The quantum state of a d-dimensional system can be represented by a probability distribution over the d 2 outcomes of a Symmetric Informationally Complete Positive Operator Valued Measure (SIC-POVM), and then this probability distribution can be represented by a vector of $\mathbb {R}^{d^{2}-1}$ in a (d 2−1)-dimensional simplex, we will call this set of vectors $\mathcal{Q}$ . Other way of represent a d-dimensional system is by the corresponding Bloch vector also in $\mathbb {R}^{d^{2}-1}$ , we will call (...) this set of vectors $\mathcal{B}$ . In this paper it is proved that with the adequate scaling $\mathcal{B}=\mathcal{Q}$ . Also we indicate some features of the shape of $\mathcal{Q}$. (shrink)

The logical hexagon (or hexagon of opposition) is a strange, yet beautiful, highly symmetrical mathematical figure, mysteriously intertwining fundamental logical and geometrical features. It was discovered more or less at the same time (i.e. around 1950), independently, by a few scholars. It is the successor of an equally strange (but mathematically less impressive) structure, the “logical square” (or “square of opposition”), of which it is a much more general and powerful “relative”. The discovery of the former did not raise interest, (...) neither among logicians, nor among philosophers of logic, whereas the latter played a very important theoretical role (both for logic and philosophy) for nearly two thousand years, before falling in disgrace in the first half of the twentieth century: it was, so to say, “sentenced to death” by the so-called analytical philosophers and logicians. Contrary to this, since 2004 a new, unexpected promising branch of mathematics (dealing with “oppositions”) has appeared, “oppositional geometry” (also called “n-opposition theory”, “NOT”), inside which the logical hexagon (as well as its predecessor, the logical square) is only one term of an infinite series of “logical bi-simplexes of dimension m”, itself just one term of the more general infinite series (of series) of the “logical poly-simplexes of dimension m”. In this paper we recall the main historical and the main theoretical elements of these neglected recent discoveries. After proposing some new results, among which the notion of “hybrid logical hexagon”, we show which strong reasons, inside oppositional geometry, make understand that the logical hexagon is in fact a very important and profound mathematical structure, destined to many future fruitful developments and probably bearer of a major epistemological paradigm change. (shrink)

We show that every state on an interval pseudo effect algebra E satisfying an appropriate version of the Riesz Decomposition Property (RDP for short) is an integral through a regular Borel probability measure defined on the Borel σ-algebra of a Choquet simplex K. In particular, if E satisfies the strongest type of RDP, the representing Borel probability measure can be uniquely chosen to have its support in the set of the extreme points of K.

