It is common lore that standard, Kripke-style semantics for quantified modal logic is incompatible with the view that no individual may belong to more than one possible world, a view that seems to require a counterpart-theoretic semantics instead. Strictly speaking, however, this thought is wrong-headed. This note explains why.

In previous work I have argued that talk about negative events should not be taken at face value: typically, what we are inclined to think of as a negative event (John’s failure to go jogging) is just an ordinary, positive event (his going to the movie instead); it is a positive event under a negative description. Here I consider more closely the difficulties that arise in those cases where no positive event seems available to do the job, as with putative (...) cases of causation by omission. In particular, I elaborate on Helen Beebee’s idea that not all causal explanations are reports of causation. When we mention John’s failure to turn off the gas as an explanans of why there was an explosion, we do not say what caused the explosion. We do not mention any of the relevant causes. We just remark that one sort of event that was supposed to occur, and whose occurrence would have prevented the explosion, did not in fact occur. (shrink)

According to a popular line of reasoning, diachronic vagueness creates a problem for the endurantist conception of persistence. Some authors have replied that this line of reasoning is inconclusive, since the endurantist can subscribe to a principle of Diachronic Unrestricted Composition (DUC) that is perfectly parallel to the principle required by the perdurantist’s semantic account. I object that the endurantist should better avoid DUC. And I argue that even DUC, if accepted, would fail to provide the endurantist with the necessary (...) resources for explaining diachronic vagueness in familiar semantic terms. (shrink)

This is a supplement to our book "Le tribolazioni del filosofare. Comedia metaphysica ne la quale si tratta de li errori & de le pene de l’Infero". It features an entirely new canto of the poem (originally thought to be lost) along with an extensive commentary. The canto covers the first ring of the circle of the Sullen, which hosts the Adverse to the Possible, and deals with several philosophical questions concerning the metaphysics of modality.

L’intérêt que Bergson porte aux arts est bien connu. À travers l’ensemble de son œuvre, les exemples souvent inspirés par la littérature et la lecture semblent révéler une certaine affinité pour cette forme d’art. Pourtant, malgré sa récurrence, ce thème n’est jamais étudié frontalement ni profondément. Cette brève étude se veut un tour d’horizon du répertoire bergsonien, une recherche d’éléments qui permettraient peut-être d’articuler une pensée bergsonienne de la lecture. Plus précisément, nous examinons les exemples utilisés par Bergson pour illustrer (...) les notions de suggestion, d’attention et de sympathie, pour déterminer si ces descriptions du phénomène de lecture ne sont que des exemples, ou s’ils ont une valeur philosophique propre. (shrink)

An overview of the way I picture the amorphous world we live in, built around my comments and responses to nine festschrift essays by A. Borghini (on the Fedro metaphor and the art of butchery), F. Calemi (on the predication principle and metalinguistic nominalism), C. Calosi (on the argument from mereological universalism to extensonality), E. Casetta (on the role of “monsters” in the realism/antirealism debate), V. Giardino (on inductive reasoning, spatial representation, and problem solving), P. Graziani (on mereological notation), P. (...) Pedrini (on the distinction between natural and artificial boundaries), D. Santoro (on causation by omission), and G. Torrengo (on absolute vs. relational space and the problem of incongruent counterparts). (shrink)

There are two ways of understanding the notion of a contradiction: as a conjunction of a statement and its negation, or as a pair of statements one of which is the negation of the other. Correspondingly, there are two ways of understanding the Law of Non-Contradiction (LNC), i.e., the law that says that no contradictions can be true. In this paper I offer some arguments to the effect that on the first (collective) reading LNC is non-negotiable, but on the second (...) (distributive) reading it is perfectly plausible to suppose that LNC may, in some rather special and perhaps undesirable circumstances, fail to hold. (shrink)

That parthood is a transitive relation is among the most basic principles of classical mereology. Alas, it is also very controversial. In a recent paper, Ingvar Johansson has put forward a novel diagnosis of the problem, along with a corresponding solution. The diagnosis is on the right track, I argue, but the solution is misleading. And once the pieces are properly put together, we end up with a reinforcement of the standard defense of transitivity on behalf of classical mereology.

