Leibniz's Argument Research Articles

A New Defense of the Principle of Sufficient Reason

This paper offers a defense of a much-maligned Leibnizian argument for the Principle of Sufficient Reason, the principle according to which whatever is has a sufficient reason or explanation. While Leibniz’s argument is widely thought to rely on a question-begging premise, the paper offers a wholly original and non-question-begging defense of that premise, a defense that Leibniz did not anticipate. The paper does not present this defense of Leibniz's argument as an interpretation of Leibniz; rather, the paper—more modestly in one way, less modestly in another—simply claims that this argument succeeds.

The Role of Plurality in Leibniz's Argument from Unity

The Role of Plurality in Leibniz's Argument from Unity

A relevância da carta de Leibniz para Casati

n this article I discuss the problematic of the letter of 1689, from Leibniz to Ludovico Casati. This letter from Leibniz's intermediate phase, Leibniz argues the possibility that extrinsic properties as well as intrinsic properties can not distinguish completely similar things. For Leibniz the existence of indiscernible things is absurd, since the infinite intellect accompanies the multiplicity of all created things. Therefore, all things must be varied and distinct, even when it is not possible to distinguish things by their intrinsic and extrinsic properties. In this way, I analyze the letter with the intuition of understanding Leibniz's argument to Casati, as well as delimiting the Principle of the identity of the indiscernibles, as a principle of distinction. In arguing to Casati that the best possible world is guided by a reason that establishes that things are different. At the end, I provide a translation in Portuguese of this letter.

Temporal Creation and Cosmological Arguments in Early-Modern Calvinism

ABSTRACTThis study examines the varieties of cosmological arguments deployed in the natural theologies of early-modern Calvinism. Some of the first Reformed forays into theistic proofs make use of Thomist arguments which allow for the logical possibility of creation from eternity. In the seventeenth century, many Reformed theologians prefer to use arguments against the possibility of an eternal world – arguments which had been defended by medieval theologians such as Bonaventure. But these arguments in turn faced criticism in the seventeenth century, and many of the Reformed supplemented them or replaced them with others. The argument from the mutability of the world to its temporal beginning became increasingly popular among Reformed thinkers. Historical arguments from the recent rise of arts and sciences or biological species supplemented the philosophical arguments for the world's beginning. Their theological commitment to the impossibility of eternal creation may explain why the Reformed did not typically use the Clarke and Leibniz argument from contingency.

Leibniz on Infinite Numbers, Infinite Wholes, and Composite Substances

Leibniz claims that nature is actually infinite but rejects infinite number. Are his mathematical commitments out of step with his metaphysical ones? It is widely accepted that Leibniz has a viable response to this problem: there can be infinitely many created substances, but no infinite number of them. But there is a second problem that has not been satisfactorily resolved. It has been suggested that Leibniz's argument against the world soul relies on his rejection of infinite number, and, as such, Leibniz cannot assert that any body has a soul without also accepting infinite number, since any body has infinitely many parts. Previous attempts to address this concern have misunderstood the character of Leibniz's rejection of infinite number. I argue that Leibniz draws an important distinction between ‘wholes’ – collections of parts that can be thought of as a single thing – and ‘fictional wholes’ – collections of parts that cannot be thought of as a single thing, which allows us to make sense of his rejection of infinite number in a way that does not conflict either with his view that the world is actually infinite or that the bodies of substances have infinitely many parts.

