- Department of Philosophy
University of St Andrews
Edgecliffe, The Scores
St Andrews, Fife KY16 9AL
United Kingdom
Institute for Logic, Language and Computation
University of Amsterdam
Oude Turfmarkt 141
1012 GC Amsterdam
The Netherlands
Francesco Berto
University of St Andrews, Philosophy, Faculty Member
- Ontology, Logic, Paradoxes, Alexius Meinong, Modality, Metaphysics, and 47 moreComputational Philosophy, Philosophical Logic, Modal Logic, Mereology, Ontology (Computer Science), Metaphysics of Modality, G.W.F. Hegel, Philosophy, Aristotle, Epistemic Logic, Possible World Semantics, David K Lewis, Possible Worlds, Paraconsistent logic, Aristotle's Metaphysics, Logical Paradox, Negation (Logic), Dialetheism, Impossible Worlds, Modal realism (Philosophy), Liar Paradox, Relevance Logic, Inconsistency Management, Modelling System Inconsistencies and Consistencies, Ersatzism, Set-theoretic paradoxes, Contradiction, Philosophy of Science, Philosophy Of Language, Metaphilosophy, Modal Meinongianism, Semantics for Hegel's logical vocabulary, Dialettica Hegeliana, Wittgenstein Godel, Hegel Logic Semantic, Hegel Semantics, Exclusion Negation, Hegelian Dialectic, Philosophy Of Mathematics, History of Philosophy, Gödel's Incompleteness Theorems, Epistemology, Dynamic Epistemic Logic, Imagination, Philosophy of Mind, Philosophy of Mind: Imagination, and Knowledge Representation and Reasoningedit
- I teach and work on logic, ontology, and epistemology at the Department of Philosophy, University of St Andrews, and ... moreI teach and work on logic, ontology, and epistemology at the Department of Philosophy, University of St Andrews, and at the Institute for Logic, Language and Computation (ILLC), University of Amsterdam.
Before this, I’ve been doing more or less the same at the University of Aberdeen UK, at the Institute for Advanced Study, University of Notre Dame IN-USA, at the Sorbonne-Ecole Normale Supérieure in Paris, at the Universities of Padua, Venice and Milan-San Raffaele in Italy.
I love logical paradoxes, impossible worlds, nonexistent objects, and philosophers who don’t take themselves too seriously.
My ORCID ID: 0000-0003-3246-657Xedit
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... more
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.
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When do two sentences say the same thing, that is, express the same content? We defend two-component (2C) semantics: the view that propositional contents comprise (at least) two irreducibly distinct constituents, (1) truth-conditions, and... more
When do two sentences say the same thing, that is, express the same content? We defend two-component (2C) semantics: the view that propositional contents comprise (at least) two irreducibly distinct constituents, (1) truth-conditions, and (2) subject-matter. We contrast 2C with one-component (1C) semantics, focusing on the view that subject-matter is reducible to truth conditions. We identify exponents of this view and argue in favor of 2C. An appendix proposes a general formal template for propositional 2C semantics.
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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... more
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.
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Sentences φ and ψ are cognitive synonyms for one when they play the same role in one's cognitive life. The notion is pervasive (§ 1), but elusive: it is bound to be hyperintensional (§ 2), but excessive fine-graining would trivialize it... more
Sentences φ and ψ are cognitive synonyms for one when they play the same role in one's cognitive life. The notion is pervasive (§ 1), but elusive: it is bound to be hyperintensional (§ 2), but excessive fine-graining would trivialize it and there are reasons for some coarse graining (§ 2.1). Conceptual limitations stand in the way of a natural algebra (§ 2.2), and it should be sensitive to subject matters (§ 2.3). A cognitively adequate individuation of content may be intransitive (§ 3) due to 'dead parrot' series: sequences of sentences φ1 ,... , φn where adjacent φi and φi+1 are cognitive synonyms while φ1 and φn are not (§ 3.1). Finding an intransitive account is hard: Fregean equipollence won't do (§ 3.2) and a result by Leitgeb shows that it wouldn't satisfy a minimal compositionality principle (§ 3.3). Sed contra, there are reasons for transitivity, too (§ 3.4). In § 4, we come up with a formal semantics capturing this jumble of desiderata, thereby showing that the notion is coherent. In § 5, we reassess the desiderata in its light.
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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... more
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.
