Papers (EN) by Achille C . Varzi
To appear in Logica Universalis
A complementary system for a given logic is a proof system whose theorems are exactly the formula... more A complementary system for a given logic is a proof system whose theorems are exactly the formulas that are not valid according to the logic in question. This article is a contribution to the complementary proof theory of classical propositional logic. In particular, we present a complementary proof-net system, CPN, that is sound and complete with respect to the set of all classically invalid (one-side) sequents. We also show that cut elimination in CPN enjoys strong normalization along with strong confluence (and, hence, uniqueness of normal forms).
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Journal of Philosophical Logic, 2023
This paper extends the axiomatic treatment of intuitionistic mereology by examining the behavior ... more This paper extends the axiomatic treatment of intuitionistic mereology by examining the behavior of constructive notions of overlap and disjointness. We consider both (i) various ways of defining such notions in terms of other intuitionistic mereological primitives, and (ii) the possibility of treating them as mereological primitives of their own.
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Gestalt Theoy, 2022
Can we really perceive absences? Sartre tells us that when he arrived late for his appointment at... more Can we really perceive absences? Sartre tells us that when he arrived late for his appointment at the café, he saw the absence of his friend Pierre. Is that really what he saw? Where was it, exactly? Why didn’t Sartre see the absence of other people who were not there? Why did other people who were there not see the absence of Pierre? The perception of absences gives rise to a host of conundrums and is constantly on the verge of conceptual confusion. Here I focus on the need to be clear about four sorts of distinctions: (i) the difference between perceiving an absence and perceiving something that is absent; (ii) the difference between perceiving an absence and an absence of perceiving; (iii) the difference between perceiving an absence and perceiving something as an ab-sence; and (iv) the difference between perceiving an absence and perceiving that something is absent.
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in F. Mariani Zini (ed.), The Meaning of Something. Rethinking the Logic and the Unity of Ontology, Cham, Springer, 2022
Universalist and nihilist answers to philosophical questions may be extreme, but they are clear e... more Universalist and nihilist answers to philosophical questions may be extreme, but they are clear enough. Aliquidist answers, by contrast, are typically caught between the Scylla of vagueness and indeterminacy and the Charybdis of ungroundedness and arbitrariness, and steering a proper middle course—saying exactly where in the middle one is going to settle—demands exceptional navigating powers. I myself tend to favor extreme answers precisely for this reason. Here, however, I consider one sense in which Something may claim superiority over its polar competitors, Everything and Nothing, when it comes to answerting the ontological question, “What is there?”.
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in M. Fitting (ed.), Selected Topics from Contemporary Logics, London, College Publications, 2021
We offer a critical overview of two sorts of proof systems that may be said to characterize class... more 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.
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Synthese, 2021
We present two mereological theories based on a primitive apartness relation along with binary re... more We present two mereological theories based on a primitive apartness relation along with binary relations of mereological excess and weak excess , respectively. Both theories are shown to be acceptable from the standpoint of constructive reasoning while remaining faithful to the spirit of classical mereology. The two theories are then compared and assessed with regard to their extensional import.
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in S. Shapiro and G. Hellman (eds.), The History of Continua: Philosophical and Mathematical Perspectives, Oxford, Oxford University Press, 2021
Euclid’s definition of a point as “that which has no part” has been a major source of controversy... more 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). Here I focus 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).
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Topoi, 2021
Cities are mysteriously attractive. The more we get used to being citizens of the world, the more... more Cities are mysteriously attractive. The more we get used to being citizens of the world, the more we feel the need to identify ourselves with a city. Moreover, this need seems in no way distressed by the fact that the urban landscape around us changes continuously: new buildings rise, new restaurants open, new stores, new parks, new infrastructures… Cities seem to vindicate Heraclitus’s dictum: you cannot step twice into the same river; you cannot walk twice through the same city. But, as with the river, we want and need to say that it is the same city we are walking through every day. It is always different, but numerically self-identical. How is that possible? What sort of mysterious thing is a city?
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in S. Bernstein and T. Goldschmidt (eds.), Non-Being: New Essay on the Metaphysics of Non-Existence, Oxford, Oxford University Press, 2021
The U.S. presidential election of 2000 was crucially decided in Florida. And, in Florida, the ele... more The U.S. presidential election of 2000 was crucially decided in Florida. And, in Florida, the election hinged crucially on a peculiar sort of question: Does this ballot have a hole? “Yes, it does”, so the ballot is valid and ought to be counted. “No it doesn’t”, and the ballot must be discarded. If only one could tell! Where were the hole experts when we needed them? Eventually the matter was thwarted by the Supreme Court and we all gave up. But we did learn something. We learned that even the destiny of a Presidential Election, if not more, might ultimately depend on one’s criteria for identifying holes—not their material surroundings, which everyone could detect, but the holes themselves.
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Synthese, 2020
David Lewis's Counterpart Theory (CT) is often seen as involving a radical departure from the sta... more David Lewis's Counterpart Theory (CT) is often seen as involving a radical departure from the standard, Kripke-style semantics for Modal Logic (ML), suggesting that we are dealing with deeply divergent accounts of our modal talk. However, CT captures but one version of the relevant semantic intuition, and does so on the basis of metaphysical assumptions (all worlds are equally real, individuals are world-bound) that are ostensibly discretionary. Just as ML can be translated into a language that quantifies explicitly over worlds, CT may be formulated as a semantic theory in which world quantification is purely metalinguistic. And just as Kripke-style semantics is formally compatible with the doctrine of world-boundedness, a counterpart-based semantics may in principle allow for cases of trans world identity. In fact, one may welcome a framework that is general enough to include both Lewis's counterpart-based account and Kripke's identity-based account as distinguished special cases. There are several ways of doing so. The purpose of this paper is to outline a fully general option and to illustrate its philosophical significance, showing how the large variety of intermediate relations that lie between Lewisian counterparthood and Kripkean identity yield a corresponding variety of modal theories that would otherwise remain uncharted.
