Work of Eagle, Farah, Goldbring, Kirchberg, and Vignati shows that the only separable C*‐algebras that admit quantifier elimination in continuous logic are,,, and the continuous functions on the Cantor set. We show that, among finite dimensional C*‐algebras, quantifier elimination does hold if the language is expanded to include two new predicate symbols: One for minimal projections, and one for pairs of unitarily conjugate elements. Both of these predicates are definable, but not quantifier‐free definable, in the usual language of C*‐algebras. (...) We also show that adding just the predicate for minimal projections is sufficient in the case of full matrix algebras, but that in general both new predicate symbols are required. (shrink)

Recently, many philosophers have been interested in using locative relations to clarify and pursue debates in the metaphysics of material objects. Most begin with the relation of exact location. But what if we begin instead with the relation known as weak location – the relation an object x bears to any region not completely bereft of x? I explore some of the consequences of pursuing this route for issues including coincidence, extended simples, and endurance, with an eye to evaluating the (...) prospects for taking weak location as our fundamental locative relation. (shrink)

Causation appears to present us with an interpretative difficulty. While arguably a redundant relation given fundamental physics, it is nevertheless apparently pragmatically indispensable. This chapter revisits certain arguments made previously by the author for these claims with the benefit of hindsight, starting with the role of causal models in the human sciences, and attempting to explain why it is not possible to straightforwardly ground such models in fundamental physics. This suggests that further constraints, going beyond physics, are needed to legitimate (...) such models. These supplementary constraints could be reified, but that would seem to conflict with the completeness of physics. A response is to emphasize the practical role of causal talk, and the author suggests that a fictionalist approach might be worth exploring. After clarifying fictionalism as a general approach, they carry out in some detail the project of clarifying what a fictionalist attitude to causation would involve. (shrink)

There will be a surprise party for Mark tonight. He loves surprise parties, because he loves the surprise—but he'll feel terrible if the surprise is spoiled, and not want to go. He has a reason to go to the party—the surprise—; but if he knew or even believed what that reason was, he would have a reason not to go. It looks like in this case there can be really good reasons for someone without the person being aware of what (...) those reasons are (and in this case, it wouldn't even be a reason to go anymore if he was aware of it). Now presumably this reason isn't motivating Mark to go to the party. But it is a fact that counts in favour of Mark's going to the party even without motivating him to do it. (shrink)

Metaphysics, having long since recovered the logical positivist/empiricist objections that were supposed to signal its death, is once again coming under sustained criticism, and from a similar direction. Once it was realised that speculative systematic metaphysics needn’t be abandoned in light of empiricist scruples, metaphysics flourished. But it’s become increasingly clear that, even if the logical empiricists didn’t exactly get their objections right, there is something worrying about the evidential basis for contemporary metaphysics. Not that metaphysicians are unaware of this. (...) There is lots of recent activity in metametaphysics, and much of this research is more or less connected to worries about whether we can have evidence in favour of a metaphysical hypothesis. Roughly: there are alternative views according to which metaphysical disputes variously.. (shrink)

This book consists thematically of three broad sections: a lengthy introduction in which Grünbaum critically assesses the hermeneutic construal of psychoanalysis, as represented in the work of Habermas, G. S. Klein, and Ricoeur; a critical examination of Popper's assessment of both psychoanalysis and inductivism; and a logical analysis of core psychoanalytic ideas that constitute the foundation for much of psychoanalytic theory. This last section is, in my view, the heart of the book and therefore, it is that section on which (...) I will focus in this review. (shrink)

The notion of multiple location plays an important role in the characterization of endurantism. Several authors have recently offered cases intended to demonstrate the incoherence of multiple location. I argue that these cases do not succeed in making multiple location problematic. Along the way, several crucial issues about multiple location and its use by endurantists are clarified.

I argue that any broadly dispositional analysis of probability will either fail to give an adequate explication of probability, or else will fail to provide an explication that can be gainfully employed elsewhere (for instance, in empirical science or in the regulation of credence). The diversity and number of arguments suggests that there is little prospect of any successful analysis along these lines.