In lieu of an abstract, here is a brief excerpt of the content:POETRY AS THE NAMING OF THE GODS by Phyllis Zagano There have been many attempts to define poetry, and there is copious advice to would-be poets. Horace writes somewhere "Sit quod vis, simplex dumtaxat et unum" which can be comfortably rendered as "make anything at all, so long as it hangs together." The hanging together is the quality most writers point to as evidence of success: simply, it (...) works. What poetry does is the more complex question, since it is the understanding of its internal kinesis which allows for its definition. Essentially, it takes an object from objective reality (insofar as we can agree such exists) and creates an oxymoronic entity: a static consciousness. This is always seen in phenomenological terms, that is, it must be consciousness of something. The poet recognizes this in deference to the common consciousness and the common understanding of the everyday, by the use of metaphor, simile, and the other accouterments of the trade. Things must be as they appear, and they must be as they appear to some majority of the people, in order for the poet to argue his private vision with clarity. The analogy must have some common ground before it has meaning, before the "naming" takes place. For Martin Heidegger the activity of creating poetry, dichten, is not only an indispensable part of human life, it signals the humanness of the person. He has two principal essays on poetry which show how this activity ofdichten combines his concepts Dasein and Vorhandenheit (despite his later abandonment of Dasein for Lichtung). Heidegger's essay, "Hölderlin and the Essence of Poetry," seeks to determine what is common to poetry, that is, what constitutes its essence. 340 Phyllis Zagano341 Another ofhis essays, "What are Poets For?" begins where the first ends (with considerations of Friedrich Hölderlin's "Bread and Wine"). Each essay comments on specific poems and somewhat imperfectly attempts a poetic theory in consonance with the rest of Heidegger's work. Since "Hölderlin and the Essence of Poetry" concentrates more on poetic theory than "What are Poets For?," investigation of it will prove more helpful in understanding and appropriating Heidegger's contention that "The writing of poetry is the fundamental naming of the Gods____"· In his "Letter on Humanism," Heidegger calls language the "House of Being," while man is the "Shepherd of Being." This understanding ofthe function oflanguage and the methodweuse tocreateand recreate ourselves and our world recurs often in Heidegger's work. The essay, "Hölderlin and the Essence of Poetry," stands as a seeking after what is common to poetry and, while Heidegger recognizes that Hölderlin's work is "only one among many others" (p. 294) and therefore cannot be used as the sole criterion to determine what constitutes poetry, he says that if what we recognize as the "essence of poetry" is present in a universal concept, then it ought to be able to be extrapolated from Hölderlin's poetry as well as from that of any other poet. What constitutes the "essence" of poetry, Heidegger argues, ought to be equally valid in every poem, but it is perhaps well to remind him that what ought to be equally valid in every poem is only equally valid in every poem which "hangs together," that is, every poem which performs its function as poem. Such insistence is ofcourse mere definition of terms, but in this case, without prior argument on the metaphysics of art, it is necessary. In any event, Heidegger concludes that the essence of Hölderlin's poetry is the "essence ofpoetry" itself (p. 294), and that what is common to poetry is found in it. While some critics might argue that Heidegger makes too much of Hölderlin here, the more dangerous weakness in this method of argumentation is the possibility that an idiosyncrasy might be mistaken for an essential element or, more probably, that too much will be generalized from this particular example or set of examples. The trained literary critic can cast a cold eye on such magnification of a single poet as the presenter of both form and content for the meaning of the "essence of poetry." In fact, it... (shrink)

In this book a noted physiologist and neuroscientist introduces the concept of simplexity, the set of solutions living organisms find that enable them to deal with information and situations, while taking into account past experiences and anticipating future ones. Such solutions are new ways of addressing problems so that actions may be taken more quickly, more elegantly, and more efficiently. In a sense, the history of living organisms may be summed up by their remarkable ability to find solutions that avoid (...) the world's complexity by imposing on it their own rules and functions. Evolution has resolved the problem of complexity not by simplifying but by finding solutions whose processes--though they can sometimes be complex--allow us to act in the midst of complexity and of uncertainty. Nature can inspire us by making us realize that simplification is never simple and requires instead that we choose, refuse, connect, and imagine, in order to act in the best possible manner. Such solutions are already being applied in design and engineering and are significant in biology, medicine, economics, and the behavioral sciences. (shrink)

The concept of simplexity, as proposed by Alain Berthoz, is based on the assumption that solutions elaborated by living organisms to decipher and face complexity could be applicable to all complex adaptive systems. Within the pedagogical and didactic context the proposai of the French physiologist could provide a scientific research trajectory aiming at solving the tension between theory, praxis, descriptive approaches and practical needs. Thus, simplexity seems to be an operational strategy based on the identification of the principles that rule (...) and guide the didactic action through patterns of adaptation, which allow to decipher complexity in terms of data elaboration and decision making among different opportunities. (shrink)

We propose a reconstruction of the constellation of problems and philosophical positions on the nature and number of the primitives of logic in four authors of the nineteenth century logical scene: Peano, Padoa, Frege and Peirce. We argue that the proposed reconstruction forces us to recognize that it is in at least four different senses that a notation can be said to be simpler than another, and we trace the origins of these four senses in the writings of these authors. (...) We conclude that Frege, and even more so Peirce, developed new notations not to make drawing logical conclusions easier but in order to answer the needs of logical analysis. (shrink)

This book offers a concise survey of basic probability theory from a thoroughly subjective point of view whereby probability is a mode of judgment. Written by one of the greatest figures in the field of probability theory, the book is both a summation and synthesis of a lifetime of wrestling with these problems and issues. After an introduction to basic probability theory, there are chapters on scientific hypothesis-testing, on changing your mind in response to generally uncertain (...) observations, on expectations of the values of random variables, on de Finetti's dissolution of the so-called problem of induction, and on decision theory. (shrink)

