This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is shown that Fitting’s nested calculi naturally arise from their corresponding labelled calculi—for each of the aforementioned logics—via the elimination of structural rules in labelled derivations. The translational correspondence between the two types of systems is leveraged to show that the nested calculi inherit proof-theoretic properties from their associated labelled calculi, such as (...) completeness, invertibility of rules and cut admissibility. Since labelled calculi are easily obtained via a logic’s semantics, the method presented in this paper can be seen as one whereby refined versions of labelled calculi (containing nested calculi as fragments) with favourable properties are derived directly from a logic’s semantics. (shrink)

This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic paradigms: labelled and nested sequent calculi. The formalism of labelled sequents has been successful in that cut-free calculi in possession of desirable proof-theoretic properties can be automatically generated for large classes of logics. Despite these qualities, labelled systems make use of a complicated syntax that explicitly incorporates the (...) semantics of the associated logic, and such systems typically violate the subformula property to a high degree. By contrast, nested sequent calculi employ a simpler syntax and adhere to a strict reading of the subformula property, making such systems useful in the design of automated reasoning algorithms. However, the downside of the nested sequent paradigm is that a general theory concerning the automated construction of such calculi (as in the labelled setting) is essentially absent, meaning that the construction of nested systems and the confirmation of their properties is usually done on a case-by-case basis. The refinement method connects both paradigms in a fruitful way, by transforming labelled systems into nested (or, refined labelled) systems with the properties of the former preserved throughout the transformation process. To demonstrate the method of refinement and some of its applications, we consider grammar logics, first-order intuitionistic logics, and deontic STIT logics. The introduced refined labelled calculi will be used to provide the first proof-search algorithms for deontic STIT logics. Furthermore, we employ our refined labelled calculi for grammar logics to show that every logic in the class possesses the effective Lyndon interpolation property. (shrink)

We provide a direct method for proving Craig interpolation for a range of modal and intuitionistic logics, including those containing a "converse" modality. We demonstrate this method for classical tense logic, its extensions with path axioms, and for bi-intuitionistic logic. These logics do not have straightforward formalisations in the traditional Gentzen-style sequent calculus, but have all been shown to have cut-free nested sequent calculi. The proof of the interpolation theorem uses these calculi and is purely syntactic, without resorting to embeddings, (...) semantic arguments, or interpreted connectives external to the underlying logical language. A novel feature of our proof includes an orthogonality condition for defining duality between interpolants. (shrink)

This work provides proof-search algorithms and automated counter-model extraction for a class of STIT logics. With this, we answer an open problem concerning syntactic decision procedures and cut-free calculi for STIT logics. A new class of cut-free complete labelled sequent calculi G3LdmL^m_n, for multi-agent STIT with at most n-many choices, is introduced. We refine the calculi G3LdmL^m_n through the use of propagation rules and demonstrate the admissibility of their structural rules, resulting in auxiliary calculi Ldm^m_nL. In the single-agent case, we (...) show that the refined calculi Ldm^m_nL derive theorems within a restricted class of (forestlike) sequents, allowing us to provide proof-search algorithms that decide single-agent STIT logics. We prove that the proof-search algorithms are correct and terminate. (shrink)

This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more refined formalism of nested sequents. The extraction of nested calculi from labelled calculi obtains via considerations pertaining to the elimination of structural rules in labelled derivations. Each aspect of the extraction process is motivated and detailed, showing that each nested calculus inherits favorable proof-theoretic properties from its associated (...) labelled calculus. (shrink)

We introduce translations between display calculus proofs and labeled calculus proofs in the context of tense logics. First, we show that every derivation in the display calculus for the minimal tense logic Kt extended with general path axioms can be effectively transformed into a derivation in the corresponding labeled calculus. Concerning the converse translation, we show that for Kt extended with path axioms, every derivation in the corresponding labeled calculus can be put into a special form that is translatable to (...) a derivation in the associated display calculus. A key insight in this converse translation is a canonical representation of display sequents as labeled polytrees. Labeled polytrees, which represent equivalence classes of display sequents modulo display postulates, also shed light on related correspondence results for tense logics. (shrink)

We employ a recently developed methodology -- called "structural refinement" -- to extract nested sequent systems for a sizable class of intuitionistic modal logics from their respective labelled sequent systems. This method can be seen as a means by which labelled sequent systems can be transformed into nested sequent systems through the introduction of propagation rules and the elimination of structural rules, followed by a notational translation. The nested systems we obtain incorporate propagation rules that are parameterized with formal grammars, (...) and which encode certain frame conditions expressible as first-order Horn formulae that correspond to a subclass of the Scott-Lemmon axioms. We show that our nested systems are sound, cut-free complete, and admit hp-admissibility of typical structural rules. (shrink)

