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)

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)

This article surveys recent literature by Parsons, McGee, Shapiro and others on the significance of categoricity arguments in the philosophy of mathematics. After discussing whether categoricity arguments are sufficient to secure reference to mathematical structures up to isomorphism, we assess what exactly is achieved by recent ‘internal’ renditions of the famous categoricity arguments for arithmetic and set theory.

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)

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)

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)

In "What the Nose Doesn't Know", I argue that there are no olfactory illusions. Central to the traditional notions of illusion and hallucination is a notion of object-failure—the failure of an experience to represent particular objects. Because there are no presented objects in the case of olfactory experience, I argue that the traditional ways of categorizing non-veridical experience do not apply to the olfactory case. In their place, I propose a novel notion of non-veridical experience for the olfactory case. In (...) his (2011), Stevenson responds to my claim that there are no olfactory illusions. Although he agrees that it is natural—or at least commonplace—to think there are no olfactory illusions, he argues that there are and provides examples of them, many of which he suggests have analogues in the visual and auditory domains. In this paper, I examine the nature of the disagreement between us. I argue that Stevenson fails to argue against my conclusion that there are no olfactory illusions. (shrink)

Much of the philosophical work on perception has focused on vision. Recently, however, philosophers have begun to correct this ‘tunnel vision’ by considering other modalities. Nevertheless, relatively little has been written about the chemical senses—olfaction and gustation. The focus of this paper is olfaction. In this paper, I consider the question: does human olfactory experience represents objects as thus and so? If we take visual experience as the paradigm of how experience can achieve object representation, we might think that the (...) answer to this question is no. I argue that olfactory experience does indeed represent objects—just not in a way that is easily read from the dominant visual case. (shrink)

Universals are putative objects like wisdom, morality, redness, etc. Although we believe in properties (which, we argue, are not a kind of object), we do not believe in universals. However, a number of ordinary, natural language constructions seem to commit us to their existence. In this paper, we provide a fictionalist theory of universals, which allows us to speak as if universals existed, whilst denying that any really do.

We can learn much about perceptual experience by thinking about how it can mislead us. In this paper, I explore whether, and how, olfactory experience can mislead. I argue that, in the case of olfactory experience, the traditional distinction between illusion and hallucination does not apply. Integral to the traditional distinction is a notion of ‘object-failure’—the failure of an experience to present objects accurately. I argue that there are no such presented objects in olfactory experience. As a result, olfactory experience (...) can only mislead by means of a kind of property hallucination. The implications of my arguments are twofold. First, we see that accounts of representational content cannot always be based on the visual model. And, secondly, we see that we must recast the notion of nonveridicality, allowing for a notion of non-veridical experience that is disengaged from any particular object. (shrink)

Amie Thomasson and Eli Hirsch have both attempted to deflate metaphysics, by combining Carnapian ideas with an appeal to ordinary language. My main aim in this paper is to critique such deflationary appeals to ordinary language. Focussing on Thomasson, I draw two very general conclusions. First: ordinary language is a wildly complicated phenomenon. Its implicit ontological commitments can only be tackled by invoking a context principle; but this will mean that ordinary language ontology is not a trivial enterprise. Second: ordinary (...) language often points in different directions simultaneously, so that a wide variety of existence questions cannot be deflated merely by appealing to ordinary language. (shrink)

This book questions what sovereignty looks like when it is de-ontologised; when the nothingness at the heart of claims to sovereignty is unmasked and laid bare. Drawing on critical thinkers in political theology, such as Schmitt, Agamben, Nancy, Blanchot, Paulhan, The Politics of Nothing asks what happens to the political when considered in the frame of the productive potential of the nothing? The answers are framed in terms of the deep intellectual histories at our disposal for considering these fundamental questions, (...) carving out trajectories inspired by, for example, Peter Lombard, Shakespeare and Spinoza. This book offers a series of sensitive and creative reflections that suggest the possibilities offered by thinking through sovereignty via the frame of nihilism. This book was originally published as a special issue of Culture, Theory and Critique. (shrink)