A. J. Ayer was one of the foremost analytical philosophers of the twentieth century, and was known as a brilliant and engaging speaker. In essays based on his influential Dewey Lectures, Ayer addresses some of the most critical and controversial questions in epistemology and the philosophy of science, examining the nature of inductive reasoning and grappling with the issues that most concerned him as a philosopher. This edition contains revised and expanded versions of the lectures and two additional essays. Ayer (...) begins by considering Hume's formulation of the problem of induction and then explores the inferences on which we base our beliefs in factual matters. In other essays, he defines the three kinds of probability that inform inductive reasoning and examines the various criteria for verifiability and falsifiability. In his extensive introduction, Graham Macdonald discusses the arguments in _Probability and Evidence_, how they relate to Ayer's other works, and their influence in contemporary philosophy. He also provides a brief biographical sketch of Ayer, and includes a bibliography of works about and in response to _Probability and Evidence_. (shrink)

How do we ascribe subjective probability? In decision theory, this question is often addressed by representation theorems, going back to Ramsey (1926), which tell us how to define or measure subjective probability by observable preferences. However, standard representation theorems make strong rationality assumptions, in particular expected utility maximization. How do we ascribe subjective probability to agents which do not satisfy these strong rationality assumptions? I present a representation theorem with weak rationality assumptions which can be used to (...) define or measure subjective probability for partly irrational agents. (shrink)

This book explores a question central to philosophy--namely, what does it take for a belief to be justified or rational? According to a widespread view, whether one has justification for believing a proposition is determined by how probable that proposition is, given one's evidence. In this book this view is rejected and replaced with another: in order for one to have justification for believing a proposition, one's evidence must normically support it--roughly, one's evidence must make the falsity of that proposition (...) abnormal in the sense of calling for special, independent explanation. This conception of justification bears upon a range of topics in epistemology and beyond. Ultimately, this way of looking at justification guides us to a new, unfamiliar picture of how we should respond to our evidence and manage our own fallibility. This picture is developed here. (shrink)

When a doctor tells you there’s a one percent chance that an operation will result in your death, or a scientist claims that his theory is probably true, what exactly does that mean? Understanding probability is clearly very important, if we are to make good theoretical and practical choices. In this engaging and highly accessible introduction to the philosophy of probability, Darrell Rowbottom takes the reader on a journey through all the major interpretations of probability, with reference (...) to real–world situations. In lucid prose, he explores the many fallacies of probabilistic reasoning, such as the ‘gambler’s fallacy’ and the ‘inverse fallacy’, and shows how we can avoid falling into these traps by using the interpretations presented. He also illustrates the relevance of the interpretation of probability across disciplinary boundaries, by examining which interpretations of probability are appropriate in diverse areas such as quantum mechanics, game theory, and genetics. Using entertaining dialogues to draw out the key issues at stake, this unique book will appeal to students and scholars across philosophy, the social sciences, and the natural sciences. (shrink)

Richard Jeffrey is beyond dispute one of the most distinguished and influential philosophers working in the field of decision theory and the theory of knowledge. His work is distinctive in showing the interplay of epistemological concerns with probability and utility theory. Not only has he made use of standard probabilistic and decision theoretic tools to clarify concepts of evidential support and informed choice, he has also proposed significant modifications of the standard Bayesian position in order that it provide a (...) better fit with actual human experience. Probability logic is viewed not as a source of judgment but as a framework for explaining the implications of probabilistic judgments and their mutual compatability. This collection of essays spans a period of some 35 years and includes what have become some of the classic works in the literature. There is also one completely new piece, while in many instances Jeffrey includes afterthoughts on the older essays. (shrink)

As a student at Cambridge forty years ago I received a good training in the language and literature of classical Greece, and had the good fortune to study paleography under the late E. H. Minns. For all this I am deeply grateful. But I had no training in Byzantine Greek. It was only later, and more or less by accident, that I discovered Byzantine and Modern Greek. It is not my intention to discuss the wider aspects of this question now, (...) but to appeal, on the basis of some passages in the Oresteia, for a new approach to textual criticism, or rather for the renewal of an old approach. (shrink)

