip11 Alternatively). From this, Spinoza provides a proof of substance by analyzing that it is impossible for there to be a reason for the nonexistence of substance. For something to not exist, it must either be limited by something external to it or be self-contradictory. There cannot be something external to substance because substance is unique. Substance is unique because no two substances of the same nature can exist (Ip5). If more than one substance of identical nature existed, they would be undifferentiable and therefore not distinct. Essentially, uniqueness means that there cannot be more than one totality of existence because the totalities would be undifferentiable. It follows that there cannot exist any external entity that shares the same nature as/is commensurable with substance. Here, one may object that there it is possible for an external entity that is not a substance to exist. However, this is implausible as there cannot be an existent that is not within the totality of existence. As there cannot be any external entity commensurable with substance, and commensurability is necessary for affections, no external entity can limit substance. This demonstration may seem abstruse, but it essentially states that there cannot exist anything distinct from the totality of existence. If there were an entity distinct from all of existence, it would either 1. Exist and be commensurable with substance – which means it would be a part of the totality, not distinct from substance/not differentiable from substance, or 2. Not exist and be incommensurable, being unable to limit substance. Thus, there cannot be any external entity that limits substance.
The other sufficient reason for nonexistence is self-contradiction. Entities that have self-contradictory natures cannot exist (like a cuboid sphere). Spinoza states that substance is not self-contradictory: “it is absurd to affirm this of a Being absolutely infinite and supremely perfect” (Ip11 Alternatively). One way to interpret this is: because the totality of existence is the affirmation of all existents (affirms that all that exists exists), there is no ‘imperfection’ in God’s/Substance’s nature – there cannot be any contradictions in substance because contradictions necessarily do not exist and nonexistence cannot be in the totality of existence. It follows from these two demonstrations that there cannot be a reason for God’s nonexistence. Thus, God/Substance necessarily exists.
I now explicate Leibniz’s proof of God. Leibniz’s definition of God is of a choice-making (has free will) supremely perfect being. Leibniz states that God “acts always in the most perfect and desirable way” (Dis. 4), that God “has chosen the most perfect world…” (Dis. 6) and that God is “an absolutely perfect being” (Dis. 1). Leibniz’s definition of God is in line with the typical definition of an all-powerful, all-knowing creator of everything there is. A significant difference between Leibniz’s God and Spinoza’s God is that Leibniz’s God has free will and created everything.
Leibniz also provides a proof of God using the PSR. Leibniz represents the PSR as “we can find no true or existent fact, no true assertion, without there being a sufficient reason why it is thus and not otherwise” (Mon. 32). Leibniz claims that these true facts are contingent facts that depend on the sufficient reasons that they have for being the case (Mon. 33). The facts that Leibniz is referring to here are matters of fact (contingent facts about the world). For example, the fact that someone is currently sleeping. This is contingent upon humans requiring sleep, and the proliferation of humanity to the extent that this fact is true throughout the day. However, every sufficient reason for every contingent fact is also a contingent fact. This requires another sufficient reason, ad infinitum. Leibniz extrapolates that this infinite chain of contingent facts (the infinite chain of matters of fact) requires an external sufficient reason for being the case. “It must be the case that the sufficient or ultimate reason is outside the sequence or series of this multiplicity of contingencies, however infinite it may be” (Mon. 37). To motivate Leibniz’s extrapolation, I examine the definition of contingence. To be contingent is to depend on something for existence. Leibniz claims that the sequence of contingencies requires a sufficient reason for existence. This sufficient reason is not within the sequence of contingencies because the sufficient reason cannot be a contingent fact. Thus, this reason is external to the sequence of contingencies. Leibniz claims that this reason is an independent and necessary existent which we call God (Mon. 38). He also claims that this cause has “the reason of its existence in itself” (Mon. 45). Here, Leibniz is extrapolating that PSR necessitates an existent whose sufficient reason for its own existence is in itself (which Leibniz defines as God). Having explicated both philosopher’s arguments from PSR, I now analyze which is more compelling with the concept of contingence as my focus.
