Why should moral philosophers, moral psychologists, and machine ethicists care about computational complexity? Debates on whether artificial intelligence (AI) can or should be used to solve problems in ethical domains have mainly been driven by what AI can or cannot do in terms of human capacities. In this paper, we tackle the problem from the other end by exploring what kind of moral machines are possible based on what computational systems can or cannot do. To do so, we analyze normative (...) ethics through the lens of computational complexity. First, we introduce computational complexity for the uninitiated reader and discuss how the complexity of ethical problems can be framed within Marr’s three levels of analysis. We then study a range of ethical problems based on consequentialism, deontology, and virtue ethics, with the aim of elucidating the complexity associated with the problems themselves (e.g., due to combinatorics, uncertainty, strategic dynamics), the computational methods employed (e.g., probability, logic, learning), and the available resources (e.g., time, knowledge, learning). The results indicate that most problems the normative frameworks pose lead to tractability issues in every category analyzed. Our investigation also provides several insights about the computational nature of normative ethics, including the differences between rule- and outcome-based moral strategies, and the implementation-variance with regard to moral resources. We then discuss the consequences complexity results have for the prospect of moral machines in virtue of the trade-off between optimality and efficiency. Finally, we elucidate how computational complexity can be used to inform both philosophical and cognitive-psychological research on human morality by advancing the moral tractability thesis. (shrink)

The paper proposes a synthesis between human scientists and artificial representation learning models as a way of augmenting epistemic warrants of realist theories against various anti-realist attempts. Towards this end, the paper fleshes out unconceived alternatives not as a critique of scientific realism but rather a reinforcement, as it rejects the retrospective interpretations of scientific progress, which brought about the problem of alternatives in the first place. By utilising adversarial machine learning, the synthesis explores possibility spaces of available evidence for (...) unconceived alternatives providing modal knowledge of what is possible therein. As a result, the epistemic warrant of synthesised realist theories should emerge bolstered as the underdetermination by available evidence gets reduced. While shifting the realist commitment away from theoretical artefacts towards modalities of the possibility spaces, the synthesis comes out as a kind of perspectival modelling. (shrink)

In this paper, we offer reasons to justify the explanatory credentials of dynamical modeling in the context of the metaplasticity thesis, located within a larger grouping of views known as 4E Cognition. Our focus is on showing that dynamicism is consistent with interventionism, and therefore with a difference-making account at the scale of system topologies that makes sui generis explanatory differences to the overall behavior of a cognitive system. In so doing, we provide a general overview of the interventionist approach. (...) We then argue that recent mechanistic attempts at reducing dynamical modeling to a merely descriptive enterprise fail given that the explanatory standard in dynamical modeling can be shown to rest on interventionism. We conclude that dynamical modeling captures features of nested and developmentally plastic cognitive systems that cannot be explained by appeal to underlying mechanisms alone. (shrink)

The idea that perceptual and cognitive systems must incorporate knowledge about the structure of the environment has become a central dogma of cognitive theory. In a Bayesian context, this idea is often realized in terms of “tuning the prior”—widely assumed to mean adjusting prior probabilities so that they match the frequencies of events in the world. This kind of “ecological” tuning has often been held up as an ideal of inference, in fact defining an “ideal observer.” But widespread as this (...) viewpoint is, it directly contradicts Bayesian philosophy of probability, which views probabilities as degrees of belief rather than relative frequencies, and explicitly denies that they are objective characteristics of the world. Moreover, tuning the prior to observed environmental frequencies is subject to overfitting, meaning in this context overtuning to the environment, which leads (ironically) to poor performance in future encounters with the same environment. Whenever there is uncertainty about the environment—which there almost always is—an agent's prior should be biased away from ecological relative frequencies and toward simpler and more entropic priors. (shrink)

