We prove that the set of properties describable by a uniform sequence of first-order sentences using at most k + 1 distinct variables is exactly equal to the set of properties checkable by a Turing machine in DSPACE[n k ] (where n is the size of the universe). This set is also equal to the set of properties describable using an iterative definition for a finite set of relations of arity k. This is a refinement of the theorem PSPACE = (...) VAR[O[1]] [8]. We suggest some directions for exploiting this result to derive trade-offs between the number of variables and the quantifier depth in descriptive complexity. (shrink)

In 1960, E. P. Wigner, a joint winner of the 1963 Nobel Prize for Physics, published a paper titled On the Unreasonable Effectiveness of Mathematics in the Natural Sciences [61]. This paper can be construed as an examination and affirmation of Galileo's tenet that “The book of nature is written in the language of mathematics”. To this effect, Wigner presented a large number of examples that demonstrate the effectiveness of mathematics in accurately describing physical phenomena. Wigner viewed these examples as (...) illustrations of what he called the empirical law of epistemology, which asserts that the mathematical formulation of the laws of nature is both appropriate and accurate, and that mathematics is actually the correct language for formulating the laws of nature. At the same time, Wigner pointed out that the reasons for the success of mathematics in the natural sciences are not completely understood; in fact, he went as far as asserting that “… the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation for it.”. (shrink)

This book challenges the view that bad beliefs - beliefs that blatantly conflict with easily available evidence - can largely be explained by widespread irrationality, instead arguing that ordinary people are rational agents whose beliefs are the result of their rational response to the evidence they're presented with.

What is posthumanism and why does it matter? This book offers an introduction to the ways in which humanism's belief in the natural supremacy of the Family of Man has been called into question at different moments and from different theoretical positions. What is the relationship between posthumanism and technology? Can posthumanism have a politics—postcolonial or feminist? Are postmodernism and poststructuralism posthumanist? What happens when critical theory meets Hollywood cinema? What links posthumanism to science fiction. Posthumanism addresses these and other (...) questions in an attempt to come to terms with one of the most pressing issues facing contemporary society. (shrink)

The Taming of the True poses a broad challenge to realist views of meaning and truth that have been prominent in recent philosophy. Neil Tennant argues compellingly that every truth is knowable, and that an effective logical system can be based on this principle. He lays the foundations for global semantic anti-realism and extends its consequences from the philosophy of mathematics and logic to the theory of meaning, metaphysics, and epistemology.

McKenna’s critique (rather than criticisms) of idealized approaches to epistemology is an important contribution to the literature. In this brief discussion, I set out his main concerns about more idealized approaches, within and beyond social epistemology, before turning to some issues I think he neglects. I suggest that it’s important to pay attention to the prestige hierarchy in philosophy, and to how that hierarchy can serve ideological purposes. The greater prestige of more abstract approaches plays a role in determining what (...) issues and what voices we attend to. (shrink)

How may we characterize the intrinsic structure of physical quantities such as mass, length, or electric charge? This article shows that group-theoretic methods—specifically, the notion of a free and transitive group action—provide an elegant way of characterizing the structure of scalar quantities, and uses this to give an intrinsic treatment of vector quantities. It also gives a general account of how different scalar or vector quantities may be algebraically combined with one another. Finally, it uses this apparatus to give a (...) simple intrinsic treatment of Newtonian gravitation. (shrink)

Informed consent is a central topic in contemporary biomedical ethics. Yet attempts to set defensible and feasible standards for consenting have led to persistent difficulties. In Rethinking Informed Consent in Bioethics Neil Manson and Onora O'Neill set debates about informed consent in medicine and research in a fresh light. They show why informed consent cannot be fully specific or fully explicit, and why more specific consent is not always ethically better. They argue that consent needs distinctive communicative transactions, by (...) which other obligations, prohibitions, and rights can be waived or set aside in controlled and specific ways. Their book offers a coherent, wide-ranging and practical account of the role of consent in biomedicine which will be valuable to readers working in a range of areas in bioethics, medicine and law. (shrink)

Most philosophers think that phenomenal consciousness underlies, or at any rate makes a large contribution, to moral considerability. This paper argues that many such accounts invoke question-begging arguments. Moreover, they’re unable to explain apparent differences in moral status across and within different species. In the light of these problems, I argue that we ought to take very seriously a view according to which moral considerability is grounded in functional properties. Phenomenal consciousness may be sufficient for having a moral value, but (...) it may not be necessary, and it may contribute relatively little to our overall considerability. (shrink)