Much of the philosophical work on perception has focused on vision. Recently, however, philosophers have begun to correct this ‘tunnel vision’ by considering other modalities. Nevertheless, relatively little has been written about the chemical senses—olfaction and gustation. The focus of this paper is olfaction. In light of new physiological and psychophysical research on olfaction, I consider whether olfactory experience is object-based. In particular, I explore the claim that “odor objects” constitute sensory individuals. It isn’t obvious—at least at the outset—whether they (...) meet the widely accepted principles of object individuation and recognition at work in the visual and auditory cases. Among the general issues I consider, then, is whether these traditional principles form necessary, or simply sufficient, conditions on object perception. As we see, at the very least, considering the object-recognition model of olfaction challenges us to look more closely at well-entrenched models of object perception. But the payoff of doing so is high. We not only learn something about a modality that philosophers have historically neglected; by asking new questions and challenging old assumptions, we also further our understanding of perception in general. (shrink)

Hilary Putnam’s BIV argument first occurred to him when ‘thinking about a theorem in modern logic, the “Skolem–Löwenheim Theorem”’ (Putnam 1981: 7). One of my aims in this paper is to explore the connection between the argument and the Theorem. But I also want to draw some further connections. In particular, I think that Putnam’s BIV argument provides us with an impressively versatile template for dealing with sceptical challenges. Indeed, this template allows us to unify some of Putnam’s most enduring (...) contributions to the realism/antirealism debate: his discussions of brains-in-vats, of Skolem’s Paradox, and of permutations. In all three cases, we have an argument which does not merely defeat the sceptic; it also shows us that we must reject some prima facie plausible philosophical picture. (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)

There are several relations which may fall short of genuine identity, but which behave like identity in important respects. Such grades of discrimination have recently been the subject of much philosophical and technical discussion. This paper aims to complete their technical investigation. Grades of indiscernibility are defined in terms of satisfaction of certain first-order formulas. Grades of symmetry are defined in terms of symmetries on a structure. Both of these families of grades of discrimination have been studied in some detail. (...) However, this paper also introduces grades of relativity, defined in terms of relativeness correspondences. This paper explores the relationships between all the grades of discrimination, exhaustively answering several natural questions that have so far received only partial answers. It also establishes which grades can be captured in terms of satisfaction of object-language formulas and draws connections with definability theory. (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)

I introduce a perceptual phenomenon so far overlooked in the philosophical literature: ‘visual evanescence’. ‘Evanescent’ objects are those that due to their structured visible appearances have a tendency to vanish or evanesce from sight at certain places and for certain ‘biologically apt’ perceivers. Paradigmatically evanescent objects are those associated with certain forms of animal camouflage. I show that reflection on visual evanescence helps create conceptual room for a treatment of looks statements not explicit in the contemporary literature, one which takes (...) its cue from the relatively neglected philosophy of perception of G.E.M. Anscombe. In sensory contexts in which evanescence is known to have occurred, the use of ‘looks invisible’ seems to be intelligible, a fact that sensationalist and objectivist treatments of the nature of looks, as I call them, cannot obviously accommodate - at least, as I explain, when coupled with what Cora Diamond (1981) describes as a ‘natural’ understanding of nonsense. Focusing on a number of imaginative scenarios in which the statement ‘looks invisible’ is permissible, I oppose these ontological treatments with the grammatical approach I draw from Anscombe and in doing so I uncover a degree of unity across the cases I consider: something can intelligibly be said to ‘look invisible’ if one can see or appears to see the entirety of the region that the ‘invisible’ thing occupies. The region ‘looks empty’ but is full. (shrink)

