A subtheory of the theory of self-referential truth known as FS is shown to be weak as a theory of truth but equivalent to full FS in its proof-theoretic strength.

In a language for arithmetic with a predicate T, intended to mean “ x is the Gödel number of a true sentence”, a set S of axioms and rules of inference has the truth disjunction property if whenever S ⊢ T ∨ T, either S ⊢ T or S ⊢ T. Similarly, S has the truth existence property if whenever S ⊢ ∃χ T ), there is some n such that S ⊢ T ). Continuing previous work, we establish whether (...) these properties hold or fail for a large collection of possible axiomatic systems. (shrink)

We define a class of functions, the descent recursive functions, relative to an arbitrary elementary recursive system of ordinal notations. By means of these functions, we provide a general technique for measuring the proof-theoretic strength of a variety of systems of first-order arithmetic. We characterize the provable well-orderings and provably recursive functions of these systems, and derive various conservation and equiconsistency results.

Probably the two most famous examples of elementary embeddings between inner models of set theory are the embeddings of the universe into an inner model given by a measurable cardinal and the embeddings of the constructible universeLinto itself given by 0#. In both of these examples, the “target model” is a subclass of the “ground model”. It is not hard to find examples of embeddings in which the target model is not a subclass of the ground model: ifis a generic (...) ultrafilter arising from forcing with a precipitous ideal on a successor cardinalκ, then the ultraproduct of the ground model viacollapsesκ. Such considerations suggest a classification of how close the target model comes to “fitting inside” the ground model.Definition 1.1. LetMandNbe inner models of ZFC, and letj:M→Nbe an elementary embedding. Theco-critical pointofjis the least ordinalλ, if any exist, such that there isX⊆λ, X∈NbutX∉M. Such anXis called anew subsetofλ.It is easy to see that the co-critical point ofj:M→Nis a cardinal inN. (shrink)

In a modal system of arithmetic, a theory S has the modal disjunction property if whenever $S \vdash \square\varphi \vee \square\psi$ , either $S \vdash \square\varphi$ or $S \vdash \square\psi. S$ has the modal numerical existence property if whenever $S \vdash \exists x\square\varphi(x)$ , there is some natural number n such that $S \vdash \square\varphi(\mathbf{n})$ . Under certain broadly applicable assumptions, these two properties are equivalent.

History and Philosophy of Logic, Volume 33, Issue 1, Page 99-100, February 2012.

This article examines the development of the concept of the value chain from the linear to the virtual conception of the chain, through the evolution of the literature from Michael Porter’s writings of the mid 1990s to the theorists of e-business and e-commerce in the later 1990s I argue that Porter’s account employs white metaphors and that writings on the virtual value chain both extend the white metaphors of Porter’s linear chain, and suggest a pronouncedly metaphysical system of thought (...) — one which has correlates in areas of thought, including Renaissance Neo-Platonism, cybernetics and the discourse of cyberspace. I suggest that this offers a model of the advance of metaphor — of its usure, as described by Derrida in his White Mythology — and that this model can be synthesised with the views of Ricoeur about the evolution of metaphor towards symbolism. When we apply these ideas of Derrida and Ricoeur to the development of the White Metaphor of the linear chain towards a progressive symbolism, we can see a correlation between the complex causality inferred as a feature of the virtual chain and the cosmological affinities of Renaissance notions of causation. (shrink)

This paper compares the roles classical and intuitionistic logic play in restricting the free use of truth principles in arithmetic. We consider fifteen of the most commonly used axiomatic principles of truth and classify every subset of them as either consistent or inconsistent over a weak purely intuitionistic theory of truth.

The first attempt at a systematic approach to axiomatic theories of truth was undertaken by Friedman and Sheard (Ann Pure Appl Log 33:1–21, 1987). There twelve principles consisting of axioms, axiom schemata and rules of inference, each embodying a reasonable property of truth were isolated for study. Working with a base theory of truth conservative over PA, Friedman and Sheard raised the following questions. Which subsets of the Optional Axioms are consistent over the base theory? What are the (...) proof-theoretic strengths of the consistent theories? The first question was answered completely by Friedman and Sheard; all subsets of the Optional Axioms were classified as either consistent or inconsistent giving rise to nine maximal consistent theories of truth.They also determined the proof-theoretic strength of two subsets of the Optional Axioms. The aim of this paper is to continue the work begun by Friedman and Sheard. We will establish the proof-theoretic strength of all the remaining seven theories and relate their arithmetic part to well-known theories ranging from PA to the theory of ${\Sigma^1_1}$ dependent choice. (shrink)

This is a revision of game theory which takes account of agents' own descriptions of their situations, and which allows people to reason as members of groups.

