This definitive survey of the hottest issues in inductive logic sets the stage for further classroom discussion.

Preface. I. BASICS OF LOGIC. Introduction. The Structure of Simple Statements. The Structure of Complex Statements. Simple and Complex Properties. Validity. 2. PROBABILITY AND INDUCTIVE LOGIC. Introduction. Arguments. Logic. Inductive versus Deductive Logic. Epistemic Probability. Probability and the Problems of Inductive Logic. 3. THE TRADITIONAL PROBLEM OF INDUCTION. Introduction. Hume’s Argument. The Inductive Justification of Induction. The Pragmatic Justification of Induction. Summary. IV. THE GOODMAN PARADOX AND THE NEW RIDDLE OF INDUCTION. Introduction. Regularities and Projection. The Goodman Paradox. The Goodman (...) Paradox, Regularity, and the Principle of the Uniformity of Nature. Summary. 5. MILL’S METHODS OF EXPERIMENTAL INQUIRY AND THE NATURE OF CAUSALITY. Introduction. Causality and Necessary and Sufficient Conditions. Mill’s Methods. The Direct Method of Agreement. The Inverse Method of Agreement. The Method of Difference. The Combined Methods. The Application of Mill’s Methods. Sufficient Conditions and Functional Relationships. Lawlike and Accidental Conditions. 6. THE PROBABILITY CALCULUS. Introduction. Probability, Arguments, Statements, and Properties. Disjunction and Negation Rules. Conjunction Rules and Conditional Probability. Expected Value of a Gamble. Bayes’ Theorem. Probability and Causality. 7. KINDS OF PROBABILITY. Introduction. Rational Degree of Belief. Utility. Ramsey. Relative Frequency. Chance. 8. PROBABILITY AND SCIENTIFIC INDUCTIVE LOGIC. Introduction. Hypothesis and Deduction. Quantity and Variety of Evidence. Total Evidence. Convergence to the Truth. ANSWERS TO SELECTED EXERCISES. INDEX. (shrink)

The question of coherence of rules for changing degrees of belief in the light of new evidence is studied, with special attention being given to cases in which evidence is uncertain. Belief change by the rule of conditionalization on an appropriate proposition and belief change by "probability kinematics" on an appropriate partition are shown to have like status.

A brief account of the work of Giorgio Agamben and its relation to the work of Jean-Luc Nancy.

Maher (1992b) advances an objection to dynamic Dutch-book arguments, partly inspired by the discussion in Levi (1987; in particular by Levi's case 2, p. 204). Informally, the objection is that the decision maker will "see the dutch book coming" and consequently refuse to bet, thus escaping the Dutch book. Maher makes this explicit by modeling the decision maker's choices as a sequential decision problem. On this basis he claims that there is a mistake in dynamic coherence arguments. There is really (...) no formal mistake in classical dynamic coherence arguments, but the discussions in Maher and Levi do suggest interesting ways in which the definition of dynamic coherence might be strengthened. Such a strengthened "sequentialized" notion of dynamic coherence is explored here. It so happens that even on the strengthened standards for a Dutch book, the classic dynamic coherence argument for conditioning still goes through. (shrink)

Explore 2,500 years of Western philosophy, from the ancient Greeks to modern thinkers, with this ultimate guide’s stunning and simple approach to some of history’s biggest ideas. This essential guide to philosophy includes thoughts on our modern society, exploring science and democracy, and posing the question: where do we go from here? Easy-to-understand text is accompanied by works of art and artifacts from history, as the big ideas and important thinkers are introduced through time. Famous quotes are highlighted, and the (...) sidebars discuss other ideas or key works to include extra context around the theories and people. Celebrate the world's most revolutionary concepts and understand how these ideas continue to shape our world. Develop your own perspectives and explore relevant issues such as modern logic and religion with this wonderfully comprehensive illustrated guide. In a world of evolving ideas, The Story of Philosophy is a fantastic resource to revisit again and again. (shrink)

This contribution is part of the special series of Inaugural Articles by members of the National Academy of Sciences elected on April 27, 1999.