Tennenbaum's Theorem yields an elegant characterisation of the standard model of arithmetic. Several authors have recently claimed that this result has important philosophical consequences: in particular, it offers us a way of responding to model-theoretic worries about how we manage to grasp the standard model. We disagree. If there ever was such a problem about how we come to grasp the standard model, then Tennenbaum's Theorem does not help. We show this by examining a parallel argument, from a simpler model-theoretic (...) result. (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 this paper, I explore a noted empirical link between regret and insomnia. Drawing on Brian O’Shaughnessy analysis of wakeful consciousness, I sketch three candidate ways of excavating a conceptual connection. Regret involves a certain kind of temporal orientation that, for O’Shaughnessy, only the state of wakefulness makes possible. Regret involves mental activity – it is productive of and precipitates patterns of counterfactual thought and imagining. Further, picking up a cue from Bernard Williams’ celebrated conception of agent-regret in ‘Moral Luck’, (...) sometimes the mental activity that occurs in regret is affective and expressive – as I argue, it is expressive of the wish that things were otherwise were satisfied now. Finally, I take up the puzzle as to why occurrent regret is not merely incompatible with sleep – insofar as it necessitates wakefulness - but may preclude falling asleep and I offer a tentative solution, focusing on the self-conscious character of occurrent regret. (shrink)

It is a metaphysical orthodoxy that interesting non-symmetric relations cannot be reduced to symmetric ones. This orthodoxy is wrong. I show this by exploring the expressive power of symmetric theories, i.e. theories which use only symmetric predicates. Such theories are powerful enough to raise the possibility of Pythagrapheanism, i.e. the possibility that the world is just a vast, unlabelled, undirected graph.

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)

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)

Can we quantify over everything: absolutely, positively, definitely, totally, every thing? Some philosophers have claimed that we must be able to do so, since the doctrine that we cannot is self-stultifying. But this treats restrictivism as a positive doctrine. Restrictivism is much better viewed as a kind of militant quietism, which I call dadaism. Dadaists advance a hostile challenge, with the aim of silencing everyone who holds a positive position about ‘absolute generality’.

On a very natural conception of sets, every set has an absolute complement. The ordinary cumulative hierarchy dismisses this idea outright. But we can rectify this, whilst retaining classical logic. Indeed, we can develop a boolean algebra of sets arranged in well-ordered levels. I show this by presenting Boolean Level Theory, which fuses ordinary Level Theory (from Part 1) with ideas due to Thomas Forster, Alonzo Church, and Urs Oswald. BLT neatly implement Conway’s games and surreal numbers; and a natural (...) extension of BLT is definitionally equivalent with ZF. (shrink)

Potentialists think that the concept of set is importantly modal. Using tensed language as an heuristic, the following bar-bones story introduces the idea of a potential hierarchy of sets: 'Always: for any sets that existed, there is a set whose members are exactly those sets; there are no other sets.' Surprisingly, this story already guarantees well-foundedness and persistence. Moreover, if we assume that time is linear, the ensuing modal set theory is almost definitionally equivalent with non-modal set theories; specifically, with (...) Level Theory, as developed in Part 1. (shrink)

Hilary Putnam once suggested that “the actual existence of sets as ‘intangible objects’ suffers… from a generalization of a problem first pointed out by Paul Benacerraf… are sets a kind of function or are functions a sort of set?” Sadly, he did not elaborate; my aim, here, is to do so on his behalf. There are well-known methods for treating sets as functions and functions as sets. But these do not raise any obvious philosophical or foundational puzzles. For that, we (...) first need to provide a full-fledged function theory. I supply such a theory: it axiomatizes the iterative notion of function in exactly the same sense that ZF axiomatizes the iterative notion of set. Indeed, this function theory is synonymous with ZF. It might seem that set theory and function theory present us with rival foundations for mathematics, since they postulate different ontologies. But appearances are deceptive. Set theory and function theory provide the very same judicial foundation for mathematics. They do not supply rival metaphysical foundations; indeed, if they supply metaphysical foundations at all, then they supply the very same metaphysical foundations. (shrink)

