Achille C. Varzi

This major bibliography offers a comprehensive overview of the recent literature on the nature of events and the place they occupy in our conceptual scheme. The subject has received extensive consideration in the philosophical debate over the last few decades, with ramifications reaching far into the domains of allied disciplines such as linguistics and the cognitive sciences. The starting point for this work is Hans Reichenbach's pioneering contribution on the logical form of action sentences, and the broad scope includes entries from the philosophy of action, the philosophy of mind, the philosophy of space, time, and causation, and situation theory. Approximately 1,850 entries from more than 900 authors are listed in alphabetical/chronological order by author, and most entries are annotated. This excellent work also includes Subject, Name, and Second and Subsequent Authors indexes.

Is a whole something more than the sum of its parts? Are there things composed of the same parts? If you divide an object into parts, and divide those parts into smaller parts, will this process ever come to an end? Can something lose parts or gain new ones without ceasing to be the thing it is? Does any multitude of things (including disparate things such as you, this book, and the tail of a cat) compose a whole of some sort? Questions such as these have occupied us for at least as long as philosophy has existed. They define the field that has come to be known as mereology-the study of all relations of part to whole and of part to part within a whole-and have deep and far-reaching ramifications in metaphysics as well as in logic, the foundations of mathematics, the philosophy of language, the philosophy of science, and beyond. In Mereology, A. J. Cotnoir and Achille C. Varzi have compiled decades of advanced research into a comprehensive, up-to-date, and formally rigorous picture. The early chapters cover the more classical aspects of mereology; the rest of the book deals with variants and extensions. Whether you are an established professional philosopher, an interested student, or a newcomer, inside you will find all the tools you need to join this ever-evolving field of inquiry and theorize about all things mereological.

We offer a critical overview of two sorts of proof systems that may be said to characterize classical propositional logic indirectly (and non-standardly): refutation systems, which prove sound and complete with respect to classical contradictions, and rejection systems, which prove sound and complete with respect to the larger set of all classical non-tautologies. Systems of the latter sort are especially interesting, as they show that classical propositional logic can be given a paraconsistent characterization. In both cases, we consider Hilbert-style systems as well as Gentzen-style sequent calculi and natural-deduction formalisms.

Universalist and nihilist answers to philosophical questions may be extreme, but they are clear enough. Aliquidist answers, by contrast, are typically caught between the Scylla of vagueness and indeterminacy and the Charybdis of ungroundedness and arbitrariness, and steering a proper middle course—saying exactly where in the middle one is going to settle—demands exceptional navigating powers. I myself tend to favor extreme answers precisely for this reason. Here, however, I consider one sense in which Something may claim superiority over its polar competitors, Everything and Nothing, when it comes to answerting the ontological question, “What is there?”.

Cities are mysteriously attractive. The more we get used to being citizens of the world, the more we feel the need to identify ourselves with a city. Moreover, this need seems in no way distressed by the fact that the urban landscape around us changes continuously: new buildings rise, new restaurants open, new stores, new parks, new infrastructures… Cities seem to vindicate Heraclitus’s dictum: you cannot step twice into the same river; you cannot walk twice through the same city. But, as with the river, we want and need to say that it is the same city we are walking through every day. It is always different, but numerically self-identical. How is that possible? What sort of mysterious thing is a city? The answer, I submit, is that cities aren’t things. They are processes. Like rivers, cities unfold in time just as they extend in space, by having different temporal parts for each time at which they exist. And walking though one part and then again through another is, literally, walking through the same whole.

There is no doughnut without a hole, the saying goes. And that’s true. If you think you can come up with an exception, it simply wouldn’t be a doughnut. Holeless doughnuts are like extensionless color, or durationless sound—nonsense. Does it follow, then, that when we buy a doughnut we really purchase two sorts of thing—the edible stuff plus the little chunk of void in the middle? Surely we cannot just take the doughnut and leave the hole at the grocery store, as we cannot just eat the doughnut and save the hole for later. But then, again, surely when we eat a doughnut we do not also eat the hole. Or do we?

The U.S. presidential election of 2000 was crucially decided in Florida. And, in Florida, the election hinged crucially on a peculiar sort of question: Does this ballot have a hole? “Yes, it does”, so the ballot is valid and ought to be counted. “No it doesn’t”, and the ballot must be discarded. If only one could tell! Where were the hole experts when we needed them? Eventually the matter was thwarted by the Supreme Court and we all gave up. But we did learn something. We learned that even the destiny of a Presidential Election, if not more, might ultimately depend on one’s criteria for identifying holes—not their material surroundings, which everyone could detect, but the holes themselves.

