We analyze common reasoning about admissibility in the strategic and extensive form of a game. We define a notion of sequential proper admissibility in the extensive form, and show that, in finite extensive games with perfect recall, the strategies that are consistent with common reasoning about sequential proper admissibility in the extensive form are exactly those that are consistent with common reasoning about admissibility in the strategic form representation of the game. Thus in such games the solution given by common (...) reasoning about admissibility does not depend on how the strategic situation is represented. We further explore the links between iterated admissibility and backward and forward induction. (shrink)

This paper pursues a thorough-going instrumentalist, or means-ends, approach to the theory of inductive inference. I consider three epistemic aims: convergence to a correct theory, fast convergence to a correct theory and steady convergence to a correct theory (avoiding retractions). For each of these, two questions arise: (1) What is the structure of inductive problems in which these aims are feasible? (2) When feasible, what are the inference methods that attain them? Formal learning theory provides the tools for a complete (...) set of answers to these questions. As an illustration of the results, I apply means-ends analysis to various versions of Goodman's Riddle of Induction. (shrink)

Formal learning theory is the mathematical embodiment of a normative epistemology. It deals with the question of how an agent should use observations about her environment to arrive at correct and informative conclusions. Philosophers such as Putnam, Glymour and Kelly have developed learning theory as a normative framework for scientific reasoning and inductive inference.

This paper places formal learning theory in a broader philosophical context and provides a glimpse of what the philosophy of induction looks like from a learning-theoretic point of view. Formal learning theory is compared with other standard approaches to the philosophy of induction. Thereafter, we present some results and examples indicating its unique character and philosophical interest, with special attention to its unified perspective on inductive uncertainty and uncomputability.

Philosophical logicians proposing theories of rational belief revision have had little to say about whether their proposals assist or impede the agent's ability to reliably arrive at the truth as his beliefs change through time. On the other hand, reliability is the central concern of formal learning theory. In this paper we investigate the belief revision theory of Alchourron, Gardenfors and Makinson from a learning theoretic point of view.

This paper develops a means–end analysis of an inductive problem that arises in particle physics: how to infer from observed reactions conservation principles that govern all reactions among elementary particles. I show that there is a reliable inference procedure that is guaranteed to arrive at an empirically adequate set of conservation principles as more and more evidence is obtained. An interesting feature of reliable procedures for finding conservation principles is that in certain precisely defined circumstances they must introduce hidden particles. (...) Among the reliable inductive methods there is a unique procedure that minimizes convergence time as well as the number of times that the method revises its conservation principles. Thus the aims of reliable, fast and steady convergence to an empirically adequate theory single out a unique optimal inference for a given set of observed reactions—including prescriptions for when exactly to introduce hidden particles. (shrink)

This paper studies efficient learning with respect to mind changes. Our starting point is the idea that a learner that is efficient with respect to mind changes minimizes mind changes not only globally in the entire learning problem, but also locally in subproblems after receiving some evidence. Formalizing this idea leads to the notion of uniform mind change optimality. We characterize the structure of language classes that can be identified with at most α mind changes by some learner (not necessarily (...) effective): A language class L is identifiable with α mind changes iff the accumulation order of L is at most α. Accumulation order is a classic concept from point-set topology. To aid the construction of learning algorithms, we show that the characteristic property of uniformly mind change optimal learners is that they output conjectures (languages) with maximal accumulation order. We illustrate the theory by describing mind change optimal learners for various problems such as identifying linear subspaces and one-variable patterns. (shrink)

Occam’s razor directs us to adopt the simplest hypothesis consistent with the evidence. Learning theory provides a precise definition of the inductive simplicity of a hypothesis for a given learning problem. This definition specifies a learning method that implements an inductive version of Occam’s razor. As a case study, we apply Occam’s inductive razor to causal learning. We consider two causal learning problems: learning a causal graph structure that presents global causal connections among a set of domain variables, and learning (...) context-sensitive causal relationships that hold not globally, but only relative to a context. For causal graph learning, Occam’s inductive razor directs us to adopt the model that explains the observed correlations with a minimum number of direct causal connections. For expanding a causal graph structure to include context-sensitive relationships, Occam’s inductive razor directs us to adopt the expansion that explains the observed correlations with a minimum number of free parameters. This is equivalent to explaining the correlations with a minimum number of probabilistic logical rules. The paper provides a gentle introduction to the learning-theoretic definition of inductive simplicity and the application of Occam’s razor for causal learning. (shrink)