In this work we answer a long standing request for temporal embeddings of deontic STIT logics by introducing the multi-agent STIT logic TDS . The logic is based upon atemporal utilitarian STIT logic. Yet, the logic presented here will be neutral: instead of committing ourselves to utilitarian theories, we prove the logic TDS sound and complete with respect to relational frames not employing any utilitarian function. We demonstrate how these neutral frames can be transformed into utilitarian temporal frames, while preserving (...) validity. Last, we discuss problems that arise from employing binary utility functions in a temporal setting. (shrink)

Standpoint logic is a recently proposed formalism in the context of knowledge integration, which advocates a multi-perspective approach permitting reasoning with a selection of diverse and possibly conflicting standpoints rather than forcing their unification. In this paper, we introduce nested sequent calculi for propositional standpoint logics---proof systems that manipulate trees whose nodes are multisets of formulae---and show how to automate standpoint reasoning by means of non-deterministic proof-search algorithms. To obtain worst-case complexity-optimal proof-search, we introduce a novel technique in the context (...) of nested sequents, referred to as "coloring," which consists of taking a formula as input, guessing a certain coloring of its subformulae, and then running proof-search in a nested sequent calculus on the colored input. Our technique lets us decide the validity of standpoint formulae in CoNP since proof-search only produces a partial proof relative to each permitted coloring of the input. We show how all partial proofs can be fused together to construct a complete proof when the input is valid, and how certain partial proofs can be transformed into a counter-model when the input is invalid. These "certificates" (i.e. proofs and counter-models) serve as explanations of the (in)validity of the input. (shrink)

We generalize intuitionistic tense logics to the multi-modal case by placing grammar logics on an intuitionistic footing. We provide axiomatizations for a class of base intuitionistic grammar logics as well as provide axiomatizations for extensions with combinations of seriality axioms and what we call "intuitionistic path axioms". We show that each axiomatization is sound and complete with completeness being shown via a typical canonical model construction.

We introduce a framework that allows for the construction of sequent systems for expressive description logics extending ALC. Our framework not only covers a wide array of common description logics, but also allows for sequent systems to be obtained for extensions of description logics with special formulae that we call "role relational axioms." All sequent systems are sound, complete, and possess favorable properties such as height-preserving admissibility of common structural rules and height-preserving invertibility of rules.

We present cut-free labelled sequent calculi for a central formalism in logics of agency: STIT logics with temporal operators. These include sequent systems for Ldm , Tstit and Xstit. All calculi presented possess essential structural properties such as contraction- and cut-admissibility. The labelled calculi G3Ldm and G3Tstit are shown sound and complete relative to irreflexive temporal frames. Additionally, we extend current results by showing that also Xstit can be characterized through relational frames, omitting the use of BT+AC frames.

The aim of this paper is to introduce and explain display calculi for a variety of logics. We provide a survey of key results concerning such calculi, though we focus mainly on the global cut elimination theorem. Propositional, first-order, and modal display calculi are considered and their properties detailed.

We formally introduce a novel, yet ubiquitous, category of norms: norms of instrumentality. Norms of this category describe which actions are obligatory, or prohibited, as instruments for certain purposes. We propose the Logic of Agency and Norms (LAN) that enables reasoning about actions, instrumentality, and normative principles in a multi-agent setting. Leveraging LAN , we formalize norms of instrumentality and compare them to two prevalent norm categories: norms to be and norms to do. Last, we pose principles relating the three (...) categories and evaluate their validity vis-à-vis notions of deliberative acting. On a technical note, the logic will be shown decidable via the finite model property. (shrink)

We introduce an effective translation from proofs in the display calculus to proofs in the labelled calculus in the context of tense logics. We identify the labelled calculus proofs in the image of this translation as those built from labelled sequents whose underlying directed graph possesses certain properties. For the basic normal tense logic Kt, the image is shown to be the set of all proofs in the labelled calculus G3Kt.

The purpose of this paper is to review and discuss Luciano Floridi’s 2019 book The Logic of Information: A Theory of Philosophy as Conceptual Design, the latest instalment in his philosophy of information (PI) tetralogy, particularly with respect to its implications for library and information studies (LIS) .