As a student at Cambridge forty years ago I received a good training in the language and literature of classical Greece, and had the good fortune to study paleography under the late E. H. Minns. For all this I am deeply grateful. But I had no training in Byzantine Greek. It was only later, and more or less by accident, that I discovered Byzantine and Modern Greek. It is not my intention to discuss the wider aspects of this question now, (...) but to appeal, on the basis of some passages in the Oresteia, for a new approach to textual criticism, or rather for the renewal of an old approach. (shrink)

The aim of this article is to reconstruct the theory of simple apprehension held in the Kiev-Mohyla Academy in the seventeenth and eighteenth centuries. We start from Aristotle’s idea of two kinds of knowing and from the Thomist theory of the two operations of the intellect in view of the ontological distinction between essence and actuality. In dealing with the theory of the activities of the intellect in the Kiev-MohylaAcademy, we consider simple apprehension as a form of Aristotle’s immediate knowledge. (...) We conclude by introducing the notion of non-representational simple apprehension. (shrink)

The aim of this article is to reconstruct the theory of simple apprehension held in the Kiev-Mohyla Academy in the seventeenth and eighteenth centuries. We start from Aristotle’s idea of two kinds of knowing and from the Thomist theory of the two operations of the intellect in view of the ontological distinction between essence and actuality. In dealing with the theory of the activities of the intellect in the Kiev-MohylaAcademy, we consider simple apprehension as a form of Aristotle’s immediate knowledge. (...) We conclude by introducing the notion of non-representational simple apprehension. (shrink)

This volume is the first to provide a philosophical appraisal of probabilities in all of physics.

Recognizing that probability (the Greek doxa) was understood in pre-modern theories as the polar opposite of certainty (episteme), the author of this study elaborates the forms which these polar opposites have taken in some twentieth century writers and then, in greater detail, in the writings of Thomas Aquinas. Profiting from subsequent more sophisticated theories of probability, he examines how Aquinas’s judgments about everything from God to gossip depend on schematizations of the polarity between the systematic and the non-systematic: (...) revelation/reason, science/opinion, saints/philosophers, Aristotle/others. Post-medieval developments have provided the means to discern within Thomas’s thought both a logical theory and a kind of relative frequency theory of probability. The former depends on Aristotle’s theory of demonstration, the latter on his theory of an orderly cosmos; but each as used by Thomas lead to convictions that are sometimes naive, sometimes amusing or even terrifying. (shrink)

In _Probability and Evidence_, one of Britain's foremost twentieth-century philosophers addresses central questions in the theory of knowledge and the philosophy of science. This book contains A.J. Ayer's John Dewey Lectures delivered at Columbia University, together with two additional essays, "Has Harrod Answered Hume?" and "The Problem of Conditionals.".

Science is the basis for managing the affairs of life and human activities, and living without knowledge is a form of wandering and a kind of loss. Using scientific methods helps us understand the foundations of choice, decision-making, and adopting the right solutions when solutions abound and options are numerous. Operational research is considered the best that scientific development has provided because its methods depend on the application of scientific methods in solving complex issues and the optimal use of available (...) resources in various fields, private and governmental work in peace and war, in politics and economics, in planning and implementation, and in various aspects of life. Its basic essence is to use the data provided for the issue under study to build a mathematical model that is the optimal solution. It is the basis on which decision makers rely in managing institutions and companies, and when operations research methods meet with the neutrosophic teacher, we get ideal solutions that take into account all the circumstances and fluctuations that may occur in the work environment over time. One of the most important operations research methods is the linear programming method. Which prompted us to reformulate the linear models, the graphical method, and the simplex method, which are used to obtain the optimal solution for linear models using the concepts of neutrosophic science. In this research, and as a continuation of what we presented previously, we will reformulate the modified simplex algorithm that was presented to address the difficulty that we were facing when applying the direct simplex algorithm. It is the large number of calculations required to be performed in each step of the solution, which requires a lot of time and effort. (shrink)

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)

In two recent papers Barry Loewer (2001, 2004) has suggested to interpret probabilities in statistical mechanics as Humean chances in David Lewis’ (1994) sense. I first give a precise formulation of this proposal, then raise two fundamental objections, and finally conclude that these can be overcome only at the price of interpreting these probabilities epistemically.

