Sometimes mereologists have problems with counting. We often don't want to count the parts of maximally connected objects as full‐fledged objects themselves, and we don't want to count discontinuous objects as parts of further, full‐fledged objects. But whatever one takes “full‐fledged object” to mean, the axioms and theorems of classical, extensional mereology commit us to the existence both of parts and of wholes – all on a par, included in the domain of quantification – and this makes mereology look counterintuitive (...) to various philosophers.In recent years, a proposal has been advanced to solve the tension between mereology and familiar ways of counting objects, under the label of Minimalist View. The Minimalist View may be summarized in the slogan: “Count x as an object iff it does not overlap with any y you have already counted as an object”. The motto seems prima facie very promising but, we shall argue, when one looks at it more closely, it is not. On the contrary, the Minimalist View involves an ambiguity that can be solved in quite different directions. We argue that one resolution of the ambiguity makes it incompatible with mereology. This way, the Minimalist View can lend no support to mereology at all.We suggest that the Minimalist View can become compatible with mereology once its ambiguity is solved by interpreting it in what we call an epistemic or conceptual fashion: whereas mereology has full metaphysical import, the Minimalist View may account for our ways of selecting “conceptually salient” entities. But even once it is so disambiguated, it is doubtful that the Minimalist View can help to make mereology more palatable, for it cannot make it any more compatible with commonsensical ways of counting objects. (shrink)

A counterpossible conditional is a counterfactual with an impossible antecedent. Common sense delivers the view that some such conditionals are true, and some are false. In recent publications, Timothy Williamson has defended the view that all are true. In this paper we defend the common sense view against Williamson’s objections.

Impossible Worlds focuses on an exciting new theory in philosophy, with applications in metaphysics, logic, and the theory of meaning. Its central topic is: how do we meaningfully talk and reason about situations which, unbeknownst to us, are impossible? This issue emerges as a central problem in contemporary philosophical accounts of meaning, information, knowledge, belief, fiction, conditionality, and counterfactual supposition. The book is written bytwo of the leading philosophers in the area and contains original research of relevance to professional philosophers (...) and logicians working in metaphysics, philosophy of language, formal logic, and adjacentareas. (shrink)

A hyperintensional epistemic logic would take the contents which can be known or believed as more fine-grained than sets of possible worlds. I consider one objection to the idea: Williamson’s Objection from Overfitting. I propose a hyperintensional account of propositions as sets of worlds enriched with topics: what those propositions, and so the attitudes having them as contents, are about. I show that the account captures the conditions under which sentences express the same content; that it can be pervasively applied (...) in formal and mainstream epistemology; and that it is left unscathed by the objection. (shrink)

In this paper we reply to arguments of Kroon (“Characterization and Existence in Modal Meinongianism”. Grazer Philosophische Studien 86, 23–34) to the effect that Modal Meinongianism cannot do justice to Meinongian claims such as that the golden mountain is golden, and that it does not exist.

Is there a notion of contradiction—let us call it, for dramatic effect, “absolute”—making all contradictions, so understood, unacceptable also for dialetheists? It is argued in this paper that there is, and that spelling it out brings some theoretical benefits. First it gives us a foothold on undisputed ground in the methodologically difficult debate on dialetheism. Second, we can use it to express, without begging questions, the disagreement between dialetheists and their rivals on the nature of truth. Third, dialetheism has an (...) operator allowing it, against the opinion of many critics, to rule things out and manifest disagreement: for unlike other proposed exclusion-expressing-devices (for instance, the entailment of triviality), the operator used to formulate the notion of absolute contradiction appears to be immune both from crippling expressive limitations and from revenge paradoxes—pending a rigorous nontriviality proof for a formal dialetheic theory including it. (shrink)

We propose a dynamic hyperintensional logic of belief revision for non-omniscient agents, reducing the logical omniscience phenomena affecting standard doxastic/epistemic logic as well as AGM belief revision theory. Our agents don’t know all a priori truths; their belief states are not closed under classical logical consequence; and their belief update policies are such that logically or necessarily equivalent contents can lead to different revisions. We model both plain and conditional belief, then focus on dynamic belief revision. The key idea we (...) exploit to achieve non-omniscience focuses on topic- or subject matter-sensitivity: a feature of belief states which is gaining growing attention in the recent literature. (shrink)