Although computation and the science of physical systems would appear to be unrelated, there are a number of ways in which computational and physical concepts can be brought together in ways that illuminate both. This volume examines fundamental questions which connect scholars from both disciplines: is the universe a computer? Can a universal computing machine simulate every physical process? What is the source of the computational power of quantum computers? Are computational approaches to solving physical problems and paradoxes always fruitful? (...) Contributors from multiple perspectives reflecting the diversity of thought regarding these interconnections address many of the most important developments and debates within this exciting area of research. Both a reference to the state of the art and a valuable and accessible entry to interdisciplinary work, the volume will interest researchers and students working in physics, computer science, and philosophy of science and mathematics. (shrink)

For Kant, Fichte, and Hegel, secondary literature on Kant, Fichte, and Hegel is not philosophy in the proper sense. It is best to think the relation between the history of philosophy, philosophy, and its future in terms of a set of virtues that should be binding both for the historians of philosophy and philosophers.

This paper investigates the lived experience of alienation as a form of mental strife or pathology as it is connected to the digitalization of modern life. To do so, I deploy the concept of affordances from ecological psychology, phenomenology, and embodied cognition. I propose an affordance-based model for understanding digitalized alienation. First, I argue that the lived sense of alienation is best understood as a fracturing of the affordance space, where possibilities for action are lived as disconnected from one another (...) and therefore from one’s personal development and search for meaning. Using this model, I show how the process of digitalization can lead to a lived sense of alienation for modern subjects. On this model, digitalization is alienating insofar as it fractures the affordance space into disconnected fields that invite determinate, separate, and repeatable tasks—swiping, clicking, scrolling, etc.—rather than offering opportunities for the development of new cognitive and bodily skills that are mutually informing and enriching across different affordance fields. (shrink)

Philosophers conceptualize a lot, generate, analyze, and engineer concepts. They often either equate ‘words’ and ‘concepts’ or consider words only as means of expression of their ‘concepts’. I suggest that philosophers should learn to distinguish between ‘words’ and ‘concepts’. Philosophers’ terms are often incompatible or partially incompatible with philosophers’ ‘concepts’. Examples are ‘isms’ in philosophy and the conception of reason. If ‘talking about the same matter’ is a prerequisite for fruitful philosophical debates, words and their analysis should have at least (...) some limiting and guiding power over concepts. (shrink)

Whataboutism, eine weit verbreitete Argumentationsstrategie in Debatten über den Israel-Gaza-Krieg, lenkt oft durch Gegenfragen von der eigentlichen Kritik ab. Doch trotz seines schlechten Rufs kann Whataboutism auch positive Auswirkungen haben.

Whataboutism is een strategie waarbij op een beschuldiging wordt gereageerd met een wedervraag die eveneens een beschuldiging impliceert, waardoor de oorspronkelijke vraag eerder wordt ontweken dan beantwoord. Het is een effectieve methode om de aandacht te verplaatsen naar een andere situatie door een vergelijkbaar, dan wel onvergelijkbaar, contrast te bieden, waardoor de beschuldigde het eigen gedrag probeert te rechtvaardigen en verantwoordelijkheid probeert te ontlopen. Maar niet alle vormen van whataboutism impliceren echter een drogredenering, noch worden ze altijd verkeerd toegepast. Het (...) contrast dat voortkomt uit de vraag ‘what about’ kan dan een cruciale bijdrage leveren aan een situatie die een verdere kritische analyse vereist, en daarmee de geloofwaardigheid van de argumentatie versterken. (shrink)

_The Metaphysics of Perfect Beings_ addresses the problems an Anselmian perfect being faces in contexts involving unlimited options. Recent advances in the theory of vagueness, the metaphysics of multiverses and hyperspace, the theory of dynamic or sequential choice, the logic of moral and rational dilemmas, and metaethical theory provide the resources to formulate the new challenges and the Anselmian responses with an unusual degree of precision. Almeida shows that the challenges arising in the unusual contexts involving unlimited options sometimes produce (...) metaphysical surprise. (shrink)

This is a book about the concept of a physical thing and about how the names of things relate to the things they name. It questions the prevalent view that names 'refer to' or 'denote' the things they name. Instead it presents a new theory of proper names, according to which names express certain special properties that the things they name exhibit. This theory leads to some important conclusions about whether things have any of their properties as a matter of (...) necessity. This will be an important book for philosophers in metaphysics and the philosophy of language, though it will also interest linguists concerned with the semantics of natural language. (shrink)

Hilary Putnam (1981) proposed an interesting and much discussed attempt to refute a skeptical argument that is based on one form of the brain-in-a-vat scenario. In turn, Putnam’s attempted refutation is based on content externalism (also known as semantic externalism). On this view, the referents and meanings of various types of singular and general terms, as well as the propositions expressed by sentences containing such terms, are determined by aspects of the speaker’s external environment. In this entry, we will consider (...) the basic features of and problems with Putnam’s original argument, and we will also present and discuss several of the most important attempts to reconstruct or improve upon that argument. (shrink)