Anscombe’s published writings, lectures and notes on sensation point toward a sophisticated critique of sense-data, representationalist and direct realist theories of perception (in both their historical and contemporary forms), and a novel analysis of the concept of sensation. Her philosophy of perception begins with the traditional question, ‘What are the objects of sensation?’, but the response is a grammatical rather than ontological enquiry. What, she asks, are the characteristics of the grammatical object of sensation verbs? Anscombe’s answer is: sensation verbs (...) take ‘intentional objects’, where an ‘intentional object’ is a description which has the characteristics of the concept of intention—characteristics elucidated in great detail in her Intention. This simple manoeuvre allows Anscombe to reject two opposing positions in the philosophy of perception - that the objects of sensation are sense-data and that the objects of sensation are tables and chairs (etc). Both views, she argues, fail to recognise the grammatical fact that the verbs of sensation take intentional objects. This chapter outlines the case for a grammatical methodology in philosophy of perception, by framing an analysis of the ways in which the sense-data and direct-realist theories of perception arise out of the theoretical demands that are generated when the grammar of the concept of sensation is left unexplored. Along the way, it will be shown that Anscombe’s philosophy of perception should not be read as fore-running contemporary representationalism, and that reading it as such in fact runs counter not only to the letter but the spirit of Ancombe’s proposal. (shrink)

We argue against the halving response to Sleeping Beauty. First, we outline an appealing constraint on probability assignments: the Principle of Irrelevant Information. Roughly, this says: if you don’t know whether C, but you would assign probability p to X regardless of whether C or not-C, then you should assign p to X. This Principle is deeply plausible, but we show that it contradicts halving. Second, we show that halving either violates solid statistical reasoning or draws absurd distinctions.

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.

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)

Health institutions recommend that young infants be exclusively breastfed on demand, and it is widely held that parents who can breastfeed have an obligation to do so. This has been challenged in recent philosophical work, especially by Fiona Woollard. Woollard’s work critically engages with two distinct views of parental obligation that might ground such an obligation—based on maximal benefit and avoidance of significant harm—to reject an obligation to breastfeed. While agreeing with Woollard’s substantive conclusion, this paper (drawing on philosophical discussion (...) of the ‘right to rear’) argues that there are several more moderate views of parental obligation which might also be thought to ground parental obligation. We first show that an obligation to breastfeed might result not from a general obligation to maximally benefit one’s child, but from what we call ‘choice-specific’ obligations to maximise benefit within particular activities. We then develop this idea through two views of parental obligation—the Dual Interest view, and the Best Custodian view—to ground an obligation to exclusively breastfeed on demand, before showing how both these more moderate views fail. Finally, we argue that not only is there no general obligation to breastfeed children, but that it is often morally right not to do so. Since much advice from health institutions on this issue implies that exclusive breastfeeding on demand is the best option for all families, our argument drives the feeding debate forward by showing that this advice often misrepresents parents’ moral obligations in potentially harmful ways. (shrink)

I offer a reading of Murdoch's conception of concrete universality as it appears in 'The Idea of Perfection', the first essay in the Sovereignty of Good. I show that it has British Idealist overtones that are inflected by Wittgenstein, a thought I try to illuminate by drawing an analogy with Wittgenstein's discussion of the metre stick in Paris in Philosophical Investigations §50. In the last part of the paper, I appeal to the work of Murdoch's erstwhile tutor Donald MacKinnon to (...) respond to an objection to my strategy, which I draw from Murdoch's later work, Metaphysics as a Guide to Morals. (shrink)

This article is about the manifestations of similarities between two seemingly distinct groups of Nigerians: cybercriminals and politicians. Which linguistic strategies do Twitter users use to express their opinions on cybercriminals and politicians? The study undertakes a qualitative analysis of ‘engaged’ tweets of an elite law enforcement agency in West Africa. We analyzed and coded over 100,000 ‘engaged’ tweets based on a component of mechanisms of moral disengagement (i.e., advantageous comparison), a linguistic device. The results reveal how respondents defend the (...) actions of online fraudsters (“the deviant group”) by strategically comparing them to the wrongful acts of corrupt politicians (“the respectable group”). Similarly, the results show how respondents positioned this linguistic strategy to compare “the powerless group” (online fraudsters) and “the powerful group” (politicians) in society. Indeed, tweet responses suggest that the Economic and Financial Crimes Commission (EFCC) generally looks downwards for culprits (i.e., online fraudsters) while ignoring fraudulent politicians. We conclude that the process by which some actions are interpreted as a crime compared to others is a moral enterprise. (shrink)