Christology and Time: Prolegomena to Any Future Apocalyptic

I. Enigma of Time WHEN WRITERS TAKE UP the knotty issue of time, they often acknowledge their frustration by invoking this famous passage from St. Augustine's Confessions: So just what he asks. If no one asks me, I know. But if I wish to explain it to anyone who asks, I know not. (1) Perhaps these same writers, once they have admitted their despair, will go on to invoke another famous line from one of Shakespeare's sonnets: And time that gave doth now his gift confound. (2) Taken together, these two passages sum up the strange paradox of time: it both inexorably ubiquitous, yet also maddeningly difficult to talk about. Lots of things, after all, are difficult on their own terms without their being familiar to us in our ordinary lives--and in fact are difficult precisely in their unfamiliarity. One thinks here of cryptography, the Latin of Duns Scotus or the Greek of Maximus the Confessor, the chemistry of polymers, Attic epigraphy, Kremlin politics. But time, weirdly, both difficult to analyze yet inescapable. As science writer Dan Falk says, The great paradox of time that it at once intimately familiar and yet deeply mysterious: nothing more central and yet so remote. To be human to be aware of the passage of time; no concept lies closer to the core of our consciousness. Yet who can say just what time is? It thoroughly intangible. We cannot see, hear, smell, taste, or touch Yet we do feel Or at least we think we feel it. (3) Despite this ineluctable dilemma, perhaps there a way out. One way of beginning to say something meaningful about time might be to look at an eighteenth-century debate between Isaac Newton and Gottfried Leibniz. Newton had claimed that time was absolute, that is, that it served as the presupposition for nondivine reality inside of which the universe was created. Leibniz disagreed and held instead that time was entirely relational, allowing one event to be related to another. In other words, without a universe of interrelated events there would be no time. Leibniz's argument rested--as did so much of his philosophy--on his most fundamental bedrock, the so-called Principle of Sufficient Reason, which says that nothing happens without there first being a reason for it to happen. In other words, this principle insists that the universe rational through and through: there can be no event without a precedent cause that brings about that event. Without a reason for it to occur, an event simply doesn't happen. Period. But for Leibniz the same principle applies, much more controversially, to God: God does nothing on a whim but always motivated by a sufficient reason for doing so. It was this principle of course that got Leibniz into so much trouble when he said that, out of all the possible worlds God could have created, he pick what he called the of all possible worlds. Any other possible world would lack a sufficient reason to exist. As everyone knows, this conclusion threw theodicy (a word he invented) into disrepute thereafter. But he was on surer ground when he invoked that same principle to dispute Newton's notion of absolute time, as Falk explains: Leibniz believed that if time were absolute--continuing even when no change observed--then time must have been passing even before God created the universe. In that case, God created the universe at some particular time. But why that particular time? Why not five minutes earlier or five minutes later? After all, in the Newtonian scheme, every moment alike. (The best that Newton's ally [Samuel] Clarke could offer in reply was that sometimes God did do certain things on a whim. That did not satisfy Leibniz, who said such a notion is plainly maintaining that God wills something, without any sufficient reason for his will.) (4) We know Leibniz's argument ultimately proved successful (albeit shorn of its reliance on the Principle of Sufficient Reason) because of Albert Einstein's later theory of relativity. …

Leibniz's Cosmological Argument for the Existence of God

In this article, I discuss Leibniz's interpretation of the cosmological argument for the existence of God. In particular, I consider whether Leibniz's position on this point was developed partly in reference to Spinoza's position. First, I analyze Leibniz's annotations from 1676 on Spinoza's Letter 12. The traditional cosmological argument, as found in Avicenna and Saint Thomas for example, relies on the Aristotelian assumption that an actual infinite is impossible and on the idea that there can be no effect without a cause. From these premises, the argument concludes that God must be the uncaused first cause of all things. In Letter 12, Spinoza follows Chasdai Crescas and rejects this proof. Instead, he develops a variant of the cosmological argument which depicts God as the self-caused ground of all causes or things. In his annotations, Leibniz agrees with Spinoza about the inadequacy of the traditional argument, but remains ambiguous as to Spinoza's conception of God as a self-caused being. Next, I turn to Leibniz's comments from 1678 on Spinoza's Ethics. Here, Leibniz develops an original interpretation of the cosmological argument based entirely on the consideration of conceptual relations. Leibniz's argument depicts God as an uncaused being conceived through itself which is the condition of conceivability of all things. I argue that Leibniz developed this argument in deliberate opposition to Spinoza's conception of God as the self-caused ground of all causes or things.

Is Leibniz's argument against the No Shared Attribute Proposition justifiable?

Is Leibniz's argument against the No Shared Attribute Proposition justifiable?

What is Leibniz's argument for the identity of indiscernibles in his correspondence with Clarke?*

Leibniz's last public remarks on his Principle of the Identity of Indiscernibles (abbreviated ‘PII’) were written three months before his death in November 1716. In the fifth letter of his correspo...

Leibniz, creation and the best of all possible worlds

Leibniz argued that God would not create a world unless it was the best possible world. I defend Leibniz's argument. I then consider whether God could refrain from creating if there were no best possible world. I argue that God, on pain of contradiction, could not refrain from creating in such a situation. I conclude that either this is the best possible world or God is not our creator.