We propose a solution to the problem of logical omniscience in what we take to be its fundamental version: as concerning arbitrary agents and the knowledge attitude per se. Our logic of knowledge is a spin-off from a general theory of thick content, whereby the content of a sentence has two components: an intension, taking care of truth conditions; and a topic, taking care of subject matter. We present a list of plausible logical validities and invalidities for the logic of (...) knowledge per se for arbitrary agents, and isolate three explanatory factors for them: the topic-sensitivity of content; the fragmentation of knowledge states; the defeasibility of knowledge acquisition. We then present a novel dynamic epistemic logic that yields precisely the desired validities and invalidities, for which we provide expressivity and completeness results. We contrast this with related systems and address possible objections. (shrink)

It is a venerable slogan due to David Hume, and inherited by the empiricist tradition, that the impossible cannot be believed, or even conceived. In Positivismus und Realismus, Moritz Schlick claimed that, while the merely practically impossible is still conceivable, the logically impossible, such as an explicit inconsistency, is simply unthinkable. -/- An opposite philosophical tradition, however, maintains that inconsistencies and logical impossibilities are thinkable, and sometimes believable, too. In the Science of Logic, Hegel already complained against “one of the (...) fundamental prejudices of logic as hitherto understood”, namely that “the contradictory cannot be imagined or thought” (Hegel 1931: 430). Our representational capabilities are not limited to the possible, for we appear to be able to imagine and describe also impossibilities — perhaps without being aware that they are impossible. -/- Such impossibilities and inconsistencies are what this entry is about... (shrink)

I want to model a finite, fallible cognitive agent who imagines that p in the sense of mentally representing a scenario—a configuration of objects and properties—correctly described by p. I propose to capture imagination, so understood, via variably strict world quantifiers, in a modal framework including both possible and so-called impossible worlds. The latter secure lack of classical logical closure for the relevant mental states, while the variability of strictness captures how the agent imports information from actuality in the imagined (...) non-actual scenarios. Imagination turns out to be highly hyperintensional, but not logically anarchic. Section 1 sets the stage and impossible worlds are quickly introduced in Sect. 2. Section 3 proposes to model imagination via variably strict world quantifiers. Section 4 introduces the formal semantics. Section 5 argues that imagination has a minimal mereological structure validating some logical inferences. Section 6 deals with how imagination under-determines the represented contents. Section 7 proposes additional constraints on the semantics, validating further inferences. Section 8 describes some welcome invalidities. Section 9 examines the effects of importing false beliefs into the imagined scenarios. Finally, Sect. 10 hints at possible developments of the theory in the direction of two-dimensional semantics. (shrink)

We present and defend the Australian Plan semantics for negation. This is a comprehensive account, suitable for a variety of different logics. It is based on two ideas. The first is that negation is an exclusion-expressing device: we utter negations to express incompatibilities. The second is that, because incompatibility is modal, negation is a modal operator as well. It can, then, be modelled as a quantifier over points in frames, restricted by accessibility relations representing compatibilities and incompatibilities between such points. (...) We defuse a number of objections to this Plan, raised by supporters of the American Plan for negation, in which negation is handled via a many-valued semantics. We show that the Australian Plan has substantial advantages over the American Plan. (shrink)

We present a theory of truth in fiction that improves on Lewis's [1978] ‘Analysis 2’ in two ways. First, we expand Lewis's possible worlds apparatus by adding non-normal or impossible worlds. Second, we model truth in fiction as belief revision via ideas from dynamic epistemic logic. We explain the major objections raised against Lewis's original view and show that our theory overcomes them.

There is some consensus on the claim that imagination as suppositional thinking can have epistemic value insofar as it’s constrained by a principle of minimal alteration of how we know or believe reality to be – compatibly with the need to accommodate the supposition initiating the imaginative exercise. But in the philosophy of imagination there is no formally precise account of how exactly such minimal alteration is to work. I propose one. I focus on counterfactual imagination, arguing that this can (...) be modeled as simulated belief revision governed by Laplacian imaging. So understood, it can be rationally justified by accuracy considerations: it minimizes expected belief inaccuracy, as measured by the Brier score. (shrink)