STIT logic is a prominent framework for the analysis of multi-agent choice-making. In the available deontic extensions of STIT, the principle of Ought-implies-Can (OiC) fulfills a central role. However, in the philosophical literature a variety of alternative OiC interpretations have been proposed and discussed. This paper provides a modular framework for deontic STIT that accounts for a multitude of OiC readings. In particular, we discuss, compare, and formalize ten such readings. We provide sound and complete sequent-style calculi for all of (...) the various STIT logics accommodating these OiC principles. We formally analyze the resulting logics and discuss how the different OiC principles are logically related. In particular, we propose an endorsement principle describing which OiC readings logically commit one to other OiC readings. (shrink)

Standard Type Theory, STT, tells us that b^n(a^m) is well-formed iff n=m+1. However, Linnebo and Rayo have advocated the use of Cumulative Type Theory, CTT, has more relaxed type-restrictions: according to CTT, b^β(a^α) is well-formed iff β > α. In this paper, we set ourselves against CTT. We begin our case by arguing against Linnebo and Rayo’s claim that CTT sheds new philosophical light on set theory. We then argue that, while CTT ’s type-restrictions are unjustifiable, the type-restrictions imposed by (...) STT are justified by a Fregean semantics. What is more, this Fregean semantics provides us with a principled way to resist Linnebo and Rayo’s Semantic Argument for CTT. We end by examining an alternative approach to cumulative types due to Florio and Jones; we argue that their theory is best seen as a misleadingly formulated version of STT. (shrink)

Tim Button explores the relationship between words and world; between semantics and scepticism. -/- A certain kind of philosopher – the external realist – worries that appearances might be radically deceptive. For example, she allows that we might all be brains in vats, stimulated by an infernal machine. But anyone who entertains the possibility of radical deception must also entertain a further worry: that all of our thoughts are totally contentless. That worry is just incoherent. -/- We cannot, then, be (...) external realists, who worry about the possibility of radical deception. Equally, however, we cannot be internal realists, who reject all possibility of deception. We must position ourselves somewhere between internal realism and external realism, but we cannot hope to say exactly where. We must be realists, for what that is worth, and realists within limits. -/- In establishing these claims, The Limits of Realism critically explores and develops several themes from Hilary Putnam’s work: the model-theoretic arguments; the connection between truth and justification; the brain-in-vat argument; semantic externalism; and conceptual relativity. The book establishes the continued significance of these topics for all philosophers interested in mind, logic, language, or the possibility of metaphysics. (shrink)

No-futurists ('growing block theorists') hold that that the past and the present are real, but that the future is not. The present moment is therefore privileged: it is the last moment of time. Craig Bourne (2002) and David Braddon-Mitchell (2004) have argued that this position is unmotivated, since the privilege of presentness comes apart from the indexicality of 'this moment'. I respond that no-futurists should treat 'x is real-as-of y' as a nonsymmetric relation. Then different moments are real-as-of different times. (...) This reunites privilege with indexicality, but entails that no-futurists must believe in ineliminably tensed facts. (shrink)

By definition, pain is a sensory and emotional experience that is felt in a particular part of the body. The precise relationship between somatic events at the site where pain is experienced, and central processing giving rise to the mental experience of pain remains the subject of debate, but there is little disagreement in scholarly circles that both aspects of pain are critical to its experience. Recent experimental work, however, suggests a public view that is at odds with this conceptualisation. (...) By demonstrating that the public does not necessarily endorse central tenets of the “mental” view of pain (subjectivity, privacy, and incorrigibility), experimental philosophers have argued that the public holds a more “body-centric” view than most clinicians and scholars. Such a discrepancy would have important implications for how the public interacts with pain science and clinical care. In response, we tested the hypothesis that the public is capable of a more “mind-centric” view of pain. Using a series of vignettes, we demonstrate that in situations which highlight mental aspects of pain the public can, and does, recognize pain as a mental phenomenon. We also demonstrate that the public view is subject to context effects, by showing that the public’s view is modified when situations emphasizing mental and somatic aspects of pain are presented together. (shrink)

Keränen (2001) raises an argument against realistic (ante rem) structuralism: where a mathematical structure has a non-trivial automorphism, distinct indiscernible positions within the structure cannot be shown to be non-identical using only the properties and relations of that structure. Ladyman (2005) responds by allowing our identity criterion to include 'irreflexive two-place relations'. I note that this does not solve the problem for structures with indistinguishable positions, i.e. positions that have all the same properties as each other and exactly the same (...) relations to all objects (including themselves). I conclude that realistic structuralists must compromise and treat some structures eliminativistically. (shrink)

