Spinoza or Leibniz

In his excellent book, Before Logic, Richard Mason (who also has a nice book on Spinoza, The God of Spinoza) argues that problems in logic as logicians understand them, and as they attempt to resolve them, are themselves consequences of particular choices, choices that exclude options that might have been on the table had another choice been made. Mason is quite adamant that this does not involve historicizing logic, nor does he adhere to an ahistorical view of logic. The arguments of Mason’s small book are all ‘intended,’ as he claims in the final lines of his book, ‘to show how logic must be part of philosophy, not in any sense before it. Too much must come first.’ And some of what comes first are particular interests and choices that set the stage for the logical developments to follow. One such choice is between Spinoza and Leibniz.

In typically straightforward fashion, Leibniz states the choice, as he sees it, between his philosophy and Spinoza’s: ‘You know,’ says Theophilius, the spokesperson for Leibniz’s thought in the New Essays, ‘I once strayed a little too far in another direction, and began to incline to the Spinozist view which allows God infinite power only, not granting him either perfection or wisdom, and which dismisses the search for final causes and explains everything through brute necessity.’ (p. 73). This will be a choice that will continue to haunt Leibniz, and a choice Samuel Clarke will press Leibniz on when, in their correspondence towards the end of Leibniz’s life, Clarke will seek to understand how Leibniz’s philosophy is not forced into the view that God’s choice of the best of all possible worlds is not itself determined by the laws of necessity. As this relates to logic, Mason sees the difference between Spinoza and Leibniz as one of choosing to emphasize the causes of things in the case of Spinoza and the truth of propositions in the case of Leibniz. A consequence of this, as Mason sees it, is that ‘Spinoza had no interest in explaining the sense of what might be said or thought. His approach to modality was concerned with existence, not with the meaning or truth of statements of possibility or necessity.’ To rephrase this difference in terms I used in an earlier post (here), Spinoza is indeed interested in the infinite, but the infinite enjoyment and power of existing, whereas Leibniz is interested in the infinite analysis that will justify the truth of contingent or necessary propositions. For Spinoza, a consequence of his approach is that rather than trouble over a logical analysis to demonstrate the truth of a proposition, he argues in the Theological-Political Treatise that ‘we ought to define and explain things through their proximate causes. Generalizations about fate and the interconnection of causes can be of no service to us in forming or ordering our thoughts concerning particular things.’ In other words, once we have understood the proximate cause of a thing, we have understood the thing. Nothing more is needed. For Leibniz, by contrast, to understand why Adam sinned, for example, it is not sufficient to understand the proximate causes of this sin, for if God willfully created the best of all possible worlds then he created an Adam who sinned. However, for Leibniz God did not create a sinning Adam but an infinite series within which Adam sinned, and a series of which an infinite analysis (that only God can do) would reveal that it is the best of all possible series (or worlds) that God could have created, including series where Adam does not sin. Although it might not initially seem so, Mason arges that the Leibnizian choice in favor of an analysis of the relationship of true propositions to reality rather than an analysis of proximate causes has become the road most travelled by logicians. This approach is not without its problems. In particular, as Mason shows, the Leibnizian problem of accounting for the relationship between the truths of propositions and concepts and reality ‘became an openly epistemological problem: how are the judgments that I make possible?’ (Before Logic, 64). From Kant onwards the attempts to resolve this problem took a decidedly subjectivist turn – viz. Kant’s Copernican Revolution. This is not to say that Leibniz is wrong and Spinoza right. As Mason goes on to argue, ‘For Spinoza there seems to have been no doubt that the basis for his form of necessity was in the things we talk about, and not in the way in which we talk about things. That, too, left large questions of epistemology, but in a different direction.’ (65). Namely, since the mind is the idea of the body, and a body that is a mode of the infinite power and enjoyment of existing, then this mind already contains within itself God’s causal power (our body is nothing less than a modification of God’s power). As a result, for Spinoza, ‘most controversies arise from this, that men do not correctly express what is in their mind.’ (E II 47 schol). The problem is thus not one of determining how our judgments are possible, and the various forms they can take, but instead it becomes the problem of knowing what a body can do, its powers and capacities, and in understanding this we understand the thing without recourse to logical relations and the orderings of our thoughts and propositions. As Donald Davidson argued, and as Mason cites, ‘it is sentences (or statements or propositions), or the relations between them, that are properly classified as contingent or logical; if causal relations are “in nature,” it makes no sense to classify them as logical or contingent.’ (“Causal Relations” in Essays on Actions and Events).