Achille Varzi è uno dei maggiori metafisici viventi. Nel corso degli anni ha scritto testi fondamentali di logica, metafisica, mereologia, filosofia del linguaggio. Ha sconfinato nella topologia, nella geografia, nella matematica, ha ragionato di mostri e confini, percezione e buchi, viaggi nel tempo, nicchie, eventi e ciambelle; e non ha disdegnato di dialogare con gli abitanti di Flatlandia, con Neo e con Terminator. Tra le sue opere principali: Holes and Other Superficialities e Parts and Places. The Structures of Spatial (...) Representation, entrambi scritti insieme a R. Casati per MIT Press; Il mondo messo a fuoco, Laterza; e il suo libro più recente: Le tribolazioni del filosofare, con C. Calosi, per Laterza. -/- Da una giornata all’Università di Urbino nasce questa conversazione a molte voci sulla e con la filosofia di Achille C. Varzi. In un dialogo critico al quale l’Autore si presta con generosità e onestà intellettuale, Andrea Borghini, Francesco Calemi, Claudio Calosi, Elena Casetta, Valeria Giardino, Pierluigi Graziani, Patrizia Pedrini, Daniele Santoro e Giuliano Torrengo lo interrogano e mettono alla prova sui temi affrontati, nel corso degli anni, in campi diversi. Il risultato è un percorso che si snoda attraverso molti mondi, dalla logica alla metafisica, dalla filosofia del linguaggio alla filosofia della matematica, dalla mereologia alla filosofia del tempo, spingendosi in qualche caso oltre i confini del saggio filosofico. (shrink)

A lot of work in metaphysics relies on linguistic analysis and intuitions. Do we want to know what sort of things there are or could be? Then let’s see what sort of things there must be in order for what we truthfully say to be true. Do we want to see whether x is distinct from y? Then let’s see whether there is any statement that is true of x but not of y. And so on. In this paper I (...) argue that this way of proceeding is full of traps and is bound to be pretty useless unless we already have a good idea of what sort of things there are, and of how we are going to count them. (shrink)

A compact overview of the main formal theories of parthood and of their mutual relationships, up to Classical Extensional Mereology. Written as an Appendix to the other essays included in the volume.

In ‘Towards a Solution to the Sorites Paradox’, Graham Priest gives us a new account of the sorites based on fuzzy logic. The novelty lies in the suggestion that truth-value assignments should themselves be treated as fuzzy objects, i.e., objects about which we can make fuzzy identity statements. I argue that Priest’s solution does not have the explanatory force that Priest advocates. That is, it does not explain why we find the existence of a cut-off point counter-intuitive. I also argue (...) that this sort of explanation calls for a general theory that goes beyond the special case of linguistic vagueness, for the phenomenon is at bottom not linguistic. (shrink)

What sort of logic do we get if we adopt a supervaluational semantics for vagueness? As it turns out, the answer depends crucially on how the standard notion of validity as truth preservation is recasted. There are several ways of doing that within a supervaluational framework, the main alternative being between “global” construals (e.g., an argument is valid iff it preserves truth-under-all-precisifications) and “local” construals (an argument is valid iff, under all precisifications, it preserves truth). The former alternative is by (...) far more popular, but I argue in favor of the latter, for (i) it does not suffer from a number of serious objections, and (ii) it makes it possible to restore global validity as a defined notion. (shrink)

There is a natural philosophical impulse (and, correspondingly, a great deal of pressure) to always ask for explanations, for example, explanations of why we act as we do. Kevin Mulligan has gone a very long way in disentangling the many different because’s, and the many senses of ‘because’, that tend to clutter our efforts to manage that impulse. This short dialogue is meant as a humble tribute to his work in this area.

