The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed description of higher-order logic, including a comprehensive discussion of its semantics. He goes on to demonstrate the prevalence of second-order concepts in mathematics and the extent to which mathematical ideas can be formulated in higher-order logic. He also shows how first-order languages are often insufficient to codify (...) many concepts in contemporary mathematics, and thus that both first- and higher-order logics are needed to fully reflect current work. Throughout, the emphasis is on discussing the associated philosophical and historical issues and the implications they have for foundational studies. For the most part, the author assumes little more than a familiarity with logic comparable to that provided in a beginning graduate course which includes the incompleteness of arithmetic and the Lowenheim-Skolem theorems. All those concerned with the foundations of mathematics will find this a thought-provoking discussion of some of the central issues in the field today. (shrink)

Enth.: Dugoald Stewart's account of Adam Smith / ed. by I.S. Ross.

Moving beyond both realist and anti-realist accounts of mathematics, Shapiro articulates a "structuralist" approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers that exist independent of each other, but rather is the natural structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle.

This paper defends the view that standards, which are typically social in nature, play a role in determining whether a subject has knowledge. While the argument focuses on standards that pertain to reasoning, I also consider whether there are similar standards for memory and perception.Ultimately, I argue that the standards are context sensitive and, as such, we must view attributions of knowledge as indexical. I exploit similarities between this view and a version of the relevant alternatives reply to skepticism in (...) order to defend this reply against the objection that it is ad hoc. (shrink)

This chapter provides broad coverage of the notion of logical consequence, exploring its modal, semantic, and epistemic aspects. It develops the contrast between proof-theoretic notion of consequence, in terms of deduction, and a model-theoretic approach, in terms of truth-conditions. The main purpose is to relate the formal, technical work in logic to the philosophical concepts that underlie reasoning.

Recent writing on the idea of a form of life has tended to be critical of the use made of this notion by writers such as Peter Winch, D. Z. Phillips and Norman Malcolm. Rightly or wrongly these writers have been regarded as meaning by ‘a form of life’, something like ‘a way or style of life’, and recent explicatory work on the notion has largely tended to discount this as a plausible interpretation of what Wittgenstein meant in his use (...) of the expression. The intention of this paper is not that of direct intervention in this particular dispute, though the conclusions drawn, if correct, would have some bearing on it. The intention is rather to develop, in order to make use of it, the idea of a form of life within the context of a number of philosophical difficulties. I should certainly claim to be drawing upon the remarks made by Wittgenstein in his own use of the expression: but I should not claim to be expounding Wittgenstein. Hence I do not wish to enter into the disputes referred to above about what precisely Wittgenstein meant by the expression, though again, what I say, if not wholly misguided, should have some bearing on these disputes. (shrink)

According to ante rem structuralism a branch of mathematics, such as arithmetic, is about a structure, or structures, that exist independent of the mathematician, and independent of any systems that exemplify the structure. A structure is a universal of sorts: structure is to exemplified system as property is to object. So ante rem structuralist is a form of ante rem realism concerning universals. Since the appearance of my Philosophy of mathematics: Structure and ontology, a number of criticisms of the idea (...) of ante rem structures have appeared. Some argue that it is impossible to give identity conditions for places in homogeneous ante rem structures, invoking a version of the identity of indiscernibles. Others raise issues concerning the identity and distinctness of places in different structures, such as the the natural number 2 and the real number 2. The purpose of this paper is to take the measure of these objections, and to further articulate ante rem structuralism to take them into account. (shrink)

ABSTRACTExperts use their superior skills and understanding to mediate between evidence in some domain and non-experts. But how should we understand the proper relationship between experts and non-experts? In this paper, I present two ways of conceiving experts’ mediating role from the perspective of non-experts: the Authority View and the Advisor View. Jennifer Lackey has criticized the Authority View and defended the Advisor View. I defend an account of epistemic authority that avoids her criticisms while arguing the Advisor View lacks (...) the advantages she claims. Ultimately, I present a hybrid approach according to which whether we should treat experts as authorities or advisors varies depending upon the presence of certain epistemic and moral concerns. (shrink)

Typically, a logic consists of a formal or informal language together with a deductive system and/or a model-theoretic semantics. The language is, or corresponds to, a part of a natural language like English or Greek. The deductive system is to capture, codify, or simply record which inferences are correct for the given language, and the semantics is to capture, codify, or record the meanings, or truth-conditions, or possible truth conditions, for at least part of the language.