This choice between Spinoza or Leibniz, or their intellectual mitosis (as I discuss this here) between the things we talk about (Spinoza) or the way we talk about things (Leibniz), is itself symptomatic of a deeper, shared problem—namely, the problem of reconciling the finite with the infinite. For Spinoza, as I discussed in earlier posts (here, here, and here), this emerges as a decidedly ethical problem for individuals. More precisely, Spinoza sets out in his Treatise on the Emendation of the Intellect (TIE) ‘to enquire whether there existed a true good, one which was capable of communicating itself and could alone effect the mind to the exclusion of all else, whether, in fact, there was something whose discovery and acquisition would afford me a continuous and supreme joy to all eternity.’ As I argue in these earlier posts and in Philosophy at the Edge of Chaos, Spinoza was unable to adequately reconcile the infinite with the finite mind and thereby adequately address his ethical problem. When Spinoza acquires the use of common notions that are neither axiomatic first principles or simple inductive generalizations, but rather objective zones of indetermination, Spinoza abandons the TIE and reworks his ethical problem in his appropriately titled masterpiece, Ethics. Carrying the insight derived from common notions further, Spinoza develops an understanding of substance that I read as problematic substance, or as in-determinate and in-finite insofar as it is only determinate and identifiable as actualized in determinate and finite modes. For Spinoza, then, substance does indeed turn on its modes. This is no forced reading as I see it but one perfectly in accord with Spinoza’s ethical problem of reconciling a finite mind (or mode) with God or the infinite enjoyment of existing as Spinoza calls it, a reconciliation that will afford individuals ‘a continuous and supreme joy to all eternity.’

For Leibniz the problem of reconciling the finite and the infinite is a decidedly logical problem. Since Leibniz does not begin with the notion of one infinite substance but rather with infinite individual substances (or what he calls monads), the problem becomes one of relating each individual substance to the infinity of other individual substances. The watershed idea that Leibniz credits for enabling him to resolve this problem is that of a complete notion. As Leibniz states it,

If a notion is complete, i.e is such that from it a reason can be given for all the predicates of the subject to which this notion can be attributed, this will be the notion of an individual substance and conversely. For an individual substance is a subject which is not in another subject, but others are in it, and so all the predicates of that subject are all the predicates of the individual substance.’ (“The Nature of Truth”).

As Leibniz will repeatedly state this point, a true proposition is one whereby ‘the predicate is in the subject’. This is the case even of contingent truths, such as Caesar crossed the Rubicon or I am a professor of philosophy. To say that the complete notion of Caesar is such that it includes all the predicates that are true of this individual substance, then the complete notion of Caesar necessarily includes the predicate of crossing the Rubicon, and for me it includes being a professor of philosophy. The problem with this, as Leibniz recognized, is that the complete analysis of such necessary contingent truths requires an infinite analysis that only God can do:

In the case of a contingent truth, even though the predicate is really in the subject, yet one never arrives at a demonstration or an identity, even though the resolution of each term is continued indefinitely. In such cases it is only God, who comprehends the infinite at once, who can see how the one is in the other, and can understand a priori the perfect reason for contingency; in creatures this is supplied a posteriori, by experience.

Even if we could carry out the infinite analysis and demonstrate how each individual substance necessarily involves every other individual substance, we could still not give the reason for the infinite series itself. This is where Leibniz is able to rescue the perfection and wisdom of God who chooses the best of all possible worlds, or the best infinite series. A consequence of this move is that Leibniz separates mind, the mind that chooses and understands reasons, from matter. One of the central tenets of Locke’s philosophy that Leibniz attacks in his New Essays, and by extension in Spinoza as well, is precisely the view that ‘matter might think’. Since matter, for Leibniz, is infinitely divisible one can always find extrinsic relationships within relationships, simpler bodies within any given body, but as Leibniz understands it, ‘in each individual substance, God perceives the truth of all its accidents from its very notion, without calling in anything extrinsic; for each in its own way involves others, and the whole universe.’ (“Necessary and Contingent Truths” emphasis mine). The notion or concept of an individual substance is thus distinct from, and not to be confused with, the material constituents of a substance, or matter does not think. Spinoza, by contrast, by taking the road less travelled and not attempting to reconcile the infinite with the finite logically and by way of true propositions and concepts, is able to accept the claim that matter thinks, or better said that thought and matter are each expressions of the same infinite enjoyment of existing that is substance (God or Nature) as Spinoza understands it. So we come, finally, to another choice that Spinoza and Leibniz leave us with: either matter is self-moving and is its own reason for existing (Spinoza) or matter is not self-moving and is in need of the perfection and wisdom of God in order to have its reason for existing (Leibniz).