_Framing effects_ concern the having of different attitudes towards logically or necessarily equivalent contents. Framing is of crucial importance for cognitive science, behavioral economics, decision theory, and the social sciences at large. We model a typical kind of framing, grounded in (i) the structural distinction between beliefs activated in working memory and beliefs left inactive in long term memory, and (ii) the topic- or subject matter-sensitivity of belief: a feature of propositional attitudes which is attracting growing research attention. We introduce (...) a class of models featuring (i) and (ii) to represent, and reason about, agents whose belief states can be subject to framing effects. We axiomatize a logic which we prove to be sound and complete with respect to the class. (shrink)

The Humean view that conceivability entails possibility can be criticized via input from cognitive psychology. A mainstream view here has it that there are two candidate codings for mental representations (one of them being, according to some, reducible to the other): the linguistic and the pictorial, the difference between the two consisting in the degree of arbitrariness of the representation relation. If the conceivability of P at issue for Humeans involves the having of a linguistic mental representation, then it is (...) easy to show that we can conceive the impossible, for impossibilities can be represented by meaningful bits of language. If the conceivability of P amounts to the pictorial imaginability of a situation verifying P, then the question is whether the imagination at issue works purely qualitatively, that is, only by phenomenological resemblance with the imagined scenario. If so, the range of situations imaginable in this way is too limited to have a significant role in modal epistemology. If not, imagination will involve some arbitrary labeling component, which turns out to be sufficient for imagining the impossible. And if the relevant imagination is neither linguistic nor pictorial, Humeans will appear to resort to some representational magic, until they come up with a theory of a ‘third code’ for mental representations. (shrink)

An overview of hyperintensionality is provided. Hyperintensional languages have expressions with meanings that are more fine-grained than necessary equivalence. That is, the expressions may necessarily co-apply and yet be distinct in meaning. Adequately accounting for theories cast in hyperintensional languages is important in the philosophy of language; the philosophy of mind; metaphysics; and elsewhere. This entry presents a number of areas in which hyperintensionality is important; a range of approaches to theorising about hyperintensional matters; and a range of debates that (...) attention to hyperintensional constructions has generated. (shrink)

We study imagination as reality-oriented mental simulation : the activity of simulating nonactual scenarios in one’s mind, to investigate what would happen if they were realized. Three connected questions concerning ROMS are: What is the logic, if there is one, of such an activity? How can we gain new knowledge via it? What is voluntary in it and what is not? We address them by building a list of core features of imagination as ROMS, drawing on research in cognitive psychology (...) and the philosophy of mind. We then provide a logic of imagination as ROMS which models such features, combining techniques from epistemic logic, action logic, and subject matter semantics. Our logic comprises a modal propositional language with non-monotonic imagination operators, a formal semantics, and an axiomatization. (shrink)

This book is both an introduction to and a research work on Meinongianism. “Meinongianism” is taken here, in accordance with the common philosophical jargon, as a general label for a set of theories of existence – probably the most basic notion of ontology. As an introduction, the book provides the first comprehensive survey and guide to Meinongianism and non-standard theories of existence in all their main forms. As a research work, the book exposes and develops the most up-to-date Meinongian theory (...) (called modal Meinongianism), applies it to specific fields, and discusses its open problems. Part I of the book provides a historical introduction to, and critical discussion of, the dominant philosophical view of existence: the “Kantian-Fregean-Quinean” perspective. Part II is the full-fledged introduction to the Meinongian theories of existence as a real property of individuals: after starting with the so-called naïve Meinongian conception and its problems, it provides a self-contained presentation of the main neo-Meinongian proposals, and a detailed discussion of their strengths and weaknesses. Part III develops a specific neo-Meinongian theory of existence employing a model-theoretic semantic framework. It discusses its application to the ontology and semantics of fictional objects, and its open problems. The methodology of the book follows the most recent trends in analytic ontology. In particular, the meta-ontological point of view is largely privileged. (shrink)

A dialetheia is a sentence, A, such that both it and its negation, ¬A, are true (we shall talk of sentences throughout this entry; but one could run the definition in terms of propositions, statements, or whatever one takes as her favourite truth-bearer: this would make little difference in the context). Assuming the fairly uncontroversial view that falsity just is the truth of negation, it can equally be claimed that a dialetheia is a sentence which is both true and false.