The evolution of life on Earth has produced an organism that is beginning to model and understand its own evolution and the possible future evolution of life in the universe. These models and associated evidence show that evolution on Earth has a trajectory. The scale over which living processes are organized cooperatively has increased progressively, as has its evolvability. Recent theoretical advances raise the possibility that this trajectory is itself part of a wider developmental process. According to these theories, the (...) developmental process has been shaped by a yet larger evolutionary dynamic that involves the reproduction of universes. This evolutionary dynamic has tuned the key parameters of the universe to increase the likelihood that life will emerge and produce outcomes that are successful in the larger process (e.g. a key outcome may be to produce life and intelligence that intentionally reproduces the universe and tunes the parameters of ‘offspring’ universes). Theory suggests that when life emerges on a planet, it moves along this trajectory of its own accord. However, at a particular point evolution will continue to advance only if organisms emerge that decide to advance the developmental process intentionally. The organisms must be prepared to make this commitment even though the ultimate nature and destination of the process is uncertain, and may forever remain unknown. Organisms that complete this transition to intentional evolution will drive the further development of life and intelligence in the universe. Humanity’s increasing understanding of the evolution of life in the universe is rapidly bringing it to the threshold of this major evolutionary transition. (shrink)

An option for Business Ethics course offered in business schools or in philosophy departments, this text balances the perspectives of business and philosophy in the cases and readings. The focus of this text is on the benefits of good corporate conduct to the companies who practice good business ethics.

ABSTRACT Michael Rescorla has argued that it makes sense to compute directly with numbers, and he faulted Turing for not giving an analysis of number-theoretic computability. However, in line with a later paper of his, it only makes sense to compute directly with syntactic entities, such as strings on a given alphabet. Computing with numbers goes via notation. This raises broader issues involving de re propositional attitudes towards numbers and other non-syntactic abstract entities.

Argues against naturalism, or the idea that natural physical processes explain everything, the mind and soul do not exist, and consciousness and causality may have no basis, and suggests that it does not account for human--or any--action.

The presumption of innocence has often been understood as a doctrine that can be explained primarily by instrumental concerns relating to accurate fact-finding in the criminal trial and that has few if any implications outside the trial itself. In this paper, I argue, in contrast, that in a liberal legal order everyone has a right to be presumed innocent simply in virtue of being a person. Every person has a right not to be subjected to criminal punishment unless and until (...) he or she has done something that is criminally wrong. Since disagreements about allegations of criminal wrongdoing are inevitable, the liberal legal order requires a process for determining whether wrongdoing has occurred. In order to preserve the right not to be punished without wrongdoing, the accused person must be presumed innocent throughout this process. The presumption of innocence is therefore as much a basic human right as, for example, the right to bodily integrity or the right to freedom of expression. Specifications of and limitations on the right should therefore be justified not primarily in terms of their instrumental effectiveness in fact-finding or crime control but in terms of the role of the criminal process in a liberal legal order. I consider some implications of this view of the presumption of innocence for the pre-trial process and for substantive criminal law. I argue that the presumption of innocence, understood as a basic human right, should condition the entire pre-trial process; it has, however, minimal implications for the definition of offences. (shrink)

We show that, by choosing definitions carefully, a version of Frege's theorem can be proved in intuitionistic logic.

In the early years of the eighteenth century Leibniz had several interactions with John Toland. These included, from 1702 to 1704, discussions of materialism. Those discussions culminated with the consideration of Toland's 1704 Letters to Serena, where Toland argued that matter is necessarily active. In this paper I argue for two main theses about this exchange and its consequences for our wider understanding. The first is that, despite many claims that Toland was at the time of Letters to Serena a (...) Spinozist, we can make better sense of him as a sort of Hobbesian materialist. The second main point concerns reasons for materialism, and in particular a story Locke tells in the Essay about materialists' motives. Toland defends his materialism by arguing that matter is active, and argues that matter is active by using a conceivability argument. But this is not the crude conceivability argument that Locke suggests motivates materialists. This (together with reflecting on some of Hobbes's arguments) suggests that we might well tell a Lockean story about reasons for early modern materialism, but not Locke's story. (shrink)