Section 2: Analysis of Contingence
First, a brief explanation of the significance of the philosophers’ conceptions of contingence. Having a different conception of contingence directly impacts the definitions that the philosophers assign to God. Leibniz argues that: As all matters of fact are contingent, there needs to be an independent external reason for these matters of fact, and that reason is God. Spinoza argues that: everything is necessary (nothing is contingent), and this necessary entity (everything that exists) is God/substance. The fundamental difference in the existential claims of Spinoza and Leibniz is God’s relation to existents. In other words, God as metaphysically distinct from all other existing entities (Leibniz), or God/substance as equivalent to all existing entities (Spinoza). To clarify, Leibniz does hold that the sequence of contingencies is dependent on God for existence. However, Leibniz’s God is fundamentally distinguishable from other entities, while Spinoza holds an equivalence claim between God/substance and all entities.
Differing accounts of contingence results in their differing definitions of God. For Leibniz, as God is distinguishable from other existing entities, God must have created them. This is a natural conclusion from his claim that all other existing entities depend on God for existence. It follows for Leibniz that God has the ability to choose, act and think. Hence, it is consistent for Leibniz to conclude that God has free will. For Spinoza, substance/God is equivalent to the totality of existents. Although it follows that substance/God is a thinking thing (IIp1), what Spinoza means is different from Leibniz. For Spinoza, substance/God is only a thinking thing insofar as it contains thought (there are thinking beings within the totality of existence). It does not follow for Spinoza that God/substance has independent and self-conscious thought (or free will). Thus, their differing conceptions of contingence greatly influence their metaphysical conclusions about God.
I now analyze and compare the two accounts of contingence, starting with Spinoza. Spinoza holds that everything that was, is and will be is necessarily the way it is/was/will-be (the totality of existence is not contingent). This claim is backed by Spinoza’s aforementioned proof of the necessity of substance. Furthermore, it can be compelled by analysis of the definition of substance that it is absurd to consider substance contingent. The argument is as follows:
P1: Substance is contingent.
P2: For any contingent entity, it has to be contingent upon A where A is external to itself (being contingent upon something within itself or being contingent upon itself would be self-contingence, which is non-contingence).
P3: For all A where substance is contingent upon A, A necessarily exists.
P4: For all A where A exists, A is within the totality of existence (substance).
C: A is external to and within substance.
From P1, P2 and P3, substance is contingent upon some existent A that is external to itself. However, from P4, A is within substance. Hence, it is absurd that substance is contingent.
This proof is a reductio ad absurdum. It demonstrates that holding substance as contingent results in absurdity, which means that substance is necessary.
For Leibniz, all matters of fact are contingent upon other matters of fact. He extrapolates from this that the sequence of matters of fact is contingent – and hence requires an external sufficient reason for its existence. This is not deductively valid. Leibniz assumes that the sequence of matters of fact is contingent because matters of fact are contingent – but this is not logically necessary. The sequence is the sum/totality of all matters of fact and is not a matter of fact in-itself. Although all matters of fact are contingent, it does not follow that the sequence is contingent. An example of a similar logical flaw is in the following reasoning: All lines that make up a triangle are one-dimensional. Hence, a triangle is one-dimensional. Although all the parts have a predicate (one-dimensional/is-contingent), it does not follow that the whole has that same predicate. Hence, Leibniz’s argument is unable to prove the existence of God because his argument relies on the contingence of the sequence.
Conclusion
Leibniz’s argument ambitiously sought to prove the existence of an in-itself independent entity (which he calls God) that is distinct from all matters of fact. On the other hand, Spinoza’s arguments, though seemingly ambitious, seeks only to demonstrate certain definitional truths about the totality of existence. In the end, Spinoza simply proves that all that exists necessarily exists. After analysis of the definitions and arguments put forth, this is compelling. In comparison, Leibniz’s use of the aforementioned logical flaw makes his ambitious argument significantly less compelling.
Editor’s Note:
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Works Cited
Leibniz, Gottfried Wilhelm, et al. Discourse on Metaphysics and Other Essays. Hackett, 1991.
Spinoza, Benedict de, et al. Ethics. Penguin, 1996.
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