The book was planned and written as a single, sustained argument. But earlier versions of a few parts of it have appeared separately. The object of this book is both to establish the existence of the paradoxes, and also to describe a non-Pascalian concept of probability in terms of which one can analyse the structure of forensic proof without giving rise to such typical signs of theoretical misfit. Neither the complementational principle for negation nor the multiplicative principle for conjunction (...) applies to the central core of any forensic proof in the Anglo-American legal system. There are four parts included in this book. Accordingly, these parts have been written in such a way that they may be read in different orders by different kinds of reader. (shrink)

APA PsycNET abstract: This is the first volume of a two-volume work on Probability and Induction. Because the writer holds that probability logic is identical with inductive logic, this work is devoted to philosophical problems concerning the nature of probability and inductive reasoning. The author rejects a statistical frequency basis for probability in favor of a logical relation between two statements or propositions. Probability "is the degree of confirmation of a hypothesis (or conclusion) on the (...) basis of some given evidence (or premises)." Furthermore, all principles and theorems of inductive logic are analytic, and the entire system is to be constructed by means of symbolic logic and semantic methods. This means that the author confines himself to the formalistic procedures of word and symbol systems. The resulting sentence or language structures are presumed to separate off logic from all subjectivist or psychological elements. Despite the abstractionism, the claim is made that if an inductive probability system of logic can be constructed it will have its practical application in mathematical statistics, and in various sciences. 16-page bibliography. (PsycINFO Database Record (c) 2016 APA, all rights reserved). (shrink)

Once upon a time, some thought that indicative conditionals could be effectively analyzed as material conditionals. Later on, an alternative theoretical construct has prevailed and received wide acceptance, namely, the conditional probability of the consequent given the antecedent. Partly following critical remarks recently ap- peared in the literature, we suggest that evidential support—rather than conditional probability alone—is key to understand indicative conditionals. There have been motivated concerns that a theory of evidential conditionals (unlike their more tra- ditional counterparts) (...) cannot generate a sufficiently interesting logical system. Here, we will describe results dispelling these worries. Happily, and perhaps surprisingly, appropriate technical variations of Ernst Adams’s classical approach allow for the construction of a logic of evidential conditionals with distinctive fea- tures, which is also well-behaved and reasonably strong. (shrink)

Emch, G.G., Liu, C.: The Logic of Thermostatistical Physics. Springer, Berlin/ Heidelberg (2002) 11. Frigg, R., Werndl, C.: Entropy – a guide for the perplexed. Forthcoming in: Beisbart, C., Hartmann, S. (eds.) Probabilities in Physics. Oxford  ...

I argue that when we use ‘probability’ language in epistemic contexts—e.g., when we ask how probable some hypothesis is, given the evidence available to us—we are talking about degrees of support, rather than degrees of belief. The epistemic probability of A given B is the mind-independent degree to which B supports A, not the degree to which someone with B as their evidence believes A, or the degree to which someone would or should believe A if they had (...) B as their evidence. My central argument is that the degree-of-support interpretation lets us better model good reasoning in certain cases involving old evidence. Degree-of-belief interpretations make the wrong predictions not only about whether old evidence confirms new hypotheses, but about the values of the probabilities that enter into Bayes’ Theorem when we calculate the probability of hypotheses conditional on old evidence and new background information. (shrink)

Quantum mechanics and probability theory share one peculiarity. Both have well established mathematical formalisms, yet both are subject to controversy about the meaning and interpretation of their basic concepts. Since probability plays a fundamental role in QM, the conceptual problems of one theory can affect the other. We first classify the interpretations of probability into three major classes: inferential probability, ensemble probability, and propensity. Class is the basis of inductive logic; deals with the frequencies of (...) events in repeatable experiments; describes a form of causality that is weaker than determinism. An important, but neglected, paper by P. Humphreys demonstrated that propensity must differ mathematically, as well as conceptually, from probability, but he did not develop a theory of propensity. Such a theory is developed in this paper. Propensity theory shares many, but not all, of the axioms of probability theory. As a consequence, propensity supports the Law of Large Numbers from probability theory, but does not support Bayes theorem. Although there are particular problems within QM to which any of the classes of probability may be applied, it is argued that the intrinsic quantum probabilities are most naturally interpreted as quantum propensities. This does not alter the familiar statistical interpretation of QM. But the interpretation of quantum states as representing knowledge is untenable. Examples show that a density matrix fails to represent knowledge. (shrink)