I propose a comprehensive account of negation as a modal operator, vindicating a moderate logical pluralism. Negation is taken as a quantifier on worlds, restricted by an accessibility relation encoding the basic concept of compatibility. This latter captures the core meaning of the operator. While some candidate negations are then ruled out as violating plausible constraints on compatibility, different specifications of the notion of world support different logical conducts for negations. The approach unifies in a philosophically motivated picture the following (...) results: nothing can be called a negation properly if it does not satisfy Contraposition and Double Negation Introduction; the pair consisting of two split or Galois negations encodes a distinction without a difference; some paraconsistent negations also fail to count as real negations, but others may; intuitionistic negation qualifies as real negation, and classical Boolean negation does as well, to the extent that constructivist and paraconsistent doubts on it do not turn on the basic concept of compatibility but rather on the interpretation of worlds. (shrink)

'Ontology and Metaontology: A Contemporary Guide' is a clear and accessible survey of ontology, focussing on the most recent trends in the discipline. -/- Divided into parts, the first half characterizes metaontology: the discourse on the methodology of ontological inquiry, covering the main concepts, tools, and methods of the discipline, exploring the notions of being and existence, ontological commitment, paraphrase strategies, fictionalist strategies, and other metaontological questions. The second half considers a series of case studies, introducing and familiarizing the reader (...) with concrete examples of the latest research in the field. The basic sub-fields of ontology are covered here via an accessible and captivating exposition: events, properties, universals, abstract objects, possible worlds, material beings, mereology, fictional objects. -/- The guide's modular structure allows for a flexible approach to the subject, making it suitable for both undergraduates and postgraduates looking to better understand and apply the exciting developments and debates taking place in ontology today. (shrink)

We outline a neo-Meinongian framework labeled as Modal Meinongian Metaphysics (MMM) to account for the ontology and semantics of fictional discourse. Several competing accounts of fictional objects are originated by the fact that our talking of them mirrors incoherent intuitions: mainstream theories of fiction privilege some such intuitions, but are forced to account for others via complicated paraphrases of the relevant sentences. An ideal theory should resort to as few paraphrases as possible. In Sect. 1, we make this explicit via (...) two methodological principles, called the Minimal Revision and the Acceptability Constraint. In Sect. 2, we introduce the standard distinction between internal and external fictional discourse. In Sects. 3–5, we discuss the approaches of (traditional) Meinongianism, Fictionalism, and Realism—and their main troubles. In Sect. 6 we propose our MMM approach. This is based upon (1) a modal semantics including impossible worlds (Subsect. 6.1); (2) a qualified Comprehension Principle for objects (Subsect. 6.2); (3) a notion of existence-entailment for properties (Subsect. 6.3). In Sect. 7 we present a formal semantics for MMM based upon a representation operator. And in Sect. 8 we have a look at how MMM solves the problems of the three aforementioned theories. (shrink)

There is a principle in things, about which we cannot be deceived, but must always, on the contrary, recognize the truth – viz. that the same thing cannot at one and the same time be and not be": with these words of the Metaphysics, Aristotle introduced the Law of Non-Contradiction, which was to become the most authoritative principle in the history of Western thought. However, things have recently changed, and nowadays various philosophers, called dialetheists, claim that this Law does not (...) hold unrestrictedly – that in peculiar circumstances the same thing may at the same time be and not be, and contradictions may obtain in the world. This book opens with an examination of the famous logical paradoxes that appear to speak on behalf of contradictions (e.g., the Liar paradox, the set-theoretic paradoxes such as Cantor’s and Russell’s), and of the reasons for the failure of the standard attempts to solve them. It provides, then, an introduction to paraconsistent logics – non-classical logics in which the admission of contradictions does not lead to logical chaos –, and their astonishing applications, going from inconsistent data base management to contradictory arithmetics capable of circumventing Gödel’s celebrated Incompleteness Theorem. The final part of the book discusses the philosophical motivations and difficulties of dialetheism, and shows how to extract from Aristotle’s ancient words a possible reply to the dialetheic challenge. How to Sell a Contradiction will appeal to anyone interested in non-classical logics, analytic metaphysics, and philosophy of mathematics, and especially to those who consider challenging our most entrenched beliefs the main duty of philosophical inquiry. (shrink)

Accounts of propositions as sets of possible worlds have been criticized for conflating distinct impossible propositions. In response to this problem, some have proposed to introduce impossible worlds to represent distinct impossibilities, endorsing the thesis that impossible worlds must be of the same kind; this has been called the parity thesis. I show that this thesis faces problems, and propose a hybrid account which rejects it: possible worlds are taken as concrete Lewisian worlds, and impossibilities are represented as set-theoretic constructions (...) out of them. This hybrid account (1) distinguishes many intuitively distinct impossible propositions; (2) identifies impossible propositions with extensional constructions; (3) avoids resorting to primitive modality, at least so far as Lewisian modal realism does. (shrink)