Because harm is an important notion in ethics, it’s worth investigating what it amounts to. The counterfactual comparative account of harm, commonly thought to be the most promising account of harm, analyzes harm by comparing what actually happened with what would have happened in some counterfactual situation. But it faces the preemption problem, a problem so serious that it has driven some to suggest we abandon the counterfactual comparative account and maybe even abandon the notion of harm altogether. This paper (...) defends a version of the counterfactual comparative account that solves the preemption problem, a version called the “worse than nothing account.” It says that you harm someone just in case you leave them worse off than if you’d done nothing at all. (shrink)

The two of us commonly know a proposition just in case (i) we both know it, (ii) we both know that we both know it, (iii) we both know that we both know that we both know it, and so on. In a recent paper titled ‘Uncommon Knowledge’, Harvey Lederman (2018) argues against the possibility of common knowledge. His argument rests on the empirical claim that there are minor individual variations in how we perceive things. This motivates a principle about (...) perception: when two people are perceiving something and it perceptually appears a certain way to one of them, then for all that person knows, it perceptually appears a slightly different way to the other. In this paper, I challenge Lederman’s perceptual principle and thereby his argument. In particular, I argue that there are some circumstances in which things perceptually appear a certain way to me and nonetheless I know that they don’t perceptually appear in a slightly different way to you. Indeed, I argue that not only are there exceptions to the perceptual principle, but they are widespread. (shrink)

Parents play a critical role in their child’s personal development and day-to-day experiences. However, as digital technologies are increasingly embedded in most New Zealand children’s everyday life activities parents face the task of ensuring their child’s online safety. To do so, they need to understand the way their child engages with and through these tools and make sense of the rapidly changing, and more technically complex, nature of digital devices. This presents a digital parenting dilemma: maximising children’s online opportunities while (...) minimising online risks and potential harm. This factsheet presents evidence about digital parenting in New Zealand based on nationally representative data collected from parents, caregivers and whānau and their children aged 9-17. It uses measures from the Global Kids Online project to explore the prevalence of different practices used by New Zealand parents to influence or mediate children’s internet use. (shrink)

Multiverse Views in set theory advocate the claim that there are many universes of sets, no-one of which is canonical, and have risen to prominence over the last few years. One motivating factor is that such positions are often argued to account very elegantly for technical practice. While there is much discussion of the technical aspects of these views, in this paper I analyse a radical form of Multiversism on largely philosophical grounds. Of particular importance will be an account of (...) reference on the Multiversist conception, and the relativism that it implies. I argue that analysis of this central issue in the Philosophy of Mathematics indicates that Radical Multiversism must be algebraic, and cannot be viewed as an attempt to provide an account of reference without a softening of the position. (shrink)

A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often forcing constructions that add subsets to models are cited as evidence in favour of the latter. This paper informs this debate by analysing ways the Universist might interpret this discourse that seems (...) to necessitate the addition of subsets to V. We argue that despite the prima facie incoherence of such talk for the Universist, she nonetheless has reason to try and provide interpretation of this discourse. We analyse extant interpretations of such talk, and analyse various tradeoffs in naturality that might be made. We conclude that the Universist has promising options for interpreting different forcing constructions. (shrink)

An account of how a rational agent should revise beliefs in the light of new evidence.

Nietzsche takes moral judgments to be false beliefs, and encourages us to pursue subjective nonmoral value arising from our passions. His view that strong and unified passions make one virtuous is mathematically derivable from this subjectivism and a conceptual analysis of virtue, explaining his evaluations of character and the nature of the Overman.

The independence phenomenon in set theory, while pervasive, can be partially addressed through the use of large cardinal axioms. A commonly assumed idea is that large cardinal axioms are species of maximality principles. In this paper I question this claim. I show that there is a kind of maximality (namely absoluteness) on which large cardinal axioms come out as restrictive relative to a formal notion of restrictiveness. Within this framework, I argue that large cardinal axioms can still play many of (...) their usual foundational roles. (shrink)

Often philosophers, logicians, and mathematicians employ a notion of intended structure when talking about a branch of mathematics. In addition, we know that there are foundational mathematical theories that can find representatives for the objects of informal mathematics. In this paper, we examine how faithfully foundational theories can represent intended structures, and show that this question is closely linked to the decidability of the theory of the intended structure. We argue that this sheds light on the trade-off between expressive power (...) and meta-theoretic properties when comparing first-order and second-order logic. (shrink)

Essays devoted to the work of the late Neil Wilson, Canadian philosopher and contributor to the field of semantic analysis that emerged from the fusion of logic, pragmatism, and ontology. Many of the essays in this volume take their initial inspiration from Wilson's seminal work Substances Without Substrata.

