Paul Lodge

Between 1698 and 1706 Leibniz was engaged in one of his most interesting correspondences, with the Dutch philosopher and physicist Burcher de Volder. The two men were concerned primarily with the question of how the motion of bodies can be explained without appeal to the direct intervention of God. Leibniz presented a naturalistic account of motion to De Volder, but failed to convince him of its adequacy. I shall examine one reason for this failure - the disagreement that arose over the issue of whether there is a substance whose nature is constituted by extension.

Section 17 of Leibniz’s Monadology contains a famous argument in which considerations of what it would be like to enter a machine that was as large as a mill are offered as reasons to reject materialism about the mental. In this paper, I provide a critical discussion of Leibniz’s mill argument, but, unlike most treatments, my discussion will focus on texts other than the Monadology in which considerations of the mill also appear. I provide a survey of three previous interpretations of the argument and a partial defence of one of them, namely the one that Marc Bobro and I offered in Stepping Back Insider Leibniz's Mill (The Monist, 1998). However, I also argue that a fourth interpretation is necessary to account for the appearances of Leibniz’s mill in at least some of his writings.

According to Robert Sleigh Jr., “The opening remarks of DM.18 make it clear that Leibniz took the results of DM.17 as either establishing, or at least going a long way toward establishing, that force is not identifiable with any mode characterizable terms of size, shape, and motion.” Sleigh finds this puzzling and suggests that other commentators have generally been insufficiently perplexed by the bearing that the DM.17 has on the metaphysical issue. He notes that §17 of the Discourse is a presentation of “the argument of the Brevis demonstratio to the effect that Descartes erred in measuring force in terms of mass and velocity, rather than in terms of mass and the square of velocity,” and observes that, given this, it is initially plausible to think that Leibniz ought to have concluded the very opposite, for “if force were measurable in terms of mass and the square of velocity—then force would be characterizable in terms of size and motion.”

In discussion of Leibniz’s philosophical methodology Donald Rutherford defends the view that Leibniz regarded metaphysics as an a priori demonstrative science. In the course of this discussion Rutherford isolates and tries to deflect a significant challenge for his view, namely the observation that in many of his mature writings on metaphysics Leibniz appears to defend his views by means of a posteriori arguments. I present some prima facie difficulties with Rutherford’s position and then offer an alternative account of how Leibniz thought he needed to establish metaphysical claims. My suggestion is that the challenge that Rutherford poses may be best answered by attending to the fact that Leibniz recognized a kind of metaphysical enquiry, ‘real metaphysics’, that is essentially a posteriori, in virtue of the fact that it is concerned not just with possible kinds of beings, but with the kinds of beings that God actually created.

Seine Kritik an Descartes' Auffassung vom Körper gründet Leibniz bekanntlich auf Erörterungen zur Teilbarkeit und Ausdehnung. Obgleich jene Argumentation im Fokus einer Auseinandersetzung mit Leibniz' Metaphysik angesiedelt werden muss, ist sie bisher nicht recht verstanden worden. Mein Anliegen hier ist im Kern, Leibniz' Gedankengang zu explizieren und dessen Stichhaltigkeit auszuleuchten. Das Argument, um das es geht, ist wohl am ehesten aus der Darlegung in Leibniz' Korrespondenz mit Antoine Arnauld bekannt, findet sich jedoch zudem im späteren Briefwechsel mit De Volder. Neben Parallelen gibt es zwischen den Verfahrensweisen, die Leibniz in den zwei Korrespondenzen jeweils favorisiert, gleichwohl derart signifikante Differenzen, dass es nicht unbegründet scheint, ihm auch zwei Argumentationslinien zuzuschreiben -die Unterschiede dieser Linien werde ich im Folgenden auch hinsichtlich ihres Entstehungszusammenhangs beleuchten und einen Ausblick auf weitere Forschungserfordernisse wagen

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

In this paper I offer a discussion of chapter 3 of Adrian Moore’s The Evolution of Modern Metaphysics, which is titled “Leibniz: Metaphysics in the Service of Theodicy.” Here Moore discusses the philosophy of Leibniz and comes to a damning conclusion. My main aim is to suggest that such a conclusion might be a little premature. I begin by outlining Moore’s discussion of Leibniz and then raise some problems for the objections that Moore presents. I follow this by raising a Moore-inspired problem of my own and offer a possible response. The response is based on a little-known essay of Leibniz’s called “Leibniz’s Philosophical Dream” and leads me to consider Leibniz’s deepest motivations for engaging in philosophical reflection.