I present an approach to our conceiving absolute impossibilities—things which obtain at no possible world—in terms of ceteris paribus intentional operators: variably restricted quantifiers on possible and impossible worlds based on world similarity. The explicit content of a representation plays a role similar in some respects to the one of a ceteris paribus conditional antecedent. I discuss how such operators invalidate logical closure for conceivability, and how similarity works when impossible worlds are around. Unlike what happens with ceteris paribus counterfactual (...) conditionals, the closest worlds are relevantly closest belief-worlds: closest to how things are believed to be, rather than to how they are. Also, closeness takes into account apriority and the opacity of intentional contexts. (shrink)

A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change (...) this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more 'big picture' ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics. (shrink)

We reply to various arguments by Otavio Bueno and Edward Zalta (‘Object Theory and Modal Meinongianism’) against Modal Meinongianism, including that it presupposes, but cannot maintain, a unique denotation for names of fictional characters, and that it is not generalizable to higher-order objects. We individuate the crucial difference between Modal Meinongianism and Object Theory in the former’s resorting to an apparatus of worlds, possible and impossible, for the representational purposes for which the latter resorts to a distinction between two kinds (...) of predication, exemplification and encoding. We show that encoding has fewer forerunners in the history of philosophy than Bueno and Zalta want, and that there’s a reason why the notion has been found baffling by some. (shrink)

Philosophical dialetheism, whose main exponent is Graham Priest, claims that some contradictions hold, are true, and it is rational to accept and assert them. Such a position is naturally portrayed as a challenge to the Law of Non-Contradiction (LNC). But all the classic formulations of the LNC are, in a sense, not questioned by a typical dialetheist, since she is (cheerfully) required to accept them by her own theory. The goal of this paper is to develop a formulation of the (...) Law which appears to be unquestionable, in the sense that the Priestian dialetheist is committed to accept it without also accepting something inconsistent with it, on pain of trivialism—that is to say, on pain of lapsing into the position according to which everything is the case. This will be achieved via (a) a discussion of Priest's dialetheic treatment of the notions of rejection and denial; and (b) the characterization of a negation via the primitive intuition of content exclusion. Such a result will not constitute a cheap victory for the friends of consistency. We may just learn that different things have been historically conflated under the label of 'Law of Non-Contradiction'; that dialetheists rightly attack some formulations of the Law, and orthodox logicians and philosophers have been mistaken in assimilating them to the indisputable one. (shrink)

This research is published within the project ‘The Logic of Conceivability’, funded by the European Research Council, Grant Number 681404.

We address an argument by Floridi (Synthese 168(1):151–178, 2009; 2011a), to the effect that digital and analogue are not features of reality, only of modes of presentation of reality. One can therefore have an informational ontology, like Floridi’s Informational Structural Realism, without commitment to a supposedly digital or analogue world. After introducing the topic in Sect. 1, in Sect. 2 we explain what the proposition expressed by the title of our paper means. In Sect. 3, we describe Floridi’s argument. In (...) the following three sections, we raise three difficulties for it, (i) an objection from intuitions: Floridi’s view is not supported by the intuitions embedded in the scientific views he exploits (Sect. 4); (ii) an objection from mereology: the view is incompatible with the world’s having parts (Sect. 5); (iii) an objection from counting: the view entails that the question of how many things there are doesn’t make sense (Sect. 6). In Sect. 7, we outline two possible ways out for Floridi’s position. Such ways out involve tampering with the logical properties of identity, and this may be bothersome enough. Thus, Floridi’s modus ponens will be our (and most ontologists’) modus tollens. (shrink)