I describe a realist, ontologically objective interpretation of probability, "far-flung frequency (FFF) mechanistic probability". FFF mechanistic probability is defined in terms of facts about the causal structure of devices and certain sets of frequencies in the actual world. Though defined partly in terms of frequencies, FFF mechanistic probability avoids many drawbacks of well-known frequency theories and helps causally explain stable frequencies, which will usually be close to the values of mechanistic probabilities. I also argue that it's (...) a virtue rather than a failing of FFF mechanistic probability that it does not define single-case chances, and compare some aspects of my interpretation to a recent interpretation proposed by Strevens. (shrink)

This book provides a systematic treatment of Locke's theory of probable assent. It shows how the theory applies to Locke's philosophy of science, moral epistemology, and religious epistemology. There is a powerful case to be made that the most important dimension of Locke's philosophy is his theory of rational probable assent, rather than his theory of knowledge. According to Locke, we largely live our lives in the "twilight of probability" rather than in "the sunshine of certain knowledge". Locke's theory (...) of probable assent is towering insofar as it contains a wealth of novel, independently interesting, and prescient elements that precede the modern field of formal epistemology. In this book, the author argues for the central role of probable assent in Locke's philosophy. Locke's theory of probable assent is based on an epistemic modesty that claims, roughly, that our cognitive abilities are quite limited and that we ought to carry ourselves in believing with due caution. This modesty motivates the author's discussion of other aspects of Locke's epistemology, notably his principle of proportionality, his doxastic involuntarism, his epistemological pragmatism, and his theory of testimony. The book concludes by connecting the theory of probable assent with Locke's views on the limits of science, moral epistemology, and the rationality of faith. Locke's Twilight of Probability will appeal to scholars and advanced students working on Locke and the history of early modern philosophy. (shrink)

This paper develops an information-sensitive theory of the semantics and probability of conditionals and statements involving epistemic modals. The theory validates a number of principles linking probability and modality, including the principle that the probability of a conditional If A, then C equals the probability of C, updated with A. The theory avoids so-called triviality results, which are standardly taken to show that principles of this sort cannot be validated. To achieve this, we deny that rational (...) agents update their credences via conditionalization. We offer a new rule of update, Hyperconditionalization, which agrees with Conditionalization whenever nonmodal statements are at stake but differs for modal and conditional sentences. (shrink)

We propose a model of uncertain belief. This models coherent beliefs by a filter, ????, on the set of probabilities. That is, it is given by a collection of sets of probabilities which are closed under supersets and finite intersections. This can naturally capture your probabilistic judgements. When you think that it is more likely to be sunny than rainy, we have{????|????(????????????????????)>????(????????????????????)}∈????. When you think that a gamble ???? is desirable, we have {????|Exp????[????]>0}∈????. It naturally extends the model of credal (...) sets; and we will show it captures all the expressive power of the desirable gambles model. It also captures the expressive power of sets of desirable gamble sets (with a mixing axiom, but no Archimadean axiom). (shrink)

There are two central questions concerning probability. First, what are its formal features? That is a mathematical question, to which there is a standard, widely (though not universally) agreed upon answer. This answer is reviewed in the next section. Second, what sorts of things are probabilities---what, that is, is the subject matter of probability theory? This is a philosophical question, and while the mathematical theory of probability certainly bears on it, the answer must come from elsewhere. To (...) see why, observe that there are many things in the world that have the mathematical structure of probabilities---the set of measurable regions on the surface of a table, for example---but that one would never mistake for being probabilities. So probability is distinguished by more than just its formal characteristics. The bulk of this essay will be taken up with the central question of what this “more” might be. (shrink)

This is a study in the meaning of natural language probability operators, sentential operators such as probably and likely. We ask what sort of formal structure is required to model the logic and semantics of these operators. Along the way we investigate their deep connections to indicative conditionals and epistemic modals, probe their scalar structure, observe their sensitivity to contex- tually salient contrasts, and explore some of their scopal idiosyncrasies.