When trust is broken, how should we determine who is at fault? Previous discus- sions of broken trust typically attribute the fault to trusters who place trust foolishly or trustees who act in an untrustworthy manner. These discussions take for granted the ability of the truster and trustee to communicate and understand the boundaries of what is being entrusted, that is, the domain of trust. However, the boundaries of entrusted domains are not always clear to either party which can result (...) in broken trust despite the best efforts of both truster and trustee. In this paper, I argue that deter- mining who to blame when trust is broken is a messy affair in which disagreements over fault regularly arise. I introduce three features of trust domains that take center stage in negotiations regarding who is at fault when trust is broken: scope, rigidity and ordering. (shrink)

is true, there is a truth-maker (e.g., a fact) with which it is identical and the truth of the former consists in its identity with the latter. The theory is best understood as a reaction to the correspondence theory, according to which the relation of truth-bearer to truth-maker is correspondence. A correspondence theory is vulnerable to the nagging suspicion that if the best we can do is make statements that merely correspond to the truth, then we inevitably fail to capture (...) the reality they are about and thus fall short of the truth we aim at. An identity theory is designed to overcome this suspicion. (shrink)

Catalysed by conversations amongst a group of colleagues, this article is an initial exploration of what happens to women academics aged 60+ who work in a university in Aotearoa New Zealand. This work is an example of when academic theories, in this case feminism, are called forth by real-world experiences – in this case, increasing academic job insecurity, catalysed by post-pandemic economic shortfalls. We blend together personal anecdotes and feminist analysis to show how women’s academic careers, which are commonly constrained (...) by motherhood in their younger years, are also curtailed at the senior end by processes of voluntary/involuntary retirement, as and when demanded by adverse fiscal conditions. (shrink)

Language was central to Hobbes's understanding of human beings and their mental abilities, and criticism of other philosophers' uses of language became a favorite critical tool for him. This paper connects Hobbes's theories about language to his criticisms of others' language, examining Hobbes's theories of propositions and truth, and how they relate to his claims that various sorts of proposition are absurd. It considers whether Hobbes in fact means anything more by 'absurd' than 'false'. And it pays particular attention to (...) Hobbes's categorization of causes of absurdity and of types of incoherent proposition, arguing that Hobbes's approach is only loosely related to later discussions of category mistakes. (shrink)

The purpose of this edited book is to provide new insight into the understanding of ethics as they relate to organization practice and managerial behavior in todays economy. It provides an overview and critique of ethics as it relates to key contemporary challenges and issues for organizations these include globalization, sustainability, consumerism, neo-liberalism, corporate collapses, leadership and corporate regulation. The book is organized around the core question: What are the ethics of organizing in todays institutional environment and what does this (...) mean for the practice of management and the organization of business? In responding to this question, the contributors examine ethics as it is deeply embedded in the everyday practice of management. Interdisciplinary contributions from sociology, philosophy, management, organization studies, and public administration provide unique perspectives, while case studies and examples drawn from practice illustrate the challenges and dilemmas faced in practice. Each chapter has a brief overview and introduction written by the editors which summarize the main points of each chapter in terms of their contributions to the overall aims of the book as well as drawing connections between the different chapters. (shrink)

The purpose of this paper is to present a thought experiment and argument that spells trouble for “radical” deflationism concerning meaning and truth such as that advocated by the staunch nominalist Hartry Field. The thought experiment does not sit well with any view that limits a truth predicate to sentences understood by a given speaker or to sentences in (or translatable into) a given language, unless that language is universal. The scenario in question concerns sentences that are not understood but (...) are known to be logical consequences of known and understood sentences. Ultimately, the issue turns on the notion of logical consequence that is available to various versions of deflationism. (shrink)

This collection of new papers on Scottish philosophy in the age of Hutcheson and Hume pays close attention to the study of context and the use of original historical sources as a key to philosophical interpretation. The book includes revolutionary new research on Hume's early reading in science and religion and its impact of his thought.

Hobbes denies in Leviathan that we have an idea of God. He does think, though, that God exists, and does not even deny that we can think about God, even though he says we have no idea of God. There is, Hobbes thinks, another cognitive mechanism by means of which we can think about God. That mechanism allows us only to think a few things about God though. This constrains what Hobbes can say about our knowledge of God, and grounds (...) his belief in a fairly strong version of the thesis that God is incomprehensible. (shrink)