Since its first appearance in 1966, the notion of a supervaluation has been regarded by many as a powerful tool for dealing with semantic gaps. Only recently, however, applications to semantic gluts have also been considered. In previous work I proposed a general framework exploiting the intrinsic gap/glut duality. Here I also examine an alternative account where gaps and gluts are treated on a par: although they reflect opposite situations, the semantic upshot is the same in both cases--the value of (...) some expressions is not uniquely defined. Other strategies for generalizing supervaluations are considered and some comparative facts are discussed. (shrink)

I focus on three mereological principles: the Extensionality of Parthood (EP), the Uniqueness of Composition (UC), and the Extensionality of Composition (EC). These principles are not equivalent. Nonetheless, they are closely related (and often equated) as they all reflect the basic nominalistic dictum, No difference without a difference maker. And each one of them—individually or collectively—has been challenged on philosophical grounds. In the first part I argue that such challenges do not quite threaten EP insofar as they are either self-defeating (...) or unsupported. In the second part I argue that they hardly undermine the tenability of EC and UC as well. (shrink)

I argue that the conjunction of perdurantism (the view that objects are temporally extended) and universalism (the thesis that any old class of things has a mereological fusion) gives rise to undesired complications when combined with certain plausible assumptions concerning the semantics of tensed statements.

Ci imbattiamo in un confine ogni volta che pensiamo a un’entità demarcata rispetto a ciò che la circonda. C’è un confine (una superficie) che delimita l’interno di una sfera dal suo esterno; c’è un confine (una frontiera) che separa il Maryland dalla Pennsylvania. Talvolta la collocazione esatta di un confine non è chiara o è in qualche modo controversa (come quando si cerchi di tracciare i limiti del monte Everest, o il confine del nostro corpo). Talaltra il confine non corrisponde (...) a una discontinuità fisica o a una differenziazione qualitativa (come nel caso dei confini del Wyoming, o della demarcazione tra la metà superiore e la metà inferiore di una sfera omogenea). Ma, che sia netto o confuso, naturale o artificiale, sembra esservi per ogni oggetto un confine che lo separa dal resto del mondo. Anche gli eventi hanno confini, quantomeno confini temporali. Le nostre vite sono delimitate dalle nostre nascite e morti; una partita di calcio comincia alle quindici in punto e termina col fischio finale dell’arbitro alle sedici e quarantacinque. E a volte si dice che anche le entità astratte, come i concetti o gli insiemi, hanno dei propri confini. Se tutto questo parlare di confini abbia davvero un senso, e se rifletta la struttura del mondo o solo l’attività organizzatrice del nostro intelletto, è però oggetto di profonda controversia filosofica. (shrink)

Mereotopology is today regarded as a major tool for ontological analysis, and for many good reasons. There are, however, a number of open questions that call for an answer. Some are philosophical, others have direct applicative import, but all are crucial for a proper assessment of the strengths and limits of mereotopology. This paper is an attempt to put sum order in this area.

A philosophical exchange broadly inspired by the characters of Berkeley’s Three Dialogues. Hylas is the realist philosopher: the view he stands up for reflects a robust metaphysic that is reassuringly close to common sense, grounded on the twofold persuasion that the world comes structured into entities of various kinds and at various levels and that it is the task of philosophy, if not of science generally, to “bring to light” that structure. Philonous, by contrast, is the anti-realist philosopher (though not (...) necessarily an idealist): his metaphysic is stark, arid, dishearteningly bone-dry, and stems from the conviction that a great deal of the structure that we are used to attribute to the world out there lies, on closer inspection, in our head, in our “organizing practices”, in the complex system of concepts and categories that unrerlie our representation of experience and our need to represent it that way. (shrink)

There is a basic distinction, in the realm of spatial boundaries, between bona fide boundaries on the one hand, and fiat boundaries on the other. The former are just the physical boundaries of old. The latter are exemplified especially by boundaries induced through human demarcation, for example in the geographic domain. The classical problems connected with the notions of adjacency, contact, separation and division can be resolved in an intuitive way by recognizing this two-sorted ontology of boundaries. Bona fide boundaries (...) yield a notion of contact that is effectively modeled by classical topology; the analogue of contact involving fiat boundaries calls, however, for a different account, based on the intuition that fiat boundaries do not support the open/closed distinction on which classical topology is based. In the presence of this two-sorted ontology it then transpires that mereotopology—topology erected on a mereological basis—is more than a trivial formal variant of classical point-set topology. (shrink)