Leibniz's Argument for Primitive Concepts

On its face, Leibniz's argument for primitive concepts seems to imply that unless we can analyze non-primitive concepts into their primitive constituents, we cannot grasp them. This implication, together with Leibniz's belief that we do conceive of some non-primitive concepts, entails that we can analyze some non-primitive concepts into their primitive components. However, Leibniz claims elsewhere that we are incapable of doing this. To resolve this inconsistency, I argue that, for Leibniz, grasping a concept is not an all-or-nothing affair; instead we possess concepts in degrees. When reinterpreted in line with this, Leibniz's argument can avoid the inconsistency.

Leibniz on Relativity and the Motion of Bodies

In a number of writings Leibniz argued that it follows from the Cartesian account of motion as change of relative position that individual bodies cannot be said to move at all.1 In this paper, I shall be concerned with some additional consequences that Leibniz drew from this that shed important light on the relationship between physics and metaphysics within his philosophy. I begin with an account of Leibniz's argument from relativity that differs from those previously offered in the literature. But I am also concerned with the way in which Leibniz uses the as a platform from which he can offer his own view of what it is for individual bodies to move. Leibniz provides three such accounts during his career and I shall discuss all three below. However, the first one that I shall discuss is far less significant since it appears only once, relatively early in Leibniz's life. Commentators have suggested that the remaining two discussions provide competing accounts of what is required for a body to move, the presence of which indicates a significant change in Leibniz's thinking about the issues over time. I argue instead that they are complementary components of a unified account of bodily motion that Leibniz adopted throughout his mature writings.

Two caricatures, II: Leibniz's best world

Leibniz's best-of-all-possible worlds solution to the problem of evil is defended. Enlightenment misrepresentations are removed. The apparent obviousness of the possib- ility of better worlds is undermined by the much better understanding achieved in modern mathematical sciences of how global structure constrains local possibilities. It is argued that alternative views, especially standard materialism, fail to make sense of the problem of evil, by implying that evil does not matter, absolutely speaking. Finally, it is shown how ordinary religious thinking incorporates the essentials of Leibniz's view. When Leibniz maintained that the solution to the problem of evil was that this was the Best of All Possible Worlds, the almost universal reaction was that his theory combined the lack of rationality exhibited by Pascal's Wager with a repulsive failure of compassion possible only in an unfeeling Enlight- enment mathematician. It was argued in an earlier article 1 that Pascal's Wager had been widely caricatured, that it had merit, and that it was a central part of thinking about faith. The present article argues that the same is true of Leibniz's best-world theory. Where Pascal's argument motivates the first step in the journey to faith, Leibniz's argument comes into play at the last. We should imagine the seeker having examined the claims of religion with a suitable combination of sympathy and scepticism, and found them of some force. Perhaps he has found the traditional arguments for the existence of God satisfying (assuming they have been cleared of the barnacles of travesty, accreted over the centuries through the untiring efforts of the Enlightened). Or some particular religion has seemed a sound candidate for an argument to the best explanation, being a coherent explanation of all facts (including moral ones) superior to alterna- tives. Or perhaps the logical tension has just become too great between a materialistic view of the world which implies that humans do not matter, and moral statements, which imply they do. Or maybe God's grace has acted directly in the manner Pascal promised. The last hurdle is then the problem of evil. Leibniz's Theodicy offers a simple solution to the problem of evil: that this is the best of all possible worlds.

Leibniz's argument for the identity of indiscernibles in his correspondence with Clarke1

(1999). Leibniz's argument for the identity of indiscernibles in his correspondence with Clarke. Australasian Journal of Philosophy: Vol. 77, No. 4, pp. 429-438.

Leibniz and the Possibility of God's Existence

Toward the end of 1676 Leibniz met Spinoza a number of times. In one of those meetings Leibniz presented a proof of the possibility of God's existence. In his proof Leibniz presupposed that a proposition is necessarily true only if its truth is either demonstrable or self-evident and that the divine perfections are simple and affirmative qualities. I contend that Leibniz's presuppositions undermine, rather than establish, the necessary existence of ‘a God of the kind in whom the pious believe’. My assessment is based upon a consideration of Leibniz's argument in the context of other early papers, works written before the Discourse on Metaphysics in 1686.