In this paper, I present what I call the symmetry conception of God within 1st order, extensional, non-well-founded set theory. The symmetry conception comes in two versions. According to the first, God is that unique being that is universally symmetrical with respect to set membership. According to the second, God is the universally symmetrical set of all sets that are universally symmetrical with respect to set membership. I present a number of theorems, most importantly that any universally symmetrical set is (...) identical to its essence, that show that the two symmetry conceptions intersect with some dominant theological conceptions of God. The theorems also show that both of the symmetry conceptions of God entail that God has a fractal like structure. (shrink)

Aristotle's categorial scheme had an unparalleled effect not only on his own philosophical system, but also on the systems of many of the greatest philosophers in the Western tradition. The set of doctrines in the Categories, known as categorialism, play, for instance, a central role in Aristotle's discussion of change in the Physics, in the science of being qua being in the Metaphysics, and in the rejection of Platonic ethics in the Nicomachean Ethics. Plainly, the enterprise of categorialism inaugurated by (...) Aristotle runs deep in the philosophical psyche. Even so, despite its wide-reaching influence—and, indeed owing to that influence—any attempt to describe categorialism faces a significant difficulty: experts disagree on many of its most important and fundamental aspects. This article argues that Aristotle's categorial scheme, as is the case with many works in the history of philosophy, is best illuminated by opposing beams of interpretive light. It examines how Aristotle arrived at his list of categories and considers the connection between Aristotle's categories and his hylomorphism. (shrink)

According to Augustine, abstract objects are ideas in the mind of God. Because numbers are a type of abstract object, it would follow that numbers are ideas in the mind of God. Call such a view the “Augustinian View of Numbers” (AVN). In this paper, I present a formal theory for AVN. The theory stems from the symmetry conception of God as it appears in Studtmann (2021). I show that the theory in Studtmann’s paper can interpret the axioms (...) of Peano Arithmetic minus the induction schema. This fact allows for the development of arithmetic in a natural way. The development eventuates in a theory that can interpret second-order arithmetic. The conception of God that emerges by the end of the discussion is a conception of an infinite, ineffable, self-cause that contains objects that not only serve as numbers but also encode information about each other. (shrink)

The traditional problem of free will has reached an impasse; we are unlikely to see progress without rethinking the terms in which the problem had been cast. Our approach offers an alternative to the standard terms of the debate, by developing an authorially parameterized approach articulated within a two-dimensional semantics for temporal predicates.

Empiricism and the Problem of Metaphysics develops and defends an empiricist solution to the problem of metaphysics, then examines the implications of such a solution for skeptical arguments and the is-ought gap. At the heart of the solution is an empirically verifiable empiricist view of the a priori.

In this note, I discuss a very simple time-dependent formula and its relation to the cosmological constant. I first note that the the formula yields an exact match of the cosmological constant on the assumption that the age of the universe is 8.08×10^60 in Planck units. I then suggest a physical interpretation of the formula according to which the cosmological constant is the result of a magnetic field.

According to Augustine, abstract objects are ideas in the Mind of God. Because numbers are a type of abstract object, it would follow that numbers are ideas in the Mind of God. Let us call such a view the Augustinian View of Numbers (AVN). In this paper, I present a formal theory for AVN. The theory stems from the symmetry conception of God as it appears in Studtmann (2021). I show that Robinson’s Arithmetic is a conservative extension of the (...) axioms in Studtmann’s original paper. The extension is made possible by identifying the set of natural numbers with God, 0 with Being, and the successor function with the essence function. The resulting theory can then be augmented to include Peano Arithmetic by adding a set-theoretic version of induction and a comprehension schema restricted to arithmetically definable properties. In addition to these formal matters, the paper provides a characterization of the mind of God. According to the characterization, the Being essences that constitute God’s mind act as both numbers and representations – each (except for Being itself) has all the properties of some number and encodes all the properties of that number’s predecessor. The conception of God that emerges by the end of the discussion is a conception of an infinite, ineffable, axiologically and metaphysically ultimate entity that contains objects that not only serve as numbers but also encode information about each other. (shrink)