I would like to attack a certain view: The view that the concept of identity can fail to apply to some things although, for some positive integer n, we have n of them. The idea of entities without self-identity is seriously entertained in the philosophy of quantum mechanics. It is so pervasive that it has been labelled the Received View. I introduce the Received View in Section 1. In Section 2 I explain what I mean by entity, and I argue (...) that supporters of the Received View should agree with my characterization of the corresponding notion of entity. I also explain what I mean by identity, and I show that supporters of the Received View agree with my characterization of that notion. In Section 3 I argue that the concept of identity, so characterized, is one with the concept of oneness. Thus, it cannot but apply to what belongs to a collection with n elements, n being a positive integer. In Section 4 I add some considerations on the primitiveness of identity or unity and the status of the Identity of Indiscernibles. In Section 5 I address the problem of how reference to indiscernible objects with identity can be achieved. (shrink)

Sentences \(\varphi\) and \(\psi\) are _cognitive synonyms_ for one when they play the same role in one’s cognitive life. The notion is pervasive (Sect. 1 ), but elusive: it is bound to be hyperintensional (Sect. 2 ), but excessive fine-graining would trivialize it and there are reasons for some coarse-graining (Sect. 2.1 ). Conceptual limitations stand in the way of a natural algebra (Sect. 2.2 ), and it should be sensitive to subject matters (Sect. 2.3 ). A cognitively adequate individuation (...) of content may be intransitive (Sect. 3 ) due to ‘dead parrot’ series: sequences of sentences \(\varphi _1, \ldots, \varphi _n\) where adjacent \(\varphi _i\) and \(\varphi _{i+1}\) are cognitive synonyms while \(\varphi _1\) and \(\varphi _n\) are not (Sect. 3.1 ). Finding an intransitive account is hard: Fregean equipollence won’t do (Sect. 3.2 ) and a result by Leitgeb shows that it wouldn’t satisfy a minimal compositionality principle (Sect. 3.3 )._Sed contra_, there are reasons for transitivity, too (Sect. 3.4 ). In Sect. 4, we come up with a formal semantics capturing this jumble of desiderata, thereby showing that the notion is coherent. In Sect. 5, we re-assess the desiderata in its light. (shrink)

An interpretation of Wittgenstein’s much criticized remarks on Gödel’s First Incompleteness Theorem is provided in the light of paraconsistent arithmetic: in taking Gödel’s proof as a paradoxical derivation, Wittgenstein was drawing the consequences of his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. It is shown that the features of paraconsistent arithmetics match (...) with some intuitions underlying Wittgenstein’s philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any mathematical question. (shrink)

Drawing on different suggestions from the literature, we outline a unified metaphysical framework, labeled as Modal Meinongian Metaphysics (MMM), combining Meinongian themes with a non-standard modal ontology. The MMM approach is based on (1) a comprehension principle (CP) for objects in unrestricted, but qualified form, and (2) the employment of an ontology of impossible worlds, besides possible ones. In §§1–2, we introduce the classical Meinongian metaphysics and consider two famous Russellian criticisms, namely (a) the charge of inconsistency and (b) the (...) claim that naïve Meinongianism allows one to prove that anything exists. In §3, we have impossible worlds enter the stage and provide independent justification for their use. In §4, we introduce our revised comprehension principle: our CP has no restriction on the (sets of) properties that can characterize objects, but parameterizes them to worlds, therefore having modality explicitly built into it. In §5, we propose an application of the MMM apparatus to fictional objects and defend the naturalness of our treatment against alternative approaches. Finally, in §6, we consider David Lewis’ notorious objection to impossibilia, and provide a reply to it by resorting to an ersatz account of worlds. (shrink)

Cellular automata (henceforth: CA) are discrete, abstract computational systems that have proved useful both as general models of complexity and as more specific representations of non-linear dynamics in a variety of scientific fields. Firstly, CA are (typically) spatially and temporally discrete: they are composed of a finite or denumerable set of homogeneous, simple units, the atoms or cells. At each time unit, the cells instantiate one of a finite set of states. They evolve in parallel at discrete time steps, following (...) state update functions or dynamical transition rules: the update of a cell state obtains by taking into account the states of cells in its local neighborhood (there are, therefore, no actions at a distance). Secondly, CA are abstract, as they can be specified in purely mathematical terms and implemented in physical structures. Thirdly, CA are computational systems: they can compute functions and solve algorithmic problems. Despite functioning in a different way from traditional, Turing machine-like devices, CA with suitable rules can emulate a universal Turing machine, and therefore compute, given Turing's Thesis, anything computable.... (shrink)