We can see mereology as a theory of parthood and topology as a theory of wholeness. How can these be combined to obtain a unified theory of parts and wholes? This paper examines various non-equivalent ways of pursuing this task, with specific reference to its relevance to spatio-temporal reasoning. In particular, three main strategies are compared: (i) mereology and topology as two independent (though mutually related) chapters; (ii) mereology as a general theory subsuming topology; (iii) topology as a general theory (...) subsuming mereology. Some more speculative strategies and directions for further research are also considered. (shrink)

I argue that Universalism (the thesis that mereological composition is unrestricted) entails Extensionalism (the thesis that sameness of composition is sufficient for identity) as long as the parthood relation is transitive and satisfies the Weak Supplementation principle (to the effect that whenever a thing has a proper part, it has another part disjoint from the first).

This is a position article summarizing our approach to the philosophy of space and spatial representation. Our concern is mostly methodological: above all, we argue that a number of philosophical puzzles that arise in this field—puzzles concerning the nature of spatial entities, their material and mereological constitution, their relationship with the space that they occupy—stem from a confusion between semantic issues and true metaphysical concerns.

Most event-referring expressions are vague; it is utterly difficult, if not impossible, to specify the exact spatiotemporal location of an event from the words that we use to refer to it. We argue that in spite of certain prima facie obstacles, such vagueness can be given a purely semantic (broadly supervaluational) account.

There are conflicting intuitions concerning the status of a boundary separating two adjacent entities (or two parts of the same entity). The boundary cannot belong to both things, for adjacency excludes overlap; and it cannot belong to neither, for nothing lies between two adjacent things. Yet how can the dilemma be avoided without assigning the boundary to one thing or the other at random? Some philosophers regard this as a reductio of the very notion of a boundary, which should accordingly (...) be treated a mere façon de parler. In this paper I resist this temptation and examine some ways of taking the puzzle at face value within a realist perspective—treating boundaries as ontologically on a par with (albeit parasitic upon) extended parts. (shrink)

Some have argued that the vagueness exhibited by geographic names and descriptions such as ‘Albuquerque’, ‘the Outback’, or ‘Mount Everest’ is ultimately ontological: these terms are vague because they refer to vague objects, objects with fuzzy boundaries. I take the opposite stand and hold the view that geographic vagueness is exclusively semantic, or conceptual at large. There is no such thing as a vague mountain. Rather, there are many things where we conceive a mountain to be, each with its precise (...) boundary, and when we say ‘Everest’ we are just being vague as to which thing we are referring to. This paper defends this view against some plausible objections. (shrink)

One logic or many? I say—many. Or rather, I say there is one logic for each way of specifying the class of all possible circumstances, or models, i.e., all ways of interpreting a given language. But because there is no unique way of doing this, I say there is no unique logic except in a relative sense. Indeed, given any two competing logical theories T1 and T2 (in the same language) one could always consider their common core, T, and settle (...) on that theory. So, given any language L, one could settle on the minimal logic T0 corresponding to the common core shared by all competitors. That would be a way of resisting relativism, as long as one is willing to redraw the bounds of logic accordingly. However, such a minimal theory T0 may be empty if the syntax of L contains no special ingredients the interpretation of which is independent of the specification of the relevant L-models. And generally—I argue—this is indeed the case. (shrink)

Assuming that events form a genuine ontological category, shall we say that a good inventory of the world ought to include “negative” events—failures, omissions, things that didn’t happen—along with positive ones? I argue that we shouldn’t. Talk of non-occurring events is like talk of non-existing objects and should not be taken at face value. We often speak as though there were such things, but deep down we want our words to be interpreted in such a way as to avoid serious (...) ontological commitment. (shrink)

Are there any bona fide boundaries, i.e., boundaries that carve at the joints? Or is any boundary —hence any object—the result of a fiat articulation reflecting our cognitive biases and our so-cial practices and conventions? Does the choice between these two options amount to a choice between realism and wholesome relativism?