The proper treatment of correlation in evolutionary game theory has unexpected connections with recent philosophical discussions of the theory of rational decision. The Logic of Decision (Jeffrey 1983) provides the correct framework for correlated evolutionary game theory and a variant of "ratifiability" is the appropriate generalization of "evolutionarily stable strategy". The resulting theory unifies the treatment of correlation due to kin, population viscosity, detection, signaling, reciprocal altruism, and behavior-dependent contexts. It is shown that (1) a strictly dominated strategy may be (...) selected, and (2) under conditions of perfect correlation a strictly efficient strategy must be selected. (shrink)

I argue in this paper that Immanuel Kant's account of the moral wrongness of contempt in the Metaphysics of Morals provides important resources for our understanding of the nature of moral subjectivity. Although Kant typically emphasizes the subject's position as autonomous addressor of the moral law, his remarks on contempt bring into relief a dynamic relationship at the heart of practical subjectivity between the addressor and addressee positions. After tracing the development of reflection concerning the addressor and addressee positions in (...) early modern philosophy, beginning with Francisco Suarez and Samuel Pufendorf, I articulate and defend what I take to be a Kantian conception of the relation between those positions. More specifically, I argue that to be a moral subject at all is necessarily to position oneself as the addressor of the moral law, but that one must at the same time maintain oneself in the addressee position, resisting the full conversion to the addressor position that autonomy seems to demand. (shrink)

We consider the following signaling game. Nature plays first from the set {1, 2}. Player 1 (the Sender) sees this and plays from the set {A, B}. Player 2 (the Receiver) sees only Player 1’s play and plays from the set {1, 2}. Both players win if Player 2’s play equals Nature’s play and lose otherwise. Players are told whether they have won or lost, and the game is repeated. An urn scheme for learning coordination in this game is as (...) follows. Each node of the desicion tree for Players 1 and 2 contains an urn with balls of two colors for the two possible decisions. Players make decisions by drawing from the appropriate urns. After a win, each ball that was drawn is reinforced by adding another of the same color to the urn. A number of equilibria are possible for this game other than the optimal ones. However, we show that the urn scheme achieves asymptotically optimal coordination. (shrink)

My dissertation presents a comprehensive rethinking of the Kantian imperative, articulating it on the basis of what I call originary sense. Calling primarily upon the works of Maurice Merleau-Ponty, Gilles Deleuze, and Jean-François Lyotard, I show (1) that sense constitutes the ontologically most basic dimension of our worldly being and (2) that the way in which this sense happens is determinative for our experience of the ethical imperative. By originary sense I mean to name something that is neither sensible sense (...) (sensation) nor intelligible sense (meaning), but rather a kind of unity of these two that is ontologically anterior to their separation. In the first chapter I follow Merleau-Ponty’s argument in Phenomenology of Perception that sensible sense and intelligible sense belong originarily together at the level of the lived body. We are able to intend the meaning of worldly situations (Husserl’s Sinngebung) only insofar as we are responsive in an embodied way to the imperatives that are given in the sensible itself. The intelligible lawfulness so characteristic of the Kantian imperative is thus shown to be grounded in a more fundamental unity of intelligible and sensible sense. The second chapter follows Merleau-Ponty’s later works, especially The Prose of the World and The Visible and the Invisible, showing how the sensibility that is inseparable from the imperative introduces important limitations to the universalizing tendencies of Kant’s moral philosophy, drawing us back to the irreducible situatedness of ethical situations. In the third chapter I turn to the very different articulation of sense given by Gilles Deleuze, primarily in his Logic of Sense. I show there that Merleau-Ponty’s phenomenological conception of sense does not allow us to think the singularity of the imperative, the fact that the ethical command weighs on a me that cannot be grasped in terms of the generalities of my public identity. This singularity corresponds broadly to the idea of dignity in Kant’s moral philosophy. I argue that Deleuze, who conceptualizes sense as an event, gives us the resources to think singularity and to understand what it entails for our ethical practice. Finally, I attempt in the fourth chapter to think these two sides of the imperative—its demand for universality and its emphasis on singularity and dignity— together in the idea of libidinal sense. Calling on Jean-François Lyotard’s Libidinal Economy and, to a lesser extent, on Deleuze and Guattari’s Anti-Oedipus, I show that these two apparently incompatible requirements of the imperative have a common source in the event of libidinal investment (cathexis). In thus locating the source of the imperative in originary, libidinal sense, I hope both to shed some light on the irreducible complexity of our ethical being and to present a more humane, less moralizing version of the imperative than is typically articulated in moral philosophy. (shrink)

In this article, we aim to illustrate evolutionary explanations for the emergence of framing effects, discussed in detail in Cristina Bicchieri’s The Grammar of Society . We show how framing effects might evolve which coalesce two economically distinct interactions into a single one, leading to apparently irrational behavior in each individual interaction. Here we consider the now well-known example of the ultimatum game, and show how this ‘irrational’ behavior might result from a single norm which governs behavior in multiple games. (...) We also show how framing effects might result in radically different play in strategically identical situations. We consider the Hawk-Dove game (the game of chicken) and also the Nash bargaining game. Here arbitrary tags or signals might result in one party doing better than another. (shrink)

We provide an intuitive motivation for the hyperreal numbers via electoral axioms. We do so in the form of a Socratic dialogue, in which Protagoras suggests replacing big-oh complexity classes by real numbers, and Socrates asks some troubling questions about what would happen if one tried to do that. The dialogue is followed by an appendix containing additional commentary and a more formal proof.

