This article is very different from other philosophy articles: it really is a manifesto addressed to Chinese philosophers. On the whole, Western thought has been exceedingly intellectualistic and rationalistic, and in this article I outline some of the ways in which those deep one-sided tendencies need to be corrected or rebalanced. However, I also claim that the Chinese are in the best position to correct and rebalance philosophy as a discipline. Chinese thought has never gone to the extremes of Western (...) rationalism, and there is every reason to think that as China gains in power and prestige throughout the world, Chinese philosophers and thinkers will be in a position to correct or reset Western philosophy by drawing on their own deepest historical traditions, traditions which have recognized the value of emotion and sane ordinary living much more than has been typical in the West. You Chinese should realize that you have much to offer the West and not be too modest with your self-image or reticent with your philosophical ambitions. (shrink)

This article investigates Michael Slote’s call for rebalancing Western moral philosophy by using Chinese philosophy, especially Confucianism, as a form of moral sentimentalism. I agree with the need for a correction of the over reliance on reason in Western moral philosophy, but I reject the rational/sentimental dichotomy and focus on the importance of the will. I make use of the important contribution made by Daoism and the conduct concept of wu-wei 無為. I explain the use of wu-wei in Daoist texts (...) as a nominative to denote a type of conduct, as a verb in moral imperatives, and as an aspiration for human moral behavior. I consider how appropriating this concept into Western moral thought offers significant solutions to three seemingly intractable problems: weakness of will, universalization of moral duties, and the conception of life as plagued by moral dilemmas. I conclude that wu-wei is not the result of some experience of alternative consciousness. It is an alternative consciousness that is shown in behavior, but not able to be said in language. (shrink)

Necessitists about set theory think that the pure sets exists, and are the way they are, as a matter of necessity. They cannot explain why the sets (de rebus) are all the sets. This constitutes the Ur-Objection against necessitism; it is the primary motivation cited by potentialists about set theory. -/- At least three families of potentialism draw motivation from the Ur-Objection. Contingentists think that any things could form a set even if they actually did not. Prioritists think that sets (...) hyperintensionally depend upon their members. Structural-potentialists think that any possible set-hierarchy could be extended. However, once we have disentangled these three versions of potentialism, we see that the Ur-Objection should not motivate anyone. (shrink)

Philosophy and model theory frequently meet one another. Philosophy and Model Theory aims to understand their interactions -/- Model theory is used in every ‘theoretical’ branch of analytic philosophy: in philosophy of mathematics, in philosophy of science, in philosophy of language, in philosophical logic, and in metaphysics. But these wide-ranging appeals to model theory have created a highly fragmented literature. On the one hand, many philosophically significant mathematical results are found only in mathematics textbooks: these are aimed squarely at mathematicians; (...) they typically presuppose that the reader has a significant background in mathematics; and little clue is given as to their philosophical significance. On the other hand, the philosophical applications of these results are then scattered across disconnected pockets of papers, separated by decades or more. -/- The first aim of Philosophy and Model Theory, then, is to consider the philosophical uses of model theory. On a technical level, we try to show how philosophically significant results connect to one another, and also to state the best version of a result for philosophical purposes. On a philosophical level, we show how similar dialectical situations arise repeatedly, across fragmented debates in varied philosophical areas. -/- The second aim of Philosophy and Model Theory, though, is to consider the philosophy of model theory. Model theory itself is rarely taken as the subject matter of philosophising (contrast this, say, with the philosophy of biology, or the philosophy of set theory). But model theory is a beautiful part of pure mathematics, and worthy of philosophical study in its own right. (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)

A judgement analysis of people's social inferences of attitudes and ability was conducted. University students were asked to infer the liberalness ( N = 60; Study 1) or intelligence ( N = 40; Study 2) of targets seen in pictures. Multiple regression analyses revealed that attractiveness was the most important cue for predicting inferences of liberalness, while an ethnic cue (i.e., being Asian) was the most important cue for judgements about intelligence. Results also showed that a single-cue model was less (...) susceptible to overfitting, but significantly less accurate than a multiple-cue model in predicting participant's intelligence judgements. Although the multiple regression models suffered a degree of overfitting, cross validation showed that they continued to have significant predictive value when applied to new data. Furthermore, a “random partner” method (comparing each participant's own regression equation with that of another, randomly selected, participant) provided evidence of significant idiosyncratic variation in the way intelligence judgements were made. (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)

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)

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)

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’.

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)

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)

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.

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.