In The Divine Fractal, Studtmann (2021) introduced a novel conception of God, what he calls the symmetry conception, and showed that such a conception not only can be formalized within extensional non-well-founded set theory but also entails the Thomistic view that God is identical to her essence. In this paper, I show that Studtmann’s symmetry conception of God can be integrated into a recent approach to quantum gravity, namely causal set theory. The theory that results has two significant (...) consequences. First, God is the necessarily existing set of spacetime events. Second, the square root of the probability that a spacetime event randomly chosen from N spacetime events is uncaused is given by the following formula: ((Harmonic [N])/N)^(1/2). I conclude the paper by briefly discussing a connection between this formula and the cosmological constant. (shrink)

In this paper, we provide a game-theoretic examination of indirect utilitarianism by comparing the expected payoffs of attempts to apply a deontological principle and a utilitarian principle within the context of the Prisoner’s Dilemma (PD). Although many of the best-known utilitarians and consequentialists have accepted some indirect form of their respective views, the results in this paper suggest that they have been overly quick to dismiss altogether the benefits of directly enacting utilitarian principles. We show that for infallible moral agents, (...) what we call ‘non-autonomous agents’, direct utilitarianism dominates indirect utilitarianism via deontology in terms of achieving the maximized utilitarian outcome, but only in underlying games where the maximized utilitarian outcome involves unequal payoffs. In other situations, indirect utilitarianism implemented through Kantian deontology either ties or dominates direct utilitarianism in terms of achieving the maximized utilitarian outcome. We also examine the two different moralities on the assumption that fallibility, which is a form of autonomy, is an aspect of moral agency by introducing Endogenized Morality Models (EMM’s). We believe that just as indirect utilitarians worry about the cost of applying moral principles, so too they should worry about the fact that humans have both pro-social and materialistically selfish motivations and hence are fallible moral agents. We show that there are conditions under which fallible autonomous utilitarians achieve higher expected material and psychic payoffs than fallible autonomous deontologists and conditions under which they do not. (shrink)

The use of evolutionary game theory to explain the evolution of human norms and the behavior of humans who act according to those norms is widespread. Both the aims and motivation for its use are clearly articulated by Harms and Skyrms (2008) in the following passage: "A good theory of evolution of norms might start by explaining the evolution of altruism in Prisoner’s Dilemma, of Stag Hunting, and of the equal split in the symmetric bargaining game. These are not well-explained (...) by classical game theory based on rational choice. From a technical point of view, they present different theoretical challenges. In the bargaining game, there are an infinite number of equilibria with no principled (rational choice) way to select the cooperative one. In Stag Hunt there are only two, but the non-cooperative one is selected by risk-dominance. In Prisoner’s Dilemma the state of mutual cooperation is not a Nash equilibrium at all, and cooperation flies in the face of the rational-choice principle that one does not choose less rather than more. In contrast to rational choice theory, the most common tool of evolutionary game theory is the replicator dynamics, in which the propagation rate of each strategy is determined by its current payoffs. These dynamics have a rationale in both biological and cultural evolutionary modeling, and sometimes tell us things that rational choice theory does not." We agree with the first sentence in this quotation: a good theory about the behavior under norms ought to explain altruism in the Prisoner’s Dilemma (PD), playing Stag in Stag Hunt (SH), and offering equal splits in the symmetric Nash bargaining game (NB). We also agree with Harms and Skyrms about the difference in technical challenges each of these games poses. Finding a single mechanism, even one as broadly understood as evolution, that could solve these challenges en masse is no doubt a tall order. Nonetheless, in this paper, we present a single, simple, modification to SH, NB, and a general n-player PD that does just that: we introduce deontological autonomy into the models. (shrink)

The idea that a being can be identical to its own essence has a long and venerable history in theological speculation. As with many ideas in theology, however, such an idea has never been given an adequate mathematical formulation. The key to such a formulation, I argue, is introducing an essence axiom into non-well-founded set theory. According to such an axiom, for every set, x, there is a set that contains all and only those sets that contain x. With such (...) an axiom, it becomes possible to introduce an essence function that takes each set to its essence. An object that is identical to its essence, then, is simply a fixed point of the essence function. In this paper, I first discuss a theorem according to which any fixed point of the essence function is universally symmetrical with respect to the set membership relation. After proving the theorem, I discuss its theological implications. I go on to argue that the process of counting the members of a set that is identical to its essence is a Sisyphusian process. Such a fact I suggest shows that the absurdity of human existence is not alleviated by the existence of God but rather is entailed by it. (shrink)

