Achille C. Varzi

La metafisica è quel ramo della filosofia che ha come oggetto la realtà considerata nei suoi aspetti più fondamentali e generali. L’origine del termine (letteralmente: ‘dopo’ o ‘oltre la fisica’) risale agli editori delle opere di Aristotele nel I secolo a.C., che lo usarono per classificare gli scritti dedicati a quest’argomento e ritenuti, appunto, posteriori a quelli dedicati alla fisica. L’essere si dice in molti modi, scriveva Aristotele in quelle pagine, e a questa molteplicità di significati corrispondono domini d’interesse specifici. La matematica, per esempio, si occupa dell’essere sotto il profilo quantitativo, la fisica sotto il profilo naturale. La metafisica (che Aristotele chiamava ‘sapienza’ o ‘filosofia prima’) si occupa invece dell’essere nel suo complesso, considerato sotto il profilo generalissimo della sua esistenza: l’essere in quanto essere.

This is a revised and extended version of the formal theory of holes outlined in the Appendix to the book "Holes and Other Superficialities". The first part summarizes the basic framework (ontology, mereology, topology, morphology). The second part emphasizes its relevance to spatial reasoning and to the semantics of spatial prepositions in natural language. In particular, I discuss the semantics of ‘in’ and provide an account of such fallacious arguments as “There is a hole in the sheet. The sheet is in the drawer. Ergo *there is a hole in the drawer”.

Ci imbattiamo in un confine ogni volta che pensiamo a un’entità demarcata rispetto a ciò che la circonda. C’è un confine (una superficie) che delimita l’interno di una sfera dal suo esterno; c’è un confine (una frontiera) che separa il Maryland dalla Pennsylvania. Talvolta la collocazione esatta di un confine non è chiara o è in qualche modo controversa (come quando si cerchi di tracciare i limiti del monte Everest, o il confine del nostro corpo). Talaltra il confine non corrisponde a una discontinuità fisica o a una differenziazione qualitativa (come nel caso dei confini del Wyoming, o della demarcazione tra la metà superiore e la metà inferiore di una sfera omogenea). Ma, che sia netto o confuso, naturale o artificiale, sembra esservi per ogni oggetto un confine che lo separa dal resto del mondo. Anche gli eventi hanno confini, quantomeno confini temporali. Le nostre vite sono delimitate dalle nostre nascite e morti; una partita di calcio comincia alle quindici in punto e termina col fischio finale dell’arbitro alle sedici e quarantacinque. E a volte si dice che anche le entità astratte, come i concetti o gli insiemi, hanno dei propri confini. Se tutto questo parlare di confini abbia davvero un senso, e se rifletta la struttura del mondo o solo l’attività organizzatrice del nostro intelletto, è però oggetto di profonda controversia filosofica.

La filosofia non è una scienza empirica e si regge in buona misura sull’argomenta- zione (→), cioè sulla capacità di giustificare certe affermazioni, o tesi, sulla base di altre ritenute vere. Sin dall’antichità la teoria dell’argomentazione ha pertanto occupato una posizione di rilievo nella ricerca filosofica, e già a partire da Aristotele ha contribuito a definire quel settore disciplinare che oggi chiamiamo logica (dalla parola greca logos, che significa tra l’altro ‘discorso’, ‘ragionamento’). Aristotele stesso codificò la materia in maniera sistematica, secondo schemi e principi che rimasero insuperati per oltre due millenni (→ sillogistica). A partire dal XIX secolo la teoria logica subì però mutamenti profondi, grazie soprattutto all’opera del matematico inglese George Boole e del filosofo tedesco Gottlob Frege, e nel XX secolo si è assistito a sviluppi straordinari che hanno portato all’applicazione della logica non solo in filosofia ma anche in altri ambiti di ricerca (dalla linguistica al diritto sino all’informatica).

The paper investigates the link between the theory of modal occurrents (where individuals are allowed to stretch across possible worlds) and Lewis’s counterpart theory (where all individuals are world-bound but have counterparts in other worlds). First I show how to interpret modal talk extensionally within the theory of modal occurrents. Then I show that the assumption that worlds be pairwise discrete is all that is needed to reconstruct the bulk of counterpart theory (i.e., to define the concept of a counterpart and to derive the standard postulates governing that concept) in terms of the theory of modal occurrents. Finally, I argue that this reconstruction allows us to view the indeterminacy of our modal intuitions as being part and parcel with the indeterminacy of our criteria for individuating modal occurrents, and that this indeterminacy is naturally explained in terms of linguistic (as opposed to ontic) vagueness.

Some philosophers have argued that the vagueness exhibited by names and descriptions such as ‘Mount Everest’, ‘Downtown Manhattan’, or ‘that cloud in the sky’ is ultimately ontological: they are vague because they refer to vague objects, objects with fuzzy boundaries. I take the opposite stand and argue for the view that all vagueness is semantic. There is no such thing as a vague mountain. Rather, there are many things where we conceive the 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.

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.

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.

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.

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.

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.

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.

The “Game of the Rule” is easy enough: I give you the beginning of a sequence of numbers (say) and you have to figure out how the sequence continues, to uncover the rule by means of which the sequence is generated. The game depends on two obvious constraints, namely (1) that the initial segment uniquely identify the sequence, and (2) that the sequence be non-random. As it turns out, neither constraint can fully be met, among other reasons because the relevant notion of randomness is either vacuous or undecidable. This may not be a problem when we play for fun. It is, however, a serious problem when it comes to playing the game for real, i.e., when the player to issue the initial segment is not one of us but the world out there, the sequence consisting not of numbers (say) but of the events that make up our history. Moreover, when we play for fun we know exactly what initial segment to focus on, but when we play for real we don’t even know that. This is the core difficulty in the philosophy of the inductive sciences.

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?

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.