Recently, Cody Gilmore has deployed an ingenious case involving backwards time travel to highlight an apparent conflict between the theory that objects persist by perduring, and the thesis that wholly coincident objects are impossible. However, careful attention to the concepts of location and parthood that Gilmore’s cases involve shows that the perdurantist faces no genuine objection from these cases, and that the perdurantist has a number of plausible and dialectically appropriate ways to avoid the supposed conflict.

This article discusses two arguments in favor of perdurance. The first is Sider’s argument from vagueness, “one of the most powerful” in favor of perdurantism. I make the observation that endurantists have principled grounds to claim that the argument is unsound, at least if endurance is formulated in locative rather than mereological terms. Having made this observation, I use it to emphasize a somewhat neglected difference between endurantists and perdurantists with respect to their views on material objects. These views, in (...) the case of endurantists, lead to a further, less than conclusive but nevertheless interesting argument against endurantism—the anti-fundamentality argument—which I discuss and tentatively endorse. That argument posits that endurantists must take location to be a fundamental relation, and that this has as a consequence the metaphysical possibility of some rather unwelcome scenarios. Perdurantists may avoid this consequence by denying that location is fundamental, perhaps by embracing supersubstantivalism. (shrink)

A previously unrecognised argument against deterministic chance is introduced. The argument rests on the twin ideas that determined outcomes are settled, while chancy outcomes are unsettled, thus making cases of determined but chancy outcomes impossible. Closer attention to tacit assumptions about settledness makes available some principled lines of resistance to the argument for compatibilists about chance and determinism. Yet the costs of maintaining compatibilism may be higher with respect to this argument than with respect to existing incompatibilist arguments.

This article explores the connection between objective chance and the randomness of a sequence of outcomes. Discussion is focussed around the claim that something happens by chance iff it is random. This claim is subject to many objections. Attempts to save it by providing alternative theories of chance and randomness, involving indeterminism, unpredictability, and reductionism about chance, are canvassed. The article is largely expository, with particular attention being paid to the details of algorithmic randomness, a topic relatively unfamiliar to philosophers.

We describe an infinitary logic for metric structures which is analogous to Lω1,ω. We show that this logic is capable of expressing several concepts from analysis that cannot be expressed in finitary continuous logic. Using topological methods, we prove an omitting types theorem for countable fragments of our infinitary logic. We use omitting types to prove a two-cardinal theorem, which yields a strengthening of a result of Ben Yaacov and Iovino concerning separable quotients of Banach spaces.

The special theory of relativity (STR) is widely supposed to be in tension with A-theories of time, those giving special significance to the present moment. A-theories are diverse in the features they regard as distinctive of the present, but all agree that there is an absolute fact of the matter about which events have the feature of presentness. Famously, the standard notion of simultaneity operationalised within the theory of relativity is not absolute. If A-theorists accept relativistic physics, they must either (...) refine their A-theory and sever joint presentness from simultaneity (‘conciliatory’ responses to the problem), or supplement standard relativity by adding further spacetime structure that grounds a relation of absolute simultaneity (‘supplementing’ responses). This chapter considers the prospects for such approaches, concluding that while there is no knock-down argument from relativity against the A-theory, attempts to marry the A-theory with STR are more trouble than they are worth. (shrink)

Early work on the frequency theory of probability made extensive use of the notion of randomness, conceived of as a property possessed by disorderly collections of outcomes. Growing out of this work, a rich mathematical literature on algorithmic randomness and Kolmogorov complexity developed through the twentieth century, but largely lost contact with the philosophical literature on physical probability. The present chapter begins with a clarification of the notions of randomness and probability, conceiving of the former as a property of a (...) sequence of outcomes, and the latter as a property of the process generating those outcomes. A discussion follows of the nature and limits of the relationship between the two notions, with largely negative verdicts on the prospects for any reduction of one to the other, although the existence of an apparently random sequence of outcomes is good evidence for the involvement of a genuinely chancy process. (shrink)