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Timothy Williamson has defended the claim that the semantics of the indicative 'if' is given by the material conditional. Putative counterexamples can be handled by better understanding the role played in our assessment of indicatives by... more
Timothy Williamson has defended the claim that the semantics of the indicative 'if' is given by the material conditional. Putative counterexamples can be handled by better understanding the role played in our assessment of indicatives by a fallible cognitive heuristic, called the Suppositional Procedure. Williamson's Suppositional Conjecture has it that the Suppositional Procedure is humans' primary way of prospectively assessing conditionals. This paper raises some doubts on the Suppositional Procedure and Conjecture.
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We propose a new account of indicative conditionals, giving acceptability and logical closure conditions for them. We start from Adams' Thesis: the claim that the acceptability of a simple indicative equals the corresponding conditional... more
We propose a new account of indicative conditionals, giving acceptability and logical closure conditions for them. We start from Adams' Thesis: the claim that the acceptability of a simple indicative equals the corresponding conditional probability. The Thesis is widely endorsed, but arguably false and refuted by empirical research. To fix it, we submit, we need a relevance constraint: we accept a simple conditional 'If φ, then ψ' to the extent that (i) the conditional probability p(ψ|φ) is high, provided that (ii) φ is relevant for ψ. How (i) should work is well-understood. It is (ii) that holds the key to improve our understanding of conditionals. Our account has (i) a probabilistic component, using Popper functions; (ii) a relevance component, given via an algebraic structure of topics or subject matters. We present a probabilistic logic for simple indicatives, and argue that its (in)validities are both theoretically desirable and in line with empirical results on how people reason with conditionals.
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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... more
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.
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We study imagination as reality-oriented mental simulation (ROMS): the activity of simulating non-actual scenarios in one’s mind, to investigate what would happen if they were realized. Three connected questions concerning ROMS are: What... more
We study imagination as reality-oriented mental simulation (ROMS): the activity of simulating non-actual 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.
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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... more
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: (i) an intension, taking care of truth conditions; and (ii) 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: (1) the topic-sensitivity of content; (2) the fragmentation of knowledge states; (3) 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.
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We reply to arguments by Otávio Bueno and Edward Zalta ('Object Theory and Modal Meinongianism', Australasian Journal of Philosophy, 2017) against Modal Meinongianism, including that it presupposes, but cannot maintain, a unique... more
We reply to arguments by Otávio Bueno and Edward Zalta ('Object Theory and Modal Meinongianism', Australasian Journal of Philosophy, 2017) against Modal Meinongianism, including that it presupposes, but cannot maintain, a unique denotation for names of fictional characters, and that it is not generalized to higher-order objects. We individuate the crucial difference between Modal Meinongianism and Object Theory in the for-mer's resorting to an apparatus of worlds for the representational purposes for which the latter resorts to a distinction between two kinds of predi-cation, exemplification and encoding. We argue that the distinction has fewer supporters than Bueno and Zalta want, and that there's a reason why the notion of encoding has been found baffling by some.
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We present a formal semantics for epistemic logic, capturing the notion of 'knowability relative to information' (KRI). Like Dretske, we move from the platitude that what an agent can know depends on her (empirical) information. We treat... more
We present a formal semantics for epistemic logic, capturing the notion of 'knowability relative to information' (KRI). Like Dretske, we move from the platitude that what an agent can know depends on her (empirical) information. We treat operators of the form K_AB ('B is knowable on the basis of information A') as variably strict quantifiers over worlds with a topic- or aboutness- preservation constraint. Variable strictness models the non-monotonicity of knowledge acquisition while allowing knowledge to be intrinsically stable. Aboutness-preservation models the topic-sensitivity of information, allowing us to invalidate controversial forms of epistemic closure while validating less controversial ones. Thus, unlike the standard modal framework for epistemic logic, KRI accommodates plausible approaches to the Kripke-Harman dogmatism paradox, which bear on non-monotonicity, or on topic-sensitivity. KRI also strikes a better balance between agent idealization and a non-trivial logic of knowledge ascriptions.
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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... more
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.
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We present a framework for epistemic logic, modeling the logical aspects of System 1 ("fast") and System 2 ("slow") cognitive processes, as per dual process theories of reasoning. The framework combines non-normal worlds semantics with... more
We present a framework for epistemic logic, modeling the logical aspects of System 1 ("fast") and System 2 ("slow") cognitive processes, as per dual process theories of reasoning. The framework combines non-normal worlds semantics with the techniques of Dynamic Epistemic Logic. It models non-logically-omniscient, but moderately rational agents: their System 1 makes fast sense of incoming information by integrating it on the basis of their background knowledge and beliefs. Their System 2 allows them to slowly, step-wise unpack some of the logical consequences of such knowledge and beliefs, by paying a cognitive cost. The framework is applied to three instances of limited rationality, widely discussed in cognitive psychology: Stereotypical Thinking, the Framing Effect, and the Anchoring Effect.
