Achille C. Varzi

We can see mereology as a theory of parthood and topology as a theory of wholeness. How can these be combined to obtain a unified theory of parts and wholes? This paper examines various non-equivalent ways of pursuing this task, with specific reference to its relevance to spatio-temporal reasoning. In particular, three main strategies are compared: (i) mereology and topology as two independent (though mutually related) chapters; (ii) mereology as a general theory subsuming topology; (iii) topology as a general theory subsuming mereology. Some more speculative strategies and directions for further research are also considered.

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.

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.

In previous work I have argued that talk about negative events should not be taken at face value: typically, what we are inclined to think of as a negative event (John’s failure to go jogging) is just an ordinary, positive event (his going to the movie instead); it is a positive event under a negative description. Here I consider more closely the difficulties that arise in those cases where no positive event seems available to do the job, as with putative cases of causation by omission. In particular, I elaborate on Helen Beebee’s idea that not all causal explanations are reports of causation. When we mention John’s failure to turn off the gas as an explanans of why there was an explosion, we do not say what caused the explosion. We do not mention any of the relevant causes. We just remark that one sort of event that was supposed to occur, and whose occurrence would have prevented the explosion, did not in fact occur.

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.

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).

Abstract. As a general theory of reasoning—and as a general theory of what holds true under every possible circumstance—logic is supposed to be ontologically neutral. It ought to have nothing to do with questions concerning what there is, or whether there is anything at all. It is for this reason that traditional Aristotelian logic, with its tacit existential presuppositions, was eventually deemed inadequate as a canon of pure logic. And it is for this reason that modern quantification theory, too, with its residue of existentially loaded theorems and patterns of inference, has been claimed to suffer from a defect of logical purity. The law of non-contradiction rules out certain circumstances as impossible—circumstances in which a statement is both true and false, or perhaps circumstances where something both is and is not the case. Is this to be regarded as a further ontological bias?

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.

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.

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.

Some philosophers have gone a long way towards a clarification and a defense of the view that there is genuine (worldly) indeterminacy of identity. Among his reasons for taking this view seriously is the contention that extant formulations of the alternative conception, according to which all indeterminacy lies in the semantics of our language (or in the system of concepts embodied in our language), are not fitted for dealing with a host of identity puzzles. I this paper I take issue with that contention and argue that the semantic conception, if charitably construed, can meet such challenges.

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 theory according to which most ordinary objects are mere “entia successiva”—sequences of distinct mereological aggregates, whose unity resides exclusively in our minds—is a variant of the standard, three-dimensional conception of objects. For the aggregates are, at bottom, endurants, i.e., entities that persist through time by being fully present at any time at which they exist. In this paper I compare this theory with the so-called “stage view”, according to which ordinary objects—indeed, all objects—are sequences of momentary entities that cannot truly be said to persist through time. Both theories face a number of intuitive difficulties but the stage view, I argue, has a lot more to offer in return.