In his recent address to the Aristotelian Society, Aurel Kolnai suggests that games exhibit what he calls a “genuine paradoxy.” I do not believe that he has shown this to be the case, even on the most permissive interpretation of what it means to be a paradox. Kolnai has, however, called attention to an aspect of games which invites further investigation, and I should like to advance the following considerations not so much as a criticism of Kolnai as an attempt to take the investigation along a path which Kolnai has indicated, but which he has not himself, in my opinion, followed. It is not that Kolnai does not say many interesting, indeed penetrating, things about games, for he does. That Kolnai's inquiry is an important contribution to the philosophy of games is not in question. What is questionable is whether paradox has very much to do with that contribution.

This paper argues that a notion of statistical explanation, based on Salmon’s statistical relevance model, can help us better understand deep neural networks. It is proved that homogeneous partitions, the core notion of Salmon’s model, are equivalent to minimal sufficient statistics, an important notion from statistical inference. This establishes a link to deep neural networks via the so-called Information Bottleneck method, an information-theoretic framework, according to which deep neural networks implicitly solve an optimization problem that generalizes minimal sufficient statistics. The resulting notion of statistical explanation is general, mathematical, and subcausal.

Do evolutionary processes such as selection and random drift cause evolutionary change, or are they merely convenient ways of describing or summarizing it? Philosophers have lined up on both sides of this question. One recent defense (Reisman and Forber 2005) of the causal status of selection and drift appeals to a manipulability theory of causation. Yet, even if one accepts manipulability, there are still reasons to doubt that genetic drift, in particular, is genuinely causal. We will address two challenges to treating drift as causal within a manipulation framework. We will argue that both challenges ultimately fail, but that they raise interesting and subtle issues about the nature of causation and the differences between selection and drift.

It is shown that three common conditions for scientific explanations are violated by a widely used class of domain-independent explanations. These explanations can accommodate both complex and noncomplex systems and do not require the use of detailed models of system-specific processes for their effectiveness, although they are compatible with such model-based explanations. The approach also shows how a clean separation can be maintained between mathematical representations and empirical content.

Based partly on proving that algebraic relativistic quantum field theory (ARQFT) is a stochastic Einstein local (SEL) theory in the sense of SEL which was introduced by Hellman (1982b) and which is adapted in this paper to ARQFT, the recently proved maximal and typical violation of Bell's inequalities in ARQFT (Summers and Werner 1987a–c) is interpreted in this paper as showing that Bell's inequalities are, in a sense, irrelevant for the problem of Einstein local stochastic hidden variables, especially if this problem is raised in connection with ARQFT. This leads to the question of how to formulate the problem of local hidden variables in ARQFT. By giving a precise definition of hidden-variable theory within the operator algebraic framework of quantum mechanics, it will be argued that the aim of hidden-variable investigations is to determine those classes of quantum theories whose elements represent a statistical content that cannot be reduced in a given way. In some particular way to be stated, a proposition will be stated which distinguishes quantum field theories whose statistical content cannot be reduced without violating some relativistic locality principle.

All natural languages exhibit a distinction between content words (nouns, verbs, etc.) and function words (determiners, auxiliaries, tenses, etc.). Yet surprisingly little has been said about the emergence of this universal architectural feature of human language. This article argues that the existence of this distinction requires the presence of nontrivial compositionality and identifies assumptions that have previously been made in the literature that provably guarantee only trivial composition. It then presents a signaling game with variable contexts and shows how the distinction can emerge via reinforcement learning.

According to the diversity-beats-ability theorem, groups of diverse problem solvers can outperform groups of high-ability problem solvers. We argue that the model introduced by Lu Hong and Scott Page is inadequate for exploring the trade-off between diversity and ability. This is because the model employs an impoverished implementation of the problem-solving task. We present a new version of the model that captures the role of ‘ability’ in a meaningful way, and we use it to explore the trade-offs between diversity and ability in scientific problem solving.

According to Hempel, all scientific explanations and predictions which are produced exclusively with deterministic laws must be deductive, in the sense that the explanandum or the prediction must be a logical consequence of the laws and the initial (and boundary) conditions in the explanans. This deducibility thesis (DT) has been attacked from several quarters. Some time ago Canfield and Lehrer presented a “refutation” of DT as applied to predictions, in which they tried to prove that “if the deductive reconstruction [DT for predictions] were an adequate reconstruction, then scientific prediction would be impossible” ([2], p. 204). Their argument seems to have been uncontested except for an inconclusive rejoinder by Beard (cf. [1]). Moreover, Stegmüller has recently argued that “it may turn out that all or at least most of the so-called deductive-nomological explanations are in truth inductive and not deductive arguments, in view of the difficulty which has been pointed out by Canfield and Lehrer” ([3], p. 7). It seems it would be worth investigating whether Canfield and Lehrer's argument is, indeed, correct.

