Online research in philosophy

Leibniz filters play a prominent role in the theory of protoalgebraic logics. In [3] the problem of the definability of Leibniz filters is considered. Here we study the definability of Leibniz filters with parameters. The main result of the paper says that a protoalgebraic logic S has its strong version weakly algebraizable iff it has its Leibniz filters explicitly definable with parameters.

Leibniz's philosophy of time, often seen as a precursor to current forms of relationalism and causal theories of time, has rightly earned the admiration of his more recent counterparts in the philosophy of science. In this article, I examine Leibniz's philosophy of time from a new perspective: the role that tense and non-tensed temporal properties/relations play in it. Specifically, I argue that Leibniz's philosophy of time is best (and non-anachronistically) construed as a non-tensed theory of time, one that dispenses with tensed temporal properties such as past, present, and future. In arguing for this thesis, I focus on the three facets of Leibniz's philosophy most relevant for evaluating his commitment to a B-theory of time: (1) the nature of change, (2) the reality of the future, and (3) the truth-conditions for tensed temporal statements. Despite prima facie evidence to the contrary, I show that a close examination of Leibniz's views on these topics provides compelling evidence for interpreting his philosophy of time as a B-theory of time.

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.

In this paper, I aim to offer a clear explanation of what monadic domination, understood as a relation obtaining exclusively among monads, amounts to in the philosophy of Leibniz (and this insofar as monadic domination is conceived by Leibniz not to account for the substantial unity of composite substances). Central to my account is the Aristotelian notion of a hierarchy of activities, as well as a particular understanding of the relations that obtain among the perceptions of monads that stand in relations of monadic domination and subordination.

Did God give things 'accidental powers not rooted in their natures', powers not rooted in intrinsic properties? For Leibniz, no. For Locke, the answer is disputed. On a voluntarist reading, yes, secondary and tertiary qualities are superadded (Margaret Wilson). On a mechanist reading, no, as for Leibniz (Michael Ayers). Since Locke viewed these qualities as relational, his view of relations ought to bear on the dispute. Locke said relation is 'not contained in the real existence of things'. Bennett says Locke means relations are reducible (as Leibniz thought), which supports the mechanist reading. Bennett is mistaken: Locke means relations are irreducible, in harmony with his voluntarism.

In the Discourse on Metaphysics Leibniz writes, 'Our perceptions are always true, it is our judgments that come from ourselves that deceive us' (section 14). Leroy Loemker in his 'Leibniz's Doctrine of Ideas' criticizes this account of error. His main worry can be presented in the form of the following syllogistic argument, which he derives from Leibniz's doctrine of ideas: (a) There cannot be a false perception; (b) All judgments are perceptions; and therefore (c) There cannot be a false judgment. However, in this paper I argue that Leibniz can distinguish between a perception and a judgment in their semantic aspect. The sense in which a perception turns out to be false (or true) for Leibniz is different from the sense in which a judgment turns out to be false (or true). This is because, while a perception, understood in Leibniz's terms, lacks truth-conditions, a judgment, in being representational, has such conditions. Thus while a perception remains true always, a judgment can be false. Pointing to the equivocal use of 'false' in (a) and (c) above, I conclude that (c) does not follow from (a) and (b).

This paper discusses Leibniz's Trinitarian doctrine in the light of his philosophy, as revealed by a set of virtually unstudied texts. The first part of the paper examines Leibniz's defence of the Trinity against the charge of contradiction as a necessary precondition to the development of his own conception of the Trinity. The second part discusses some of the key features of Leibniz's Trinitarian doctrine, notably his conception of person, the analogy between the human mind and the Trinity, and the problem of Trinitarian relations.

Leibniz, it seems, wishes to reduce statements involving relations or extrinsic denominations to ones solely in terms of individual accidents or, respectively, intrinsic denominations. His reasons for this appear to be that relations are merely mental things (since they cannot be individual accidents) and that extrinsic denominations do not represent substances as they are on their own. Three interpretations of Leibniz''s reductionism may be distinguished: First, he allowed only monadic predicates in reducing statements (hard reductionism); second, he allowed also `implicitly relational predicates'' such as `loves somebody'' (soft reductionism); third, he allowed also `explicitly relational predicates'' such as `loves Helen'' (nonreductionism). Hard reductionism is problematic with respect to Leibniz''s doctrines of universal expression and incompossibility (among other things). Nonreductionism, in turn, faces insurmountable problems with Leibniz''s doctrine of self-sufficiency and internal identification of substances, as well as with that of individual accidents. The remaining option, soft reductionism, standing between the other two interpretations, arguably avoids at least some of their problems.

Leibniz's predicate-in-notion principle and some of its alleged consequences, by C. D. Broad.--On Leibniz's metaphysics, by L. Couturat.--Philosophical reflections of Leibniz on law, politics, and the state, by C. J. Friedrich.--The root of contingency, by E. M. Curley.--Monadology, by M. Furth.--Individual substance, by I. Hacking.--Leibniz on plenitude, relations, and the "reign of the law," by J. Hintikka.--Leibniz's theory of the ideality of relations, by H. Ishiguro.--Leibniz and Spinoza on activity, by M. Kneale.--Leibniz and Newton, by A. Koyré.--Plenitude and sufficient reason in Leibniz and Spinoza, by A. O. Lovejoy.--Leibniz on possible worlds, by B. Mates.--Recent work on the philosophy of Leibniz, by B. Russell.--On Leibniz's explication of "necessary truth," by M. D. Wilson.--Bibliography (p. [421]-425).

Broad, C. D. Leibniz's predicate-in-notion principle and some of its alleged consequences.--Couturat, L. On Leibniz's metaphysics.--Friedrich, C. J. Philosophical reflections of Leibniz on law, politics, and the state.--Curley, E. M. The root of contingency. Furth, M. Monadology.--Hacking, I. Individual substance.--Hintikka, J. Leibniz on plenitude, relations, and the "reign of law."--Ishiguro, H. Leibniz's theory of the ideality of relations.--Kneale, M. Leibniz and Spinoza on activity.--Koyré, A. Leibniz and Newton.--Lovejoy, A. O. Plenitude and sufficient reason in Leibniz and Spinoza.--Mates, B. Leibniz on possible worlds.--Russell, B. Recent work on the philosophy of Leibniz.--Wilson, M. D. On Leibniz's explication of "necessary truth.".