Berto’s highly readable and lucid guide introduces students and the interested reader to Gödel’s celebrated _Incompleteness Theorem_, and discusses some of the most famous - and infamous - claims arising from Gödel's arguments. Offers a clear understanding of this difficult subject by presenting each of the key steps of the _Theorem_ in separate chapters Discusses interpretations of the _Theorem_ made by celebrated contemporary thinkers Sheds light on the wider extra-mathematical and philosophical implications of Gödel’s theories Written in an accessible, (...) non-technical style. (shrink)

Sometimes mereologists have problems with counting. We often don't want to count the parts of maximally connected objects as full-fledged objects themselves, and we don't want to count discontinuous objects as parts of further, full-fledged objects. But whatever one takes "full-fledged object" to mean, the axioms and theorems of classical, extensional mereology commit us to the existence both of parts and of wholes – all on a par, included in the domain of quantification – and this makes mereology look counterintuitive (...) to various philosophers. In recent years, a proposal has been advanced to solve the tension between mereology and familiar ways of counting objects, under the label of Minimalist View . The Minimalist View may be summarized in the slogan: "Count x as an object iff it does not overlap with any y you have already counted as an object". The motto seems prima facie very promising but, we shall argue, when one looks at it more closely, it is not. On the contrary, the Minimalist View involves an ambiguity that can be solved in quite different directions. We argue that one resolution of the ambiguity makes it incompatible with mereology. This way, the Minimalist View can lend no support to mereology at all. We suggest that the Minimalist View can become compatible with mereology once its ambiguity is solved by interpreting it in what we call an epistemic or conceptual fashion: whereas mereology has full metaphysical import, the Minimalist View may account for our ways of selecting "conceptually salient" entities. But even once it is so disambiguated, it is doubtful that the Minimalist View can help to make mereology more palatable, for it cannot make it any more compatible with commonsensical ways of counting objects. (shrink)

In his famous work on vagueness, Russell named “fallacy of verbalism” the fallacy that consists in mistaking the properties of words for the properties of things. In this paper, I examine two (clusters of) mainstream paraconsistent logical theories – the non-adjunctive and relevant approaches –, and show that, if they are given a strongly paraconsistent or dialetheic reading, the charge of committing the Russellian Fallacy can be raised against them in a sophisticated way, by appealing to the intuitive reading of (...) their underlying semantics. The meaning of “intuitive reading” is clarified by exploiting a well-established distinction between pure and applied semantics. If the proposed arguments go through, the dialetheist or strong paraconsistentist faces the following Dilemma: either she must withdraw her claim to have exhibited true contradictions in a metaphysically robust sense – therefore, inconsistent objects and/or states of affairs that make those contradictions true; or she has to give up realism on truth, and embrace some form of anti-realistic (idealistic, or broadly constructivist) metaphysics. Sticking to the second horn of the Dilemma, though, appears to be promising: it could lead to a collapse of the very distinction, commonly held in the literature, between a weak and a strong form of paraconsistency – and this could be a welcome result for a dialetheist. (shrink)

I provide an interpretation of Wittgenstein's much criticized remarks on Gödel's First Incompleteness Theorem in the light of paraconsistent arithmetics: in taking Gödel's proof as a paradoxical derivation, Wittgenstein was right, given his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. I show that the models of paraconsistent arithmetics (obtained via the Meyer-Mortensen (...) collapsing filter on the standard model) match with many intuitions underlying Wittgensteins philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any meaningful mathematical question. (shrink)

Modal Meinongianism is the most recent neo-Meinongian theory. Its main innovation consists in a Comprehension Principle which, unlike other neo-Meinongian approaches, seemingly avoids limitations on the properties that can characterize objects. However, in a recent paper A. Sauchelli has raised an objection against modal Meinongianism, to the effect that properties and relations involving reference to worlds at which they are instantiated, and specifically to the actual world or parts thereof, force a limitation of its Comprehension Principle. The theory, thus, is (...) no better off than other neo-Meinongian views in this respect. This article shows that the notion part of actuality in Sauchelli’s paper is ambiguous from the modal Meinongian viewpoint. Accordingly, his objection splits into two, depending on its disambiguation. It is then explained how neither interpretation forces modal Meinongianism to limit its Comprehension Principle. A third problem connected to Sauchelli’s objection is addressed: how to account for our felicitously referring to nonexistent objects via descriptions that embed reference to properties not actually instantiated by the objects. Overall, the replies to these difficulties provide good insights into the workings of the new Meinongian theory. (shrink)