Carnap's Inductive Logic, like most philosophical discussions of induction, is designed for the case of independent trials. To take account of periodicities, and more generally of order, the account must be extended. From both a physical and a probabilistic point of view, the first and fundamental step is to extend Carnap's inductive logic to the case of finite Markov chains. Kuipers (1988) and Martin (1967) suggest a natural way in which this can be done. The probabilistic character of Carnapian inductive (...) logic(s) for Markov chains and their relationship to Carnap's inductive logic(s) is discussed at various levels of Bayesian analysis. (shrink)

We revisit classical Utilitarianism by connecting and generalizing two ideas. The first is that there is a representation theorem possible for hedonic value similar to, but also importantly different from, the one provided by von Neumann and Morgenstern to measure decision utility. The idea is to use objective time, in place of objective chance, to measure hedonic value. This representation for hedonic value delivers a stronger kind of scale than von Neumann–Morgenstern utility, a ratio scale rather than merely an interval (...) scale. The second idea is that measurement on a ratio scale allows the meaningful aggregation of utilities over a group. This is aggregation by product rather than sum. Aggregation by product is known to have interesting Prioritarian consequences. Aggregation becomes complicated when the two approaches are mixed, when hedonic value is mixed with uncertainly. It becomes problematic when pain as well as pleasure is taken into account. (shrink)

Game theory based on rational choice is compared with game theory based on evolutionary, or other adaptive, dynamics. The Nash equilibrium concept has a central role to play in both theories, even though one makes extremely strong assumptions about cognitive capacities and common knowledge of the players, and the other does not. Nevertheless, there are also important differences between the two theories. These differences are illustrated in a number of games that model types of interaction that are key ingredients for (...) any theory of the social contract. (shrink)

"Under Magee's sensitive guidance a remarkably coherent interpretation of this period emerges."--Marshall Cohen, Listener. "The whole book has a marvellous air of casualness and clarity that makes it a delight to read."--Colin Wilson. Contemporary British philosophy is experiencing unprecedented openness to influences from abroad. New growth is evident in many areas of traditional philosophy which had been neglected by the logical positivists and the linguistic analysts. This sense of freedom permeates Magee's volume of conversations with leading British philosophers. Under Magee's (...) direction, the philosophers discuss other influential thinkers, such as Wittgenstein, Russell, Moore, and Austin, as well as ideas of universal interest, such as morality, art, religion, and social theory. As an introduction to contemporary British philosophy, a unique collection of candid commentaries by important thinkers, and study of fresh ideas, Modern British Philosophy is consistently lively and authoritative. (shrink)

Fifteen dialogues drawn from the highly acclaimed BBC series review the tenets and theories of moral philosophy, poliitcal philosophy, the philosophy of language, and the philosophy of science.

To coordinate action, information must be transmitted, processed, and utilized to make decisions. Transmission of information requires the existence of a signaling system in which the signals that are exchanged are coordinated with the appropriate content. Signaling systems in nature range from quorum signaling in bacteria [Schauder and Bassler, Kaiser ], through the dance of the bees [Dyer and Seeley ], birdcalls [Hailman, Ficken, and Ficken, Gyger, Marler and Pickert, Evans, Evans, and Marler, Charrier and Sturdy ], and alarm calls (...) in many species [Seyfarth and Cheney, Green and Maegner,Manser, Seyfarth and Cheney ], up to human language. Information processing includes filtering – that is discarding irrelevant information and passing along what is important – and integration of multiple pieces of information. Integration includes logical inference and voting. Finally, the information must be used to make decisions with consequences for payoffs that drive evolution or learning. (shrink)

Bell's Theorem is proved for locality and conservation formulated in terms of subjunctive conditionals with chance consequents, rather than the usual conditional probability formulation. This brings into sharp focus the minimal counterfactual assumptions needed for Bell's theorem.