Radical ecology typically brings to mind media images of ecological activists standing before loggers' saws, staging anti-nuclear marches, and confronting polluters on the high seas. Yet for more than twenty years, the activities of organizations such as the Greens and Earth First! have been influenced by a diverse, less-publicized group of radical ecological philosophers. It is their work—the philosophical underpinnings of the radical ecological movement—that is the subject of _Contesting Earth's Future_. The book offers a much-needed, balanced appraisal of radical (...) ecology's principles, goals, and limitations. Michael Zimmerman critically examines the movement's three major branches—deep ecology, social ecology, and ecofeminism. He also situates radical ecology within the complex cultural and political terrain of the late twentieth century, showing its relation to Martin Heidegger's anti-technological thought, 1960s counterculturalism, and contemporary theories of poststructuralism and postmodernity. An early and influential ecological thinker, Zimmerman is uniquely qualified to provide a broad overview of radical environmentalism and delineate its various schools of thought. He clearly describes their defining arguments and internecine disputes, among them the charge that deep ecology is an anti-modern, proto-fascist ideology. Reflecting both the movement's promise and its dangers, this book is essential reading for all those concerned with the worldwide ecological crisis. (shrink)

Michael Smith has written a series of seminal essays about the nature of belief and desire, the status of normative judgment, and the relevance of the views we take on both these topics to the accounts we give of our nature as free and responsible agents. This long awaited collection comprises some of the most influential of Smith's essays. Among the topics covered are: the Humean theory of motivating reasons, the nature of normative reasons, Williams and Korsgaard on internal (...) and external reasons, the nature of self-control, weakness of will, compulsion, freedom, responsibility, the analysis of our rational capacities, moral realism, the dispositional theory of value, the supervenience of the normative on the non-normative, the error theory, rationalist treatments of moral judgment, the practicality requirement on moral judgment and non-cognivist. This collection will be of interest to students in philosophy and psychology. (shrink)

This paper argues that commonsense responses to radical skepticism can provide helpful lessons for religious epistemology—in particular, for thinking about how best to defend, and respond to, religious skepticism. Section 1 briefly summarizes of some of the main elements of the Reid-inspired epistemic-intuition-based commonsense response to radical skepticism developed in my 2021 book, "Radical Skepticism and Epistemic Intuition" and highlights the role (in our thinking about radical skepticism) of epistemic intuitions understood as seemings about epistemic value in much the same (...) way that moral intuitions are seemings about moral value. Sections 2 and 3 identify five important lessons that can be drawn from the position presented in that book, apply them to religious epistemology, and explain how they can help us to account for our religious disagreements without implausibly disparaging the rationality of those with whom we disagree. Section 4 addresses some potential concerns about Sections 2 and 3. (shrink)

It is not very surprising that it was no less true in antiquity than it is today that adult human beings are held to be responsible for most of their actions. Indeed, virtually all cultures in all historical periods seem to have had some conception of human agency which, in the absence of certain responsibility-defeating conditions, entails such responsibility. Few philosophers have had the temerity to maintain that this entailment is trivial because such responsibility-defeating conditions are always present. Another not (...) very surprising fact is that ancient thinkers tended to ascribe integrality to "what is" (to on). That is, they typically regarded "what is" as a cosmos or whole with distinguishable parts that fit together in some coherent or cohesive manner, rather than either as a "unity" with no parts or as a collection containing members (ta onta or "things that are") standing in no "natural" relations to one another. 1 The philoso phical problem of determinism and responsibility may, I think, best be characterized as follows: it is the problem of preserving the phenomenon of human agency (which would seem to require a certain separateness of individual human beings from the rest of the cosmos) when one sets about the philosophical or scientific task of explaining the integrality of "what is" by means of the development of a theory of causation or explanation ( concepts that came to be lumped together by the Greeks under the term "aitia"). (shrink)

Etic theorizing uses the theorist’s social notions to theorize about their subject. This theorist may claim that Genghis Khan was a war criminal even though his actions predate the enactment of the Geneva Conventions. Brian Epstein considers a modal etic theorist who claims that Genghis Khan would have been a war criminal even if the Geneva Conventions were never enacted. Epstein argues that this has metaphysical import: it requires postulating a novel metaphysical notion of “anchoring”. Drawing from some familiar issues (...) in modal actualism, I argue that modal etic theorizing does not support this postulate. But it does suggest a distinctive kind of modality at work in social reality. (shrink)

INTRODUCTION I first read Charles Darwin's masterpiece, On the Origin of Species , some twenty years ago. At once I fell under its spell - an emotion which ...

Michael Dummett, philosopher and social critic, is also one of the sharpest and most prominent commentators and campaigners for the fair treatment of immigrants and refugees in Britain and Europe. This book insightfully draws together his thoughts on this major issue for the first time. Exploring the confused and often highly unjust thinking about immigration, Dummett then carefully questions the principles and justifications governing state policies, pointing out that they often conflict with the rights of refugees as laid down (...) by the Geneva Convention. With compelling and often moving examples, On Immigration and Refugees points a new way forward for humane thinking and practice about a problem we cannot afford to ignore. (shrink)

From the philosopher’s perspective, the interest in quantum computation stems primarily from the way that it combines fundamental concepts from two distinct sciences: Physics, in particular Quantum Mechanics, and Computer Science, each long a subject of philosophical speculation and analysis in its own right. Quantum computing combines both of these more traditional areas of inquiry into one wholly new, if not quite independent, science. Over the course of this chapter we will be discussing some of the most important philosophical questions (...) that arise from this merger and philosophical lessons to be learned. (shrink)

This book fills a gap in studies of meaning by providing detailed case studies of attested corpus data on the meanings of words and phrases.