The Nash counterfactual considers the question: what would happen were I to change my behaviour assuming no one else does. By contrast, the Kantian counterfactual considers the question: what would happen were everyone to deviate from some behaviour. We present a model that endogenizes the decision to engage in this type of Kantian reasoning. Autonomous agents using this moral framework receive psychic payoffs equivalent to the cooperate-cooperate payoff in Prisoner’s Dilemma regardless of the other player’s action. Moreover, if both interacting (...) agents play Prisoner’s Dilemma using this moral framework, their material outcomes are a Pareto improvement over the Nash equilibrium. (shrink)

There is a very deep tension that exists at the heart of Aristotle’s metaphysical system in virtue of the fact that his works seem to contain two distinct and not obviously commensurate ontologies: an early ontology that Aristotle outlines in the Categories and a later ontology that he develops in his physical–metaphysical treatises. In this paper I briefly describe the two ontologies, discuss the sources of conflict and outline different scholarly speculations about the relationship between the two.

In this paper, I address both the interpretive and philosophical issues concerning prime matter. My aim is to show that a philosophically interesting account of prime matter can be articulated that strongly coheres with, even if it is not necessitated by, Aristotle’s texts. In articulating the interpretation, I first examine a view defended by both Richard Sorabji and Robert Sokolowski according to which prime matter is extension. Such a view, I argue, is problematic for a number of reasons. Nonetheless, it (...) provides a convenient starting point for the view I defend according to which prime matter is intimately linked to, though not identical with, extension. (shrink)

In this paper, I address both the interpretive and philosophical issues concerning prime matter. My aim is to show that a philosophically interesting account of prime matter can be articulated that strongly coheres with, even if it is not necessitated by, Aristotle’s texts. In articulating the interpretation, I first examine a view defended by both Richard Sorabji and Robert Sokolowski according to which prime matter is extension. Such a view, I argue, is problematic for a number of reasons. Nonetheless, it (...) provides a convenient starting point for the view I defend according to which prime matter is intimately linked to, though not identical with, extension. (shrink)

Whence the categories? -- The body problem in Aristotle -- Form -- Prime matter -- Quality -- Quantity -- Substance.

Evidence on the coherence between emotion and facial expression in adults from laboratory experiments is reviewed. High coherence has been found in several studies between amusement and smiling; low to moderate coherence between other positive emotions and smiling. The available evidence for surprise and disgust suggests that these emotions are accompanied by their “traditional” facial expressions, and even components of these expressions, only in a minority of cases. Evidence concerning sadness, anger, and fear is very limited. For sadness, one study (...) suggests that high emotion–expression coherence may exist in specific situations, whereas for anger and fear, the evidence points to low coherence. Insufficient emotion intensity and inhibition of facial expressions seem unable to account for the observed dissociations between emotion and facial expression. (shrink)

In some previous work, I tried to give a concept-based account of the nature of our entitlement to certain very basic inferences (see the papers in Part III of Boghossian 2008b). In this previous work, I took it for granted, along with many other philosophers, that we understood well enough what it is for a person to infer. In this paper, I turn to thinking about the nature of inference itself. This topic is of great interest in its own right (...) and surprisingly understudied by philosophers. A correct understanding of inference promises to shed light on a number of important topics. In particular, it threatens to undermine the sort of concept-based story about entitlement to which I had previously been attracted. (shrink)

Eliminative materialism is the thesis that our common-sense conception of psychological phenomena constitutes a radically false theory, a theory so fundamentally defective that both the principles and the ontology of that theory will eventually be displaced, rather than smoothly reduced, by completed neuroscience. Our mutual understanding and even our introspection may then be reconstituted within the conceptual framework of completed neuroscience, a theory we may expect to be more powerful by far than the common-sense psychology it displaces, and more substantially (...) integrated within physical science generally. My purpose in this paper is to explore these projections, especially as they bear on (1) the principal elements of common-sense psychology: the propositional attitudes (beliefs, desires, etc.), and (2) the conception of rationality in which these elements figure. (shrink)

"First published in this translation 1955; second edition (revised) 1974; reprinted with additional revisions 1987; reissued with new Further Reading 2003; reissued with new introduction 2007"--T.p. verso.