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The ‘puzzle of imaginative use’ (Kind and Kung, 2016) asks: given that imagination is arbitrary escape from reality, how can it have any epistemic value? In particular, imagination seems to be logically anarchic, like a runabout inference... more
The ‘puzzle of imaginative use’ (Kind and Kung, 2016) asks: given that imagination is arbitrary escape from reality, how can it have any epistemic value? In particular, imagination seems to be logically anarchic, like a runabout inference ticket: one who imagines A may also imagine whatever B pops to one’s mind by free mental association. This paper argues that at least a certain kind of imaginative exercise – reality-oriented mental simulation – is not logically anarchic. Showing this is part of the task of solving the puzzle. Six plausible features of imagination, so understood, are listed. Then a formal semantics is provided, whose patterns of logical validity and invalidity model the six features.
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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... more
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 (make-believed) 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.
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I present a possible worlds semantics for a hyperintensional belief revision operator, which reduces the logical idealization of cognitive agents affecting similar operators in doxastic and epistemic logics, as well as in standard AGM... more
I present a possible worlds semantics for a hyperintensional belief revision operator, which reduces the logical idealization of cognitive agents affecting similar operators in doxastic and epistemic logics, as well as in standard AGM belief revision theory. (Revised) belief states are not closed under classical logical consequence; revising by inconsistent information does not perforce lead to trivialization; and revision can be subject to ‘framing effects’: logically or necessarily equivalent contents can lead to different revisions. Such results are obtained without resorting to non-classical logics, or to non-normal or impossible worlds semantics. The framework combines, instead, a standard semantics for propositional S5 with a simple mereology of contents.
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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... more
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.
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I present a formal theory of the logic and aboutness of imagination. Aboutness is understood as the relation between meaningful items and what they concern, as per Yablo and Fine's works on the notion. Imagination is understood as per... more
I present a formal theory of the logic and aboutness of imagination. Aboutness is understood as the relation between meaningful items and what they concern, as per Yablo and Fine's works on the notion. Imagination is understood as per Chalmers' positive conceivability: the intentional state of a subject who conceives that p by imagining a situation – a configuration of objects and properties – verifying p. So far aboutness theory has been developed mainly for linguistic representation , but it is natural to extend it to intentional states. The proposed framework combines a modal semantics with a mereology of contents: imagination operators are understood as variably strict quantifiers over worlds with a content-preservation constraint.
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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... more
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 con-ceivability 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.
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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... more
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.
§1 sets the stage and impossible worlds are quickly introduced in §2. §3 proposes to model imagination via variably strict world quantifiers. §4 introduces the formal semantics. §5 argues that imagination has a minimal mereological structure validating some logical inferences. §6 deals with how imagination under-determines the represented contents. §7 proposes additional constraints on the semantics, validating further inferences. §8 describes some welcome invalidities. §9 examines the effects of importing false beliefs into the imag- ined scenarios. Finally, §10 hints at possible developments of the theory in the direction of two-dimensional semantics.
§1 sets the stage and impossible worlds are quickly introduced in §2. §3 proposes to model imagination via variably strict world quantifiers. §4 introduces the formal semantics. §5 argues that imagination has a minimal mereological structure validating some logical inferences. §6 deals with how imagination under-determines the represented contents. §7 proposes additional constraints on the semantics, validating further inferences. §8 describes some welcome invalidities. §9 examines the effects of importing false beliefs into the imag- ined scenarios. Finally, §10 hints at possible developments of the theory in the direction of two-dimensional semantics.
