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.

Standard lore has it that a proper name, or a definite description on its de re reading, is a temporally rigid designator. It picks out the same entity at every time at which it picks out an entity at all. If the entity in question is an enduring continuant then we know what this means, though we are also stuck with a host of metaphysical puzzles concerning endurance itself. If the entity in question is a perdurant then the rigidity claim is trivial, though one is left wondering how it is that different speakers ever manage to pick out one and the same entity when a host of suitable, overlapping candidates are available. But what if the entity in question is neither a continuant nor a perdurant? What if the things we talk about in ordinary language are time‐bound entities that cannot truly be said to persist through time, or stage sequences whose unity resides exclusively in our minds ‐ like the “wave” at the stadium or the characters of a cartoon? In such cases the rigidi‐ ty claim can't be right and a counterpart‐theoretic semantics seems required. Is that bad? I say it isn't. And it had better not be, if that turns out to be the best metaphysical option we have.

We tend to talk about parts in the same way in which we talk about whole objects. Yet a part is not something to be included in an inventory of the world over and above the whole to which it belongs, and a whole is not something to be included in an inventory over and above its own parts. This paper is an attempt to clarify a way of dealing with this tension which may be labeled the Minimalist View: an element in the field of a part‐whole relation is to be included in an inventory of the world if, and only if, it does not overlap any other element that is itself included in the inventory. As it turns out, a clarification of this view involves both a defense of mereological extensionality and an account of the topological distinction between detached and undetached parts.

The so-called ‘argument from vagueness’ is among the most powerful and innovative arguments offered in support of the view that objects are four-dimensional perdurants. The argument is defective – I submit – and in a number of ways that are worth looking into. But each ‘defect’, each gap in the argument, corresponds to a model of change that is independently problematic and that can hardly be built into the common-sense picture of the world. So once all the gaps of the argument are filled in, the three-dimensionalist is left with the burden of a response that cannot rely on a passive plea for common sense. The argument is not a threat to common sense as such; it is a threat to the three-dimensionalist faithfulness to common sense.

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 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 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.

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.

At the beginning, all there is is world. It’s not all alike: here is mama, there is cold, over there—noise. Soon we begin to distinguish and to recognize: more mama, more cold, more noise! Yet initially these things appear to be all of a type. Each is, in Quine’s words, just a history of sporadic encounter, a mere portion of all there is. Only with time does this fluid totality in which we are immersed begin to take shape: sensations recur; objects stick out; noise changes depending on the things around us. We learn how to act and to predict. We launch into giving names, using verbs, painting adjectives. Such marvelous unfolding is the subject of much inquiry by psychologists and biologists, and eventually by sociologists. But for a philosopher it is first and foremost the source of deep and bemusing bewilderment, if not a dilemma: Are we learning to make out the structure of the world, or are we endowing the world with a structure of our making? Is reality gradually revealing the mechanisms according to which it is organized, or is it we who progressively organize the amorphous and continuous flux of our experience?

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

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.

A rejoinder to G. Hull’s reply to my Mind 2003. Hull argues that Sorensen’s purported proof that ‘vague’ is vague--which I defended against certain familiar objections--fails. He offers three reasons: (i) the vagueness exhibited by Sorensen’s sorites is just the vagueness of ‘small’; (ii) the general assumption underlying the proof, to the effect that predicates which possess borderline cases are vague, is mistaken; (iii) the conclusion of the proof is unacceptable, for it is possible to create Sorensen-type sorites even for predicates that are paradigmatically precise. I argue that each of these points involves fallacious reasoning.

Standard lore has it that a proper name is a temporally rigid designator. It picks out the same entity at every time at which it picks out an entity at all. If the entity in question is an enduring continuant then we know what this means, though we are also stuck with a host of metaphysical puzzles concerning endurance itself. If the entity in question is a perdurant then the rigidity claim is trivial, though one is left wondering how it is that different speakers ever manage to pick out one and the same entity when a host of suitable, overlapping candidates are available. But what if the entity in question is neither a continuant nor a perdurant? What if the things we talk about in ordinary language are time-bound entities that cannot truly be said to persist through time, or stage sequences whose unity resides exclusively in our minds--like the “waves” at the stadium or the characters of a cartoon? In such cases the rigidity claim can’t be right and a counterpart-theoretic semantics seems required. Is that bad? I say it isn’t. And it had better not be, if that turns out to be the best metaphysical option we have.

Like the journal TOPOl, the TOPOl Library is based on the assumption that philosophy is a lively, provocative, delightful activity, which constantly challenges our inherited habits, painstakingly elaborates on how things could be different, in other stories, in counterfactual situations, in alternative possible worlds. Whatever its ideology, whether with the intent of uncovering a truer structure of reality or of shooting our anxiety, of exposing myths or of following them through, the outcome of philosophical activity is always the destabilizing, unsettling generation of doubts, of objections, of criticisms. It follows that this activity is intrinsically a dialogue, that philosophy is first and foremost philosophical discussion, that it requires bringing out conflicting points of view, paying careful, sympathetic attention to their structure, and using this dialectic to articulate one's approach, to make it richer, more thoughtful, more open to variation and play. And it follows that the spirit which one brings to this activity must be one of tolerance, of always suspecting one's own blindness and consequently looking with unbiased eye in every comer, without fearing to pass a (fallible) judgment on what is there but also without failing to show interest and respect.

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.

We tend to talk about (refer to, quantify over) parts in the same way in which we talk about whole objects. Yet a part is not something to be included in an inventory of the world over and above the whole to which it belongs, and a whole is not something to be included in the inventory over and above its constituent parts. This paper is an attempt to clarify a way of dealing with this tension which may be labeled the Minimalist View: An element in the field of a part-whole relation is to be included in an inventory of the world if and only if it does not overlap any distinct element that is itself included in the inventory.

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.

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.