Philosophy

The subtraction argument, originally put forward by Thomas Baldwin (1996), is intended to establish Metaphysical Nihilism, the thesis that there could have been no concrete objects. Some modified versions of the argument have been proposed in order to avoid some difficulties faced by the original argument.
In this paper I shall concentrate on two of those versions, the so-called subtraction argument* (presented and defended in Rodriguez-Pereyra 1997, 2000, 2002), and Efird and Stoneham’s recent version of the argument (Efird and Stoneham 2005). I shall defend the subtraction argument* from Alexander Paseau’s (2006) objection that because a crucial premise of the subtraction argument* may have no plausibility independent from Metaphysical Nihilism, the subtraction argument* is not suasive. Although Paseau focuses on the subtraction argument*, I shall point out that Efird and Stoneham could reply to Paseau’s objection in the same way. Thus there are (at least) two suasive versions of the subtraction argument that establish Metaphysical Nihilism. But are those two arguments equally good? I shall argue that the subtraction argument* is preferable to Efird and Stoneham’s argument.

Leibniz’s short letter to the mathematician and physicist Ludovico Casati of 1689 is a short but interesting text on the Principle of Identity of Indiscernibles, to which it is entirely dedicated. Since there is no watermark in the paper of the letter, the letter is difficult to date, but it is likely that it was written during Leibniz’s stay in Rome, sometime between April and November of 1689 (A 2 2 287–8). When addressing the letter, Leibniz wrote ‘Casani’, but this seems to be a mistake and the real addressee is thought to be Ludovico Casati, nephew of Paolo Casati, the Jesuit mathematician. The letter, reproduced in the Berlin’s Academy edition of Leibniz’s works, was first published by Gerhardt in the Archiv für Geschichte der Philosophie in 1892 (Gerhardt 1892: 53–54). It also appears in Robinet’s Iter Italicum (Robinet 1988: 134–35). But neither Gerhardt nor Robinet provide a philosophical discussion of the letter, and I am not aware of any other philosophical discussion of it. Furthermore, as far as I know, the letter has never been translated into any language. Thus I shall here provide a transcription (from A 2 2 288–89) and a translation of the letter into English, and a philosophical discussion of its treatment of the Identity of Indiscernibles.

Leibniz was a philosopher of principles: the principles of Contradiction, of Sufficient Reason, of Identity of Indiscernibles, of Plenitude, of the Best, and of Continuity are among the most famous Leibnizian principles.  In this article I shall focus on the first three principles; I shall discuss various formulations of the principles (sect. 1), what it means for these theses to have the status of principles or axioms in Leibniz’s philosophy (sect. 2), the fundamental character of the Principles of Contradiction and Sufficient Reason (sect. 3), some attempts to demonstrate the Principles of Contradiction and Sufficient Reason (sect. 4), and one attempt to demonstrate the Principle of Identity of Indiscernibles (sect. 5). The main results of the chapter are summarized in a short conclusion (sect. 6).

This paper is a response to replies by Dan López de Sa and Mark Jago to my ‘Truthmaking, Entailment, and the Conjuction Thesis’. In that paper, my main aim was to argue against the Entailment Principle by arguing against the Conjunction Thesis, which is entailed by the Entailment Principle. In the course of so doing, although not essential for my project in that paper, I defended the Disjunction Thesis. López de Sa has objected both to my defence of the Disjunction Thesis and my case against the Conjunction Thesis. I shall show that his objections are unfounded and based on serious misunderstandings of my position, what the relevant debate is, and some fundamental notions of Truthmaker Theory.
Jago argues that accepting the Disjunction Thesis and rejecting the Conjunction Thesis is hard to maintain. But I show that Jago has not shown that accepting the Disjunction Thesis while rejecting the Conjunction Thesis is impossible or even hard to maintain. Jago believes that, to accept the Disjunction Thesis while rejecting the Conjunction Thesis, one needs to reject his axiom (T3), which says that all the truthmakers for <P&P> are truthmakers for <P>. I argue that there are reasons to reject such a principle, and the version of it that says that what makes <P&P> true makes <P> true.

In the Discourse on Metaphysics Leibniz put forward his famous complete-concept definition of substance. Sometimes this definition is glossed as stating that a substance is an entity with a concept so complete that it contains all its predicates, and it is thought that it follows directly from Leibniz’s theory of truth.  Now, an adequate definition of substance should not apply to accidents. But, as I shall point out, if Leibniz’s theory of truth is correct then an accident is an entity with a concept so complete that it contains all its predicates. The aim of this paper is to clarify Leibniz’s notion of substance in the Discourse with a view to explaining how that definition successfully distinguishes between substances and accidents.

Resemblance Nominalism is the view that denies universals and tropes and claims that what makes F-things F is their resemblances. A famous argument against Resemblance Nominalism is Russell’s regress of resemblances, according to which the resemblance nominalist falls into a vicious infinite regress. Aristocratic Resemblance Nominalism, as opposed to Egalitarian Resemblance Nominalism, is the version of Resemblance Nominalism that claims that what makes F-things F is that they resemble the F-paradigms. In this paper I attempt to show that a recently advocated strategy to stop Russell’s regress by using paradigms does not succeed.