Ravit Dotan argues that a No Free Lunch theorem from machine learning shows epistemic values are insufficient for deciding the truth of scientific hypotheses. She argues that NFL shows that the best case accuracy of scientific hypotheses is no more than chance. Since accuracy underpins every epistemic value, non-epistemic values are needed to assess the truth of scientific hypotheses. However, NFL cannot be coherently applied to the problem of theory choice. The NFL theorem Dotan’s argument relies upon is a member (...) of a family of theorems in search, optimization, and machine learning. They all claim to show that if no assumptions are made about a search or optimization problem or learning situation, then the best case performance of an algorithm is that of random search or random guessing. A closer inspection shows that these theorems all rely upon assigning uniform probabilities over problems or learning situations, which is just the Principle of Indifference. A counterexample can be crafted that shows that NFL cannot be coherently applied across different descriptions of the same learning situation. To avoid this counterexample, Dotan needs to privilege some description of the learning situation faced by scientists. However, this means that NFL cannot be applied since an important assumption about the problem is being made. So Dotan faces a dilemma: either NFL leads to incoherent best-case partial beliefs or it is inapplicable to the problem of theory choice. This negative result has implications for the larger debate over theory choice. (shrink)

The idea that “simplicity is a sign of truth”, and the related “Occam’s razor” principle, stating that, all other things being equal, simpler models should be preferred to more complex ones, have been long discussed in philosophy and science. We explore these ideas in the context of supervised machine learning, namely the branch of artificial intelligence that studies algorithms which balance simplicity and accuracy in order to effectively learn about the features of the underlying domain. Focusing on statistical learning theory, (...) we show that situations exist for which a preference for simpler models provably slows down, instead of favoring, the supervised learning process. Our results shed new light on the relations between simplicity and truth approximation, which are briefly discussed in the context of both machine learning and the philosophy of science. (shrink)

As scientists start to adopt machine learning (ML) as one research tool, the security of ML and the knowledge generated become a concern. In this paper, I explain how supervised ML can be improved with better data ontology, or the way we make categories and turn information into data. More specifically, we should design data ontology in such a way that is consistent with the knowledge that we have about the target phenomenon so that such ontology can help us make (...) the inductive leap. I do so by thinking through a thought experiment, Goodman’s New Riddle of Induction (Fact, fiction, and forecast, Harvard University Press, 1955). Goodman’s riddle helps flesh out three problems of induction: (1) the problem of equal goodies, that there are often too many equally good inductive results given the same data; (2) the problem of diverging performance, that these equally good results can give opposite predictions in the future; and (3) the problem of mediocrity, that when averaged across all equally possible datasets and tasks, no inductive algorithm outperforms any other. I show that all these three problems are manifested as real obstacles in ML practice, namely, the Rashomon effect (Breiman in Stat Sci 16(3):199–231, 2001), the problem of underspecification (D’Amour et al. in J Mach Learn Res, 2020, https://doi.org/10.48550/arXiv.2011.03395 ), and the No Free Lunch theorem (Wolpert in Neural Comput 8(7):1341–90, 1996, https://doi.org/10.1162/neco.1996.8.7.1341 ). Lastly, I argue that proper data ontology can help mitigate these problems and I demonstrate how using concrete examples from climate science. This research highlights the links between philosophers’ discussions of induction and implications in ML practice. (shrink)

This paper examines a twofold tension in Gerhard Schurz’s (2019) recent proposal to solve Hume’s problem of induction. Schurz concedes to the skeptic that there is no non-circular epistemic justification of the reliability of induction, but then argues for the optimality of meta-induction so that if any prediction method is reliable, then meta-induction is. There is a tension in this proposal between meta-induction and our inductive practice: Are we supposed to abandon our inductive practice in favor of meta-induction? Schurz claims (...) that given the actual way the world has been, the meta-inductive method supports the standard inductive method. There then arises a second tension: The challenges Schurz cites against the reliability of induction—such as the anti-inductive hypothesis and the state-uniform probability distribution—cast doubt on Schurz’s claim that meta-induction supports induction. The reasoning in this paper moves in the opposite direction: There are ways of answering these challenges in defense of Schurz’s claim that meta-induction supports induction, but these ways also point to ways of defending induction directly without the mediation of meta-induction. (shrink)