In “Models and Reality” (1980), Putnam sketched a version of his internal realism as it might arise in the philosophy of mathematics. Here, I will develop that sketch. By combining Putnam’s model-theoretic arguments with Dummett’s reflections on Gödelian incompleteness, we arrive at (what I call) the Skolem-Gödel Antinomy. In brief: our mathematical concepts are perfectly precise; however, these perfectly precise mathematical concepts are manifested and acquired via a formal theory, which is understood in terms of a computable system of proof, (...) and hence is incomplete. Whilst this might initially seem strange, I show how internal categoricity results for arithmetic and set theory allow us to face up to this Antinomy. This also allows us to understand why “Models are not lost noumenal waifs looking for someone to name them,” but “constructions within our theory itself,” with “names from birth.”. (shrink)

Consider a variant of the usual story about the iterative conception of sets. As usual, at every stage, you find all the (bland) sets of objects which you found earlier. But you also find the result of tapping any earlier-found object with any magic wand (from a given stock of magic wands). -/- By varying the number and behaviour of the wands, we can flesh out this idea in many different ways. This paper's main Theorem is that any loosely constructive (...) way of fleshing out this idea is synonymous with a ZF-like theory. -/- This Theorem has rich applications; it realizes John Conway's (1976) Mathematicians' Liberation Movement; and it connects with a lovely idea due to Alonzo Church (1974). (shrink)

In the first Critique, Kant attempts to prove what we can call the "Principle of Intensive Magnitudes," according to which every possible object of experience will possess a determinate "degree" of reality. Curiously, Kant argues for this principle by inferring from a psychological premise about internal sensations (they have intensive magnitudes) to a metaphysical thesis about external objects (they also have intensive magnitudes). Most commentators dismiss the argument as a failure. In this article I give a reconstruction of Kant's argument (...) that attempts to rehabilitate the argument back into his broader transcendental theory of experience. I argue that we can make sense of the argument's central inference by appeal to Kant's theory of empirical intuition and by an analysis of the way in which Kant thinks sensory matter constitutes our most basic representations of objects. (shrink)

Craig Callender [2022] provides a novel challenge to the non-arbitrariness principle. His challenge plays an important role in his argument for the rational permissibility of a non-exponential temporal discounting rate. But the challenge is also of wider interest: it raises significant questions about whether we ought to accept the non-arbitrariness principle as a constraint on rational preferences. In this paper, I present two reasons to resist Callender’s challenge. First, I present a reason to reject his claim that the non-arbitrariness principle (...) only targets pure time preferences. Second, I criticize the inference Callender draws from a modest claim to a much stronger claim. The modest claim is that it can be hard to reveal the contents of an agent’s preferences. The stronger claim is that this provides us with a reason to reject a certain kind of normative constraint on rational preferences. I argue that the modest claim doesn’t motivate the stronger claim. The upshot of my two arguments is good news for those sympathetic to the non-arbitrariness principle: Callender’s challenge can be overcome, at least as it currently stands. (shrink)

objects are standardly taken to be causally inert, but this claim is rarely explicitly argued for. In the context of his platonism about musical works, in order for musical works to be audible, Julian Dodd argues that abstracta are causally efficacious in virtue of their concrete tokens participating in events. I attempt to provide a principled argument for the causal inertness of abstracta by first rejecting Dodd’s arguments from events, and then extending and generalizing the causal exclusion argument to the (...) abstract/concrete distinction. For reasons of parsimony, if concrete tokens or instantiations of abstract objects account for all causal work, then there is no reason to attribute causal efficacy to abstracta, and thus reason to maintain their causal inertness. I then consider how one of the main arguments against causal exclusion, namely Stephen Yablo’s notion of “proportionality”, could be modified to support the causal efficacy of abstracta. I argue that from a few simple premises Yablo’s account in fact supports their causal inertness. Having a principled reason for the causal inertness of abstracta appears to entail that the musical platonist must admit that we never literally hear the musical work, but only its performances. I sketch a solution to this problem available to Dodd, so that the musical platonist can maintain that musical works are abstract objects and are causally inert while retaining their audibility. (shrink)

Epistemic defeat is standardly understood in either evidentialist or responsibilist terms. The seminal treatment of defeat is an evidentialist one, due to John Pollock, who famously distinguishes between undercutting and rebutting defeaters. More recently, an orthogonal distinction due to Jennifer Lackey has become widely endorsed, between so-called doxastic (or psychological) and normative defeaters. We think that neither doxastic nor normative defeaters, as Lackey understands them, exist. Both of Lackey’s categories of defeat derive from implausible assumptions about epistemic responsibility. Although Pollock’s (...) evidentialist view is superior, the evidentialism per se can be purged from it, leaving a general structure of defeat that can be incorporated in a reliabilist theory that is neither evidentialist nor responsibilist in any way. (shrink)

