Substrate independence and mind-body functionalism claim that thinking does not depend on any particular kind of physical implementation. But real-world information processing depends on energy, and energy depends on material substrates. Biological evidence for these claims comes from ecology and neuroscience, while computational evidence comes from neuromorphic computing and deep learning. Attention to energy requirements undermines the use of substrate independence to support claims about the feasibility of artificial intelligence, the moral standing of robots, the possibility that we may be living in a computer simulation, the plausibility of transferring minds into computers, and the autonomy of psychology from neuroscience.

Philosophers since the ancient Greeks have investigated the nature of different kinds of inference. Although deductive inference in the form of Aristotelian syllogisms and Fregean formal logic has predominated, much attention has also been paid to induction, inference where the conclusion does not follow necessarily from the premises.

According to Church’s thesis, we can identify the intuitive concept of effective computability with such well-defined mathematical concepts as Turing computability and partial recursiveness. The almost universal acceptance of Church’s thesis among logicians and computer scientists is puzzling from some epistemological perspectives, since no formal proof is possible of a thesis that involves an informal concept such as effectiveness. Elliott Mendelson has recently argued, however, that equivalencies between intuitive notions and precise notions need not always be considered unprovable theses, and that Church’s thesis should be accepted as true.

I want to discuss a thesis that is nearly as important in current research in computer science as Church’s thesis. I call the newer thesis the tractability thesis, since it identifies the intuitive class of computationally tractable problems with a precise class of problems whose solutions can be computed in polynomial time. After briefly reviewing the theory of intractability, I compare the grounds for accepting the tractability thesis with the grounds for accepting Church's thesis. Intimately connected with the tractability thesis is the mathematical conjecture, whose meaning I shall shortly explain, that P≠NP. Unlike Church's thesis, this conjecture is precise enough to be capable of mathematical proof, but most computer scientists believe it even though no proof has been found. As we shall see below, understanding the grounds for acceptance of the conjecture that P≠NP has implications for general questions in the philosophy of mathematics and science, especially concerning the epistemological importance of explanatory and conceptual coherence.

This paper uses the economic crisis of 2008 as a case study to examine the explanatory validity of collective mental representations. Distinguished economists such as Paul Krugman and Joseph Stiglitz attribute collective beliefs, desires, intentions, and emotions to organizations such as banks and governments. I argue that the most plausible interpretation of these attributions is that they are metaphorical pointers to a complex of multilevel social, psychological, and neural mechanisms. This interpretation also applies to collective knowledge in science: scientific communities do not literally have collective representations, but social mechanisms do make important contributions to scientific knowledge.

This target article presents a new computational theory of explanatory coherence that applies to the acceptance and rejection of scientific hypotheses as well as to reasoning in everyday life. The theory consists of seven principles that establish relations of local coherence between a hypothesis and other propositions. A hypothesis coheres with propositions that it explains, or that explain it, or that participate with it in explaining other propositions, or that offer analogous explanations. Propositions are incoherent with each other if they are contradictory. Propositions that describe the results of observation have a degree of acceptability on their own. An explanatory hypothesis is accepted if it coheres better overall than its competitors. The power of the seven principles is shown by their implementation in a connectionist program called ECHO, which treats hypothesis evaluation as a constraint satisfaction problem. Inputs about the explanatory relations are used to create a network of units representing propositions, while coherence and incoherence relations are encoded by excitatory and inhibitory links. ECHO provides an algorithm for smoothly integrating theory evaluation based on considerations of explanatory breadth, simplicity, and analogy. It has been applied to such important scientific cases as Lavoisier's argument for oxygen against the phlogiston theory and Darwin's argument for evolution against creationism, and also to cases of legal reasoning. The theory of explanatory coherence has implications for artificial intelligence, psychology, and philosophy.