I sketch a new constraint on chance, which connects chance ascriptions closely with ascriptions of ability, and more specifically with 'CAN'-claims. This connection between chance and ability has some claim to be a platitude; moreover, it exposes the debate over deterministic chance to the extensive literature on (in)compatibilism about free will. The upshot is that a prima facie case for the tenability of deterministic chance can be made. But the main thrust of the paper is to draw attention to the (...) connection between the truth conditions of sentences involving 'CAN' and 'CHANCE', and argue for the context sensitivity of each term. Awareness of this context sensitivity has consequences for the evaluation of particular philosophical arguments for (in) compatibilism when they are presented in particular contexts. (shrink)

QUESTIONS Objects seem to have some properties in themselves (like shape), and some other properties that depend on other things around them (like being alone or accompanied). The distinction between primary and secondary qualities is a special case of this more general contrast: what, according to Locke, is the basis for the distinction? Is there more than one way to understand Locke’s argument: what is the best reading of Locke? What wider significance does the distinction between primary and secondary qualities (...) have? (shrink)

_Philosophy of Probability: Contemporary Readings_ is the first anthology to collect essential readings in this important area of philosophy. Featuring the work of leading philosophers in the field such as Carnap, Hájek, Jeffrey, Joyce, Lewis, Loewer, Popper, Ramsey, van Fraassen, von Mises, and many others, the book looks in depth at the following key topics: subjective probability and credence probability updating: conditionalization and reflection Bayesian confirmation theory classical, logical, and evidential probability frequentism physical probability: propensities and objective chances. The book (...) features a useful primer on the mathematics of probability, and each section includes an introduction by the editor, as well as a guide to further reading. A broad-ranging and highly accessible exploration of the subject, _Philosophy of Probability_ is ideal for any student of formal epistemology, philosophy of science, metaphysics, or philosophy of mathematics. (shrink)

The concept of randomness has been unjustly neglected in recent philosophical literature, and when philosophers have thought about it, they have usually acquiesced in views about the concept that are fundamentally flawed. After indicating the ways in which these accounts are flawed, I propose that randomness is to be understood as a special case of the epistemic concept of the unpredictability of a process. This proposal arguably captures the intuitive desiderata for the concept of randomness; at least it should suggest (...) that the commonly accepted accounts cannot be the whole story and more philosophical attention needs to be paid. 1. Randomness in science1.1Random systems1.2Random behaviour1.3Random sampling1.4Caprice, arbitrariness and noise2. Concepts of randomness2.1Von Mises/church/martin-löf randomness2.2KCS-randomness3. Randomness is unpredictability: preliminaries3.1Process and product randomness3.2Randomness is indeterminism?4. Predictability4.1Epistemic constraints on prediction4.2Computational constraints on prediction4.3Pragmatic constraints on prediction4.4Prediction defined5. Unpredictability6. Randomness is unpredictability6.1Clarification of the definition of randomness6.2Randomness and probability6.3Subjectivity and context sensitivity of randomness7. Evaluating the analysis[R]andomness … is going to be a concept which is relative to our body of knowledge, which will somehow reflect what we know and what we don't know. Henry E. Kyburg, Jr ([1974], p. 217)Phenomena that we cannot predict must be judged random. Patrick Suppes ([1984], p. 32). (shrink)

Early work on the frequency theory of probability made extensive use of the notion of randomness, conceived of as a property possessed by disorderly collections of outcomes. Growing out of this work, a rich mathematical literature on algorithmic randomness and Kolmogorov complexity developed through the twentieth century, but largely lost contact with the philosophical literature on physical probability. The present chapter begins with a clarification of the notions of randomness and probability, conceiving of the former as a property of a (...) sequence of outcomes, and the latter as a property of the process generating those outcomes. A discussion follows of the nature and limits of the relationship between the two notions, with largely negative verdicts on the prospects for any reduction of one to the other, although the existence of an apparently random sequence of outcomes is good evidence for the involvement of a genuinely chancy process. (shrink)