The sensitivity condition on knowledge says that one knows that P only if one would not believe that P if P were false. Difficulties for this condition are now well documented. Keith DeRose has recently suggested a revised sensitivity condition that is designed to avoid some of these difficulties. We argue, however, that there are decisive objections to DeRose’s revised condition. Yet rather than simply abandoning his proposed condition, we uncover a rationale for its adoption, a rationale which suggests a (...) further revision that avoids our objections as well as others. The payoff is considerable: along the way to our revision, we learn lessons about the epistemic significance of certain explanatory relations, about how we ought to envisage epistemic closure principles, and about the epistemic significance of methods of belief formation. (shrink)

The following bare-bones story introduces the idea of a cumulative hierarchy of pure sets: 'Sets are arranged in stages. Every set is found at some stage. At any stage S: for any sets found before S, we find a set whose members are exactly those sets. We find nothing else at S.' Surprisingly, this story already guarantees that the sets are arranged in well-ordered levels, and suffices for quasi-categoricity. I show this by presenting Level Theory, a simplification of set theories (...) due to Scott, Montague, Derrick, and Potter. (shrink)

Tallant (2007) has challenged my recent defence of no-futurism (Button 2006), but he does not discuss the key to that defence: that no-futurism's primitive relation 'x is real-as-of y' is not symmetric. I therefore answer Tallant's challenge in the same way as I originally defended no-futurism. I also clarify no-futurism by rejecting a common mis-characterisation of the growing-block theorist. By supplying a semantics for no-futurists, I demonstrate that no-futurism faces no sceptical challenges. I conclude by considering the problem of how (...) to interpret the relation 'x is real-as-of y'. -/- (NB: A correction to this article appears in Analysis 68.1.). (shrink)

According to conventional wisdom, the split-brain syndrome puts paid to the thesis that consciousness is necessarily unified. The aim of this paper is to challenge that view. I argue both that disunity models of the split-brain are highly problematic, and that there is much to recommend a model of the split-brain—the switch model—according to which split-brain patients retain a fully unified consciousness at all times. Although the task of examining the unity of consciousness through the lens of the split-brain syndrome (...) is not a new one—such projects date back to Nagel’s seminal paper on the topic—the time is ripe for a re-evaluation of the issues. (shrink)

Putnam famously attempted to use model theory to draw metaphysical conclusions. His Skolemisation argument sought to show metaphysical realists that their favourite theories have countable models. His permutation argument sought to show that they have permuted models. His constructivisation argument sought to show that any empirical evidence is compatible with the Axiom of Constructibility. Here, I examine the metamathematics of all three model-theoretic arguments, and I argue against Bays (2001, 2007) that Putnam is largely immune to metamathematical challenges.

We argue that S is in a position to know that p iff S can know that p. Thus, what makes position-to-know-ascriptions true is just a special case of what makes ability-ascriptions true: compossibility. The novelty of our compossibility theory of epistemic modality lies in its subsuming epistemic modality under agentive modality, the modality characterizing what agents can do.

Minimalists, such as Paul Horwich, claim that the notions of truth, reference and satisfaction are exhausted by some very simple schemes. Unfortunately, there are subtle difficulties with treating these as schemes, in the ordinary sense. So instead, minimalists regard them as illustrating one-place functions, into which we can input propositions (when considering truth) or propositional constituents (when considering reference and satisfaction). However, Bertrand Russell's Gray's Elegy argument teaches us some important lessons about propositions and propositional constituents. When applied to minimalism, (...) these lessons show us why we should abandon it. (shrink)

Suppose we can save either a larger group of persons or a distinct, smaller group from some harm. Many people think that, all else equal, we ought to save the greater number. This article defends this view (with qualifications). But unlike earlier theories, it does not rely on the idea that several people's interests or claims receive greater aggregate weight. The argument starts from the idea that due to their stakes, the affected people have claims to have a say in (...) the rescue decision. As rescuers, our primary duty is to respect these procedural claims, which we must do by doing what these people would decide, in a process where each is given an equal vote on the matter. So in cases where each votes in their own self-interest, respect for their equal right to decide, or their autonomy, will lead us to save the greater number. The argument is explained in detail, with special attention to the questions of how, exactly, it avoids aggregation, and of why majority rule is superior to lottery procedures. The view has further advantages. Especially, it explains the “partial” relevance of numbers in cases involving unequal harms, and it does so in a way that dissolves the appearance of paradox that besets theories of “partial aggregation.”. (shrink)