In 1907–8, Russell and Stout presented an objection against James and Schiller, to which both James and Schiller replied. In this paper, I shall revisit their transatlantic exchange. Doing so will yield a better understanding of Schiller’s relationship to a worryingly solipsistic brand of phenomenalism. It will also allow us to appreciate a crucial difference between Schiller and James; a difference which James explicitly downplayed.

Wittgenstein’s atomist picture, as embodied in his Tractatus, is initially very appealing. However, it faces the famous colour-exclusion problem. In this paper, I shall explain when the atomist picture can be defended in the face of that problem; and, in the light of this, why the atomist picture should be rejected. I outline the atomist picture in Section 1. In Section 2, I present a very simple necessary and sufficient condition for the tenability of the atomist picture. The condition is: (...) logical space is a power of two. In Sections 3 and 4, I outline the colour-exclusion problem, and then show how the cardinality-condition supplies a response to exclusion problems. In Section 5, I explain how this amounts to a distillation of a proposal due to Moss, which goes back to Carruthers. And in Section 6, I show how all this vindicates Wittgenstein’s ultimate rejection of the atomist picture. The brief reason is that we have no guarantee that there are any solutions to a given exclusion problem but, if there are any, then there are far too many. (shrink)

The United Nations Framework Convention on Climate Change principle of ‘common but differentiated responsibility’ admits many interpretations. In the philosophical literature on climate justice, it has typically been cashed out in terms of the following three principles: the ability to pay principle (APP), the beneficiary pays principle (BPP), and the contribution to problem principle (CPP). Many of these accounts have given prominence to the CPP and APP, but there are some who argue that the BPP deserves greater consideration. In this (...) paper, I want to ask whether the BPP must feature in any plausible account of remedial responsibility for climate change. I examine this question by looking at three different ways in which the BPP has been incorporated into accounts of climate burden-sharing. In each case, there are questions about the particular role that the BPP is assigned and it looks like either the BPP must be given equal prominence to the CPP, or the BPP might be redundant when it comes to specific task of remedying the injustices of climate change. I suggest in the conclusion one possible reason to maintain the BPP. (shrink)

In the early-to-mid 1930s, Wittgenstein investigated solipsism via the philosophy of language. In this paper, I want to reopen Wittgenstein's ‘grammatical’ examination of solipsism.Wittgenstein begins by considering the thesis that only I can feel my pains. Whilst this thesis may tempt us towards solipsism, Wittgenstein points out that this temptation rests on a grammatical confusion concerning the phrase ‘my pains’. In Section 1, I unpack and vindicate his thinking. After discussing ‘my pains’, Wittgenstein makes his now famous suggestion that the (...) word ‘I’ has two distinct uses: a subject-use and an object-use. The purpose of Wittgenstein's suggestion has, however, been widely misunderstood. I unpack it in Section 2, explaining how the subject-use connects with a phenomenological language, and so again tempts us into solipsism. In Sections 3–4, I consider various stages of Wittgenstein's engagement with this kind of solipsism, culminating in a rejection of solipsism via reflections on private languages. (shrink)

This paper develops my (BJPS 2009) criticisms of the philosophical significance of a certain sort of infinitary computational process, a hyperloop. I start by considering whether hyperloops suggest that "effectively computable" is vague (in some sense). I then consider and criticise two arguments by Hogarth, who maintains that hyperloops undermine the very idea of effective computability. I conclude that hyperloops, on their own, cannot threaten the notion of an effective procedure.

