Papers by Filippo Costantini
The art of estimation and the mathematization of force in Leibniz
Studies in History and Philosophy of Science, 2025
From 1686 onward, Leibniz is engaged in a dispute with Cartesian physicists on the correct expres... more From 1686 onward, Leibniz is engaged in a dispute with Cartesian physicists on the correct expression for the quantity of force in moving bodies. In the 1690s, he puts forth an argument for his own expression that is allegedly based on the science of quantity in general (or the art of estimation). Leibniz states that the latter requires the quantity of force to be determined by the real repetitions of a measure. It would follow that his expression for force is the correct one. Now, commentators have not been sensitive to the ingenuity of the argument presented here. In this paper, focussing on the exchange between Johann Bernoulli and Leibniz, we want to show how this argument consists essentially in pushing for a certain conception of the mathematization of force based, in turn, on a serious conception of measurement of quantities. This conception exploits the conservative properties of physical systems in order to apply general principles of determination of quantity to the special case of the quantity of force. We conclude by confronting our interpretation with others which posit a stronger connection between measurement and metaphysics in Leibniz.
JoLMA. The Journal for the Philosophy of Language, Mind and the Arts, 2024
In contrast to Quine’s (meta-)ontology and his preference for desert landscapes, recent years hav... more In contrast to Quine’s (meta-)ontology and his preference for desert landscapes, recent years have seen a renewed interest in ‘non-being’: non-existent entities, mere possibilia, negative properties, negative facts, absences, nothingness, voids, holes, etc. Interest in the category of non-being is not limited to ontology but has also found applications in the philosophy of mind, particularly regarding the role intentionality plays in relation to non-entities and the problem of perceiving absences. Additionally, it has influenced the philosophy of art, especially in discussions about absence art – i.e., art that features absences as aesthetic objects. This issue of JoLMA highlights the richness of the topic by presenting eight fresh papers that range from metaphysics, ontology, and epistemology, to philosophy of language, aesthetics, and philosophy of mind.
Leibniz’s Mereology: A Logical Reconstruction
The Review of Symbolic Logic, 2025
The aim of this paper is to give a full exposition of Leibniz’s mereological system. My starting ... more 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, I expound the Real Addition calculus; in the second part, 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, I scrutinize some of the applications of the containment-parthood distinction showing that a number of famous Leibnizian doctrines depend on it.
There is No Anima Mundi: Leibniz on the Impossibility of a Soul of the World
ERGO. A Journal of Philosophy, 2024
The main source of perplexity raised by Leibniz’s (mathematical) argument against the soul of the... more 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.
Élenchos e Trivialismo
In Élenchos. La forma del filosofare (a cura di Simoncelli D. e Pellegrino V.), 2024
Il contributo analizza la difesa elenctica del principio di non-contraddizione in rapporto alla t... more Il contributo analizza la difesa elenctica del principio di non-contraddizione in rapporto alla tesi trivialista, secondo cui tutte le proposizioni sono vere (e di conseguenza anche tutte le contraddizioni lo sono). L'articolo difende 5 tesi: 1. L'élenchos mostra che il trivialismo è una tesi irrazionale, non che esso sia falso. 2. Affinché riesca a confutare il trivialismo, l’argomentazione elenctica deve essere integrata dalla “tesi dell’unità di essere e pensiero”. 3) La tesi dell’unità di essere e pensiero, all’interno della tradizione “neoclassica” in cui si è formato Severino, è difesa facendo ricorso a una ulteriore argomentazione di tipo elenctico. 4) La dimostrazione elenctica al punto 3 non è sufficiente a mostrare la verità di tale tesi; infatti, per funzionare, tale argomentazione richiede la validità della stessa tesi che vorrebbe giustificare. Abbiamo così una palese petizione di principio. 5) Dunque, la difesa elenctica del PDNC non riesce a confutare il trivialista. Lungi dal rappresentare una difesa del trivialismo, il presente articolo ha lo scopo di evidenziare i limiti della difesa elenctica del PDNC.
Definitions by abstraction and Leibniz's notion of quantity
Theoria (Wiley), volume 90, Issue 12, 2024
This paper analyses the abstractionist account of quantity championed by Leibniz, especially in t... more This paper analyses the abstractionist account of quantity championed by Leibniz, especially in the 1680s. Leibniz intro- duced 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.
Composition as Identiy and the Logical Roots of Leibniz's Nominalism
Global Philosophy, 2023
Free available here: https://link.springer.com/article/10.1007/s10516-023-09665-3
The paper deal... more Free available here: https://link.springer.com/article/10.1007/s10516-023-09665-3
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.
The Leibniz Review
This paper won the 2022 Leibniz Society of North America Essay Competition.
This paper deals wit... more This paper won the 2022 Leibniz Society of North America Essay Competition.
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 I this way it links Leibniz’s metaphysics with his conception of Mathesis Universalis), it allows the use of metaphysics to clarify the features of his mathematical notion of quantity. This task is accomplished in §5 and §6. Finally, §7 discusses a possible objection.
JOLMA. The Journal for the Philosophy of Language, Mind and the Arts, 2021
This paper discusses Leibniz's treatment of the term 'nihil' that appears in some logical papers ... more This paper discusses Leibniz's treatment of the term 'nihil' that appears in some logical papers about the notion of Real Addition. First, the paper argues that the term should be understood as an empty (singular) term and that sentences with empty terms can be true (§2). Second, it sketches a positive free logic to describe the logical behaviour of empty terms (§3). After explaining how this approach avoids a contradiction that threatens the introduction of the term 'nihil' in the Real Addition calculus (§4), and how this approach should be understood within Leibniz's philosophy (§5), the paper assesses the prospects of such an approach with regard to two fundamental issues in Leibniz's thought: the fictional nature of infinitesimals (§6), and the occurrence of the term 'nothing' in the proof of the existence of God that we find in the New Essays (§7).
