Filippo Costantini

The paper deals with Leibniz’s ontology and the metaphysics of the aggregate. Concerning the ontology of aggregates, the main aim is to provide a new argument in favor of the claim that an aggregate and its constituents have the same ontological import. This argument takes the form of a weakening of a principle known in the contemporary literature of mereology as ‘composition as identity’ (CAI). The paper shows that Leibniz’s nominalism toward aggregates is a direct consequence of two elements: the way in which he considers the relationship between aggregates and their constituents in his logical calculus; and his theory of identity (and more generally, equivalence relations) as providing us with the ground for substitution salva veritate. It is concluded that Leibniz is committed to a principle that the author dubs Ontological-CAI: the aggregate/whole is ontologically identical (i.e. it has the same ontological import) as its constituents/parts. Concerning the metaphysics of aggregates, the paper outlines in what sense aggregates are grounded on their constituents: arguing that Leibniz is committed to a further principle that the author calls Metaphysical-CAI: the aggregate/whole is metaphysically grounded on its constituents/parts. From this it can be understood in which sense Leibniz could be considered a mereological nihilist, and in which sense not. The paper also sets out two different and competing readings of Metaphysical-CAI, and argues that Leibniz accepted both of them by interpreting them as different levels of explanation of the nature of aggregates.

In this paper I present a dilemma for Casati’s dialetheist interpretation of Heidegger. On the one hand, Casati’s main argument in favour of the ontological difference requires that loops of grounding are vicious; on the other hand, the two para-consistent models of the grounding relation discussed in chapter 6 require that loops of grounding are not vicious. We thus face a dilemma: either loops of grounding are vicious (and must therefore be rejected), or they are not. If the former, then Casati can exploit them to argue for the ontological difference, but then he cannot accept the two para-consistent models, since they validate loops. By contrast, if Casati thinks that loops of grounding are not vicious, then he has no problem with the models, but he loses his main argument for the ontological difference. After discussing the prospects of responding to this dilemma, I scrutinize Casati’s second argument in favour of the ontological difference and argue that it can be resisted.

Many scholars hold that Leibniz's monads are not located in space at all, and some attribute situations to simple substances directly. A more nuanced position is that monads have a situation only indirectly, namely through the situation of their bodies. It has been objected, however, that this intermediate position is untenable since it involves a viciously circular argument. Leibniz is clear that the situation is the basis for the extension. But if a substance is situated only through its own (extended) body, then the situation would appear to presuppose the extension of the body. Thus extension presupposes situation, but the situation would presuppose extension. In this paper (1) we present textual evidence that Leibniz did indeed hold that monads are situated via their own bodies; (2) we suggest that, even if what is properly speaking situated are (extended) bodies, there is no circularity in holding that the extension of a body results from the mutual situations of its parts: a non-vicious infinite regress of explanations in terms of extended parts is possible; and (3) we defend this solution against a possible objection.

The aim of this paper is to give a full exposition of Leibniz’s mereological system. My starting point will be his papers on Real Addition, and the distinction between the containment and the part-whole relation. In the first part (§2), I expound the Real Addition calculus; in the second part (§3), I introduce the mereological calculus by restricting the containment relation via the notion of homogeneity which results in the parthood relation (this corresponds to an extension of the Real Addition calculus via what I call the Homogeneity axiom). I analyze in detail such a notion, and argue that it implies a gunk conception of (proper) part. Finally, in the third part (§4), I scrutinize some of the applications of the containment-parthood distinction showing that a number of famous Leibnizian doctrines depend on it.

The main source of perplexity raised by Leibniz’s (mathematical) argument against the soul of the world stems from the idea that it is the infinity of the universe that precludes it from having a soul. But if this is so, how is it possible that organic bodies, which, having infinitely many parts, are also infinite, are endowed with a soul? The present paper aims to provide a new solution to this puzzle. The solution explains the difference between the body and the universe by looking at how their respective parts are arranged. It is the arrangement of the parts of the body that allows a body to be divided into infinitely many parts whilst, at the same time, having a finite magnitude. By contrast, the way in which the alleged parts of the world are arranged makes it impossible that the world has a finite magnitude: the world cannot be a whole, and so it cannot have a soul. The consequence is that it does not matter how many parts bodies have, but only that they have a finite magnitude. In this case, bodies respect the Part-Whole Principle (the whole is bigger than any of its proper parts) and therefore can be described as finite wholes with parts.