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" There's Plenty of Room at the Bottom " , said the title of Richard Feynman's 1959 seminal conference at the California Institute of Technology. Fifty years on, nanotechnologies have led computer scientists to pay close attention to the... more
" There's Plenty of Room at the Bottom " , said the title of Richard Feynman's 1959 seminal conference at the California Institute of Technology. Fifty years on, nanotechnologies have led computer scientists to pay close attention to the links between physical reality and information processing. Not all the physical requirements of optimal computation are captured by traditional models – one still largely missing is reversibility. The dynamic laws of physics are reversible at microphysical level, distinct initial states of a system leading to distinct final states. On the other hand, as von Neumann already conjectured, irreversible information processing is expensive: to erase a single bit of information costs ~3 ⋅ 10^-21 joules at room temperature. Information entropy is a thermodynamic cost, to be paid in non-computational energy dissipation. This paper addresses the problem drawing on Edward Fredkin's Finite Nature hypothesis: the ultimate nature of the universe is discrete and finite, satisfying the axioms of classical, atomistic mereology. The chosen model is a cellular automaton (CA) with reversible dynamics, capable of retaining memory of the information present at the beginning of the universe. Such a CA can implement the Boolean logical operations and the other building bricks of computation: it can develop and host all-purpose computers. The model is a candidate for the realization of computational systems, capable of exploiting the resources of the physical world in an efficient way, for they can host logical circuits with negligible internal energy dissipation.
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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... more
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 (QM). It is so pervasive that it has been labelled the Received View (French and Krause [2006]: 105). I introduce the Received View in Section 1. In Section 2 I explain what I mean by “entity” (synonymously, by “object” and “thing”), and I argue that supporters of the Received View should agree with my characterization of the corresponding notion of entity (object, thing). 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.
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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.... more
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 (the admissible) negations. The approach unifies in a philosophically motivated picture the following results: nothing can be called a negation properly if it does not satisfy (Minimal) 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; 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 on the interpretation of worlds.
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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... more
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 crip-pling expressive limitations and from revenge paradoxes – pending a rigorous non-triviality proof for a formal dialetheic theory including it.
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I present an approach to our conceiving absolute impossibilities based on 'ceteris paribus' intentional operators: variably restricted quantifiers on possible and impossible worlds, based on world similarity. I discuss how such operators... more
I present an approach to our conceiving absolute impossibilities based on 'ceteris paribus' intentional operators: variably restricted quantifiers on possible and impossible worlds, based on world similarity. I discuss how such operators invalidate logical closure for conceivability and how similarity works when impossible worlds are around. The closest worlds are relevantly closest belief-worlds, and closeness takes into account apriority and the opacity of intentional contexts.
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We address an argument by Floridi (2009, 2011), 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... more
We address an argument by Floridi (2009, 2011), 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 Section 1, in Section 2 we explain what the proposition expressed by the title of our paper means. In Section 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 (§ 4); (ii) an objection from mereology: the view is incompatible with the world’s having parts (§ 5); (iii) an objection from counting: the view entails that the question of how many things there are doesn’t make sense (§ 6). In Section 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.
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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... more
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.
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Noneism a is form of Meinongianism, proposed by Richard Routley and developed and improved by Graham Priest in his widely discussed book Towards Non-Being. Priest's noneism is based upon the double move of (a) building a worlds semantics... more
Noneism a is form of Meinongianism, proposed by Richard Routley and developed and improved by Graham Priest in his widely discussed book Towards Non-Being. Priest's noneism is based upon the double move of (a) building a worlds semantics including impossible worlds, besides possible ones, and (b) admitting a new comprehension principle for objects, differerent from the ones proposed in other kinds of neo-Meinongian theories, such as Parsons' and Zalta's. The new principle has no restrictions on the sets of properties that can deliver objects, but parameterizes the having of properties by objects to worlds. Modality is therefore explicitly built in - so the approach can be conveniently labeled as "modal noneism". In this paper, I put modal noneism to work by testing it against classical issues in modal logic and semantics. It turns out that - perhaps surprisingly - the theory (1) performs well in problems of transworld identity, which are frequently considered to be the difficult ones in the literature; (2) faces a limitation, albeit not a severe one, when one comes to transworld individuation, which is often taken (especially after Kripke's notorious 'stipulation' solution) as an easy issue, if not a pseudo-problem; and (3) may stumble upon a real trouble when dealing with what I shall call 'extensionally indiscernible entities' - particular nonexistent objects modal noneism is committed to.
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This is the inaugural lecture for the Chair of Metaphysics at the University of Amsterdam.
Research Interests: Metaphysics and Logic
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... more
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.
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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... more
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.
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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... more
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.
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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... more
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.
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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... more
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(s) 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.
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In 'Fiction and Fictionalism', Mark Sainsbury has recently dubbed “Selection Problem” a serious trouble for Meinongian object theories. Typically, Meinongianism has been phrased as a kind of realism on nonexistent objects : these are... more
In 'Fiction and Fictionalism', Mark Sainsbury has recently dubbed “Selection Problem” a serious trouble for Meinongian object theories. Typically, Meinongianism has been phrased as a kind of realism on nonexistent objects : these are mind-independent things, not mental simulacra, having the properties they have independently from the activity of any cognitive agent. But how can one single out an object we have no causal acquaintance with, and which is devoid of spatiotemporal location, picking it out from a pre-determined, mind-independent set ?