We argue that uncomputability and classical scepticism are both reflections of inductive underdetermination, so that Church's thesis and Hume's problem ought to receive equal emphasis in a balanced approach to the philosophy of induction. As an illustration of such an approach, we investigate how uncomputable the predictions of a hypothesis can be if the hypothesis is to be reliably investigated by a computable scientific method.

From one perspective, the fundamental notions of point-set topology have to do with sequences (of points or of numbers) and their limits. A broad class of epistemological questions also appear to be concerned with sequences and their limits. For example, problems of empirical underdetermination–which of a collection of alternative theories is true–have to do with logical properties of sequences of evidence. Underdetermination by evidence is the central problem of Plato’s Meno [Glymour and Kelly 1992], of one of Sextus Empiricus’ many (...) skeptical doubts, and arguably it is the idea in Kant’s antinomies, for example of the infinite divisibility of matter [Kelly 1995, Ch.3]. Many questions of methodology, or of the logic of discovery, have to do with sequences and their limits, for example under what conditions Bayesian procedures, which put a prior probability distribution over alternative hypotheses and possible evidence and form conditional probabilities as new evidence is obtained, converge to the truth ([Savage 1954], [Hesse 1970], [Osherson and Weinstein 1988], [Juhl 1993]). Some analyses of “S knows that p” seem to appeal to properties of actual and possible sequences of something–for example Nozick’s proposal that knowledge of p is belief in p produced by a method that would not produce belief in p if p were false and would produce belief in p if p were true. Even questions about finding the truth under a quite radical relativism, in which truth 1 depends on conceptual scheme and conceptual schemes can be altered, have been analyzed as a kind of limiting property of sequences [Kelly et al. 1994]. (shrink)

An important approach to game theory is to examine the consequences of beliefs that agents may have about each other. This paper investigates respect for public preferences. Consider an agent A who believes that B strictly prefers an option a to an option b. Then A respects B’s preference if A assigns probability 1 to the choice of a given that B chooses a or b. Respect for public preferences requires that if it is common belief that B prefers a (...) to b, then it is common belief that all other agents respect that preference. Along the lines of Blume, Brandenburger and Dekel [3] and Asheim [1], I treat respect for public preferences as a constraint on lexicographic probability systems. The main result is that given respect for public preferences and perfect recall, players choose in accordance with Iterated Backward Inference. Iterated Backward Inference is a procedure that generalizes standard backward induction reasoning for games of both perfect and imperfect information. From Asheim’s characterization of proper rationalizability [1] it follows that properly rationalizable strategies are consistent with respect for public preferences; hence strategies eliminated by Iterated Backward Inference are not properly rationalizable. (shrink)

The situation calculus is a logical formalism that has been extensively developed for planning. We apply the formalism in a complex multi-agent domain, modelled on the game of Clue. We find that the situation calculus, with suitable extensions, supplies a unified representation of (1) the interaction protocol, or structure of the game, (2) the dynamics of the knowledge and common knowledge of the agents, and (3) principles of strategic planning.

This paper aims to be a friendly introduction to formal learning theory. I introduce key concepts at a slow pace, comparing and contrasting with other approaches to inductive inference such as con…rmation theory. A number of examples are discussed, some in detail, such as Goodman’s Riddle of Induction. I outline some important results of formal learning theory that are of philosophical interest. Finally, I discuss recent developments in this approach to inductive inference.