Arthur Fine's Natural Ontological Attitude (NOA) is intended to provide an alternative to both realism and antirealism. I argue that the most plausible meaning of “natural” in NOA is “nonphilosophical,” but that Fine comes to NOA through a particular conception of philosophy. I suggest that instead of a natural attitude we should adopt a philosophical attitude. This is one that is self-conscious, pragmatic, pluralistic, and sensitive to context. I conclude that when scientific realism and antirealism are viewed with a philosophical attitude there are still legitimate philosophical questions to address.

Algorithmic information theory gives an idealized notion of compressibility that is often presented as an objective measure of simplicity. It is suggested at times that Solomonoff prediction, or algorithmic information theory in a predictive setting, can deliver an argument to justify Occam’s razor. This article explicates the relevant argument and, by converting it into a Bayesian framework, reveals why it has no such justificatory force. The supposed simplicity concept is better perceived as a specific inductive assumption, the assumption of effectiveness. It is this assumption that is the characterizing element of Solomonoff prediction and wherein its philosophical interest lies.

In a recent Philosophy of Science article, Gerhard Schurz proposes meta-inductivistic prediction strategies as a new approach to Hume's problem. This discussion examines the limitations of Schurz's approach. It can be proved that the meta-inductivistic approach does not work anymore if meta-inductivists have to face an infinite number of alternative predictors. With this limitation it remains doubtful whether the meta-inductivist can provide a full solution to the problem of induction.

It is shown that a number of questions, usually considered philosophical rather than scientific, can be reformulated to apply to a world of automata or “well-informed heat engines.” In some cases they admit of physical answers, but in many cases obtaining answers entails violation of the second law of thermodynamics. This is demonstrated explicitly for the problem of determinism and free will, for the discovery of the origin or ultimate fate of the universe, or for the discovery of causes or purposes in nature.

A philosophy might take its general inspiration from (1) commonsense; (2) careful observation; (3) philosophical argumentation; (4) the sciences; (5) “higher” sources of illumination. It is argued in this paper that it is bedrock commonsense, and the sciences, which are the most reliable foundations for a philosophy. This result is applied to the discussion and defense of a materialist theory of the mind.

In this paper I address some of the problems that the historical development of science poses for a realist and discuss whether a realist construal of scientific activity is conducive to historiographical practice. First, I discuss, by means of historical examples, Ian Hacking's defense of entity realism. Second, I try to show, drawing on Kuhn's recent work on incommensurability, that the realism problem is relevant to historiography and that a realist position entails a particular historiographical strategy, which faces problems. Finally, I suggest that for historiographical purposes an agnostic attitude with respect to scientifictheories and unobservable entities is the most appropriate.

The main scientific problems of chemical bonding were solved half a century ago, but adequate philosophical understanding of chemical combination is yet to be achieved. Chemists routinely use important terms (“element,” “atom,” “molecule,” “substance”) with more than one meaning. This can lead to misunderstandings. Eliminativists claim that what seems to be a baseball breaking a window is merely the action of “atoms, acting in concert.” They argue that statues, baseballs, and similar macroscopic things “do not exist.” When macroscopic objects like baseballs move, exceedingly large numbers (∼1025) of microscopic components coordinate their activities. Understanding how this happens requires attention to the interactions that link parts into larger units. Eliminativists say that everything that truly exists has causal relationships in addition to those of its components—“nonredundant causality.” This paper holds that if a number of entities interact in such a way that the effect of that collection on test objects is different than it would have been in the absence of the interaction, then identification of that collection as a single composite agent is warranted, for purposes to which that difference is relevant. Ordinary “chemical substances” (both elementary materials such as dihydrogen and compounds such as water) fulfill this version of the requirement of nonredundant causality. Other sorts of chemical coherences, including chemical dissipative structures (e.g., flames), also fulfill that criterion. All these types of coherences qualify as “substances” (as that term is used in philosophy) even though they are not all “chemical substances.”

This article examines the multiple realizability thesis within a causal framework. The beginnings of this framework are found in Elliott Sober’s “Multiple Realizability Argument against Reduction,” which argues that the multiple realizability thesis poses no challenge to reductive explanation. While Sober’s causal approach has the potential to reveal new insights, I argue that his setup fails to capture important aspects of the multiple realizability thesis. After correcting for these issues, I argue that this causal framework reveals something quite different. It reveals how multiple realizability relates to a common type of causal complexity in biology that poses problems for reductive explanation.

Substantive counterlegal discourse poses a problem for those according to whom the laws of nature are metaphysically necessary. I discern two types of necessitarianism about laws: dispositional essentialism and modal necessitarianism. I argue that Toby Handfield’s response to the problem of counterlegals cannot help the modal necessitarian, according to whom all possible worlds are identical with respect to the laws. I thus propose a fictionalist treatment of counterlegals. Fictions are not limited by metaphysical possibility; hence, fictionalism affords the modal necessitarian the means to account for the apparent substance of counterlegals even granting the metaphysical necessity of the laws.