In this paper, I set out a line of response by distinguishing different ways in which a thing may not exist. I show that the selection problem (a) does not arise for past, currently nonexistent objects ; (b) may not arise also for future existents (provided one massages naïve intuitions a bit) ; and (c) even for mere possibilia ; but (d) is a real snag for purely fictional objects, such as Holmes or Gandalf. As for (d), I propose a solution that forces Meinongianism to introduce a kind of ontological dependence of purely fictional nonexistents upon existents. The strategy complicates the intuitively simple, naïve Meinongian framework a bit, but looks quite promising.
In this paper, I set out a line of response by distinguishing different ways in which a thing may not exist. I show that the selection problem (a) does not arise for past, currently nonexistent objects ; (b) may not arise also for future existents (provided one massages naïve intuitions a bit) ; and (c) even for mere possibilia ; but (d) is a real snag for purely fictional objects, such as Holmes or Gandalf. As for (d), I propose a solution that forces Meinongianism to introduce a kind of ontological dependence of purely fictional nonexistents upon existents. The strategy complicates the intuitively simple, naïve Meinongian framework a bit, but looks quite promising.
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Meta-ontology (in van Inwagen's sense) concerns the methodology of ontology, and a controversial meta-ontological issue is to what extent ontology can rely on linguistic analysis while establishing the furniture of the world. This paper... more
Meta-ontology (in van Inwagen's sense) concerns the methodology of ontology, and a controversial meta-ontological issue is to what extent ontology can rely on linguistic analysis while establishing the furniture of the world. This paper discusses an argument advanced by some ontologists (I call them unifiers) against supporters of or coincident entities (I call them multipliers) and its meta-ontological import. Multipliers resort to Leibniz's Law to establish that spatiotemporally coincident entities a and b are distinct, by pointing at a predicate F() made true by a and false by b. Unifiers try to put multipliers in front of a dilemma: in attempting to introduce metaphysical differences on the basis of semantic distinctions, multipliers either (a) rest on a fallacy of verbalism, entailed by a trade-off between a de dicto and a de re reading of modal claims, or (b) beg the question against unifiers by having to assume the distinction between a and b beforehand. I shall rise a tu quoque, showing that unifiers couldn't even distinguish material objects (or events) from the spatiotemporal regions they occupy unless they also resorted to linguistic distinctions. Their methodological aim to emancipate themselves from linguistic analysis in ontological businesses is therefore problematic.
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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,... more
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.
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A he spread of paraconsistent logics and dialetheism has produced a good deal of dis? cussion of the principle referred to as "Law of Contradiction," or, better, "Law of Non... more
A he spread of paraconsistent logics and dialetheism has produced a good deal of dis? cussion of the principle referred to as "Law of Contradiction," or, better, "Law of Non Contradiction" (LNC). Dialetheists typically think that some sentences, called dialetheias, are both true ...
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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... more
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.
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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... more
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.
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Nel pieno dell'età cartesiana, Leibniz non si vergognava di dire che vi è più verità nella Fisica di Aristotele, che nelle Meditazioni sulla filosofia prima. Nel pieno dell'età postmetafisica e... more
Nel pieno dell'età cartesiana, Leibniz non si vergognava di dire che vi è più verità nella Fisica di Aristotele, che nelle Meditazioni sulla filosofia prima. Nel pieno dell'età postmetafisica e della svolta linguistica, Davidson ha affermato, in uno dei suoi saggi più celebri, che poiché ...
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... | Ayuda. Modus Tollerns. Kant, Hegel e la critica della nozione logica di sostanza. Autores: Francesco Berto; Localización: Giornale di Metafisica: revista bimestrale di filosofia, ISSN 0017-0372, Vol. 25, Nº 2, 2003 , pags. 287-304.... more
... | Ayuda. Modus Tollerns. Kant, Hegel e la critica della nozione logica di sostanza. Autores: Francesco Berto; Localización: Giornale di Metafisica: revista bimestrale di filosofia, ISSN 0017-0372, Vol. 25, Nº 2, 2003 , pags. 287-304. ...
