Achille C. Varzi

We think of a boundary whenever we think of an entity demarcated from its surroundings. There is a boundary (a line) separating Maryland and Pennsylvania. There is a boundary (a circle) isolating the interior of a disc from its exterior. There is a boundary (a surface) enclosing the bulk of this apple. Sometimes the exact location of a boundary is unclear or otherwise controversial (as when you try to trace out the margins of Mount Everest, or even the boundary of your own body). Sometimes the boundary lies skew to any physical discontinuity or qualitative differentiation (as with the border of Wyoming, or the boundary between the upper and lower halves of a homogeneous sphere). But whether sharp or blurry, natural or artificial, for every object there appears to be a boundary that marks it off from the rest of the world. Events, too, have boundaries — at least temporal boundaries. Our lives are bounded by our births and by our deaths; the soccer game began at 3pm sharp and ended with the referee's final whistle at 4:45pm. It is sometimes suggested that even abstract entities, such as concepts or sets, have boundaries of their own, and Wittgenstein could emphatically proclaim that the boundaries of our language are the boundaries of our world. Whether all this boundary talk is coherent, however, and whether it reflects the structure of the world or simply the organizing activity of our mind, are matters of deep philosophical controversy.

There are two natural ways of thinking about negation: (i) as a form of complementation and (ii) as an operation of reversal, or inversion (to deny that p is to say that things are “the other way around”). A variety of techniques exist to model conception (i), from Euler and Venn diagrams to Boolean algebras. Conception (ii), by contrast, has not been given comparable attention. In this note we outline a twofold geometric proposal, where the inversion metaphor is understoood as involving a rotation o a reflection, respectively. These two options are equivalent in classical two-valued logic but they differ significantly in many-valued logics. Here we show that they correspond to two basic sorts of negation operators—Post’s and Kleene’s—and we provide a simple group-theoretic argument demonstrating their generative power.

Fictionalism in ontology is a mixed bag. Here I focus on three main variants—which I label after the names of Pascal, Berkeley, and Hume—and consider their relative strengths and weaknesses. The first variant is just a version of the epistemic Wager, applied across the board. The second variant builds instead on the fact that ordinary language is not ontologically transparent; we speak with the vulgar, but deep down we think with the learned. Finally, on the Humean variant it’s the structure of the ontological inventory, not its content, that may turn out to involve fictional elements. That is, for the Humean the fiction lies, not in the reality of common-sense ontology, but in the laws—of unity, identity, causation, etc.—in terms of which we articulate our experience of that reality. In the end, this is the kind of fictionalism that I find most interesting, sensible, and tenable. And I argue that it is even compatible with the sort of “naive” realism we have all come to appreciate in the work of Paolo Bozzi, to whom the paper is dedicated.

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.

The theory according to which most ordinary objects are mere “entia successiva”—sequences of distinct mereological aggregates, whose unity resides exclusively in our minds—is a variant of the standard, three-dimensional conception of objects. For the aggregates are, at bottom, endurants, i.e., entities that persist through time by being fully present at any time at which they exist. In this paper I compare this theory with the so-called “stage view”, according to which ordinary objects—indeed, all objects—are sequences of momentary entities that cannot truly be said to persist through time. Both theories face a number of intuitive difficulties but the stage view, I argue, has a lot more to offer in return.

Quine’s desert is generally contrasted with Meinong’s jungle, as a sober ontological alternative to the exuberant luxuriance that comes with the latter. Here I focus instead on the desert as a sober metaphysical alternative to the Aristotelian garden, with its tidily organized varieties of flora and fauna neatly governed by fundamental laws that reflect the essence of things and the way they can be, or the way they must be. In the desert there are no “natural joints”; all the boundaries we find are lines we have drawn, artificial fencings that merely reflect of our own demarcations, our classifications, our desperate need to ward off the flux and meet an excusable but ungrounded demand for order and stability. The desert returns a picture of reality that is radically anti-realist. And yet the picture does not amount to a form of irrealism. The desert is out there and is what it is regardless of how we feel. And it is not completely structureless. It’s just that the structure it has is very thin and does not correspond to the sort of structure that so-called metaphysical realists—and scientific realists alike—tend to attribute to it.