We explain and explore class-theoretic potentialism—the view that one can always individuate more classes over a set-theoretic universe. We examine some motivations for class-theoretic potentialism, before proving some results concerning the relevant potentialist systems (in particular exhibiting failures of the $\mathsf {.2}$ and $\mathsf {.3}$ axioms). We then discuss the significance of these results for the different kinds of class-theoretic potentialists.

In the contemporary philosophy of set theory, discussion of new axioms that purport to resolve independence necessitates an explanation of how they come to be justified. Ordinarily, justification is divided into two broad kinds: intrinsic justification relates to how `intuitively plausible' an axiom is, whereas extrinsic justification supports an axiom by identifying certain `desirable' consequences. This paper puts pressure on how this distinction is formulated and construed. In particular, we argue that the distinction as often presented is neither well-demarcated nor (...) sufficiently precise. Instead, we suggest that the process of justification in set theory should not be thought of as neatly divisible in this way, but should rather be understood as a conceptually indivisible notion linked to the goal of explanation. (shrink)

This essay discusses the moral costs and benefits of sexual technology. It starts with first-wave sexual technology, such as dating apps, messaging apps, and social networks, and then discusses second-wave sexual technology, which offers users more immersive experiences, such as virtual reality and sex robots. The paper argues that, overall, such technologies provide more benefits than they incur costs. Finally, the paper discusses the rise of a new identity—digisexuality, explaining that digisexuals are people who consider sexual technology an essential part (...) of who they are, and who might forego relationships with other people. The paper argues that the development of this new identity is a good thing, and that reasons against it are not convincing. (shrink)

Zero provides a challenge for philosophers of mathematics with realist inclinations. On the one hand it is a bona fide cardinal number, yet on the other it is linked to ideas of nothingness and non-being. This paper provides an analysis of the epistemology and metaphysics of zero. We develop several constraints and then argue that a satisfactory account of zero can be obtained by integrating an account of numbers as properties of collections, work on the philosophy of absences, and recent (...) work in numerical cognition and ontogenetic studies. (shrink)

This factsheet presents findings from a quantitative study looking at adults’ experiences of sending and sharing potentially harmful digital communications in New Zealand. Typically research into harmful digital communications focuses on the experiences of those on the receiving end – the victims. However, to better address the distress and harm caused, information is needed about the people sending and sharing potentially harmful messages and posts. In this study we asked adult New Zealanders whether they had sent potentially harmful digital communications (...) in the previous year and if so, how often they had done this, who they were sent to, the channel(s) they used, and the reason for doing this. (shrink)

This paper assessed whether belief in conspiracy theories was associated with a particularly cognitive style (worldview). The sample comprised 223 volunteers recruited via convenience sampling and included undergraduates, postgraduates, university employees and alumni. Respondents completed measures assessing a range of cognitive-perceptual factors (schizotypy, delusional ideation and hallucination proneness) and conspiratorial beliefs (general attitudes towards conspiracist thinking and endorsement of individual conspiracies). Positive symptoms of schizotypy, particularly the cognitive-perceptual factor, correlated positively with conspiracist beliefs. The best predictor of belief in conspiracies (...) was delusional ideation. Consistent with the notion of a coherent conspiratorial mindset, scores across conspiracy measures correlated strongly. Whilst findings supported the view that belief in conspiracies, within the sub-clinical population, was associated with a delusional thinking style, cognitive-perceptual factors in combination accounted for only 32% of the variance. (shrink)

Neil E. Williams develops a systematic metaphysics centred on the idea of powers, as a rival to neo-Humeanism, the dominant systematic metaphysics in philosophy today. Williams takes powers to be inherently causal properties and uses them as the foundation of his explanations of causation, persistence, laws, and modality.

Suppose that one thinks that certain symmetries of a theory reveal “surplus structure”. What would a formalism without that surplus structure look like? The conventional answer is that it would be a reduced theory: a theory which traffics only in structures invariant under the relevant symmetry. In this paper, I argue that there is a neglected alternative: one can work with a sophisticated version of the theory, in which the symmetries act as isomorphisms.

This book discusses theories of legal reasoning and provides an overall view of the rhetoric of legal justification. It shows how and why lawyers arguments can be rationally persuasive even though rarely, if ever, logically conclusive or compelling. It examines the role of "legal syllogism" and universality of legal reasoning, looking at arguments of consequentialism and principle, and concludes by questioning the infallibility of judges as lawmakers.