The no-free-lunch theorems promote a skeptical conclusion that all possible machine learning algorithms equally lack justification. But how could this leave room for a learning theory, that shows that some algorithms are better than others? Drawing parallels to the philosophy of induction, we point out that the no-free-lunch results presuppose a conception of learning algorithms as purely data-driven. On this conception, every algorithm must have an inherent inductive bias, that wants justification. We argue that many standard learning algorithms should rather (...) be understood as model-dependent: in each application they also require for input a model, representing a bias. Generic algorithms themselves, they can be given a model-relative justification. (shrink)

One of the most discussed issues in psychology—presently and in the past—is how to define and measure the extent to which human cognition is rational. The rationality of human cognition is often evaluated in terms of normative standards based on a priori intuitions. Yet this approach has been challenged by two recent developments in psychology that we review in this article: ecological rationality and descriptivism. Going beyond these contributions, we consider it a good moment for psychologists and philosophers to join (...) forces and work toward a new foundation for the definition of rational cognition. We take a first step in this direction by proposing that the rationality of both cognitive and normative systems can be measured in terms of their cognitive success. Cognitive success can be defined and gauged in terms of two factors: ecological validity (the system's validity in conditions in which it is applicable) and the system's applicability (the scope of conditions under which it can be applied). As we show, prominent systems of reasoning—deductive reasoning, Bayesian reasoning, uncertain conditionals, and prediction and choice—perform rather differently on these two factors. Furthermore, we demonstrate that conceptualizing rationality according to its cognitive success offers a new perspective on the time-honored relationship between the descriptive (“is”) and the normative (“ought”) in psychology and philosophy. (shrink)

According to the paradigm of adaptive rationality, successful inference and prediction methods tend to be local and frugal. As a complement to work within this paradigm, we investigate the problem of selecting an optimal combination of prediction methods from a given toolbox of such local methods, in the context of changing environments. These selection methods are called meta-inductive strategies, if they are based on the success-records of the toolbox-methods. No absolutely optimal MI strategy exists—a fact that we call the “revenge (...) of ecological rationality”. Nevertheless one can show that a certain MI strategy exists, called “AW”, which is universally long-run optimal, with provably small short-run losses, in comparison to any set of prediction methods that it can use as input. We call this property universal access-optimality. Local and short-run improvements over AW are possible, but only at the cost of forfeiting universal access-optimality. The last part of the paper includes an empirical study of MI strategies in application to an 8-year-long data set from the Monash University Footy Tipping Competition. (shrink)

In this paper, we show how game theoretic work on conversation combined with a theory of discourse structure provides a framework for studying interpretive bias and how bias affects the production and interpretation of linguistic content. We model the influence of author bias on the discourse content and structure of the author’s linguistic production and interpreter bias on the interpretation of ambiguous or underspecified elements of that content and structure. Interpretive bias is an essential feature of learning and understanding but (...) also something that can be exploited to pervert or subvert the truth. We develop three types of games to understand and to analyze a range of interpretive biases, the factors that contribute to them, and their strategic effects. (shrink)

The basic Bayesian model of credence states, where each individual’s belief state is represented by a single probability measure, has been criticized as psychologically implausible, unable to represent the intuitive distinction between precise and imprecise probabilities, and normatively unjustifiable due to a need to adopt arbitrary, unmotivated priors. These arguments are often used to motivate a model on which imprecise credal states are represented by sets of probability measures. I connect this debate with recent work in Bayesian cognitive science, where (...) probabilistic models are typically provided with explicit hierarchical structure. Hierarchical Bayesian models are immune to many classic arguments against single-measure models. They represent grades of imprecision in probability assignments automatically, have strong psychological motivation, and can be normatively justified even when certain arbitrary decisions are required. In addition, hierarchical models show much more plausible learning behavior than flat representations in terms of sets of measures, which—on standard assumptions about update—rule out simple cases of learning from a starting point of total ignorance. (shrink)