According to the cliché a picture is worth a thousand words. But this is a canard, for it vastly underestimates the expressive power of many pictures and diagrams. In this note we show that even a simple map such as the outline of Manhattan Island, accompanied by a pointer marking North, implies a vast infinity of statements—including a vast infinity of true statements.

Book information: John Heil, From an Ontological Point of View, Oxford: Clarendon Press, 2003, xv + 267 pp, $45.00 cloth, ISBN 0-19-925974-7.

The concept of niche (setting, context, habitat, environment) has been little studied by ontologists, in spite of its wide application in a variety of disciplines from evolutionary biology to economics. What follows is a first formal theory of this concept, a theory of the relations between objects and their niches. The theory builds upon existing work on mereology, topology, and the theory of spatial location as tools of formal ontology. It will be illustrated above all by means of simple biological (...) examples, but the concept of niche should be understood as being, like concepts such as part, boundary, and location, a structural concept that is applicable in principle to a wide range of different domains. (shrink)

Peter Simons has argued that the expression ‘the universe’ is not a genuine singular term: it can name neither a single, completely encompassing individual, nor a collection of individuals. (It is, rather, a semantically plural term standing equally for every existing object.) I offer reasons for resisting Simons’s arguments on both scores.

The paper outlines a model-theoretic framework for investigating and comparing a variety of mereotopological theories. In the first part we consider different ways of characterizing a mereotopology with respect to (i) the intended interpretation of the connection primitive, and (ii) the composition of the admissible domains of quantification (e.g., whether or not they include boundary elements). The second part extends this study by considering two further dimensions along which different patterns of topological connection can be classified - the strength of (...) the connection and its multiplicity. (shrink)

Some philosophers have argued that the vagueness exhibited by names and descriptions such as ‘Mount Everest’, ‘Downtown Manhattan’, or ‘that cloud in the sky’ is ultimately ontological: they are vague because they refer to vague objects, objects with fuzzy boundaries. I take the opposite stand and argue for the view that all vagueness is semantic. There is no such thing as a vague mountain. Rather, there are many things where we conceive the mountain to be, each with its precise boundary, (...) and when we say ‘Everest’ we are just being vague as to which thing we are referring to. This paper defends this view against some plausible objections. (shrink)

A critical survey of topics that play a central role in contemporary analytic ontology and metaphysics, including, identity, persistence through time, the problem of universals, the notion of ontological commitment, and the boundary between semantic issues and metaphysics proper.

What is money? Paraphrasing Goodman, I say that’s the wrong question to ask. The right question is, When is money? And to get the answer, Searle’s general formula for social objects (X couns as Y in context C) is fine, as long as you give it a different reading.

This is a revised and extended version of the formal theory of holes outlined in the Appendix to the book "Holes and Other Superficialities". The first part summarizes the basic framework (ontology, mereology, topology, morphology). The second part emphasizes its relevance to spatial reasoning and to the semantics of spatial prepositions in natural language. In particular, I discuss the semantics of ‘in’ and provide an account of such fallacious arguments as “There is a hole in the sheet. The sheet is (...) in the drawer. Ergo *there is a hole in the drawer”. (shrink)

A dialogue among statements that try to explain to each other the mechanisms and peculiarities of self-referential assertions and, particularly, of their context-dependence.

Some reflections on Nelson Goodman’s ontological pluralism (as emerging from his Ways of Worldmaking) and its influence on contemporary philosophy, taking the querelle with Quine in the columns of The New York Review of Books as a starting point.

This is a sequel to my paper "Il denaro è un’opera d’arte", focusing on the metaphysics of those peculiar social objects that play an increasingly central role in the financial world—derivatives. On the analysis I offer, they appear to run afoul of Searle’s theory of social objects (or of the theory outlined in my earlier paper), and I put forward some suggestions on where to look for the necessary adjustments.