This contribution examines two related points in relation to Aquinas’s understanding of contemplation, which is a sorely neglected topic in scholarship. First, after having outlined that the final act of contemplation culminates in an intellective, simple apprehension of the truth, I will examine how this act relates to the three operations of the intellect (grasping of quiddity, judgement, and reasoning) Aquinas identifies in a number of places. Second, I argue that his view of contemplation as simple insight is significantly indebted (...) to Neoplatonic sources; therefore, we must pay attention to the way he introduces Neoplatonic elements into his Aristotelian framework. I conclude this contribution by suggesting some reasons—of a theological nature—why Aquinas would have been drawn towards a non-discursive or “intuitive” notion of contemplation. (shrink)

It is well known that classical, aka ‘sharp’, Bayesian decision theory, which models belief states as single probability functions, faces a number of serious difficulties with respect to its handling of agnosticism. These difficulties have led to the increasing popularity of so-called ‘imprecise’ models of decision-making, which represent belief states as sets of probability functions. In a recent paper, however, Adam Elga has argued in favour of a putative normative principle of sequential choice that he claims to be (...) borne out by the sharp model but not by any promising incarnation of its imprecise counterpart. After first pointing out that Elga has fallen short of establishing that his principle is indeed uniquely borne out by the sharp model, I cast aspersions on its plausibility. I show that a slight weakening of the principle is satisfied by at least one, but interestingly not all, varieties of the imprecise model and point out that Elga has failed to motivate his stronger commitment. (shrink)

A. J. Ayer was one of the foremost analytical philosophers of the twentieth century, and was known as a brilliant and engaging speaker. In essays based on his influential Dewey Lectures, Ayer addresses some of the most critical and controversial questions in epistemology and the philosophy of science, examining the nature of inductive reasoning and grappling with the issues that most concerned him as a philosopher. This edition contains revised and expanded versions of the lectures and two additional essays. Ayer (...) begins by considering Hume's formulation of the problem of induction and then explores the inferences on which we base our beliefs in factual matters. In other essays, he defines the three kinds of probability that inform inductive reasoning and examines the various criteria for verifiability and falsifiability. In his extensive introduction, Graham Macdonald discusses the arguments in _Probability and Evidence_, how they relate to Ayer's other works, and their influence in contemporary philosophy. He also provides a brief biographical sketch of Ayer, and includes a bibliography of works about and in response to _Probability and Evidence_. (shrink)

This paper motivates and develops a novel semantic framework for deontic modals. The framework is designed to shed light on two things: the relationship between deontic modals and substantive theories of practical rationality and the interaction of deontic modals with conditionals, epistemic modals and probability operators. I argue that, in order to model inferential connections between deontic modals and probability operators, we need more structure than is provided by classical intensional theories. In particular, we need probabilistic structure that (...) interacts directly with the compositional semantics of deontic modals. However, I reject theories that provide this probabilistic structure by claiming that the semantics of deontic modals is linked to the Bayesian notion of expectation. I offer a probabilistic premise semantics that explains all the data that create trouble for the rival theories. (shrink)

This paper articulates a way to ground a relatively high prior probability for grand explanatory theories apart from an appeal to simplicity. I explore the possibility of enumerating the space of plausible grand theories of the universe by using the explanatory properties of possible views to limit the number of plausible theories. I motivate this alternative grounding by showing that Swinburne’s appeal to simplicity is problematic along several dimensions. I then argue that there are three plausible grand views—theism, atheism, (...) and axiarchism—which satisfy explanatory requirements for plausibility. Other possible views lack the explanatory virtue of these three theories. Consequently, this explanatory grounding provides a way of securing a nontrivial prior probability for theism, atheism, and axiarchism. An important upshot of my approach is that a modest amount of empirical evidence can bear significantly on the posterior probability of grand theories of the universe. (shrink)