The theorems of the simplest and strongest sensible quantified modal logic include the Barcan Formula and its converse. Both formulas face strong intuitive objections. This paper develops a theory of possibilia to meet those objections.

The simplest quantified modal logic combines classical quantification theory with the propositional modal logic K. The models of simple QML relativize predication to possible worlds and treat the quantifier as ranging over a single fixed domain of objects. But this simple QML has features that are objectionable to actualists. By contrast, Kripke-models, with their varying domains and restricted quantifiers, seem to eliminate these features. But in fact, Kripke-models also have features to which actualists object. Though these philosophers have introduced variations (...) on Kripke-models to eliminate their objectionable features, the most well-known variations all have difficulties of their own. The present authors reexamine simple QML and discover that, in addition to having a possibilist interpretation, it has an actualist interpretation as well. By introducing a new sort of existing abstract entity, the contingently nonconcrete, they show that the seeming drawbacks of the simplest QML are not drawbacks at all. Thus, simple QML is independent of certain metaphysical questions. (shrink)

In this paper, we develop an alternative strategy, Platonized Naturalism, for reconciling naturalism and Platonism and to account for our knowledge of mathematical objects and properties. A systematic (Principled) Platonism based on a comprehension principle that asserts the existence of a plenitude of abstract objects is not just consistent with, but required (on transcendental grounds) for naturalism. Such a comprehension principle is synthetic, and it is known a priori. Its synthetic a priori character is grounded in the fact that it (...) is an essential part of the logic in which any scientific theory will be formulated and so underlies (our understanding of) the meaningfulness of any such theory (this is why it is required for naturalism). Moreover, the comprehension principle satisfies naturalist standards of reference, knowledge, and ontological parsimony! As part of our argument, we identify mathematical objects as abstract individuals in the domain governed by the comprehension principle, and we show that our knowledge of mathematical truths is linked to our knowledge of that principle. (shrink)

The paper begins with an argument against eliminativism with respect to the propositional attitudes. There follows an argument that concepts are sui generis ante rem entities. A nonreductionist view of concepts and propositions is then sketched. This provides the background for a theory of concept possession, which forms the bulk of the paper. The central idea is that concept possession is to be analyzed in terms of a certain kind of pattern of reliability in one’s intuitions regarding the behavior of (...) the concept. The challenge is to find an analysis that is at once noncircular and fully general. Environmentalism, anti-individualism, holism, analyticity, etc. provide additional hurdles. The paper closes with a discussion of the theory’s implications for the Wittgenstein-Kripke puzzle about rule-following and the Benacerraf problem concerning mathematical knowledge. (shrink)

This is the second edition of an important introduction to Leibniz's philosophy of logic and language first published in 1972. It takes issue with several traditional interpretations of Leibniz while revealing how Leibniz's thought is related to issues of great interest in current logical theory. For this new edition, the author has added new chapters on infinitesimals and conditionals as well as taking account of reviews of the first edition.

This is the second edition of an important introduction to Leibniz's philosophy of logic and language first published in 1972. It takes issue with several traditional interpretations of Leibniz (by Russell amongst others) while revealing how Leibniz's thought is related to issues of great interest in current logical theory. For this new edition, the author has added new chapters on infinitesimals and conditionals as well as taking account of reviews of the first edition.

At least some of these commentators have then, rather naturally, taken a step which it will be the business of this essay to criticize. They have suggested that Leibniz’s "counter-part theory" can be understood as providing an interpretation of counter-factuals and certain forms of modal discourse within his system. For example, Mondadori writes.

Der Aufsatz sucht die Berechtigung der Leibnizschen Unterscheidung zwischen notwendigen und kontingenten Aussagen nachzuweisen. Das entscheidende Problem ist für den Autor die Frage nach der Verbindung zwischen dem Subjektbegriff und seinen Teilbegriffen, Teilbegriffe, ohne die der Subjektbegriff nicht gedacht werden kann, kommen ihm wesentlich und notwendig zu. Teilbegriffe, deren Zukommen jedoch nur bei Hinzunahme externer Bedingungen -letzlich des göttlichen Willens und seiner Wahl der besten Welt -begründet werden kann, kommen in kontingenter Weise zu. Notwendige Sätze können durch eine Analyse der (...) Begriffe in endlich vielen Schritten bewiesen werden, kontingente Sätze erfordern eine unendliche Analyse und sind deshalb nicht beweisbar. Leibniz' Annahme kontingenter Aussagen beruht daher nach der Überzeugung des Autors nicht auf der Unterscheidung zwischen Möglichkeit und Existenz, wie z. B. Russell geglaubt hat, sondern auf der Unterscheidung von Wesensbegriffen und Individualbegriffen. Mit Hilfe dieser Unterscheidung ist die Annahme kontingenter Aussagen nach der Meinung des Autors zu rechtfertigen. (shrink)

In this paper my objective is two-fold. First, I will try to provide further arguments in favour of the view defended in my earlier paper¹. In particular, I will try to show (in § 1) that a plausible understanding of the notion of a complete concept, coupled with (what I take to be) a reasonable interpretation of Leibniz's intriguing talk of severa “possible Adams” (§ 2), leads quite naturally to the view that Leibniz was committed to the doctrine of world-bound (...) individuals. Second, I will try to show (in § 3) that a suggestive way of saving contingency in the framework of Leibniz's theory of complete concepts is bound to fail : and the reasons for this failure will provide further evidence in favour of the view under present discussion. The remaining sections of the paper (§§ 4-6), will be concerned with fixing and making precise some of the loose ends of the previous three sections. Thus §§ 4 and 5 will be devoted to an analysis of Leibniz's use and understanding of the notions of contingency and necessity, and essence and accident, respectively. It will be shown that Leibniz's use and understanding of those notions is perfectly consistent with his commitment to the doctrine of world-bound individuals. In § 6, finally, I will try to indicate exactly how David Lewis' Counterpart Theory can be brought to bear upon Leibniz's theory of complete concepts, and, specifically, how it ought to be interpreted in that context. (shrink)