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 “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)

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)

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)

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)

: Studies of Chinese dialectical materialism have long neglected the important philosophical dimension of Hegelian thought and its influence on Chinese Marxism. This essay examines the work of Zhang Shiying of Beijing University, whose studies of Hegel's works on dialectical logic in the 1950s sought to clarify the nature of Hegel's speculative dialectic and its relation to dialectical materialism. Like Lenin before him, Zhang believed that Hegel's works on logic offered a more profound reflection on materialism than had previously been (...) recognized by Marxist critics of German idealism. Zhang's sensitive reading of both Hegel's Science of Logic and the Encyclopedia Logic highlights the problem of the speculative dialectic and negativity. Examined here is Zhang's analysis of the Hegelian dialectic in light of contemporary accounts of the role of Hegelian negativity in poststructuralist thought. (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.

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.

This book provides a sustained and penetrating critique of a wide range of views in modern cognitive science and philosophy of the mind, from Turing's famous test for intelligence in machines to recent work in computational linguistic theory. While discussing many of the key arguments and topics, the authors also develop a distinctive analytic approach. Drawing on the methods of conceptual analysis first elaborated by Wittgenstein and Ryle, the authors seek to show that these methods still have a great deal (...) to offer in the field of the cognitive theory and the philosophy of mind, providing a powerful alternative to many of the positions put forward in the contemporary literature. Amoung the many issues discussed in the book are the following: the Cartesian roots of modern conceptions of mind; Searle's 'Chinese Room' thought experiment; Fodor's 'language of thought' hypothesis; the place of 'folk psychology' in cognitivist thought; and the question of whether any machine may be said to 'think' or 'understand' in the ordinary senses of these words. Wide ranging, up-to-date and forcefully argued, this book represents a major intervention in contemporary debates about the status of cognitive science an the nature of mind. It will be of particular interest to students and scholars in philosophy, psychology, linguistics and computing sciences. (shrink)

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)

Early reactions to the publication of Harold Garfinkel's Studies in Ethnomethodology, which have persisted over the passing decades, was that ethnomethodology could not address what sociology deemed to be socially significant matters such as 'power' and 'the state'. This, however, is not the case. How such matters enter into the practical everyday affairs of members is of equal interest to ethnomethodology when compared to how any matter enters into members' everyday life, and how they display that. It just does not (...) have more importance. Egon Bittner spelt this out with regard to Weber's interest in bureaucracy when he reminds sociology that when Weber talked about efficiency he was not referring to an objective standard but as something that is attuned to practical interests as they emerge in the context of everyday life. This paper examines some of the actions and interactions that were encountered in a Governmental Department in one of the European countries. It makes visible how characterisations of bureaucracy such as 'rational', and 'efficient' are achieved in the actions and interactions of Department employees, and some of the practices involved in that achievement. Garfinkel, and ethnomethodology in general, are not, in principle, to be found wanting where matters of overarching, primordial interest to sociology are concerned. (shrink)

We agree that conceptualisation is key in understanding the brain basis of emotion. We argue that by conflating facial emotion recognition with subjective emotion experience, Lindquist et al. understate the importance of biological predisposition in emotion. We use examples from the anxiety disorders to illustrate the distinction between these two phenomena, emphasising the importance of both emotional hardware and contextual learning.

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)

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)

Over the past several decades, scholars of liberal and democratic theory have shown a heightened interest in the role that various virtues might play in promoting the good/free society. Yet within this recent "return" to the virtues, one quality that has been almost entirely left out of the discussion is humility. In this essay, I critically address this lacuna and offer a defense of a particular form of humility, what I call democratic humility. After considering a range of moral and (...) political objections to the concept of humility, Iprovide an account that seeks to address some of these long-standing difficulties while arguing that the idea of humility, recuperated as an ethos of civic attentiveness, may be one of the most important virtues for late-modern societies marked by ethical and cultural pluralism. (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.

In 1919 the Animal Breeding Research Department was established in Edinburgh. This Department, later renamed the Institute of Animal Genetics, forged an international reputation, eventually becoming the centrepiece of a cluster of new genetics research units and institutions in Edinburgh after the Second World War. Yet despite its significance for institutionalising animal genetics research in the UK, the origins and development of the Department have not received as much scholarly attention as its importance warrants. This paper sheds new light on (...) Edinburgh’s place in early British genetics by drawing upon recently catalogued archival sources including the papers of James Cossar Ewart, Regius Professor of Natural History at the University of Edinburgh between 1882 and 1927. Although presently a marginal figure in genetics historiography, Ewart established two sites for experimental animal breeding work between 1895 and 1911 and played a central role in the founding of Britain’s first genetics lectureship, also in 1911. These early efforts helped to secure government funding in 1913. However, a combination of the First World War, bureaucratic problems and Ewart’s personal ambitions delayed the creation of the Department and the appointment of its director by another six years. This paper charts the institutionalisation of animal breeding and genetics research in Edinburgh within the wider contexts of British genetics and agriculture in the early twentieth century. (shrink)

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)

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)

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)

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)

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)