For Locke, an idea is ‘the immediate object of perception, thought, or understanding’ (§8).1 Perhaps this is something like a concept: he goes on to give examples of white, cold, and round, which look like they have some representational content. What do these ideas represent? Locke defines a quality: ‘the power to produce any idea in our mind, I call quality of the subject wherein that power is’ (§8). The natural thought is that these ideas represent some quality of the (...) object, which quality just is the power that the object has to produce that idea in us. Though the idea is in us, the power or quality is clearly in the object. Sometimes, it is true, we speak loosely and refer to the quality of the object by the same name that we use to refer to the idea in us, and talk of white being in the object, for example. Locke cautions that when we speak like this, we should ‘be understood to mean those qualities in the objects which produce them [the ideas] in us’ (§8). (shrink)

Morris N. Eagle explores the understanding and role of subjective experience in the disciplines of psychology, psychoanalysis, and philosophy of mind. Elaborating how different understandings of subjective experience give rise to very different theories of the nature of the mind, Eagle then explains how these shape clinical practices. In particular, Eagle addresses the strong tendency in the disciplines concerned with the nature of the mind to overlook the centrality of subjective experience in one's life, to view it (...) with suspicion, and to reduce it to neural processes. Describing examples of research in which subjective experience is a central variable, Eagle provides an outline of a model in which the dichotomy of conscious and unconscious is supplemented by subjective experience as a continuum. This book is essential reading for psychoanalysts, psychoanalytic psychotherapists, psychologists and anyone wishing to gain a deeper understanding of the importance of theories of the mind to therapeutic practice. (shrink)

We examine topological dynamical systems on the Cantor set from the point of view of the continuous model theory of commutative C*-algebras. After some general remarks, we focus our attention on the generic homeomorphism of the Cantor set, as constructed by Akin, Glasner, and Weiss. We show that this homeomorphism is the prime model of its theory. We also show that the notion of “generic” used by Akin, Glasner, and Weiss is distinct from the notion of “generic” encountered in Fraïssé (...) theory. (shrink)

A generic quantification, like dogs have tails, has a distinctive semantics; it is certainly not synonymous with the universal quantification all dogs have tails. A generic causal claim, like smoking causes cancer, is similarly not synonymous with all smoking causes cancer. Many philosophers of science have taken this difference in meaning to demand radical treatments of causal generics, invoking such exotica as causation between properties or causation at ‘different levels’. A more sober treatment is possible, making use of a..

Dispositional essentialists are typically committed to two claims: that properties are individuated by their causal role (‘causal structuralism’), and that natural necessity is to be explained by appeal to these causal roles (‘dispositional actualism’). I argue that these two claims cannot be simultaneously maintained; and that the correct response is to deny dispositional actualism. Causal structuralism remains an attractive position, but doesn’t in fact provide much support for dispositional essentialism.

true (but not conversely); if someone is lucky in truly believing \x{D835}\x{DC5D}, their belief is not knowledge; if someone truly believes that \x{D835}\x{DC5D}, but cannot justify their belief with evidence, it is not knowledge; and so on.

Consider also what I shall call the asymmetry of openness: the obscure contrast we draw between the ‘open future’ and the ‘fixed past.’ We tend to regard the future as a multitude of alternative possibilities, a ‘garden of forking paths’ in Borges’ phrase, whereas we regard the past as a unique, settled, immutable actuality. These descriptions scarcely wear their meaning on their sleeves, yet do seem to capture some genuine and important difference between past and future. What can it be?

We provide an overview of the development of product placements within traditional and newer electronic media, followed by a critique of current regulations where they exist and highlight the challenges this form of brand promotion presents to regulators. We note the weaknesses in current theoretical perspectives on the way product placements impact more than awareness and argue that a failure to recognise the increasingly diverse nature of product placement within entertainment media content means that awareness campaigns and warnings regarding the (...) presence of product placements are unlikely to be effective in countering any negative effects of the practice on vulnerable groups such as children and young adults. While we focus on the impact of product placement activity on children and young adults, using primarily the examples of alcohol and tobacco products, we also raise concerns regarding a failure to act on the presence of a number of harmful products that fall beyond the current list of restricted products even in countries where some form of specific regulation exists. In order to aid those considering the necessity for, or scope of, any future restrictions on this form of marketing communication, it is important to determine not only what is known, but what also needs to be determined about the impact of product placements across the range of existing and evolving communication channels. (shrink)