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When one thinks—knows, believes, imagines—that something is the case, one’s thought has a topic: it is about something, towards which one’s mind is directed. What is the logic of thought, so understood? This book begins to explore the... more
When one thinks—knows, believes, imagines—that something is the case, one’s thought has a topic: it is about something, towards which one’s mind is directed. What is the logic of thought, so understood?
This book begins to explore the idea that, to answer the question, we should take topics seriously. It proposes a hyperintensional account of the propositional contents of thought, arguing that these are individuated not only by the set of possible worlds at which they are true, but also by their topic: what they are about. The book then builds epistemic, doxastic, probabilistic, and conditional logics based on this view. It applies them to issues ranging from dogmatism, scepticism, and epistemic fallibilism, to imagination and suppositional reasoning, belief revision, framing effects, and the acceptability of indicative conditionals.
This book begins to explore the idea that, to answer the question, we should take topics seriously. It proposes a hyperintensional account of the propositional contents of thought, arguing that these are individuated not only by the set of possible worlds at which they are true, but also by their topic: what they are about. The book then builds epistemic, doxastic, probabilistic, and conditional logics based on this view. It applies them to issues ranging from dogmatism, scepticism, and epistemic fallibilism, to imagination and suppositional reasoning, belief revision, framing effects, and the acceptability of indicative conditionals.
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We need to understand the impossible. Francesco Berto and Mark Jago start by considering what the concepts of meaning, information, knowledge, belief, fiction, conditionality, and counterfactual supposition have in common. They are all... more
We need to understand the impossible. Francesco Berto and Mark Jago start by considering what the concepts of meaning, information, knowledge, belief, fiction, conditionality, and counterfactual supposition have in common. They are all concepts which divide the world up more finely than logic does. Logically equivalent sentences may carry different meanings and information and may differ in how they're believed. Fictions can be inconsistent yet meaningful. We can suppose impossible things without collapsing into total incoherence. Yet for the leading philosophical theories of meaning, these phenomena are an unfathomable mystery. To understand these concepts, we need a metaphysical, logical, and conceptual grasp of situations that could not possibly exist: Impossible Worlds. This book discusses the metaphysics of impossible worlds and applies the concept to a range of central topics and open issues in logic, semantics, and philosophy. It considers problems in the logic of knowledge, the meaning of alternative logics, models of imagination and mental simulation, the theory of information, truth in fiction, the meaning of conditional statements, and reasoning about the impossible. In all these cases, impossible worlds have an essential role to play.
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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... more
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.
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.
Research Interests: Metaphysics, Ontology, Philosophy Of Mathematics, States of Affairs, Facts, Propositions, Mereology, and 12 moreMeta-Ontology, Rudolf Carnap, Willard Van Orman Quine, Possible Worlds, Metaontology, Metaphysical grounding, Peter van Inwagen, Fictionalism, Abstract Objects, Ontological Pluralism, Meinongianism, and Modal Meinongianism
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... more
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.
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.
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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... more
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. The unifying focus of the work is a single, basic philosophical notion: the notion of existence. Each main theory of the notion available in philosophy is introduced via a detailed, self-contained exposition, and critically evaluated, with the original research emerging in the final Chapters. 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
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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,... more
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.
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One sense of 'imagination' that matters in epistemology has the word mean 'reality-oriented mental simulation' (ROMS): we suppose that something is the case; develop the supposition by importing background knowledge and beliefs; and check... more
One sense of 'imagination' that matters in epistemology has the word mean 'reality-oriented mental simulation' (ROMS): we suppose that something is the case; develop the supposition by importing background knowledge and beliefs; and check what is true in the imagined scenario.
What is the logic of ROMS? Imagination has a reputation for being logically anarchic. In particular, it's hyperintensional: we can imagine A without imagining a necessarily equivalent B. This work considers a Principle of Equivalence in Imagination which, if accepted, will limit the anarchy: when A and B are equivalent in imagination, one will imagine the same things after supposing either in ROMS.
What is equivalence in imagination? It is suggested that it's cognitive equivalence. A and B are cognitively equivalent for one when they play the same role in one's cognitive life: whatever one understands, concludes, etc., given either, one does, given the other. ROMS is logically modelled via variably strict modals. Two formal semantics are proposed for them: one uses possible worlds plus an algebra of topics; the other resorts to impossible worlds. The two deal with equivalence in imagination in subtly different ways.
What is the logic of ROMS? Imagination has a reputation for being logically anarchic. In particular, it's hyperintensional: we can imagine A without imagining a necessarily equivalent B. This work considers a Principle of Equivalence in Imagination which, if accepted, will limit the anarchy: when A and B are equivalent in imagination, one will imagine the same things after supposing either in ROMS.