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Perception, 2020
A new type of impossible picture is presented and described. The picture involves an object along... more A new type of impossible picture is presented and described. The picture involves an object along with its reflection in a plane mirror, delivering two apparently irreconcilable views of the object itself when seen simultaneously in its flesh and in the mirror. Contrary to other, more familiar impossible pictures, its interpretation requires explicit reasoning about the represented reality. It is a slow impossible picture.
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Analytic Philosophy, 2020
I am a friend of supervaluationism. A statement lacks a definite truth value if, and only if, it ... more I am a friend of supervaluationism. A statement lacks a definite truth value if, and only if, it comes out true on some admissible ways of precisifying the semantics of the relevant vocabulary and false on others. In this paper, I focus on the special case of identity statements. I take it that such statements, too, may occasionally suffer a truth-value gap, including philosophically significant instances. Yet there is a potentially devastating objection that can be raised against the supervaluationist treatment of such cases—in fact two objections. Luckily, both can be resisted. But seeing how requires that we take a closer look at the ontological presuppositions of supervaluationism, allowing for more leeway than is usually supposed.
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The Review of Symbolic Logic, 2019
We present a new axiomatization of classical mereology in which the three components of the theor... more We present a new axiomatization of classical mereology in which the three components of the theory—ordering, composition, and decomposition principles—are neatly separated. The equivalence of our axiom system with other, more familiar systems is established by purely deductive methods, along with additional results on the relative strengths of the composition and decomposition axioms of each theory.
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in S. Borgo, R. Ferrario, C. Masolo, and L. Vieu (eds.), Ontology Makes Sense. Essays in Honor of Nicola Guarino, Amsterdam, IOS Press, 2019
Ontology has come to gain huge currency in the information sciences, with techniques, application... more Ontology has come to gain huge currency in the information sciences, with techniques, applications, and results vastly exceeding the traditional concerns of philosophy. How did that happen? Where are we heading to? I do not have the answers. But I know what it took and what is needed. It took—and we need—the skills of a good Carnapian engineer, someone capable and willing to build bridges across fields even though each side regards them as a troublesome intruder.
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Logic and Logical Philosophy, 2019
Paul Hovda’s ‘What Is Classical Mereology?' has fruitfully reshaped the debate concerning the axi... more Paul Hovda’s ‘What Is Classical Mereology?' has fruitfully reshaped the debate concerning the axiomatic foundations of classical mereology. Precisely because of the importance of Hovda’s work and its usefulness as a reference tool, we note here that one of the five axiom systems presented therein, corresponding to the ‘Third Way’ to classical mereology, is defective and must be amended. In addition, we note that two other axiom systems, corresponding to the ‘First Way’ and to the ‘Fifth Way’, involve redundancies.
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in G. Marsico and L. Tateo (eds.), Ordinary Things and Their Extraordinary Meanings, Charlotte (NC), Information Age Publishing, 2019
Some thoughts on holes and the challenging metaphysical conundrums they raise, beginning with the... more Some thoughts on holes and the challenging metaphysical conundrums they raise, beginning with the obvious question: are there such things, or are holes mere entia representationis, as-if entities, linguistic noise?
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Synthese, 2018
Classical propositional logic can be characterized, indirectly , by means of a complementary form... more 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.
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Philosophical Studies, 2017
Mereological atomism is the thesis that everything is ultimately composed of atomic parts, i.e., ... more 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 (2015) 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 (i) the models in question are atomistic in the intended sense, and (ii) 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.
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Philosophy and Literature, 2017
Why did Carnevali submit that short poem to the 1919 Whitman issue of Poetry, if the only apparen... more Why did Carnevali submit that short poem to the 1919 Whitman issue of Poetry, if the only apparent connection with Walt Whitman is in the title? He did so, I argue, because that poem is as Whitmanesque as one could possibly imagine. Carnevali’s philosophy of the commonplace is more than just an ars poetica of sorts. It is Philosophy with the capital “P”. It is an endorsement of Whitman’s perspective on things along with that sense of wonder which, as Aristotle said (and Plato before him), is the beginning of all philosophy.
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in L. Zaibert (ed.), The Theory and Practice of Ontology, London, Palgrave Macmillian, 2016
In his Romanes Lecture of 1907, Lord Curzon emphasized the overwhelming influence of “natural” an... more In his Romanes Lecture of 1907, Lord Curzon emphasized the overwhelming influence of “natural” and “artificial” frontiers in the political history of the modern world. As Barry Smith has shown, the same could be said, more generally, of the natural and artificial boundaries that are at work in articulating every aspect of the reality with which we have to deal, not only in the world of geography, but the world of human experience at large. Moreover, once the natural/artificial distinction has been recognized, it can be drawn across the board: not merely in relation to boundaries but also in relation to those entities that may be said to have boundaries. If something enjoys a natural boundary, its identity and survival conditions do not depend on us; it is a bona fide, mind-independent entity of its own. By contrast, if its boundary is artificial, then the entity itself is to some degree a fiat entity, a product of our worldmaking. Here I am interested in limit case: what if, pace Curzon and pace Smith, all entities turned out to be of the latter sort?
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Papers (EN) by Achille C . Varzi