Gödel argued that intuition has an important role to play in mathematical epistemology, and despite the infamy of his own position, this opinion still has much to recommend it. Intuitions and folk platitudes play a central role in philosophical enquiry too, and have recently been elevated to a central position in one project for understanding philosophical methodology: the so-called ‘Canberra Plan’. This philosophical role for intuitions suggests an analogous epistemology for some fundamental parts of mathematics, which casts a number of (...) themes in recent philosophy of mathematics (concerning a priority and fictionalism, for example) in revealing new light. (shrink)

Russell famously argued that causation should be dispensed with. He gave two explicit arguments for this conclusion, both of which can be defused if we loosen the ties between causation and determinism. I show that we can define a concept of causation which meets Russell’s conditions but does not reduce to triviality. Unfortunately, a further serious problem is implicit beneath the details of Russell’s arguments, which I call the causal exclusion problem. Meeting this problem involves deploying a minimalist pragmatic account (...) of the nature and function of modal language. Russell’s scruples about causation can be accommodated, even as we partially legitimise the pervasive causal explanations in folk and scientific practice. (shrink)

Utterances within the context of telling fictional tales that appear to be assertions are nevertheless not to be taken at face value. The present paper attempts to explain exactly what such 'pseudo-assertions' are, and how they behave. Many pseudo-assertions can take on multiple roles, both within fictions and in what I call 'participatory criticism' of a fiction, especially when they occur discourse-initially. This fact, taken together with problems for replacement accounts of pseudo-assertion based on the implicit prefixing of an 'in (...) the fiction' operator, suggest that pseudo-assertion is best understood as a kind of make-believe. This proposal is elaborated and defended, and some applications to fictionalism are tentatively explored. (shrink)

and argue that (2) is similarly not true, but a convention: we use talk of pos• sibility to capture claims about consistency, or whatever. (This is merely an example; I don't suppose that (2) appeals to anyone particularly as a neces• sary truth about possibility or consistency.) Again, the kind of thing that is in..

Characteristic mental states including thinking about going on holiday, desiring to eat a peach, feeling sad, and believing that that Australia will win the world cup. Mental states are intentional (about other things) and we have privileged access to them.

In the Cratylus, Soc rates discusses with Cratylus and Hermogenes the question of whether names are merely arbitrary or in some sense ‘right,’ that is, motivated by the nature of the things they designate. In this article, I examine Heidegger’s controversial project of unearthing archē Greek terms in the specific light of the Cratylus and the tradition of “Cratylisms” which it has fostered. Having demonstrated the underlying Cratylist tendencies behind Heidegger’s conviction in the inherent ‘appropriateness’ of many Greek keywords, I (...) point out some of the problems posed by this closet Cratylism for Heidegger’s conception of primordial language as well as his critique of the correspondence theory of truth. (shrink)

By utilizing the topological concept of pseudocompactness, we simplify and improve a proof of Caicedo, Dueñez, and Iovino concerning Terence Tao's metastability. We also pinpoint the exact relationship between the Omitting Types Theorem and the Baire Category Theorem by developing a machine that turns topological spaces into abstract logics.

In this chapter, I’ll provide an introduction to the mathematics of probability theory.1 The philosophy of probability doesn’t require much mathematical sophistication, at least not to get a good grip on the main problems and views. Nothing in this chapter is particularly complicated, and even the mathematically shy should, with a little effort, find it easy to follow. I do assume familiarity with the basics of an elementary logic course, and some basic facility with the notion of a set.

Rather than entailing that a particular outcome will occur, many scientific theories only entail that an outcome will occur with a certain probability. Because scientific evidence inevitably falls short of conclusive proof, when choosing between different theories it is standard to make reference to how probable the various options are in light of the evidence. A full understanding of probability in science needs to address both the role of probabilities in theories, or chances, as well as the role of probabilistic (...) judgment in theory choice. In this chapter, the author introduces and distinguishes the two sorts of probability from one another and attempt to offer a satisfactory characterization of how the different uses for probability in science are to be understood. A closing section turns to the question of how views about the chance of some outcome should guide our confidence in that outcome. (shrink)