This paper analyzes the notion of a minimal belief change that incorporates new information. I apply the fundamental decision-theoretic principle of Pareto-optimality to derive a notion of minimal belief change, for two different representations of belief: First, for beliefs represented by a theory – a deductively closed set of sentences or propositions – and second for beliefs represented by an axiomatic base for a theory. Three postulates exactly characterize Pareto-minimal revisions of theories, yielding a weaker set of constraints than the (...) standard AGM postulates. The Levi identity characterizes Pareto-minimal revisions of belief bases: a change of belief base is Pareto-minimal if and only if the change satisfies the Levi identity (for “maxichoice” contraction operators). Thus for belief bases, Pareto-minimality imposes constraints that the AGM postulates do not. The Ramsey test is a well-known way of establishing connections between belief revision postulates and axioms for conditionals (“if p, then q”). Pareto-minimal theory change corresponds exactly to three characteristic axioms of counterfactual systems: a theory revision operator that satisfies the Ramsey test validates these axioms if and only if the revision operator is Pareto-minimal. (shrink)

This paper analyzes the notion of a minimal belief change that incorporates new information. I apply the fundamental decisiontheoretic principle of Pareto-optimality to derive a notion of minimal belief change, for two different representations of belief: First, for beliefs represented by a theory –a deductively closed set of sentences or propositions–and second for beliefs represented by an axiomatic base for a theory. Three postulates exactly characterize Pareto-minimal revisions of theories, yielding a weaker set of constraints than the standard AGM postulates. (...) The Levi identity characterizes Pareto-minimal revisions of belief bases: a change of belief base is Pareto-minimal if and only if the change satisfies the Levi identity (for “maxichoice” contraction operators). Thus for belief bases, Pareto-minimality imposes constraints that the AGM postulates do not. Keywords: belief revision, decision theory.. (shrink)

Kant taught us that there are two kinds of norms: Categorical imperatives that one ought to follow regardless of one's personal aims and circumstances, and hypothetical imperatives that direct us to employ the means towards our chosen ends. Kant's distinction separates two approaches to normative epistemology. On the one hand, we have principles of "inductive rationality", typically supported by considerations such as intuitive plausibility, conformity with exemplary practice, and internal consistency. On the other hand, we may assess rules for forming (...) belief by how well they attain the objectives that motivate inquiry; in Levi's words, "the ends of inquiry control the legitimacy of inferences" [Levi 67, p. 241]. A doctrinaire attitude would ignore one of these perspectives in favour of the other; a balanced approach is to develop both and compare [cf. Helmann 97, Sec.2]. There are three possible relationships between hypothetical and categorical imperatives for empirical inquiry. (shrink)

An important approach to game theory is to examine the consequences of beliefs that rational agents may have about each other. This paper considers respect for public preferences. Consider an agent A who believes that B strictly prefers an option a to an option b. Then A respects B’s preference if A considers the choice of a “infinitely more likely” than the choice of B; equivalently, if A assigns probability 1 to the choice of a given that B chooses a (...) or b. Respect for public preferences requires that if it is common belief that B prefers a to b, then it is common belief that all other agents respect that preference. Along the lines of Blume, Brandenburger and Dekel [4] and Asheim [1], I treat respect for public preferences as a constraint on lexicographic probability systems. The main result is that if respect for public preferences and perfect recall obtains, then players choose in accordance with Iterated Backward Inference. Iterated Backward Inference is a procedure that generalizes standard backward induction reasoning for games of both perfect and imperfect information. From Asheim’s characterization of proper rationalizability [1] it follows that properly rationalizable strategies are consistent with respect for public preferences; hence strategies eliminated by Iterated Backward Inference are not properly rationalizable. (shrink)

Sequential von Neumann–Morgernstern (VM) games are a very general formalism for representing multi-agent interactions and planning problems in a variety of types of environments. We show that sequential VM games with countably many actions and continuous utility functions have a sound and complete axiomatization in the situation calculus. This axiomatization allows us to represent game-theoretic reasoning and solution concepts such as Nash equilibrium. We discuss the application of various concepts from VM game theory to the theory of planning and multi-agent (...) interactions, such as representing concurrent actions and using the Baire topology to define continuous payoff functions. (shrink)

Philosophical logicians proposing theories of rational belief revision have had little to say about whether their proposals assist or impede the agent's ability to reliably arrive at the truth as his beliefs change through time. On the other hand, reliability is the central concern of formal learning theory. In this paper we investigate the belief revision theory of Alchourron, Gardenfors and Makinson from a learning theoretic point of view.