Dieses historische Buch kann zahlreiche Tippfehler und fehlende Textpassagen aufweisen. Kaufer konnen in der Regel eine kostenlose eingescannte Kopie des originalen Buches vom Verleger herunterladen (ohne Tippfehler). Ohne Indizes. Nicht dargestellt. 1910 edition. Auszug:...endliche als durch sie erzeugt; oder diese in jener involviert und aus ihr sich evolvierend. Der wahre Erzeuger der endlichen Grosse ist nicht die unendlichkleine" Grosse (das Unendlichkleine ware dem Grossenwert nach vielmehr Null), sondern es ist das Gesetz der Grosse (als Veranderlicher), das man sich nun wie (...) in einen Punkt zusammengezogen, d. h. fur den einzelnen Punkt ausgedruckt, oder an einer endlichen Erstreckung sich darstellend denken kann, das aber dem letzten Sachgehalt nach dasselbe ist fur den Punkt und die endliche Erstreckung, wenn es auch in Bezug auf beide verschiedene, im allgemeinen auseinander ableitbare Ausdrucke erhalten muss. Da aber die endliche Grosse uberhaupt von Punkt zu Punkt entstehend (d. h. veranderlich) gedacht wird, so ist insofern der punktuelle, d. h. infinitesimale Ausdruck der fundamentale, aus dem der extensionale gleichsam erst hervorwachst. Die Differenz entsteht eben von der Null an; nicht aus ihr; aus Null wird keine extensive Grosse; wohl aber von der Null, d. h. dem Nichtsein dessen, was werden soll, oder ganz schlicht1) vom Ausgangs wert an; woraus? Aus dem Gesetz; eine andere Antwort ist nicht zu geben und nicht zu verlangen. Durch dies Gesetz aber ist die Grosse als Eines, Identisches, im Unterschied von den sukzessiven Grossenwerten, also in ihrem Gattungsausdruck definiert. i) Vgl. oben S. 122. Fragt man also: wie soll aus der Null gewordenen, verschwundenen" Grosse die endliche Grosse wiederentstehen? so ist zu antworten: die Grosse zwar (yuantitas). (shrink)

JOURNAL OF THE HISTORY OF PHILOSOPHY PRIZE for the best published book in the history of philosophy [Awarded in 2010] _______________ -/- Although it is widely recognized that David Hume's A Treatise of Human Nature (1739-40) belongs among the greatest works of philosophy, there is little agreement about the correct way to interpret his fundamental intentions. It is an established orthodoxy among almost all commentators that skepticism and naturalism are the two dominant themes in this work. The difficulty has been, (...) however, that Hume's skeptical arguments and commitments appear to undermine and discredit his naturalistic ambition to contribute to "the science of man". This schism appears to leave his entire project broken-backed. The solution to this riddle depends on challenging another, closely related, point of orthodoxy: namely, that before Hume published the Treatise he removed almost all material concerned with problems of religion. Russell argues, contrary to this view, that irreligious aims and objectives are fundamental to the Treatise and account for its underlying unity and coherence. It is Hume's basic anti-Christian aims and objectives that serve to shape and direct both his skeptical and naturalistic commitments. When Hume's arguments are viewed from this perspective we can solve, not only puzzles arising from his discussion of various specific issues, we can also explain the intimate and intricate connections that hold his entire project together. This "irreligious" interpretation provides a comprehensive fresh account of the nature of Hume's fundamental aims and ambitions in the Treatise. It also presents a radically different picture of the way in which Hume's project was rooted in the debates and controversies of his own time, placing the Treatise in an irreligious or anti-Chrisitan philosophical tradition that includes Hobbes, Spinoza and freethinking followers. Considered in these terms, Hume's Treatise constitutes the crowning achievement of the Radical Enlightenment. (shrink)

A study of how syntax relates to meaning by a leader of the new generation of philosopher-linguists.

The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox, a challenge to 'classical' mathematics from a world-famous mathematician, a new foundational school, and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection (...) brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field. (shrink)

In this chapter, we analyze the relationships between the Internet and its users in terms of situated cognition theory. We first argue that the Internet is a new kind of cognitive ecology, providing almost constant access to a vast amount of digital information that is increasingly more integrated into our cognitive routines. We then briefly introduce situated cognition theory and its species of embedded, embodied, extended, distributed and collective cognition. Having thus set the stage, we begin by taking an embedded (...) cognition view and analyze how the Internet aids certain cognitive tasks. After that, we conceptualize how the Internet enables new kinds of embodied interaction, extends certain aspects of our embodiment, and examine how wearable technologies that monitor physiological, behavioral and contextual states transform the embodied self. On the basis of the degree of cognitive integration between a user and Internet resource, we then look at how and when the Internet extends our cognitive processes. We end this chapter with a discussion of distributed and collective cognition as facilitated by the Internet. (shrink)

The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, (...) and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field. (shrink)

The first study of this ancient text in over 70 years, Rituals of the Way explores how the Xunzi influenced Confucianism and other Chinese philosophies through its emphasis on "the Way.".