The term embodiment identifies a theory that meaning and semantics cannot be captured by abstract, logical systems, but are dependent on an agent’s experience derived from being situated in an environment. This theory has recently received a great deal of support in the cognitive science literature and is having significant impact in artificial intelligence. Memetics refers to the theory that knowledge and ideas can evolve more or less independently of their human-agent substrates. While humans provide the medium for this evolution, (...) memetics holds that ideas can be developed without human comprehension or deliberate interference. Both theories have profound implications for the study of language—its potential use by machines, its acquisition by children and of particular relevance to this special issue, its evolution. This article links the theory of memetics to the established literature on semantic space, then examines the extent to which these memetic mechanisms might account for language independently of embodiment. It then seeks to explain the evolution of language through uniquely human cognitive capacities which facilitate memetic evolution. (shrink)

The contributions to this special issue on cognitive development collectively propose ways in which learning involves developing constraints that shape subsequent learning. A learning system must be constrained to learn efficiently, but some of these constraints are themselves learnable. To know how something will behave, a learner must know what kind of thing it is. Although this has led previous researchers to argue for domain-specific constraints that are tied to different kinds/domains, an exciting possibility is that kinds/domains themselves can be (...) learned. General cognitive constraints, when combined with rich inputs, can establish domains, rather than these domains necessarily preexisting prior to learning. Knowledge is structured and richly differentiated, but its “skeleton” must not always be preestablished. Instead, the skeleton may be adapted to fit patterns of co-occurrence, task requirements, and goals. Finally, we argue that for models of development to demonstrate genuine cognitive novelty, it will be helpful for them to move beyond highly preprocessed and symbolic encodings that limit flexibility. We consider two physical models that learn to make tone discriminations. They are mechanistic models that preserve rich spatial, perceptual, dynamic, and concrete information, allowing them to form surprising new classes of hypotheses and encodings. (shrink)

The important recent book by Schurz ( 2019 ) appreciates that the no-free-lunch theorems (NFL) have major implications for the problem of (meta) induction. Here I review the NFL theorems, emphasizing that they do not only concern the case where there is a uniform prior—they prove that there are “as many priors” (loosely speaking) for which any induction algorithm _A_ out-generalizes some induction algorithm _B_ as vice-versa. Importantly though, in addition to the NFL theorems, there are many _free lunch_ theorems. (...) In particular, the NFL theorems can only be used to compare the expected performance of an induction algorithm _A_, considered in isolation, with the expected performance of an induction algorithm _B_, considered in isolation. There is a rich set of free lunches which instead concern the statistical _correlations_ among the generalization errors of induction algorithms. As I describe, the meta-induction algorithms that Schurz advocates as a “solution to Hume’s problem” are simply examples of such a free lunch based on correlations among the generalization errors of induction algorithms. I end by pointing out that the prior that Schurz advocates, which is uniform over bit frequencies rather than bit patterns, is contradicted by thousands of experiments in statistical physics and by the great success of the maximum entropy procedure in inductive inference. (shrink)

The universal optimality theorem for metainduction works for epistemic agents faced with a choice among finitely many prediction methods. Eckhart Arnold and Tom Sterkenburg objected that it breaks...

The no free lunch theorem is a radicalized version of Hume’s induction skepticism. It asserts that relative to a uniform probability distribution over all possible worlds, all computable prediction algorithms—whether ‘clever’ inductive or ‘stupid’ guessing methods —have the same expected predictive success. This theorem seems to be in conflict with results about meta-induction. According to these results, certain meta-inductive prediction strategies may dominate other methods in their predictive success. In this article this conflict is analyzed and dissolved, by means of (...) probabilistic analysis and computer simulation. (shrink)