We argue that uncomputability and classical scepticism are both re ections of inductive underdetermination, so that Church's thesis and Hume's problem ought to receive equal emphasis in a balanced approach to the philosophy of induction. As an illustration of such an approach, we investigate how uncomputable the predictions of a hypothesis can be if the hypothesis is to be reliably investigated by a computable scienti c method.

This paper reviews the hole argument as an argument against spacetime substantivalism. After a careful presentation of the argument itself, I critically review possible responses.

What is morality? How many moral values are there? And what are they? According to the theory of morality-as-cooperation, morality is a collection of biological and cultural solutions to the problems of cooperation recurrent in human social life. This theory predicts that there will be as many different types of morality as there are different types of cooperation. Previous research, drawing on evolutionary game theory, has identified at least seven different types of cooperation, and used them to explain seven different (...) types of morality: family values, group loyalty, reciprocity, heroism, deference, fairness and property rights. Here we explore the conjecture that these simple moral ‘elements’ combine to form a much larger number of more complex moral ‘molecules’, and that as such morality is a combinatorial system. For each combination of two elements, we hypothesise a candidate moral molecule, and successfully locate an example of it in the professional and popular literature. These molecules include: fraternity, blood revenge, family pride, filial piety, gavelkind, primogeniture, friendship, patriotism, tribute, diplomacy, common ownership, honour, confession, turn taking, restitution, modesty, mercy, munificence, arbitration, mendicancy, and queuing. These findings indicate that morality – like many other physical, biological, psychological and cultural systems – is indeed a combinatorial system. Thus morality-as-cooperation provides a principled and powerful theory, that explains why there are many moral values, and successfully predicts what they will be; and it generates a systematic framework that has the potential to explain all moral ideas, possible and actual. Pursuing the many implications of this theory will help to place the study of morality on a more secure scientific footing. (shrink)

Plus que de différences qui se juxtaposent, on parle aujourd'hui de processus de différenciation pour traduire le changement fondamental entraîné par la rupture du lien jusqu'ici présumé insécable entre la culture en tant que facteur d'identification collective et son inscription spatiale. A la dichotomie classique entre Nous et les Autres - fondement même du projet anthropologique - se substituent ainsi de nouvelles catégories hybrides : communautés diasporiques, transnationalisme, créolisation, autant d'indicateurs thématiques d'une véritable réorientation de la réflexion sur la culture. (...) C'est dans ce contexte que se pose, de nos jours, le problème d'une " gestion " juridique de la différence culturelle présumée ou revendiquée. Tributaires de l'émergence des peuples autochtones et des minorités " ethniques " ou " culturelles " en tant que nouveaux acteurs sur la scène nationale et internationale, les quatorze contributions à ce recueil d'orientation interdisciplinaire proposent autant de réflexions critiques sur la notion de culture dans son double rapport au Droit (c'est-à-dire au droit positif) et aux droits. Ce qui est en jeu ici, c'est la culture comme variable de l'élaboration de normes juridiques en réponse à des revendications d'ordre identitaire. (shrink)

