Achille C. Varzi

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.

Just as ontology developed over the centuries as part of philosophy, so in recent years ontology has become intertwined with the development of the information sciences. Researchers in various fields have come to realize that a solid foundation for their projects calls for an explicit theorization of the types of entities and relations that make up their respective domains of inquiry, and as the need for integrating such projects arises, so does the need to identify common ontological principles over ad hoc, case-based solutions. This volume collects the papers presented at the third international conference devoted to current research in this area, including invited papers by P. Gärdenfors and A. L. Thomasson.

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.

Might we some day be in a position to move about in time, just as we can already move about in space? Today, few would question that deliberate change in temporal location is logically possible. There is no contradiction in the thought that Tim could step into a time machine and travel backwards to visit his grandfather, or forwards to visit his grandchildren. That is, there is no contradiction provided that we take time travel to involve influencing the course of history rather than changing it. But is time travel metaphysically possible? Is there a genuinely possible world—as opposed to a merely coherent scenario—in which one can freely change one’s location in time? Here is where puzzlement and bewilderment lead to philosophical controversy. For the answer depends on one’s views concerning a wide range of other matters, and such views are themselves the subject of major philosophical controversy. Consider

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.

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).

David Lewis has argued that impossible worlds are nonsense: if there were such worlds, one would have to distinguish between the truths about their contradictory goings-on and contradictory falsehoods about them; and this--Lewis argues--is preposterous. In this paper I examine a way of resisting this argument by giving up the assumption that ‘in so-and-so world’ is a restricting modifier which passes through the truth-functional connectives The outcome is a sort of subvaluational semantics which makes a contradiction ‘A & ~A’ false even when both ‘A’ and ‘~A’ are true, just as supervaluational semantics makes a tautology ‘A v ~A’ true even when neither ‘A’ nor ‘~A’ are. Connections with discussive logics and complications of the account are discussed, and some general morals are drawn.

The “Game of the Rule” is easy enough: I give you the beginning of a sequence of numbers (say) and you have to figure out how the sequence continues, to uncover the rule by means of which the sequence is generated. The game depends on two obvious constraints, namely (1) that the initial segment uniquely identify the sequence, and (2) that the sequence be non-random. As it turns out, neither constraint can fully be met, among other reasons because the relevant notion of randomness is either vacuous or undecidable. This may not be a problem when we play for fun. It is, however, a serious problem when it comes to playing the game for real, i.e., when the player to issue the initial segment is not one of us but the world out there, the sequence consisting not of numbers (say) but of the events that make up our history. Moreover, when we play for fun we know exactly what initial segment to focus on, but when we play for real we don’t even know that. This is the core difficulty in the philosophy of the inductive sciences.

In previous work, I introduced a complete axiomatization of classical non-tautologies based essentially on Łukasiewicz’s rejection method. The present paper provides a new, Hilbert-type axiomatization (along with related systems to axiomatize classical contradictions, non-contradictions, contingencies and non-contingencies respectively). This new system is mathematically less elegant, but the format of the inferential rules and the structure of the completeness proof possess some intrinsic interest and suggests instructive comparisons with the logic of tautologies.

Remember the story of the most-most? It’s the story of that club in New York where people are the most of every type. There is the hairiest bald man and the baldest hairy man; the shortest giant and the tallest dwarf; the smartest idiot and the stupidest wise man. They are all there, including honest thieves and crippled acrobats. On Saturday night they have a party, eat, drink, dance. Then they have a contest. “And if you can tell the hairiest bald man from the baldest hairy man—we are told—you get a prize.”.

R. Sorensen’s argument to the effect that ’vague’ is a vague predicate has been used by D. Hyde to infer that vague predicates suffer from higher-order vagueness. M. Tye has objected (convincingly) that this is too strong: all that follows from Sorensen’s result is that there are some border border cases, but not necessarily border border cases of every vague predicate. I argue that this is still too strong: Sorensen’s proof presupposes the existence of border border cases, hence cannot be used to establish that fact on pain of circularity.

There are two main ways, philosophically, of characterizing the business of ontology. On one account, made popular by Quine, ontology is concerned with the material question of what there is. On the other, which made its way into our times through Brentano and his pupils, ontology is concerned with the task of laying bare the formal structure of all there is, whatever it is. My question, here, is whether one can pursue one sort of theory without also engaging in the other—whether, or to what extent, the tasks of material ontology presuppose the backing of some formal-ontological theory, and whether or to what extent formal ontology can be, in the material sense of the term, ontologically neutral.

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.

An introduction to analytic ontology. Part 1 deals with the question, What is ontology?, focusing on (i) the interplay between ontological and broadly metaphysical concerns, and (ii) the difference between material ontology and formal ontology. Part 2 deals with the question, How is ontology done?, focusing on (i) the delicate interplay between ontology and truth-making (or: between meaning and existence), and (ii) the differences between revolutionary vs. hermeneutic, prescriptive vs. descriptive, and absolute vs. relative approaches to ontology. Part 3 surveys the state of the art in a number of areas, both in material ontology (e.g., the problem of universals, the status of objects and events, the ontology of mathematics, of the physical sciences, of the social sciences) and in formal ontology (identity, ontological dependence, part-whole relations).

This original and enticing book provides a fresh, unifying perspective on many old and new logico-philosophical conundrums. Its basic thesis is that many concepts central in ordinary and philosophical discourse are inherently circular and thus cannot be fully understood as long as one remains within the confines of a standard theory of definitions. As an alternative, the authors develop a revision theory of definitions, which allows definitions to be circular without this giving rise to contradiction (but, at worst, to “vacuous” uses of definienda). The theory is applied with varying levels of detail to a circular analysis of concepts as diverse as truth, predication, necessity, physical object, etc. The focus is on truth, and hope is expressed that a deeper understanding of the Liar and related paradoxes has been provided: “We have tried to show that once the circularity of truth is recognized, a great deal of its behavior begins to make sense. In particular, from this viewpoint, the existence of the paradoxes seems as natural as the existence of the eclipses” (p. 142). We think that this hope is fully justified, although some problems remain that future research in this field should take into account.

This volume aims to offer an up-to-date indication of the on-going debate on the nature of logic. The focus is on questions pertaining to the existence and individuation of clear boundaries delineating the concerns of logic: What is their distinctive character? What makes logic a subject of its own, separate from (and generally in the background of) the concerns of other disciplines? What is it for an expression to be a logical constant? Or, perhaps equivalently, what is it for an operation or a relation to be logical? Can these questions be addressed in a general setting, or are they intrinsically unanswerable except within specific frameworks of reference (e.g., a language, or a conceptual scheme)? How are they to be addressed—are they semantic, syntactic, pragmatic? And how do semantics, syntax, or pragmatics contribute to our understanding of these questions? Are the answers fully captured by extant systems of logic? Contributors: E. Bencivenga, J. van Benthem, D. van Dalen, M. García-Carpintero and M. Pérez Otero, A. P. Hazen, A. Koslow, G. Priest, G. Sher.