The Pessimistic Induction and the Golden Rule

Nickles (2017) advocates scientific antirealism by appealing to the pessimistic induction over scientific theories, the illusion hypothesis (Quoidbach, Gilbert, and Wilson, 2013), and Darwin’s evolutionary theory. He rejects Putnam’s (1975: 73) no-miracles argument on the grounds that it uses inference to the best explanation. I object that both the illusion hypothesis and evolutionary theory clash with the pessimistic induction and with his negative attitude towards inference to the best explanation. I also argue that Nickles’s positive philosophical theories are subject to Park’s (2017a) pessimistic induction over antirealists

Induction and Natural Kinds Revisited

In ‘Induction and Natural Kinds’, I proposed a solution to the problem of induction according to which our use of inductive inference is reliable because it is grounded in the natural kind structure of the world. When we infer that unobserved members of a kind will have the same properties as observed members of the kind, we are right because all members of the kind possess the same essential properties. The claim that the existence of natural kinds is what grounds reliable use of induction is based on an inference to the best explanation of the success of our inductive practices. As such, the argument for the existence of natural kinds employs a form of ampliative inference. But induction is likewise a form of ampliative inference. Given both of these facts, my account of the reliability of induction is subject to the objection that it provides a circular justification of induction, since it employs an ampliative inference to justify an ampliative inference. In this paper, I respond to the objection of circularity by arguing that what justifies induction is not the inference to the best explanation of its reliability. The ground of induction is the natural kinds themselves

Metaphysical Explanation and the Inference to the Best Explanation (BA thesis)

Inference to the Best Explanation, roughly put, appeals to the explanatory power of a theory or hypothesis (relative to some data set) as constituting epistemic justification for it. Inference to the Best Explanation (henceforth IBE) is a tool widely employed among all reasoners alike, from the empirical sciences to ordinary life. Philosophical discussions do not differ in the usualness of explanatory appeals of this kind during serious argument. Often enough, the appeal is dialectically blocked, as many of our epistemic peers in philosophy offer reasons to be skeptical of IBE. Our aim with this monograph is to assess one worry that have been raised about this mode of inference: That explanatory power is not truth-conducive. We begin by discussing general features of inferences and then formulating IBE in detail. Afterward, we explicate and apply a canonical understanding of what an explanation is. This will lead to a certain understanding of explanatory power. We undergo a case study to defend the thesis that this kind of explanatory power is indeed epistemically irrelevant – unless, perhaps, when combined with other theoretical virtues. Our conclusion is that the measure what explanations are best requires taking other theoretical virtues into account, such as simplicity and unification. In this case, a complete assessment of IBE requires examining if, when, and how these alleged theoretical virtues are indeed truth-conducive

Transport properties of non-equilibrium systems under the application of light: Photo-induced quantum Hall insulators without Landau levels

In this paper, we study transport properties of non-equilibrium systems under the application of light in many-terminal measurements, using the Floquet picture. We propose and demonstrate that the quantum transport properties can be controlled in materials such as graphene and topological insulators, via the application of light. Remarkably, under the application of off-resonant light, topological transport properties can be induced; these systems exhibits quantum Hall effects in the absence of a magnetic field with a near quantization of the Hall conductance, realizing so-called quantum Hall systems without Landau levels first proposed by Haldane.Comment: Updated to include the detailed explanation of formalism to study the non-equilibrium transpor

Representation theories of some towers of algebras related to the symmetric groups and their Hecke algebras

We study the representation theory of three towers of algebras which are related to the symmetric groups and their Hecke algebras. The first one is constructed as the algebras generated simultaneously by the elementary transpositions and the elementary sorting operators acting on permutations. The two others are the monoid algebras of nondecreasing functions and nondecreasing parking functions. For these three towers, we describe the structure of simple and indecomposable projective modules, together with the Cartan map. The Grothendieck algebras and coalgebras given respectively by the induction product and the restriction coproduct are also given explicitly. This yields some new interpretations of the classical bases of quasi-symmetric and noncommutative symmetric functions as well as some new bases.Comment: 12 pages. Presented at FPSAC'06 San-Diego, June 2006 (minor explanation improvements w.r.t. the previous version

What Can Armstrongian Universals Do for Induction?

David Armstrong (1983) argues that necessitation relations among universals are the best explanation of some of our observations. If we consequently accept them into our ontologies, then we can justify induction, because these necessitation relations also have implications for the unobserved. By embracing Armstrongian universals, we can vindicate some of our strongest epistemological intuitions and answer the Problem of Induction. However, Armstrong’s reasoning has recently been challenged on a variety of grounds. Critics argue against both Armstrong’s usage of inference to the best explanation and even whether, by Armstrong’s own standards, necessitation relations offer a potential explanation of this explanandum, let alone the best explanation. I defend Armstrong against these particular criticisms. Firstly, even though there are reasons to think that Armstrong’s justification fails as a self-contained defence of induction, it can usefully complement several other answers to Hume. Secondly, I argue that Armstrong’s reasoning is consistent with his own standards for explanation

A mathematical theory of semantic development in deep neural networks

An extensive body of empirical research has revealed remarkable regularities in the acquisition, organization, deployment, and neural representation of human semantic knowledge, thereby raising a fundamental conceptual question: what are the theoretical principles governing the ability of neural networks to acquire, organize, and deploy abstract knowledge by integrating across many individual experiences? We address this question by mathematically analyzing the nonlinear dynamics of learning in deep linear networks. We find exact solutions to this learning dynamics that yield a conceptual explanation for the prevalence of many disparate phenomena in semantic cognition, including the hierarchical differentiation of concepts through rapid developmental transitions, the ubiquity of semantic illusions between such transitions, the emergence of item typicality and category coherence as factors controlling the speed of semantic processing, changing patterns of inductive projection over development, and the conservation of semantic similarity in neural representations across species. Thus, surprisingly, our simple neural model qualitatively recapitulates many diverse regularities underlying semantic development, while providing analytic insight into how the statistical structure of an environment can interact with nonlinear deep learning dynamics to give rise to these regularities

What inductive explanations could not be

Marc Lange argues that proofs by mathematical induction are generally not explanatory because inductive explanation is irreparably circular. He supports this circularity claim by presenting two putative inductive explanantia that are one another’s explananda. On pain of circularity, at most one of this pair may be a true explanation. But because there are no relevant differences between the two explanantia on offer, neither has the explanatory high ground. Thus, neither is an explanation. I argue that there is no important asymmetry between the two cases because they are two presentations of the same explanation. The circularity argument requires a problematic notion of identity of proofs. I argue for a criterion of proof individuation that identifies the two proofs Lange offers. This criterion can be expressed in two equivalent ways: one uses the language of homotopy type theory, and the second assigns algebraic representatives to proofs. Though I will concentrate on one example, a criterion of proof identity has much broader consequences: any investigation into mathematical practice must make use of some proof-individuation principle