In ‘Something to Do with Vagueness ...’, Linda Burns defends an analogy between the informational and the borderline-case variety of vagueness. She argues that the latter is in fact less extraordinary and less disastrous than people in the tradition of Michael Dummett and Crispin Wright have told us. However, her account involves presuppositions that cannot be taken for granted. Here we take a closer look at some of these presuppositions and argue that they may—when left unguarded—undermine much of Burns’ general account.

Abstract. As a general theory of reasoning—and as a general theory of what holds true under every possible circumstance—logic is supposed to be ontologically neutral. It ought to have nothing to do with questions concerning what there is, or whether there is anything at all. It is for this reason that traditional Aristotelian logic, with its tacit existential presuppositions, was eventually deemed inadequate as a canon of pure logic. And it is for this reason that modern quantification theory, too, with its residue of existentially loaded theorems and patterns of inference, has been claimed to suffer from a defect of logical purity. The law of non-contradiction rules out certain circumstances as impossible—circumstances in which a statement is both true and false, or perhaps circumstances where something both is and is not the case. Is this to be regarded as a further ontological bias?

In ‘Something to Do with Vagueness ...’, Linda Burns defends an analogy between the informational and the borderline-case variety of vagueness. She argues that the latter is in fact less extraordinary and less disastrous than people in the tradition of Michael Dummett and Crispin Wright have told us. However, her account involves presuppositions that cannot be taken for granted. Here is to take a closer look at some of these presuppositions and argue hat they may--when left unguarded--undermine much of Burns’ general account.

Some philosophers have gone a long way towards a clarification and a defense of the view that there is genuine (worldly) indeterminacy of identity. Among his reasons for taking this view seriously is the contention that extant formulations of the alternative conception, according to which all indeterminacy lies in the semantics of our language (or in the system of concepts embodied in our language), are not fitted for dealing with a host of identity puzzles. I this paper I take issue with that contention and argue that the semantic conception, if charitably construed, can meet such challenges.

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?

Analyses, in the simplest form assertions that aim to capture an intimate link between two concepts, are viewed since Russell's theory of definite descriptions as analyzing descriptions. Analysis therefore has to obey the laws governing definitions including some form of a Substitutivity Principle (SP). Once (SP) is accepted the road to the paradox of analysis is open. Popular reactions to the paradox involve the fundamental assumption (SV) that sentences differing only in containing an analysandum resp. an analysans express the same proposition, because analysandum and analysans are the same entity. Following suggestions of Gupta and Belnap it is argued that (SV) should be rejected.

A critical review of the main themes arising out of recent literature on the semantics of ordinary event talk. The material is organized in four sections: (i) the nature of events, with emphasis on the opposition between events as particulars and events as universals; (ii) identity and indeterminacy, with emphasis on the unifier/multiplier controversy; (iii) events and logical form, with emphasis on Davidson’s treatment of the form of action sentences; (iv) linguistic applications, with emphasis on issues concerning aspectual phenomena, the telicity/atelicity distinction, the treatment of statives, and temporal quantification.

La metafisica è quel ramo della filosofia che ha come oggetto la realtà considerata nei suoi aspetti più fondamentali e generali. L’origine del termine (letteralmente: ‘dopo’ o ‘oltre la fisica’) risale agli editori delle opere di Aristotele nel I secolo a.C., che lo usarono per classificare gli scritti dedicati a quest’argomento e ritenuti, appunto, posteriori a quelli dedicati alla fisica. L’essere si dice in molti modi, scriveva Aristotele in quelle pagine, e a questa molteplicità di significati corrispondono domini d’interesse specifici. La matematica, per esempio, si occupa dell’essere sotto il profilo quantitativo, la fisica sotto il profilo naturale. La metafisica (che Aristotele chiamava ‘sapienza’ o ‘filosofia prima’) si occupa invece dell’essere nel suo complesso, considerato sotto il profilo generalissimo della sua esistenza: l’essere in quanto essere.

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.