Many philosophers are impressed by the progress achieved by physical sciences. This has had an especially deep effect on their ontological views: it has made many of them physicalists. Physicalists believe that everything is physical: more precisely, that all entities, properties, relations, and facts are those which are studied by physics or other physical sciences. They may not all agree with the spirit of Rutherford's quoted remark that 'there is physics; and there is stamp-collecting',' but they all grant physical science (...) a unique ontological authority: the authority to tell us what there is. Physicalism is now almost orthodox in much philosophy, notably in much recent philosophy of mind. But although often invoked, it is rarely explicitly defined. It should be. The claim that everything is physical is not as clear as it seems. In this paper, we examine a number of proposed definitions of physicalism and reasons for being a physicalist. We will argue both that physicalism lacks a clear and credible definition, and that in no non-vacuous interpretation is it true. We are concerned here only with physicalism as a doctrine about the empirical world. In particular, it should not be confused with nominalism, the doctrine that there are no universals.2 Nominalism and physicalism are quite independent doctrines. Believers in universals may as consistently assert as deny that the only properties and relations are those studied by physical science. And nominalists may with equal consistency assert or deny that physical science could provide enough predicates to describe the world. That is the question which concerns physicalists, not whether physical predicates name real universals. (We will for brevity write as if they do, but we do not need that assumption.). (shrink)

Friedrich Hayek’s defense of neoliberal free market capitalism hinges on the distinction between economies and catallaxies. The former are orders instituted via planning, whereas the latter are spontaneous competitive orders resulting from human action without human design. I argue that this distinction is based on an incomplete semantic history of “economy.” By looking at the meaning of “oikonomia” in medieval providential theology as explained by Giorgio Agamben and Joseph Vogl, I argue how Hayek’s science of catallactics is itself a secularization (...) of providential theology. This exposes Hayek to three criticisms: he unjustifiably neglects the possibility of tendencies toward spontaneous disorder in free markets, he condemns the “losers” of neoliberal competition to being providential waste on the road to general prosperity, and he imposes on people the duty to consent to a neoliberal order that hinders them from cultivating their inoperativity. (shrink)

Some have claimed that people with very different beliefs literally see the world differently. Thus Thomas Kuhn: ‘what a man sees depends both upon what he looks at and also upon what his previous visual—conceptual experience has taught him to see’ (Kuhn 1970, p. ll3). This view — call it ‘Perceptual Relativism’ — entails that a scientist and a child may look at a cathode ray tube and, in a sense, the first will see it while the second won’t. The (...) claim is not, of course, that the child’s experience is ‘empty’; but that, unlike the scientist, it does not see the tube as a cathode ray tube. One way of supporting this claim is to say that one cannot see something as an F unless one has the concept F. Since the child plainly lacks the concept of a cathode ray tube, it cannot see it as a cathode ray tube. Although Perceptual Relativism is hard to believe, this supporting suggestion is not so implausible. After all, when we see (and more generally, perceive) the world, the world is presented to us in a particular way; so how can we see it as being that way unless we have some idea or conception of the way it is presented? We need not be committed to a representative theory of perception to think that perceptions in some sense represent the world. We can express this by saying that perceptions have content. Now it is a commonplace that the contents of beliefs and the other propositional attitudes involve concepts. The belief that this thing is a cathode ray tube involves, in some sense, the concept cathode ray tube. So the line of thought behind Perceptual Relativism may be expressed thus: seeing an F as an F is a state with content. (shrink)

Prior’s Tonk is a famously horrible connective. It is defined by its inference rules. My aim in this article is to compare Tonk with some hitherto unnoticed nasty connectives, which are defined in semantic terms. I first use many-valued truth-tables for classical sentential logic to define a nasty connective, Knot. I then argue that we should refuse to add Knot to our language. And I show that this reverses the standard dialectic surrounding Tonk, and yields a novel solution to the (...) problem of many-valued truth-tables for classical sentential logic. I close by outlining the technicalities surrounding nasty connectives on many-valued truth-tables. (shrink)

Recent work on hypercomputation has raised new objections against the Church–Turing Thesis. In this paper, I focus on the challenge posed by a particular kind of hypercomputer, namely, SAD computers. I first consider deterministic and probabilistic barriers to the physical possibility of SAD computation. These suggest several ways to defend a Physical version of the Church–Turing Thesis. I then argue against Hogarth's analogy between non-Turing computability and non-Euclidean geometry, showing that it is a non-sequitur. I conclude that the Effective version (...) of the Church–Turing Thesis is unaffected by SAD computation. (shrink)