Supporters of G.W.F. Hegel's philosophy have largely shied away from relating his logic to modern symbolic or mathematical approaches. While it has predominantly been the non-Greek discipline of algebra that has informed modern mathematical logic, philosopher Paul Redding argues that the approaches of Plato and Aristotle to logic were deeply shaped by the arithmetic and geometry of classical Greek culture. And by ignoring the fact that Hegel's logic also has this deep mathematical dimension, conventional Hegelians have missed some of (...) Hegel's greatest insights. In Conceptual Harmonies, Redding develops an account of Hegel's logic against a classical and modern historical background that is rarely considered. He stresses Hegel's attention to the Platonic background of Aristotle's original syllogistic and beyond. He then links these Platonic elements to Leibniz's modern revitalization of the logical tradition and then to new forms of algebraic geometry emerging in Hegel's lifetime. Redding thereby reestablishes aspects of Hegel's philosophy that are essential if Hegel is to be taken as a thinker relevant not only to contemporary philosophy, but also to current philosophical conceptions of logic. (shrink)

For over twenty years, Paul Weithman has explored the thought of John Rawls to ask how liberalism can secure the principled allegiance of those people whom Rawls called 'citizens of faith'. This volume brings together ten of his major essays, which reflect on the task and political character of political philosophy, the ways in which liberalism does and does not privatize religion, the role of liberal legitimacy in Rawls's theory, and the requirements of public reason. The essays reveal Rawls (...) as a thinker deeply engaged with political and existential questions that trouble citizens of faith, and explore how - in firm opposition to political realism - he tries to show that the possibility of liberal democracy and the natural goodness of humanity are objects of reasonable faith. The volume will be of interest to political philosophers, political theorists, moral theologians, and religious ethicists. (shrink)

According to the subset account of realization, a property, F, is realized by another property, G, whenever F is individuated by a non-empty proper subset of the causal powers by which G is individuated (and F is not a conjunctive property of which G is a conjunct). This account is especially attractive because it seems both to explain the way in which realized properties are nothing over and above their realizers, and to provide for the causal efficacy of realized properties. (...) It therefore seems to provide a way around the causal exclusion problem. There is reason to doubt, however, that the subset account can achieve both tasks. The problem arises when we look closely at the relation between properties and causal powers, specifically, at the idea that properties confer powers on the things that have them. If realizers are to be ontically prior to what they realize, then we must regard the conferral of powers by properties as a substantive relation of determination. This relation of conferral is at the heart of a kind of exclusion problem, analogous to the familiar causal exclusion problem. I argue that the subset account cannot adequately answer this new exclusion problem, and is for that reason ill-suited to be the backbone of a non-reductive physicalism. (shrink)

In 'Subjunctive Conditionals: Two Parameters vs. Three' Pavel Tichy articulates and defends a three-parameter account of counterfactuals. In the paper, he responds to a well known objection against the validity of various forms of inference, in particular strengthening of the antecedent, contraposition, and hypothetical syllogism. In this paper, I argue that his response to the objection is inadequate. I then propose an alternative form of the three-parameter account of counterfactuals that avoids the objection in question.

Although thinkers of the past might have started from presumptions of fundamental difference and inequality between (say) the genders, or people of different races, this is no longer the case. At least in mainstream political philosophy, we are all now presumed to be, in some fundamental sense, basic equals. Of course, what follows from this putative fact of basic equality remains enormously controversial: liberals, libertarians, conservatives, Marxists, republicans, and so on, continue to disagree vigorously with each other, despite all presupposing (...) some kind of basic equality. They may argue about who gets what, how much, and why, but the starting point - that all people are in some sense deserving of prima facie equal consideration - has become an axiom of our moral and political thinking. But why? Why are we basic equals? The trouble is that as soon as one asks for an explanation of this foundational premise, it begins to look shaky. After all, on any conceivable metric human beings are notably unequal, and often to striking degrees. Philosophers in this area tend to talk of equal worth, but often without trying to specify what exactly that means. Philosophically, basic equality is neither acceptable nor rejectable. It is not rejectable because we appear to be, as a matter of fact, profoundly committed to the truth of the claim that we are all one another's basic equals. But to the extent that there appear to be no philosophical arguments for believing in the truth of basic equality, it is not acceptable either. The aim of this book is to try and show why basic equality is acceptable. To do so, however, it will also contend that we need to approach the question rather differently to how it has mostly been handled so far. What's required is an exercise in what Bernard Williams called 'impure philosophy': it must include insights from other areas of human intellectual endeavour, whether psychology and history or even what we learn from how we go about practicing basic equality in our collective lives. (shrink)

