Achille C. Varzi

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

Mereological atomism is the thesis that everything is ultimately composed of atomic parts, i.e., parts lacking proper parts. Standardly, this thesis is characterized by an axiom that says, more simply, that everything has atomic parts. Anthony Shiver has argued that this characterization is satisfied by models that are not atomistic, and is therefore inadequate. I argue that Shiver’s conclusion can and ought to be resisted, for the models in question are atomistic in the intended sense, and even though the standard characterization does not say that everything is composed of atoms, it implies so. If there is a sense in which the relevant models are problematic, it lies elsewhere.

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.

We are used to regarding actions and other events, such as Brutus’ stabbing of Caesar or the sinking of the Titanic, as occupying intervals of some underlying linearly ordered temporal dimension. This attitude is so natural and compelling that one is tempted to disregard the obvious difference between time periods and actual happenings in favor of the former: events become mere “intervals cum description”.1 On the other hand, in ordinary circumstances the point of talking about time is to talk about what actually happens or might happen at some time or another. We talk about ‘now’ and ‘then’ in an effort to put some order in our description of what goes on. And since different events seem to overlap in so many different ways, a full account of their temporal relations seems to run afoul of a reductionist strategy. This raises two philosophical questions. The first is whether we can actually go beyond time, as it were, i.e., whether we can take events as bona fide entities and deal with them directly, just as we can deal with spatial entities such as physical bodies or masses without confining ourselves to their spatial representations. This is a controversial issue (though probably not as controversial as it used to be), and ties in with a number of unsettled problems concerning, e.g., the structure of causality or the definition of adequate identity and individuation criteria for events. 2 The second question is whether we can perhaps do without time, i.e., whether we can dispense with time points or intervals as an independent ontological category and focus only on actual or potential happenings, in opposition to the form of reductionism mentioned above—in short, whether we can account for the temporal dimension in terms of suitable relations among events. This is also a highly controversial issue, and relates to the classical dispute concerning relational vs. absolutist conceptions of (space and) time.3 It is this second question that we intend to focus on here..

The semantics of our event talk is a complex affair. What is it that we are talking about when we speak of Brutus’s stabbing of Caesar? Exactly where and when did it take place? Was it the same event as the killing of Caesar? Some take questions such as these to be metaphysical questions. I think they are questions of semantics—questions about the way we talk and about what we mean. And I think that this conflict between metaphysic and semantic concerns is indicative of a “deep indeterminacy” (Bennett’s phrase) in our event concept. We do talk about events; but what events a statement is about is not something that can be inferred from the event names we use; it depends heavily (more heavily than with ordinary material objects) on local context and unprincipled intuitions. This paper illustrates this view in connection with two examples: the phenomenon of vagueness and the dispute over identity statements.

In a calculation involving imaginary numbers, we begin with real numbers that represent concrete measures and we end up with numbers that are equally real, but in the course of the operation we find ourselves walking “as if on a bridge that stands on no piles”. How is that possible? How does that work? And what is involved in the as-if stance that this metaphor introduces so beautifully? These are questions that bother Törless deeply. And that Törless is bothered by such questions is a central question for any reader of Törless. Here I offer my interpretation, along with a reconstruction of the philosophical intuition that lies behind it all.

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.