What is equivalence in imagination? It is suggested that it's cognitive equivalence. A and B are cognitively equivalent for one when they play the same role in one's cognitive life: whatever one understands, concludes, etc., given either, one does, given the other. ROMS is logically modelled via variably strict modals. Two formal semantics are proposed for them: one uses possible worlds plus an algebra of topics; the other resorts to impossible worlds. The two deal with equivalence in imagination in subtly different ways.
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A Topic-Sensitive Intentional Modal (TSIM) is a two-place, variably strict modal with an aboutness or topicality constraint, of the form ‘X^φψ’ (read: ‘Given φ, the agent X’s that ψ’, X being some mental state or act). TSIMs do nice... more
A Topic-Sensitive Intentional Modal (TSIM) is a two-place, variably strict modal with an aboutness or topicality constraint, of the form ‘X^φψ’ (read: ‘Given φ, the agent X’s that ψ’, X being some mental state or act). TSIMs do nice things for mainstream and formal epistemology, belief revision theory, and mental simulation theory. I present a basic formal semantics for TSIMs and explore three readings of ‘X^φψ’ one gets by imposing different constraints on their truth conditions: (1) as expressing knowability relative to information (‘Given total information φ, one is in the position to know that ψ’), inspired by Dretske’s view that what one can know depends on the available (empirical) information; (2) as a mental simulation operator (‘In mental simulation starting with input φ, one imagines that ψ’) capturing features of mainstream mental simulation theories, like that of Nichols and Stich; (3) as a hyperintensional belief revision operator (‘After (statically) revising by φ, one believes that ψ’), reducing the idealization of cognitive agents one finds in standard doxastic logics and AGM. I close by mentioning developments of TSIM theory currently in progress.
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Tractatus 4.024 inspired the dominant semantics of our time: truth-conditional semantics. Such semantics is focused on possible worlds: the content of p is the set of worlds where p is true. It has become increasingly clear that such an... more
Tractatus 4.024 inspired the dominant semantics of our time: truth-conditional semantics. Such semantics is focused on possible worlds: the content of p is the set of worlds where p is true. It has become increasingly clear that such an account is, at best, defective: we need an ‘independent factor in meaning, constrained but not determined by truth-conditions’ (Yablo 2014, p. 2), because sentences can be differently true at the same possible worlds. I suggest a missing comment which, had it been included in the Tractatus, would have helped semantics get this right from the start. This is my 4.0241: ‘Knowing what is the case if a sentence is true is knowing its ways of being true’: knowing a sentence’s truth possibilities and what we now call its topic, or subject matter. I show that the famous ‘fundamental thought’ that ‘the “logical constants” do not represent’ (4.0312) can be understood in terms of ways-based views of meaning. Such views also help with puzzling claims like 5.122: ‘If p follows from q, the sense of “p” is contained in the that of “q”’, which are compatible with a conception of entailment combining truth-preservation with the preservation of topicality, or of ways of being true.
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Against the mainstream Quinean meta-ontology, Meinongians claim: “There are things that do not exist”. It is sometimes said that the “there are” in that sentence expresses “Meinongian quantification”. I consider two supposedly knock-down... more
Against the mainstream Quinean meta-ontology, Meinongians claim: “There are things that do not exist”. It is sometimes said that the “there are” in that sentence expresses “Meinongian quantification”. I consider two supposedly knock-down meta-ontological objections to Meinongianism from the literature: (1) an objection from equivocation, to the effect that the view displays a conceptual or semantic misunderstanding, probably of quantificational expressions; and (2) an objection from analyticity, to the effect that that sentence is Frege-analytically false i.e., it is synonymous with a logical falsity. Objection (1) is countered via a development of Williamson’s argument against epistemic conceptions of analyticity. Objection (2), which points at alleged linguistic evidence, is countered by resorting to linguistic counter-evidence. The upshot is a set-up of the debate between Quineans and Meinongians, in which the two parties disagree on substantive matters concerning de re the property of existence, taken as a natural property in the Lewis-Sider sense; and in which quick alleged refutations, such as objections from meaning-variance or analytic falsehood, rarely achieve their expected results.