This paper defends an interpretation of the representational function of sensation in Kant's theory of empirical cognition. Against those who argue that sensations are ?subjective representations? and hence can only represent the sensory state of the subject, I argue that Kant appeals to different notions of subjectivity, and that the subjectivity of sensations is consistent with sensations representing external, spatial objects. Against those who claim that sensations cannot be representational at all, because sensations are not cognitively sophisticated enough to possess (...) intentionality, I argue that Kant does not use the term ?Vorstellung? to refer to intentional mental states exclusively. Sensations do not possess their own intentionality, but they nevertheless perform a representational function in virtue of their role as the matter of empirical intuition. In empirical intuition, the sensory qualities given in sensation are combined with the representation of space to constitute the intuited appearance. The representational function of sensation consists in sensation being the medium out of which intuited appearances are constituted: the qualities of sensations stand in for what the understanding will judge (conceptualize) as material substance. (shrink)

Phenomenalist interpretations of Kant are out of fashion. The most common complaint from anti-phenomenalist critics is that a phenomenalist reading of Kant would collapse Kantian idealism into Berkeleyan idealism. This would be unacceptable because Berkeleyan idealism is incompatible with core elements of Kant’s empirical realism. In this paper, I argue that not all phenomenalist readings threaten empirical realism. First, I distinguish several variants of phenomenalism, and then show that Berkeley’s idealism is characterized by his commitment to most of them. I (...) then make the case that two forms of phenomenalism are consistent with Kant’s empirical realism. The comparison between Kant and Berkeley runs throughout the paper, with special emphasis on the significance of their theories of intentionality. (shrink)

Elements of Mind (EM) has two themes, one major and one minor. The major theme is intentionality, the mind’s direction upon its objects; the other is the mind–body problem. I treat these themes separately: chapters 1, and 3–5 are concerned with intentionality, while chapter 2 is about the mind–body problem. In this summary I will first describe my view of the mind–body problem, and then describe the book’s main theme. Like many philosophers, I see the mind–body problem as containing two (...) sub–problems: the problem of mental causation and the problem of consciousness. I see these problems forming the two horns of a dilemma. Just as the problem of mental causation pushes us towards physicalism, so the problem of consciousness pushes us away from it. Each problem reveals the inadequacy of the solution to the other. Essentially the problem of mental causation is the conflict between (i) the apparent fact that mental states and events have effects in the physical world and (ii) a general principle about the causal nature of the physical world, which is sometimes called the ‘causal closure’ or the ‘causal completeness’ of the physical world. This principle says that all physical effects have physical causes which are enough to bring them about. The problem then is simple: how can a mental cause have a physical effect if that effect also has a physical cause which is enough to bring it about? Barring massive overdetermination of our actions by independent causes, it seems that the best answer is to identify the mental and the physical causes. And this is traditionally how physicalists have argued for their identity theory of mind and body. However, many physicalists reject the identity theory, and therefore they have to solve the mental causation problem in some other way. At present, there is no consensus among physicalists on which of the currently proposed solutions is correct. In chapter 2 of EM I propose an alternative, which I call ‘emergentism’. Inspired by the rejection of the identity theory, Emergentism is the idea that mental properties are genu.. (shrink)

Franz Brentano’s attempt to distinguish mental from physical phenomena by employing the scholastic concept of intentional inexistence is often cited as reintroducing the concept of intentionality into mainstream philosophical discussion. But Brentano’s own claims about intentional inexistence are much misunderstood. In the second half of the 20th century, analytical philosophers in particular have misread Brentano’s views in misleading ways.1 It is important to correct these misunderstandings if we are to come to a proper assessment of Brentano’s worth as a philosopher (...) and his position in the history of philosophy. Good corrections have been made in the recent analytic literature by David Bell (1990), Dermot Moran (1996), and Barry Smith (1994) among others. But there is also another, more purely philosophical lesson to be learned from the proper understanding of Brentano’s views on this matter. This is that Brentano’s struggles with the concept of intentionality reveal a fundamental division between different ways of thinking about intentionality, an division which Brentano himself does not make fully clear. Making the nature of this division explicit is the aim of this paper. (shrink)