In this chapter, I show that there is at least one crucial, non-short, argument, which does not involve arguments about spatiotemporality, why Kant’s subjectivism about the possibility of knowledge, argued in the Transcendental Deduction, must lead to idealism. This has to do with the fact that given the implications of the discursivity thesis, namely, that the domain of possible determination of objects is characterised by limitation, judgements of experience can never reach the completely determined individual, i.e. the thing in itself (...) or the unlimited real, but only objects as objects of possible experience. As such, it can be shown by reference to a key argument from Kant, that Hegel’s famous criticism that Kant is not licensed, on the basis of his core arguments concerning the original-synthetic unity of apperception, to restrict our knowledge to appearances, is mistaken on purely systematic grounds. More specifically, I argue that idealism follows already from the constraints that the use of the categories, in particular the categories of quality, places on the very conceivability of things in themselves. My claim is that, although it is not only possible but also necessary to think things in themselves, it does not follow that by merely thinking them we have a full grasp of the nature of things in themselves, as some important commentators claim we have. We must therefore distinguish between two kinds of conceiving of things in themselves: conceiving in the standard sense of ‘forming the notion of’, and conceiving in the narrow sense of ‘having a determinate intellectual grasp’. So although we must be able notionally to think things in themselves, as the grounds of their appearances, we cannot even conceive, through pure concepts, of how they are in themselves in any determinate, even if merely intellectual, sense. To put it differently, we cannot have a positive conception of things in themselves (this is in line with Kant’s distinction between noumena in the negative and positive senses; cf. B307–9). For support, I resort to a much overlooked chapter in the Critique, concerning the transcendental Ideal, where Kant discusses what it is for a thing to be a thing in itself proper, namely, something that is thoroughly determined. This concerns the real ontological conditions of things, which are not satisfied by the modal categories alone, namely, their existence conditions. I claim that the chief reason why, given Kant’s view of determinative judgement, we cannot determine a thing in itself is because of two connected reasons: (1) a thing in itself is already fully determined and therefore not further determinable and (2) we cannot possibly determine all of the thing’s possible determinations. In this context, I also discuss the notion of material (not: empirical) synthesis—of which Kant speaks in the chapter on the transcendental Ideal—which must be presupposed as the ground of the formal a priori synthesis that grounds possible experience. This material synthesis, which is an idea of reason that defines a thing as thoroughly determined with regard to all of its possible predicates and has mere regulative status, can by implication not be determined by the forms of the understanding, which synthesise only a limited set of predicates. As a result, given this definition of ‘thing in itself’, any object (appearance) as at best44 a limited set of determinations of the thing can never be numerically identical to the thing in itself as thoroughly determined individual. This undercuts a standard assumption about the identity relation between appearances and things in themselves in many contemporary interpretations of Kant’s transcendental idealism. (shrink)

Introduction: The role of animals in philosophies of man -- Part I: What's wrong with animal rights? -- The right to remain silent -- Part II: Animal pedagogy -- You are what you eat : Rousseau's cat -- Say the human responded : Herder's sheep -- Part III: Difference worthy of its name -- Hair of the dog : Derrida's and Rousseau's good taste -- Sexual difference, animal difference : Derrida's sexy silkworm -- Part IV: It's our fault -- The (...) beaver's struggle with species-being : De Beauvoir and the praying mantis -- Answering the call of nature : Lacan walking the dog -- Part V: Estranged kinship -- The abyss between humans and animals : Heidegger puts the bee in being -- Strange kinship : Merleau-Ponty's sensuous stickleback -- Stopping the anthropological machine : Agamben's tick-tocking tick -- Psychoanalysis and the science of kinship -- Psychoanalysis as animal by-product : Freud's zoophilia -- Animal abjects, maternal abjects : Kristeva's strays -- Conclusion: Sustainable ethics. (shrink)

Explainable artificial intelligence (XAI) seeks to produce explanations for those machine learning methods which are deemed opaque. However, there is considerable disagreement about what this means and how to achieve it. Authors disagree on what should be explained (topic), to whom something should be explained (stakeholder), how something should be explained (instrument), and why something should be explained (goal). In this paper, I employ insights from means-end epistemology to structure the field. According to means-end epistemology, different means ought to be (...) rationally adopted to achieve different epistemic ends. Applied to XAI, different topics, stakeholders, and goals thus require different instruments. I call this the means-end account of XAI. The means-end account has a descriptive and a normative component: on the one hand, I show how the specific means-end relations give rise to a taxonomy of existing contributions to the field of XAI; on the other hand, I argue that the suitability of XAI methods can be assessed by analyzing whether they are prescribed by a given topic, stakeholder, and goal. (shrink)