David Lewis’s counterpart theory is often seen as involving a radical departure from the standard, Kripke-style semantics for modal logic, suggesting that we are dealing with deeply divergent accounts of our modal talk. However, CT captures but one version of the relevant semantic intuition, and does so on the basis of metaphysical assumptions that are ostensibly discretionary. Just as ML can be translated into a language that quantifies explicitly over worlds, CT may be formulated as a semantic theory in which world quantification is purely metalinguistic. And just as Kripke-style semantics is formally compatible with the doctrine of world-boundedness, a counterpart-based semantics may in principle allow for cases of trans-world identity. In fact, one may welcome a framework that is general enough to include both Lewis’s counterpart-based account and Kripke’s identity-based account as distinguished special cases. There are several ways of doing so. The purpose of this paper is to outline a fully general option and to illustrate its philosophical significance, showing how the large variety of intermediate relations that lie between Lewisian counterparthood and Kripkean identity yield a corresponding variety of modal theories that would otherwise remain uncharted.

Euclid’s definition of a point as “that which has no part” has been a major source of controversy in relation to the epistemological and ontological presuppositions of classical geometry, from the medieval and modern disputes on indivisibilism to the full development of point-free geometries in the 20th century. Such theories stem from the general idea that all talk of points as putative lower-dimensional entities must and can be recovered in terms of suitable higher-order constructs involving only extended regions (or bodies). Here I focus on what is arguably the first thorough proposal of this sort, Whitehead’s theory of “extensive abstraction”, offering a critical reconstruction of the theory through its successive installments: from the purely mereological version of ‘La théorie relationniste de l’espace’ (1916) to the refined versions presented in An Enquiry Concerning the Principles of Natural Knowledge (1919) and in The Concept of Nature (1920) to the last, mereotopological version of Process and Reality (1929).

I am a friend of supervaluationism. A statement lacks a definite truth value if, and only if, it comes out true on some admissible ways of precisifying the semantics of the relevant vocabulary and false on others. In this paper, I focus on the special case of identity statements. I take it that such statements, too, may occasionally suffer a truth-value gap, including philosophically significant instances. Yet there is a potentially devastating objection that can be raised against the supervaluationist treatment of such cases—in fact two objections. Luckily, both can be resisted. But seeing how requires that we take a closer look at the ontological presuppositions of supervaluationism, allowing for more leeway than is usually supposed.

We propose the beginnings of a general theory of environments, of the parts or regions of space in which organisms live and move. We draw on two sources: on the one hand on recent work on the ontology of space; and on the other hand on work by ecological scientists on concepts such as territory, habitat, and niche. An environment is in first approximation a volume of space; it is a specific habitat, location, or site that is suitable or adequate for given purposes (of foraging, resting, hunting, breeding, nesting, grooming) in the life of an organism or group of organisms. This spatial notion of environment can be drawn closer to biological and ecological science by taking account of the pertinent physical attributes realized within given spatial regions.

This paper is concerned with certain ontological issues in the foundations of geographic representation. It sets out what these basic issues are, describes the tools needed to deal with them, and draws some implications for a general theory of spatial representation. Our approach has ramifications in the domains of mereology, topology, and the theory of location, and the question of the interaction of these three domains within a unified spatial representation theory is addressed. In the final part we also consider the idea of non-standard geographies, which may be associated with geography under a classical conception in the same sense in which non-standard logics are associated with classical logic.

In his Romanes Lecture of 1907, Lord Curzon emphasized the overwhelming influence of “natural” and “artificial” frontiers in the political history of the modern world. As Barry Smith has shown, the same could be said, more generally, of the natural and artificial boundaries that are at work in articulating every aspect of the reality with which we have to deal, not only in the world of geography, but the world of human experience at large. Moreover, once the natural/artificial distinction has been recognized, it can be drawn across the board: not merely in relation to boundaries but also in relation to those entities that may be said to have boundaries. If something enjoys a natural boundary, its identity and survival conditions do not depend on us; it is a bona fide, mind-independent entity of its own. By contrast, if its boundary is artificial, then the entity itself is to some degree a fiat entity, a product of our worldmaking. Here I am interested in limit case: what if, pace Curzon and pace Smith, all entities turned out to be of the latter sort?

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.

Alexandre Koyré wrote that Newton and the science that followed led to a splitting of the world: on the one hand is the “world of qualities and of sensible perceptions”, on the other is the “world of quantities and of reified geometry”. A comparison between facts held true by common sense and false by the scientific image of the world (or vice versa) seems to confirm this view. But is the dichotomy a real one? Is the world of common sense really “another world” relative to the world of the natural sciences? In this paper we argue in support of a negative answer.

"Perhaps not all the stories that follow are true. They could, however, be true, and the Reader is invited to ponder this." So begins _Insurmountable Simplicities_, Roberto Casati and Achille Varzi's colorful incarnation of the many philosophical conundrums that hide in the wrinkles of everyday life. Why do mirrors seem to invert left and right but not up and down? How do we know whether strawberries taste the same for everyone? Where is it written that we must observe the law, and if it is not written, why should we observe it? What if we could swap brains-or the rest of our bodies? _Insurmountable Simplicities_ is filled with stories, dialogues, and epistolary exchanges that cover a range of themes-such as personal identity, causality and responsibility, fortune, the nature of things, the paradoxes of time and space, the interface between logic and language-in captivating and inventive ways. Clear, concise, and intellectually engaging, this internationally acclaimed book brilliantly demonstrates that the beauty of philosophy resides in its thorough engagement with the simplicities of the world, insurmountable as they might initially appear

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.