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

According to a certain familiar way of dividing up the business of philosophy, ontology is concerned with the question of what entities exist (a task that is often identified with that of drafting a “complete inventory” of the universe) whereas metaphysics seeks to explain, of those entities, what they are (i.e., to specify the “ultimate nature” of the items included in the inventory). This distinction carries with it a natural thought, namely, that ontology is in some way prior to metaphysics. One must first of all figure out what things exist (or might exist); then one can attend to the further question of what they are, specify their nature, speculate on those features that make each thing the thing it is. I sympathize with that thought, but there is a major worry lurking in the background and there are several complications that emerge in the foreground. The purpose of this paper is to address such worries and complications and to come up with a plausible way of understanding the “priority thesis” that makes it both reasonable and, hopefully, useful.

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.

[ES] Aquí articulo y luego defiendo las dos afirmaciones siguientes: que es un error pensar que la estructura del mundo debe reflejar la estructura de las teorías por las cuales lo representamos, y por medio de las cuales tratamos de descifrarlo, simplemente porque estas teorías parecen funcionar; entre las consecuencias más lamentables de este error está la tendencia generalizada a pensar que debe haber una pluralidad de realidades, o varios niveles diferentes e irreductibles de una realidad estratificada, simplemente porque nuestro credo incluye una pluralidad de teorías cada una de las cuales aparenta ser tan importante y confiable como es irreductible a las demás. [EN] I articulate and then defend the following two claims: it is a mistake to think that the structure of the world should mirror the structure of the theories by which we represent it, and through which we try to decipher it, simply because those theories appear to work; among the most deplorable consequences of this mistake is the widespread tendency to think that there must be a plurality of realities, or several different and irreducible levels of a stratified reality, merely because our credo includes a plurality of theories each of which appears to be as important and trustworthy as it is irreducible to the others.

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).

A scholarly annotated epic poem on the pitfalls and tribulations of “good philosophizing”. Divided into twenty-eight cantos (in medieval Italian hendecasyllabic terza rima), the poem tells of an allegorical journey through the downward spiral of the philosophers’ hell, where all sorts of thinkers are punished for their faults and mistakes, in the endeavor to reach a way out of the condition of intellectual impasse in which the narrator has found himself. The affinities with Dante’s Inferno are apparent. Whereas Dante’s poem is about human sins and moral felonies, this one is about philosophical errors and fallacies; whereas Virgil takes Dante through the gluttons, the wrathful, the violent, the traitors to parties and countries, etc., here Socrates takes us through the realists, the skeptics, the dualists, the nichilists, the worshipers of language and easy mythos, etc. And yet this is not just a philosophical counterpart of Dante’s masterpiece, even less a parody. We can’t say exactly when, how, and why it was written, but this is an authentic piece of philosophy, a poem of love, a passionate testimony of militant metaphysics. It is the inspired and inspiring journey of someone, anyone, who is truly moved by the Love for Wisdom and by the grueling purification of the intellect that it demands.

Since its first appearance in 1966, the notion of a supervaluation has been regarded by many as a powerful tool for dealing with semantic gaps. Only recently, however, applications to semantic gluts have also been considered. In previous work I proposed a general framework exploiting the intrinsic gap/glut duality. Here I also examine an alternative account where gaps and gluts are treated on a par: although they reflect opposite situations, the semantic upshot is the same in both cases--the value of some expressions is not uniquely defined. Other strategies for generalizing supervaluations are considered and some comparative facts are discussed.

A philosophical exchange broadly inspired by the characters of Berkeley’s Three Dialogues. Hylas is the realist philosopher: the view he stands up for reflects a robust metaphysic that is reassuringly close to common sense, grounded on the twofold persuasion that the world comes structured into entities of various kinds and at various levels and that it is the task of philosophy, if not of science generally, to “bring to light” that structure. Philonous, by contrast, is the anti-realist philosopher (though not necessarily an idealist): his metaphysic is stark, arid, dishearteningly bone-dry, and stems from the conviction that a great deal of the structure that we are used to attribute to the world out there lies, on closer inspection, in our head, in our “organizing practices”, in the complex system of concepts and categories that unrerlie our representation of experience and our need to represent it that way.

It is shown that a complete axiomatization of classical non-tautologies can be obtained by taking F (falsehood) as the sole axiom along with the two inference rules: (i) if A is a substitution instance of B, then A |– B; and (ii) if A is obtained from B by replacement of equivalent sentences, then A |– B (counting as equivalent the pairs {T, ~F}, {F, F&F}, {F, F&T}, {F, T&F}, {T, T&T}). Since the set of tautologies is also specifiable by purely syntactic means, the resulting picture gives an improved syntactic account of classical sentential logic. The picture can then be completed by considering related systems that prove adequate to specify the set of contradictions, the set of non-contradictions, and the set of contingencies respectively.

A lot of work in metaphysics relies on linguistic analysis and intuitions. Do we want to know what sort of things there are or could be? Then let’s see what sort of things there must be in order for what we truthfully say to be true. Do we want to see whether x is distinct from y? Then let’s see whether there is any statement that is true of x but not of y. And so on. In this paper I argue that this way of proceeding is full of traps and is bound to be pretty useless unless we already have a good idea of what sort of things there are, and of how we are going to count them.

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

On the one hand, logic has (or ought to have) nothing to do with metaphysics; it ought to have nothing to do with questions concerning what there is, or whether there is anything at all. On the other hand, metaphysics can hardly get off the ground without the help of logical analysis; to be is to be a truth-maker, and the search for truth-makers requires that we lay open the logical structure of our language. So something’s gotta give: either logical analysis is metaphysically biased, or metaphysicians must make up their mind before resorting to logical analysis. Or both.

There are two ways of understanding the notion of a contradiction: as a conjunction of a statement and its negation, or as a pair of statements one of which is the negation of the other. Correspondingly, there are two ways of understanding the Law of Non-Contradiction (LNC), i.e., the law that says that no contradictions can be true. In this paper I offer some arguments to the effect that on the first (collective) reading LNC is non-negotiable, but on the second (distributive) reading it is perfectly plausible to suppose that LNC may, in some rather special and perhaps undesirable circumstances, fail to hold.