Eternity & Contradiction. Journal of Fundamental Ontology, 2021
This paper analyzes and criticizes Emanuele Severino's resolution of the aporia of nothingness. S... more This paper analyzes and criticizes Emanuele Severino's resolution of the aporia of nothingness. Severino's solution consists in two theses: A) the meaning of 'nothingness' is self-contradictory; B) the determinate content of the meaning of nothingness is consistent (it does not imply by itself any contradiction). After distinguishing three possible interpretations of the term 'nothing' (as a quantifier, as a noun-phrase, and as a concept), the paper argues that there is no interpretation that makes both theses A) and B) simultaneously true. This shows that Severino's formulation and resolution of the problem of nothingness is untenable; moreover, it is shown that his resolution is based on an ambiguity between the nounphrase and the concept interpretation.
Eternity & Contradiction. Journal of Fundamental Ontology, 2020
In my paper ‘Elenchos Come Petitio Principii’, I argued that Severino’s elenctic argument does no... more In my paper ‘Elenchos Come Petitio Principii’, I argued that Severino’s elenctic argument does not work against a dialetheist position such as the one defended by Graham Priest. In the present paper, I will focus on some fundamental aspects of the dialetheist’s challenge to the Law of Non Contradiction that have raised many doubts, such as the claim that a true contradiction is at the same time false, or the fact that the dialetheist’s metatheory should be as inconsistent as the object theory. Moreover, I shall exploit such clarifications to reexpose some of the key passages of my critique of the elenctic strategy, in particular those regarding the second figure of elenchos. Finally, I shall reply to the objection that accuses both dialetheism and my own view of not providing incontrovertible grounds to their respective claims.
Philosophia (Springer), 2020
In this paper we offer a new solution to the old paradox of nothingness. This new solution develo... more 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 (absolute generality) and to eat it too (avoid commitment to a contradictory notion of nothingness).
History of Philosophy and Logical Analysis , 2019
This paper deals with Leibniz’s well-known reductio argument against the infinite number. I will ... more This paper deals with Leibniz’s well-known reductio argument against the infinite number. I will show that while the argument is in itself valid, the assumption that Leibniz reduces to absurdity does not play a relevant role. The last paragraph of the paper reformulates the whole Leibnizian argument in plural terms (i.e. by means of a plural logic) to show that it is possible to derive the contradiction that Leibniz uses in his argument even in the absence of the premise that he refutes.
Rivista di Filosofia Neo-Scolastica, 2018
The paper argues that the elenctic argument in defence of the Law of Non-contradiction is a Petit... more The paper argues that the elenctic argument in defence of the Law of Non-contradiction is a Petitio Principii. In the first part of the paper, Emanuele Severino’s development of an elenctic strategy in Ritornare a Parmenide is examined and compared with Graham Priest’s defence of the truth of some contradictions. The fundamental reason why the elenctic strategy begs the question is that, in order to work, it exactly presupposes that account of negation which is challenged by the friends of contradictions like Priest. In the second part, the traditional idealistic argument against the existence of the “Thing in itself” is shown to suffer from the same problem.
Kriterion - Journal of Philosophy, 2018
In this paper, we offer a contribution to the discussion of one of the most important objections ... more 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 Philosophical Forum, Inc., 2018
In the debate on absolute generality, many authors have defended a relativistic position, namely ... more In the debate on absolute generality, many authors have defended a relativistic position, namely that quantiiers are always restricted to a less than all-inclusive domain. Consequently, they hold that an unrestricted quantiication over everything is not possible. One problem for such a view is the need to explain the apparent absolute generality of logical laws. The standard response appeals to schemas. In this paper, I begin by examining the reasons why schematic generality has such a strong appeal in this debate, which rely on their open-endedness. However, I also raise an objection to show that schemas cannot be a good substitute for quantiicational generality, due to the fact that they do not express propositions with a determined truth-value. The second part of the paper is dedicated to develop a different kind of generality, which is both open-ended (as schematic generality) and expresses a proposition with a determined truth-value (as quantificational generality). From a formal point of view, I will make use of a modal approach, in which the modality must be taken as primitive. The paper ends with a comparison of this form of generality and schematism, and argues that the former is to be preferred over the latter.
Discipline Filosofiche, XXVI, 2, 2016
The aim of this paper is to understand the meaning of dialectical contradiction. I shall argue th... more 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 (§ 1); I shall show why Hegel and Adorno give two radically different interpretations of contradiction (§ 2 and § 3); why Adorno’s idea of dialectics, as showing the presence of a transcendent “nonidentical”, is not sustainable (§ 4); and, finally, that Adorno’s conception of a purely negative dialectics requires a linguistic interpretation (§ 5).
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Papers by Filippo Costantini
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, I scrutinize some of the applications of the containment-parthood distinction showing that a number of famous Leibnizian doctrines depend on it.
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.
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 I this way it links Leibniz’s metaphysics with his conception of Mathesis Universalis), it allows the use of metaphysics to clarify the features of his mathematical notion of quantity. This task is accomplished in §5 and §6. Finally, §7 discusses a possible objection.