According to Leibniz’s infinite-analysis account of contingency, any derivative truth is contingent if and only if it does not admit of a finite proof. Following a tradition that goes back at least as far as Bertrand Russell, several interpreters have been tempted to explain this biconditional in terms of two other principles: first, that a derivative truth is contingent if and only if it contains infinitely complex concepts and, second, that a derivative truth contains infinitely complex concepts if and only (...) if it does not admit of a finite proof. A consequence of this interpretation is that Leibniz’s infinite-analysis account of contingency falls prey to Robert Adams’s Problem of Lucky Proof. I will argue that this interpretation is mistaken and that, once it is properly understood how the idea of an infinite proof fits into Leibniz’s circle of modal notions, the problem of lucky proof simply disappears. (shrink)

In this paper the cosmological argument of Gottfried-Wilhelm Leibniz is revisited. We propose an interpretation of the argument as being an argument based on the structure of the logical space of all abstract facts. For this we view Leibnizian philosophy as providing a picture theory of language. This structure is given by the metaphysical foundations of Leibnizian philosophy: Leibniz’s theory of truth in the form of praedicatum inesse subiecto, the Principle of Sufficient Reason and the distinction between necessary and contingent (...) facts. The theory of truth is interpreted as being provided by a formal calculus of abstract concepts in the sense of Edward Zalta. The other metaphysical requirements are also briefly discussed. Using these the structure on logical space is realised by an antisymmetric, transitive relation which admits arbitrary joins. Such a relation must admit a minimum, which is interpreted as the existence of God. This interpretation entails the difficulties of explicating existence in Leibniz’s metaphysics, which are also discussed. (shrink)

Abstract : In this paper, it is argued that Leibniz’s view that necessity is grounded in the availability of a demonstration is incorrect and furthermore, can be shown to be so by using Leibniz’s own examples of infinite analyses. First, I show that modern mathematical logic makes clear that Leibniz’s "infinite analysis" view of contingency is incorrect. It is then argued that Leibniz's own examples of incommensurable lines and convergent series undermine, rather than bolster his view by providing examples of (...) necessary mathematical truths that are not demonstrable. Finally, it is argued that a more modern view on convergent series would, in certain respects, help support some claims he makes about the necessity of mathematical truths, but would still not yield a viable theory of necessity due to remaining problems with other logical, mathematical, and modal claims. (shrink)

Despite his commitment to freedom, Leibniz’ philosophy is also founded on pre-established harmony. Understanding the life of the individual as a spiritual automaton led Leibniz to refer to the puzzle of the way out of determinism as the Labyrinth of Freedom. Leibniz claimed that infinite complexity is the reason why it is impossible to prove a contingent truth. But by means of Leibniz’ calculus, it actually can be shown in a finite number of steps how to calculate a summation of (...) infinite parts. It appears that the analogy Leibniz drew between the mathematics of infinite series and the logic of contingent truths did more harm than good. A solution consistent with Leibniz’ perception of infinity is proposed. Alongside the existence of the aforementioned analogy, it is based on a disanalogy between the mathematics of infinite series and the logic of infinitely complex truths. This is a disanalogy that Leibniz had already used to solve the Labyrinth of Continuum which he declared more than once could, like the Labyrinth of Freedom, be solved by means of the nature of infinity. The solution of both labyrinths is based on the fictitiousness of the infinitesimal. (shrink)

According to one of Leibniz’s theories of contingency a proposition is contingent if and only if it cannot be proved in a finite number of steps. It has been argued that this faces the Problem of Lucky Proof, namely that we could begin by analysing the concept ‘Peter’ by saying that ‘Peter is a denier of Christ and …’, thereby having proved the proposition ‘Peter denies Christ’ in a finite number of steps. It also faces a more general but related (...) problem that we dub the Problem of Guaranteed Proof. We argue that Leibniz has an answer to these problems since for him one has not proved that ‘Peter denies Christ’ unless one has also proved that ‘Peter’ is a consistent concept, an impossible task since it requires the full decomposition of the infinite concept ‘Peter’. We defend this view from objections found in the literature and maintain that for Leibniz all truths about created individual beings are contingent. (shrink)

In this dissertation, I develop an interpretation of Leibniz on modality and free will. I do so for two reasons: first, I am attempting to revitalize the notion that Leibniz is the predecessor of contemporary modal semantics; second, I am using Leibniz's philosophical system to motivate responses to contemporary philosophical issues in modality and free will. In Chapter One, I argue that Leibniz's basic principles are plausible theoretical tools that ought to be used by contemporary philosophers in developing their philosophical (...) systems. In Chapter Two, I develop Leibniz's views on the nature of individuals. I argue that possible individuals are actually of the same sort as individuals in the actual world--possible individuals and actual individuals are complete creatures that do not differ ontologically from each other. In Chapter Three, I argue that Leibniz's views on possible individuals make him a modal realist and compare his view with contemporary modal realism in order to support this claim. I also argue that counterparts avoid many of the problems set for them by contemporary thinkers; I end with the ways that Leibniz's view differs from contemporary accounts. In Chapter Four, I argue that Leibniz provides two different analyses of modality. The first is an infinite analysis account; the second is a possible worlds account. I argue that these two accounts are compatible and amount to two different descriptions of the same theory of modality. I address objections to each account in order to show this. In Chapter Five, I argue that Leibniz is a compatibilist about free will. Importantly, I argue that it is precisely Leibniz's account of modality that allows for this compatibilism, as against a necessitarian like Spinoza. I then use Leibniz's account to challenge contemporary libertarians about free will on the basis of the principle of sufficient reason. I also show how Leibniz can help semicompatibilism avoid a worry concerning necessitarianism. At the end of the day, I claim that adopting elements of Leibniz's system can help us better understand modality and the freedom of the will and can be an aid in furthering contemporary philosophical theory. (shrink)