Free Will & The Tragic Predicament : Making Sense of Williams -/- The discussion in this paper aims to make better sense of free will and moral responsibility by way of making sense of Bernard Williams’ significant and substantial contribution to this subject. Williams’ fundamental objective is to vindicate moral responsibility by way of freeing it from the distortions and misrepresentations imposed on it by “the morality system”. What Williams rejects, in particular, are the efforts of “morality” to further “deepen” (...) or “refine” the notion of the voluntary, with a view to securing “ultimate justice”. It is these aims and aspirations, he argues, that take us to the precipice of scepticism. In Shame and Necessity (1993) Williams advances a vindicatory genealogy that unmasks the “illusions” and “fantasies” of our current ethical ideas as they relate to agency and responsibility. What we are then left with is the task of “recasting our ethical conceptions” . It is here that Williams is especially insistent on the importance and value of historical consciousness and reflection. The role of our reflections about the Greeks and tragedy is precisely to show that in order to move forward, into the future, we need to first look back at where we have come from. The value of these “untimely” observations is that they provide us with alternatives and options that we might otherwise lack. What we discover, when we consider the Greeks, is their commitment to a “pessimism of strength” that rests on rejecting scepticism. It is this two-sided perspective on our ethical predicament that delivers a more truthful account of our human situation, one that will help us discard those illusions and fantasies of "morality" that we are “better off” without. An account of this kind refuses to accept an optimism that insists that any form of responsible ethical life must be one that is immune to the influence of luck and fate. This is the fundamental lesson that we can learn from the ancient Greeks and that Williams seeks to “recover” for us. (shrink)

Ricoeur’s theory of productive imagination in previously unpublished lectures. The eminent philosopher Paul Ricoeur was devoted to the imagination. These previously unpublished lectures offer Ricoeur’s most significant and sustained reflections on creativity as he builds a new theory of imagination through close examination, moving from Aristotle, Pascal, Spinoza, Hume, and Kant to Ryle, Price, Wittgenstein, Husserl, and Sartre. These thinkers, he contends, underestimate humanity’s creative capacity. While the Western tradition generally views imagination as derived from the reproductive example of (...) the image, Ricoeur develops a theory about the mind’s power to produce new realities. Modeled most clearly in fiction, this productive imagination, Ricoeur argues, is available across conceptual domains. His theory provocatively suggests that we are not constrained by existing political, social, and scientific structures. Rather, our imaginations have the power to break through our conceptual horizons and remake the world. (shrink)

This is a book about the Hilbert space formulation of quantum mechanics and its measurement theory. It contains a synopsis of what became of the Mathematical Foundations of Quantum Mechanics since von Neumann's classic treatise with this title. Fundamental non-classical features of quantum mechanics-indeterminacy and incompatibility of observables, unavoidable measurement disturbance, entanglement, nonlocality-are explicated and analysed using the tools of operational quantum theory. The book is divided into four parts: 1. Mathematics provides a systematic exposition of the Hilbert space and (...) operator theoretic tools and relevant measure and integration theory leading to the Naimark and Stinespring dilation theorems; 2. Elements develops the basic concepts of quantum mechanics and measurement theory with a focus on the notion of approximate joint measurability; 3. Realisations offers in-depth studies of the fundamental observables of quantum mechanics and some of their measurement implementations; and 4. Foundations discusses a selection of foundational topics (quantum-classical contrast, Bell nonlocality, measurement limitations, measurement problem, operational axioms) from a measurement theoretic perspective. The book is addressed to physicists, mathematicians and philosophers of physics with an interest in the mathematical and conceptual foundations of quantum physics, specifically from the perspective of measurement theory. (shrink)