This paper analyses the abstractionist account of quantity championed by Leibniz, especially in the 1680s. Leibniz introduced the notion of quantity in an indirect way, via an abstraction principle. In the first part of the paper, I identify the context in which this approach arose in light of Leibniz's criticism of his earlier dream of an ‘alphabet of human thought’. Recognising the impossibility of such a project led him to realise that, when dealing with terms referring to abstract objects, we should always consider them within the true sentences in which they occur. In the second part, I describe this approach in detail. This allows us to look at some key concepts of Leibniz's theory of quantity. In particular, I raise the problem of the relationship between the two sides of the abstraction principle: how should we think of the relation between the claim that a and b are equal, and the claim that the quantity of a is identical to the quantity of b? I argue that we can find a positive answer to this problem in Leibniz.

This paper deals with the metaphysics of the notion of quantity in the philosophy of Leibniz, and its aim is to defend the following bi-conditional: for any object x, x has a certain quantity if and only if x has a (metaphysical) limit or a bound. The direction from left to right is justified in §3, while in §4 I develop an argument to justify the direction from right to left. Since the bi-conditional links the metaphysical notion of limit to the mathematical notion of quantity (and in this way it links Leibniz’s metaphysics with his conception of Mathesis Universalis), it allows the use of metaphysics to clarify the features of the mathematical notion of quantity. This task is accomplished in §5 and §6. Finally, §7 discusses a possible objection.

The paper deals with Leibniz’s ontology and the metaphysics of the aggregate. Concerning the ontology of aggregates, the main aim is to provide _a new argument_ in favor of the claim that an aggregate and its constituents have the same ontological import. This argument takes the form of a weakening of a principle known in the contemporary literature of mereology as ‘composition as identity’ (CAI). The paper shows that Leibniz’s nominalism toward aggregates is a direct consequence of two elements: the way in which he considers the relationship between aggregates and their constituents in his logical calculus; and his theory of identity (and more generally, equivalence relations) as providing us with the ground for substitution _salva veritate_. It is concluded that Leibniz is committed to a principle that the author dubs Ontological-CAI: the aggregate/whole is _ontologically identical_ (i.e. it has the same ontological import) as its constituents/parts. Concerning the metaphysics of aggregates, the paper outlines in what sense aggregates are grounded on their constituents: arguing that Leibniz is committed to a further principle that the author calls Metaphysical-CAI: the aggregate/whole is _metaphysically grounded_ on its constituents/parts. From this it can be understood in which sense Leibniz could be considered a mereological nihilist, and in which sense not. The paper also sets out two different and competing readings of Metaphysical-CAI, and argues that Leibniz accepted both of them by interpreting them as different levels of explanation of the nature of aggregates.

In this paper, we offer a contribution to the discussion of one of the most important objections against a relativist position in the absolute generality debate. The inexpressibility objection accuses the generality-relativist of not being able to coherently express her own position. First, we examine Glanzberg’s attempt to reply to this objection and we show that it fails. Second, we study the prospects of generalizing the relativist position. In particular, we analyze Fine’s and Linnebo’s modal approaches and we argue that, even though they are able to coherently express one of the core ideas of relativism while avoiding the inexpressibility objection, there is an important sense in which they are no longer relativist positions. Third, while strengthening the idea that the inexpressibility objection does succeed, we argue that this is no guarantee of the falsity of relativism. Relativism may be inexpressible but true. However, we stress that even if the inexpressibility objection does not supply a definitive, knock-down objection against relativism, if we want to discuss relativism in a rational way, the objection offers a compelling reason not to embrace generality-relativism.

The aim of this paper is to understand the meaning of dialectical contradiction. I shall argue that dialectics is mainly a linguistic phenomenon that shows the coimplication of concepts. Through a deep analysis of the notions of “contradiction” and “negation”, which lie behind Hegel’s and Adorno’s work, I shall explain the logical structure of the contradiction which Hegel and Adorno work with ; I shall show why Hegel and Adorno give two radically different interpretations of contradiction ; why Adorno’s idea of dialectics, as showing the presence of a transcendent “nonidentical”, is not sustainable ; and, finally, that Adorno’s conception of a purely negative dialectics requires a linguistic interpretation.

In this paper we offer a new solution to the old paradox of nothingness. This new solution develops in two steps. The first step consists in showing how to resolve the contradiction generated by the notion of nothingness by claiming that the contradiction shows the indefinite extensibility of the concept of object. The second step consists in showing that, having accepted the idea of indefinite extensibility, we can have absolute generality without the emergence of the contradiction connected to the absolute notion of nothingness. The idea of indefinite extensibility allows us to have our cake and to eat it too.