Some of the concerns which motivate attempts to provide a philosophical reduction of nomological necessity are briefly introduced in I. In II, Hempel's treatment of the paradoxes is contrasted with a position which holds that nomological necessity is a pragmatic dimension of laws of nature, and that this pragmatic dimension is of such a type that it prevents laws of nature from contraposing. Such a position is, however, untenable unless (i) the sense of 'pragmatics' at issue is specified, and the (...) possibility of pragmatic differences resulting in differences in confirmation is defended, and (ii) a relevant pragmatic difference between contrapositives is indicated. III attempts to satisfy condition (i) by developing a new sense of pure pragmatics and argues that some remarks by Goodman and Scheffler together with work on the logic of explanation by Dr. Rescher and myself suggest that nomological contrapositives are not pragmatically equivalent (i.e. substitutable salva veritate in the pure pragmatics of an ideal scientific language). If such is the case, condition (ii) is also satisfied. (shrink)

We investigate a simple stochastic model of social network formation by the process of reinforcement learning with discounting of the past. In the limit, for any value of the discounting parameter, small, stable cliques are formed. However, the time it takes to reach the limiting state in which cliques have formed is very sensitive to the discounting parameter. Depending on this value, the limiting result may or may not be a good predictor for realistic observation times.

The question of diachronic coherence, coherence of degrees of belief across time, is investigated within the context of Richard Jeffrey’s radical probabilism. Diachronic coherence is taken as fundamental, and coherence results for degrees of belief at a single time, such as additivity, are recovered only with additional assumptions. Additivity of probabilities of probabilities is seen to be less problematic than additivity of first-order probabilities. Without any assumed model of belief change, diachronic coherence applied to higher-order degrees of belief yields the (...) martingale property. (shrink)

This paper discusses the explanatory significance of the equilibrium concept in the context of an example of extremely complicated dynamical behavior. In particular, numerical evidence is presented for the existence of chaotic dynamics on a "strange attractor" in the evolutionary game dynamics introduced by Taylor and Jonker [also known as the "replicator dynamics"]. This phenomenon is present already in four strategy evolutionary games where the dynamics takes place in a simplex in three dimensional space-the lowest number of dimensions in which (...) such a strange attractor is possible. From a dynamical point of view, it is the attractor-rather than the equilibrium-that is of prime interest. (shrink)

This is an investigation of the emergence of signaling using one kind of trial and error learning: probe and adjust.Send article to KindleTo send this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about (...) sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.LEARNING TO SIGNAL WITH PROBE AND ADJUSTVolume 9, Issue 2Brian SkyrmsDOI: https://doi.org/10.1017/epi.2012.5Your Kindle email address Please provide your Kindle [email protected]@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. LEARNING TO SIGNAL WITH PROBE AND ADJUSTVolume 9, Issue 2Brian SkyrmsDOI: https://doi.org/10.1017/epi.2012.5Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. LEARNING TO SIGNAL WITH PROBE AND ADJUSTVolume 9, Issue 2Brian SkyrmsDOI: https://doi.org/10.1017/epi.2012.5Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation Request permission. (shrink)

The structure of Reichenbach's pragmatic vindication of induction is analysed in detail. The argument is seen to proceed in two stages, the first being a pragmatic justification of the frequency interpretation of probability which is taken as a license for considering the aim of induction to be the discovery of limiting relative frequencies, and the second being the pragmatic justification of induction itself. Both justifications are found to contain flaws, and the arguments used to support Reichenbach's definition of the aim (...) of induction presuppose the availability of a type of predicate which generates paradoxes closely related to Goodman's "grue-bleen" paradox. Next, Salmon's "Criterion of Linguistic Invariance" is evaluated as a canon of inductive logic, which singles out the "straight rule" from an infinite class of convergent inductive rules. Upon close examination, its credentials are seen to be unimpressive. In connection with Salmon's work on linguistic invariance, we take a closer look at the impact of the Goodman paradox on probability estimator rules like Reichenbach's "straight rule." We find that its undesirable consequences for such systems of inductive logic cannot be escaped by Salmon's solution, or indeed by any solution whose motivating idea is to rule "queer" predicates out of court. Finally, the discussion of the Goodman paradox leads us to a modest methodological proposal for systems of inductive logic which incorperate probability estimator rules of the type at issue. (shrink)

We show how Richard Jeffrey’s The Logic of Decision provides the proper formalism for calculating expected fitness for correlated encounters in general. As an illustration, some puzzles about kin selection are resolved.

Two examples demonstrate the possibility of extremely complicated non-convergent behavior in evolutionary game dynamics. For the Taylor-Jonker flow, the stable orbits for three strategies were investigated by Zeeman. Chaos does not occur with three strategies. This papers presents numerical evidence that chaotic dynamics on a strange attractor does occur with four strategies. Thus phenomenon is closely related to known examples of complicated behavior in Lotka-Volterra ecological models.

1 Introduction p. 3 2 Scientific Method--the Traditional View and Popper's View p. 13 3 The Criterion of Demarcation between what is and what is not Science p. 32 4 Popper's Evolutionism and his theory of World 3 p. 55 5 Objective Knowledge p. 65 6 The Open Society p. 75 7 The Enemies of the Open Society p. 90 Postscript p. 114 Bibliography p. 117.