Whatever the attractions of Tolkein's world, irrealists about fictions do not believe literally that Bilbo Baggins is a hobbit. Instead, irrealists believe that, according to The Lord of the Rings {Bilbo is a hobbit}. But when irrealists want to say something like “I am taller than Bilbo”, there is nowhere good for them to insert the operator “according to The Lord of the Rings”. This is an instance of the operator problem. In this paper, I outline and criticise Sainsbury's (2006) (...) spotty scope approach to the operator problem. Sainsbury treats the problem as syntactic, but the problem is ultimately metaphysical. (shrink)

forall x: Calgary is a full-featured textbook on formal logic. It covers key notions of logic such as consequence and validity of arguments, the syntax of truth-functional propositional logic TFL and truth-table semantics, the syntax of first-order (predicate) logic FOL with identity (first-order interpretations), symbolizing English in TFL and FOL, and Fitch-style natural deduction proof systems for both TFL and FOL. It also deals with some advanced topics such as modal logic, soundness, and functional completeness. Exercises with solutions are available. (...) It is provided in PDF (for screen reading, printing, and a special version for dyslexics), HTML, and in LaTeX source code. (shrink)

I consider the first part of Marty’s Raum und Zeit, which treats of both the nature of space and spatial perception. I begin by sketching two charges that Marty raises against Kantian and Brentanian conceptions of space (and spatial perception) respectively, before detailing what I take to be a characteristically Martyan picture of space perception, though set against the backdrop of contemporary philosophy of perception. Marty has it that spatial relations are non-real but existent, causally inert relations that are grounded (...) in space, which is itself non-real but existent. Objects do not inhere in space in the way properties inhere in substances. Rather, there is a ‘non-real’ relation of ‘fulfillment’ (Erfüllung) that holds between objects and places in space, which itself subsists. I consider whether any contemporary philosophy of perception is equipped to make sense of Martyan space perception and I suggest that the most promising conception is Naïve Realism. I then outline a difficulty for this theoretical translation. Naïve Realism is a direct theory of perception whereby S is said to perceive O just in case S stands in a psychological relation of acquaintance with O, where this relation is both non-representational and explanatorily primitive. For Marty however, all relations are non-real and, insofar as they are grounded, are neither fundamental, nor brute or primitive in an explanatory sense. I close by detailing what I thereby take a distinctively Martyan form of Naïve Realism to involve. The central theoretical tenet that phenomenal character is fundamentally constituted by worldly objects is preserved; but the manifestly relational structure of the acquaintance relation, construed in particular as a relation of awareness, is treated as derivative. I make headway in spelling out the latter claim by bringing Marty into fleeting conversation with another Thomist - G.E.M. Anscombe. (shrink)

This paper involves constructive exegesis. I consider the contrast between morality and art as sketched in Philippa Foot's 1972 paper of the same name, ‘Morality and Art’. I then consider how her views might have shifted against the background of the conceptual landscape afforded by Natural Goodness, though the topic of the relation of art and morality is not explicitly explored in that work. The method is to set out some textual fragments from Natural Goodness that can be arranged for (...) a tentative Footian ‘aesthetics’. I bring them into conversation with some ideas from Iris Murdoch to elucidate what I think the import may be, for Foot, of depicting human form. (shrink)

Ethics, Policy & Environment, Volume 14, Issue 3, Page 345-359, October 2011.

It is frequently claimed that breeding animals that we know will have unavoidable health problems is at least prima facie wrong, because it harms the animals concerned. However, if we take ‘harm’ to mean ‘makes worse off’, this claim appears false. Breeding an animal that will have unavoidable health problems does not make any particular individual animal worse off, since an animal bred without such problems would be a different individual animal. Yet, the intuition that there is something ethically wrong (...) about breeding animals—such as purebred pedigree dogs—in ways that seem negatively to affect welfare remains powerful. In this paper, an animal version of what is sometimes called the non-identity problem is explored, along with a number of possible ways of understanding what might be wrong with such breeding practices, if it is not that they harm the animal itself. These possibilities include harms to others, placeholder arguments, non-comparative ideas of harm, an ‘impersonal’ approach, and concerns about human attitudes and dispositions. (shrink)