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World semantics for relevant logics include so-called non-normal or impossible worlds providing model-theoretic counterexamples to such irrelevant entailments as (A ∧ ¬A) → B, A → (B∨¬B), or A → (B → B). Some well-known views interpret... more
World semantics for relevant logics include so-called non-normal or impossible worlds providing model-theoretic counterexamples to such irrelevant entailments as (A ∧ ¬A) → B, A → (B∨¬B), or A → (B → B). Some well-known views interpret non-normal worlds as information states. If so, they can plausibly model our ability of conceiving or representing logical impossibilities. The phenomenon is explored by combining a formal setting with philosophical discussion. I take Priest’s basic relevant logic N4 and extend it, on the syntactic side, with a representation operator, (R), and on the semantic side, with particularly anarchic non-normal worlds. This combination easily invalidates unwelcome “logical omniscience” inferences of standard epistemic logic, such as belief-consistency and closure under entailment. Some open questions are then raised on the best strategies to regiment (R) in order to express more vertebrate kinds of conceivability.
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A hyperintensional concept draws a distinction between necessarily equivalent contents. If the concept is expressed by an operator, , then is hyperintensional insofar as and can differ in truth value in spite of and 's being necessarily... more
A hyperintensional concept draws a distinction between necessarily equivalent contents. If the concept is expressed by an operator, , then is hyperintensional insofar as and can differ in truth value in spite of and 's being necessarily equivalent. Necessary equivalence of claims is standardly understood in terms of possible worlds (ways things could have been): and are necessarily equivalent when they are true at the same worlds. This is sometimes put in terms of sentences sharing an intension. An extensional operator (e.g., Boolean negation) allows substitution salva veritate of sentences with the same extension, that is, truth value: if has the same truth value as , then also has the same truth value as. An intensional operator (e.g., the box of necessity) allows substitution salva veritate of sentences that express necessary equivalents: if is necessarily equivalent to , then has the same truth value as. The expression "hyperintensional" is thus for an that defies substitution salva veritate even of expressions with the same intension. Cresswell (1975) introduced the expression "hyperintensional" to pick out a position in a sentence where substitution fails for logical equivalents. Nowadays the term is used more broadly, with unrestrictedly necessary equivalence replacing logical equivalence. Candidates for unrestricted necessity often include, besides the logical, mathematical and metaphysical necessity. We don't discuss whether one of these is reducible to the others-e.g., the mathematical to the logical, as claimed by logicists.
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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... more
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...
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"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... more
"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..."
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..."
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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.... more
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 homogenous, 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: they can be specified in purely mathematical terms and physical structures can implement them. 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 (see entry), and therefore compute, given Turing’s thesis (see entry on Church-Turing thesis), anything computable...
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October 2019 update on the Logic of Conceivability project outcomes.
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The human imagination is enormously powerful, allowing us to conceive of far-fetched scenarios that go far beyond our individual experience. Yet imagination is useful for everyday practical reasoning as well. Researchers in the Logic of... more
The human imagination is enormously powerful, allowing us to conceive of far-fetched scenarios that go far beyond our individual experience. Yet imagination is useful for everyday practical reasoning as well. Researchers in the Logic of Conceivability project are using mathematical tools to investigate the logic of the human imagination, as Dr Peter Hawke explains
Questo è un articolo per la Festschrift in onore di Vero Tarca.
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"Riuscirà il lato oscuro della filosofia de noantri a sottrarsi per sempre al referaggio anonimo? Spero di no. Sottrarsi è inaccettabile e sospetto che alcuni di coloro che lo fanno siano in malafede." Questo post è stato originariamente... more
"Riuscirà il lato oscuro della filosofia de noantri a sottrarsi per sempre al referaggio anonimo? Spero di no. Sottrarsi è inaccettabile e sospetto che alcuni di coloro che lo fanno siano in malafede."
Questo post è stato originariamente pubblicato nel blog di filosofia dell'Università di Urbino:
http://filosofia.uniurb.it/i-referaggi-e-il-lato-oscuro-della-filosofia-italiana/
Questo post è stato originariamente pubblicato nel blog di filosofia dell'Università di Urbino:
http://filosofia.uniurb.it/i-referaggi-e-il-lato-oscuro-della-filosofia-italiana/
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This is a 2016 interview on my research work.
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Profili, bacheche, post virali ed epic fail, like e dislike, ci introducono alla logica senza che ce ne accorgiamo.
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'La mia posizione filosofica in relazione al pensiero di Emanuele Severino.' -- Un piccolo intervento (Festschrift per Severino, in uscita in una collettanea).
This is a paper to to appear in "Graham Priest on Dialetheism and Paraconsistency", a volume dedicated to GP, edited by Can Başkent, and Thomas M. Ferguson.