Achille C. Varzi

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.

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.

Dear Harriet Monroe:—Your recent issue of Poetry is quite interesting. The first poem of that young Italian chap is very good, the rest—unsuccessful. You are certainly the clearinghouse for a lot of mediocre stuff—so you should be: very democratic—keep up the good work. Yours,Williams This is William Carlos Williams writing to the editor of Poetry magazine on March 12, 1918.1 We know who the young Italian chap is: Emanuel Carnevali, age twenty, who had just made his debut in Monroe’s magazine with a six-page group of poems, “The Splendid Commonplace.”2 Less clear, perhaps, is what Williams means by “the rest” —the “unsuccessful,” “mediocre stuff.” “The Splendid Commonplace” consists of six...

Classical propositional logic can be characterized, indirectly, by means of a complementary formal system whose theorems are exactly those formulas that are not classical tautologies, i.e., contradictions and truth-functional contingencies. Since a formula is contingent if and only if its negation is also contingent, the system in question is paraconsistent. Hence classical propositional logic itself admits of a paraconsistent characterization, albeit “in the negative”. More generally, any decidable logic with a syntactically incomplete proof theory allows for a paraconsistent characterization of its set of theorems. This, we note, has important bearing on the very nature of paraconsistency as standardly characterized.

Much recent work aimed at extending model-theoretic semantics has been formulated in response to specific needs, and little effort has been made in the direction of a truly "general" generalization. This work is an attempt to overcome these limitations. The unifying view is that semantics must account for the main relationships between languages and models in a uniform fashion, regardless of the specific conditions that may be imposed upon either notion. And the upshot is a general framework within which a large variety of semantic theories naturally fall and from which the semantics of a wide class of logics can be obtained as special cases. ;The presentation is organized in two parts. In the first, a suitably general notion of a language is introduced along with a correspondingly general notion of a model, allowing for the possibility that the interpretation of some expressions be incomplete or inconsistent. The notion of a valuation is then systematically characterized by exploiting the idea that the value of an expression on a given model is always a function of the values it takes on the various ways of filling in the gaps and/or weeding out the gluts in the model. This account is shown to be grounded on some fundamental properties of the lattice of all admissible models, and may be viewed as a generalization of the method of super-valuations. ;The second part investigates the major properties of the resulting semantic apparatus. In particular, it is shown that the notion of logical validity as applied to single expressions is rather standard, and in fact reduces to the corresponding classical notion when this is available. Thus, gaps and gluts can be explained away as local phenomena that do not metastasize throughout the framework. However, with regard to the more comprehensive relation of entailment between expressions, the general picture is more intricate, as the notion of argument validity appears to escape the control of recursively specifiable systems. To shed light on this picture, a cost-benefit analysis of the proposed framework is offered in the concluding part

This is a brief sequel to Max Black 's classic dialogue on the Identity of Indiscernibles. Interlocutor A defends the bundle theory by endorsing the view according to which Black 's world does not contain two indiscernible spheres but rather a single, bi-located sphere. His opponent, B, objects that A cannot distinguish such a world from a world with a single, uniquely located sphere, hence that the view in question adds nothing to A's original response to Black 's challenge. A is simply denying that there can be worlds with two or more indiscernible entities.

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.

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.

A selection of essays dedicated to Hans Herzberger with affection and gratitude for both his profound work and his lasting example. Contributors: I. Levi (on whether and how a rational agent should be seen as a maximizer of some cognitive value), C. Normore (on medieval accounts of logical validity), J. P. Tappenden (on the local influences on Frege's doctrines), A. Urquhart (on the inexpressible), A. C. Varzi (on dimensionality and the sense of possibility), and S. Yablo (on content and carvings, and from there to mathematical realism).

This work gives an extended presentation of the treatment of variable-binding operators adumbrated in [3:1993d]. Illustrative examples include elementary languages with quantifiers and lambda-equipped categorial languages. Some remarks are also offered to illustrate the philosophical import of the resulting picture. Particularly, a certain conception of logic emerges from the account: the view that logics are true theories in the model-theoretic sense, i.e. the result of selecting a certain class of models as the only “admissible” interpretation structures (for a given language).

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.

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).

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

In classical topology the only part of a doughnut that matters is the edible part. Here I review some good reasons for reversing the order and focusing on the hole instead. By studying the topology of the hole one can learn interesting things about the morphology of the doughnut (its shape), and by studying the morphology of the hole in turn one can learn a lot about the doughnut’s dynamic properties (its patterns of interaction with the environment). The price--of course--is that one must be serious about reifying voids.

This paper focuses on the semantics of statements of the form ‘x is P at t’ vis-à-vis its metaphysical underpinnings. I begin by considering four main readings, corresponding to the four basic parsings of the temporal modifier ‘at t’: (1) at-t x is P, (2) x-at-t is P, (3) x is-at-t P, and (4) x is P-at-t. Each of these readings—which correspond to different metaphysical conceptions of the nature of temporal change—is found inadequate or otherwise problematic. In the second part of the paper I therefore consider a fifth account whose advantages over (1)–(4), I argue, exceed its revisionary costs. This fifth account is based on a conception of objects as entia successiva held together by a nexus of temporal counterparthood and reads ‘x is P at t’ as ‘the t-counterpart of x is P’.

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.

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.