Achille C. Varzi

Двигаясь в направлении реалистических перспектив, мы представляем всеобщую типологиюграниц, построенную преимущественно на противопоставлении между справедливыми (илифизическим) и назначенными(определяемыми "человеческим фактором") границами. Названноеразделение конфликтует с иными принципами разделения, для примера между: полным инеполным, завершенным и проходящим, четким и неопределенным, симметричным иасимметричным. В заключительной части обсуждены формальные проблемы: представлены двеаксиоматические теории границ и проводится проверка обеих в части некоторых деталей.Результат показывает, что применять наше понимание контакта, раздела и разделения можно ковсему.

Двигаясь в направлении реалистических перспектив, мы представляем всеобщую типологиюграниц, построенную преимущественно на противопоставлении между справедливыми (илифизическим) и назначенными(определяемыми "человеческим фактором") границами. Названноеразделение конфликтует с иными принципами разделения, для примера между: полным инеполным, завершенным и проходящим, четким и неопределенным, симметричным иасимметричным. В заключительной части обсуждены формальные проблемы: представлены двеаксиоматические теории границ и проводится проверка обеих в части некоторых деталей.Результат показывает, что применять наше понимание контакта, раздела и разделения можно ковсему.

We present a hypersequent calculus that is sound and complete with respect to the truth-functionally contingent formulas of classical logic. We investigate its structural properties and provide a Gentzen-style cut-elimination procedure. The most notable feature of the calculus is that it jointly satisfies the subformula property and the property of _deductive purity_, to the effect that only contingent hypersequents occur in formal proofs. Moreover, since the negation of a contingent formula is also contingent, the calculus turns out to be _paraconsistent_, and since the conjunction of a formula with its own negation is not contingent, the paraconsistency is of the _non-adjunctive_ kind.

Euclid’s definition of a point as “that which has no part” has been a major source of controversy in relation to the epistemological and ontological presuppositions of classical geometry, from the medieval and modern disputes on indivisibilism to the full development of point-free geometries in the 20th century. Such theories stem from the general idea that all talk of points as putative lower-dimensional entities must and can be recovered in terms of suitable higher-order constructs involving only extended regions (or bodies). This chapter focuses on what is arguably the first thorough proposal of this sort, Whitehead’s theory of “extensive abstraction”, offering a critical reconstruction of the theory through its successive installments: from the purely mereological version of ‘La théorie relationniste de l’espace’ (1916) to the refined versions presented in An Enquiry Concerning the Principles of Natural Knowledge (1919) and in The Concept of Nature (1920) to the last, mereotopological version of Process and Reality (1929).

The chapter endorses Composition as Identity, broadly and loosely understood as the thesis that a composite whole is nothing over and above its parts, and the parts nothing over and above the whole. Thus, given an object, x, composed of n proper parts, y 1,..., y n, the author feels the tension between his Quinean heart and its Lewisian counterpart. There is tension between the obligation to countenance n + 1 things, x, and the y i ’s, each of which is a distinct portion of reality, and the inclination to count just one thing, x, or just n things, the y i ’s, the former encompassing the same amount of reality as the latter. This chapter is an attempt to reconstruct this tension and to explain it away without forgoing the intimate link between counting and countenancing.

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. This chapter offers 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.

We offer a critical overview of two sorts of proof systems that may be said to characterize classical propositional logic indirectly (and non-standardly): refutation systems, which prove sound and complete with respect to classical contradictions, and rejection systems, which prove sound and complete with respect to the larger set of all classical non-tautologies. Systems of the latter sort are especially interesting, as they show that classical propositional logic can be given a paraconsistent characterization. In both cases, we consider Hilbert-style systems as well as Gentzen-style sequent calculi and natural-deduction formalisms.

Everyone who endorses the categorial distinction between objects and events must confront a general question: how do these two types of entities relate to one another? Here we are especially interested in what is typically regarded as the basic relational tie between the two, namely, that objects may be said to participate or take part in events, whereas events befall or happen to their participants. The exact nature of this participation relation is philosophically contentious and may depend on how the two categories of objects and events are construed in the first place. Regardless of its metaphysical characterization, however, a number of questions arise concerning its formal features and the general laws that govern its behavior. In particular, since both objects and events can be mereologically structured, we are interested in the formal laws that govern the interaction between participation and parthood. If objects _are_ events, as some perdurantists maintain, then participation just _is_ parthood. But what if objects and events form genuinely distinct categories? What, then, is the relationship between being part of something and taking part in something?

Alexandre Koyré wrote that Newton and the science that followed led to a splitting of the world: on the one hand is the "world of qualities and of sensible perceptions", on the other is the "world of quantities and of reified geometry". A comparison between facts held true by common sense and false by the scientific image of the world (or vice versa) seems to confirm this view. But is the dichotomy a real one? Is the world of common sense really "another world" relative to the world of the natural sciences? In this paper we argue in support of a negative answer.