The Doctrine of Potential Parts says that proper undetached parts are merely potential entities, entities that do not exist but would exist if they were detached from the rest. They are just aspects of the whole to which they belong, ways in which the whole could be broken down, and talk of such parts is really just talk about the modal properties of the whole. Here I offer a reconstruction of this doctrine and present an argument to illustrate its hidden (...) kinship with another, parallel but independent doctrine Doctrine of Potential Wholes. According to this second doctrine, disconnected wholes (i.e., wholes that are not in one piece) are in turn potential entities, entities that do not exist but would exist if their parts were suitably conjoined. (shrink)

How many championships have the Lakers won? Fourteen, if one counts those won in Minneapolis; nine, otherwise. Which is the correct answer? Is it even obvious that there is a correct answer? One is tempted to identify a team with its players. But teams, like ordinary objects, seem to survive gradual turnover of their parts. Suppose players from the Lakers are gradually replaced, one by one, over the years. We have the intuition that the team persists through this change, even (...) after none of the original players remain. Suppose too that these original players wind up playing for the Celtics. Lakers fans face an awkward question: for whom should they root? On the one hand, they have the team currently playing in L.A.—a team that has continued gradually through the years, who wear the same uniforms, but now can’t make the playoffs. On the other hand, there are the beloved Lakers starting five (responsible for all those championships) now playing together in the hated Boston garden—a team which looks (despite wearing those hated Celtics jerseys) and plays just like the Lakers of old. What’s a loyal fan to do? (shrink)

A dialogue among statements that try to explain to each other the mechanisms and peculiarities of self-referential assertions and, particularly, of their context-dependence.

Ordinary reasoning about space—we argue—is first and foremost reasoning about things or events located in space. Accordingly, any theory concerned with the construction of a general model of our spatial competence must be grounded on a general account of the sort of entities that may enter into the scope of the theory. Moreover, on the methodological side the emphasis on spatial entities (as opposed to purely geometrical items such as points or regions) calls for a reexamination of the conceptual categories (...) required for this task. Building on material presented in an earlier paper, in this work we offer some examples of what this amounts to, of the difficulties involved, and of the main directions along which spatial theories should be developed so as to combine formal sophistication with some affinity with common sense. (shrink)

The semantics of our event talk is a complex affair. What is it that we are talking about when we speak of Brutus’s stabbing of Caesar? Exactly where and when did it take place? Was it the same event as the killing of Caesar? Some take questions such as these to be metaphysical questions. I think they are questions of semantics—questions about the way we talk and about what we mean. And I think that this conflict between metaphysic and semantic (...) concerns is indicative of a “deep indeterminacy” (Bennett’s phrase) in our event concept. We do talk about events; but what events a statement is about is not something that can be inferred from the event names we use; it depends heavily (more heavily than with ordinary material objects) on local context and unprincipled intuitions. This paper illustrates this view in connection with two examples: the phenomenon of vagueness and the dispute over identity statements. (shrink)

The paper investigates the link between the theory of modal occurrents (where individuals are allowed to stretch across possible worlds) and Lewis’s counterpart theory (where all individuals are world-bound but have counterparts in other worlds). First I show how to interpret modal talk extensionally within the theory of modal occurrents. Then I show that the assumption that worlds be pairwise discrete is all that is needed to reconstruct the bulk of counterpart theory (i.e., to define the concept of a counterpart (...) and to derive the standard postulates governing that concept) in terms of the theory of modal occurrents. Finally, I argue that this reconstruction allows us to view the indeterminacy of our modal intuitions as being part and parcel with the indeterminacy of our criteria for individuating modal occurrents, and that this indeterminacy is naturally explained in terms of linguistic (as opposed to ontic) vagueness. (shrink)

Human cognitive acts are directed towards objects extended in space of a wide range of different types. What follows is a new proposal for bringing order into this typological clutter. The theory of spatially extended objects should make room not only for the objects of physics but also for objects at higher levels, including the objects of geography and of related disciplines. It should leave room for different types of boundaries, including both the bona fide boundaries which we find in (...) the physical world and the fiat (or human-demarcation-induced) boundaries with which much of geography has to deal. Two distinct axiomatic theories of boundaries are accordingly presented, and the need for both is examined in some detail. The resultant dual framework is shown to have application above all for our understanding of issues involving contact, division, and separation, issues which have posed serious difficulties for the ontological theories of boundaries that have been proposed hitherto. (shrink)