A Tale of Two Nortons

This paper considers Norton’s Material Theory of Induction. The material theory aims inter alia to neutralize Hume’s Problem of Induction. The purpose of the paper is to evaluate the material theorys capacity to achieve this end. After pulling apart two versions of the theory, I argue that neither version satisfactorily neutralizes the problem

The sources of Mill's views of ratiocination and induction

Steffen Ducheyne and John P. McCaskey (2014). “The Sources of Mill’s Views of Ratiocination and Induction,” in: Antis Loizides (ed.), John Stuart Mill’s ‘A System of Logic’: A Critical Guide (London, Routledge), pp. 63-8

Observationally Indistinguishable Spacetimes: A Challenge for Any Inductivist

Results on the observational indistinguishability of spacetimes demonstrate the impossibility of determining by deductive inference which is our spacetime, no matter how extensive a portion of the spacetime is observed. These results do not illustrate an underdetermination of theory by evidence, since they make no decision between competing theories and they make little contact with the inductive considerations that must ground such a decision. Rather, these results express a variety of indeterminism in which a specification of the observable past always fails to fix the remainder of a spacetime. This form of indeterminism is more troubling than the familiar indeterminism of quantum theory. The inductive inferences that can discriminate among the different spacetime extensions of the observed past are here called "opaque," which means that we cannot readily see the warrant that lies behind them

On the functional origins of essentialism

This essay examines the proposal that psychological essentialism results from a history of natural selection acting on human representation and inference systems. It has been argued that the features that distinguish essentialist representational systems are especially well suited for representing natural kinds. If the evolved function of essentialism is to exploit the rich inductive potential of such kinds, then it must be subserved by cognitive mechanisms that carry out at least three distinct functions: identifying these kinds in the environment, constructing essentialized representations of them, and constraining inductive inferences about kinds. Moreover, there are different kinds of kinds, ranging from nonliving substances to biological taxa to within-species kinds such as sex, and the causal processes that render these categories coherent for the purposes of inductive generalization vary. If the evolved function of essentialism is to support inductive generalization under ignorance of true causes, and if kinds of kinds vary in the implicit assumptions that support valid inductive inferences about them, then we expect different, functionally incompatible modes of essentialist thinking for different kinds. In particular, there should be differences in how biological and nonbiological substances, biological taxa, and biological and social role kinds are essentialized. The functional differences between these kinds of essentialism are discussed

Practical Theory Extension in Event-B

Abstract. The Rodin tool for Event-B supports formal modelling and proof using a mathematical language that is based on predicate logic and set theory. Although Rodin has in-built support for a rich set of operators and proof rules, for some application areas there may be a need to extend the set of operators and proof rules supported by the tool. This paper outlines a new feature of the Rodin tool, the theory component, that allows users to extend the mathematical language supported by the tool. Using theories, Rodin users may define new data types and polymorphic operators in a systematic and practical way. Theories also allow users to extend the proof capabilities of Rodin by defining new proof rules that get incorporated into the proof mechanisms. Soundness of new definitions and rules is provided through validity proof obligations.

(WP 2018-02) Extending Behavioral Economics’ Methodological Critique of Rational Choice Theory to Include Counterfactual Reasoning

This paper extends behavioral economics’ realist methodological critique of rational choice theory to include the type of logical reasoning underlying its axiomatic foundations. A purely realist critique ignores Kahneman’s emphasis on how the theory’s axiomatic foundations make it normative. I extend his critique to the theory’s reliance on classical logic, which excludes the concept of possibility employed in counterfactual reasoning. Nudge theory reflects this in employing counterfactual conditionals. This answers the complaint that the Homo sapiens agent conception ultimately reduces to a Homo economicus conception, and also provides grounds for treating Homo sapiens as an adaptive, non-optimizing, reflexive agent