‘It is of the very nature of consciousness to be intentional’ said Jean-Paul Sartre, ‘and a consciousness that ceases to be a consciousness of something would ipso facto cease to exist’.1 Sartre here endorses the central doctrine of Husserl’s phenomenology, itself inspired by a famous idea of Brentano’s: that intentionality, the mind’s ‘direction upon its objects’, is what is distinctive of mental phenomena. Brentano’s originality does not lie in pointing out the existence of intentionality, or in inventing the terminology, which (...) derives from scholastic discussions of concepts or intentiones.2 Rather, his originality consists in his claim that the concept of intentionality marks out the subject matter of psychology: the mental. His view was that intentionality ‘is characteristic exclusively of mental phenomena. No physical phenomenon manifests anything like it’.3 This is Brentano’s thesis that intentionality is the mark of the mental. Despite the centrality of the concept of intentionality in contemporary philosophy of mind, and despite the customary homage paid to Brentano as the one who revived the terminology and placed the concept at the centre of philosophy, Brentano’s thesis is widely rejected by contemporary philosophers of mind. What is more, its rejection is not something which is thought to require substantial philosophical argument. Rather, the falsity of the thesis is taken as a starting-point in many contemporary discussions of intentionality, something so obvious that it only needs to be stated to be recognised as true. Consider, for instance, these remarks from the opening pages of Searle’s Intentionality: Some, not all, mental states and events have Intentionality. Beliefs, fears, hopes and desires are Intentional; but there are forms of nervousness, elation and undirected anxiety that are not Intentional.... My beliefs and desires must always be about something. But my nervousness and undirected anxiety need not in that way be about anything.4 Searle takes this as obvious, so obvious that it is not in need of further argument or elucidation. (shrink)

Equity-linked securities with a guaranteed return become popular in a volatile market environment. This paper presents a new model for valuing guaranteed equity-linked notes. We consider a security whose value depends on the performance of a basket of equities averaged over certain points in time, but that is floored by a guaranteed amount. We show that the security’s price is given by the sum of the guaranteed amount plus the price of an Asian style option on the basket above. The (...) model provides analytical formulas for the security’s price as well as for corresponding hedge ratios; these respective formulas appear to be accurate over a wide range of underlying security parameter values, based on numerical testing against a Monte Carlo benchmark, Finally, we apply our method to value a type of segregated fund with a maturity guarantee. (shrink)

A widespread intuition is that words, musical works, and flags are intentionally produced and that they’re abstract types that can have incorrect tokens. But some philosophers, notably Julian Dodd and Nicholas Wolterstorff, think intention-dependence isn’t necessary; tokens just need to have certain relevant intrinsic features to be tokens of a given type. I show how there’s an unappreciated puzzle that arises from these two views: if tokens aren’t intention-dependent and types can admit of correct and incorrect tokens, then some driftwood (...) that washes up and forms what seems like the word ‘cat’ may simultaneously be a misspelling of ‘act’ and innumerable other misspelt words. I consider various ways Dodd and Wolterstorff can respond to this counterintuitive result and argue that biting the bullet, as well as nearby views, are implausible. Thus, they need to give up one of the two commitments, and I argue that requiring the intention-dependence of tokens, rather than the mere possession of certain intrinsic properties, is the best option. (shrink)

Newcomers to the philosophy of mind are sometimes resistant to the idea that pain is a mental state. If asked to defend their view, they might say something like this: pain is a physical state, it is a state of the body. A pain in one’s leg feels to be in the leg, not ‘in the mind’. After all, sometimes people distinguish pain which is ‘all in the mind’ from a genuine pain, sometimes because the second is ‘physical’ while the (...) first is not. And we also occasionally distinguish mental pain (which is normally understood as some kind of emotional distress) from the ‘physical pain’ one feels in one’s body. So what can be meant by saying that pain is a mental state? Of course, it only takes a little reflection shows that this naive view is mistaken. Pain is a state of consciousness, or an event in consciousness, and whether or not all states of mind are conscious, it is indisputable that only minds, or states of mind, are conscious.2 But does the naive view tell us anything about the concept of pain, or the concept of mind? I think it does. In this paper, I shall give reasons for thinking that consciousness is a form of intentionality, the mind’s ‘direction upon its objects’. I shall claim that the consciousness involved in bodily sensations like pain is constituted by the mind’s direction upon the part or region of the body where the sensation feels to be. Given this, it is less surprising that the naive view of pain says what it does: the apparent ‘physicality’ of pain is a consequence of confusing the object of the intentional state—the part of the body in which the pain is felt—with the state of being in pain. (shrink)

Although delusions are typically regarded as beliefs of a certain kind, there have been worries about the doxastic conception of delusions since at least Bleuler’s time. ‘Anti-doxasticists,’ as we might call them, do not merely worry about the claim that delusions are beliefs, they reject it. Reimer’s paper weighs into the debate between ‘doxasticists’ and ‘anti-doxasticists’ by suggesting that one of the main arguments given against the doxastic conception of delusions—what we might call the functional role objection—is based on a (...) fallacy. She also draws attention to certain parallels between delusions and what she calls “nihilistic philosophical doctrines,” such as the skeptical position that we have no .. (shrink)