A functional defined on the class of generalized characteristic functions (fuzzy sets), called “entropy≓, is introduced using no probabilistic concepts in order to obtain a global measure of the indefiniteness connected with the situations described by fuzzy sets. This “entropy≓ may be regarded as a measure of a quantity of information which is not necessarily related to random experiments. Some mathematical properties of this functional are analyzed and some considerations on its applicability to pattern analysis are made.

The Logical Foundations of Probability

A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory

According to Aristotle, humans are the rational animal. The borderline between rationality and irrationality is fundamental to many aspects of human life including the law, mental health, and language interpretation. But what is it to be rational? One answer, deeply embedded in the Western intellectual tradition since ancient Greece, is that rationality concerns reasoning according to the rules of logic - the formal theory that specifies the inferential connections that hold with certainty between propositions. Piaget viewed logical reasoning as defining the end-point of cognitive development; and contemporary psychology of reasoning has focussed on comparing human reasoning against logical standards. Bayesian Rationality argues that rationality is defined instead by the ability to reason about uncertainty. Although people are typically poor at numerical reasoning about probability, human thought is sensitive to subtle patterns of qualitative Bayesian, probabilistic reasoning. In Chapters 1-4 of Bayesian Rationality (Oaksford & Chater 2007), the case is made that cognition in general, and human everyday reasoning in particular, is best viewed as solving probabilistic, rather than logical, inference problems. In Chapters 5-7 the psychology of "deductive" reasoning is tackled head-on: It is argued that purportedly "logical" reasoning problems, revealing apparently irrational behaviour, are better understood from a probabilistic point of view. Data from conditional reasoning, Wason's selection task, and syllogistic inference are captured by recasting these problems probabilistically. The probabilistic approach makes a variety of novel predictions which have been experimentally confirmed. The book considers the implications of this work, and the wider "probabilistic turn" in cognitive science and artificial intelligence, for understanding human rationality.

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Précis of Bayesian Rationality: The Probabilistic Approach to Human Reasoning

From the Publisher:
In his groundbreaking new book, John Pollock establishes an outpost at the crossroads where artificial intelligence meets philosophy. Specifically, he proposes a general theory of rationality and then describes its implementation in OSCAR, an architecture for an autonomous rational agent he claims is the "first AI system capable of performing reasoning that philosophers would regard as epistemically sophisticated."
A sequel to Pollock's How to Build a Person, this volume builds upon that theoretical groundwork for the implementation of rationality through artificial intelligence. Pollock argues that progress in AI has stalled because of its creators' reliance upon unformulated intuitions about rationality. Instead, he bases the OSCAR architecture upon an explicit philosophical theory of rationality, encompassing principles of practical cognition, epistemic cognition, and defeasible reasoning. One of the results is the world's first automated defeasible reasoner capable of reasoning in a rich, logical environment.
Underlying Pollock's thesis is a conviction that the tenets of artifical intelligence and those of philosophy can be complementary and mutually beneficial. And, while members of both camps have in recent years grown skeptical of the very possibility of "symbol processing" AI, Cognitive Carpentry establishes that such an approach to AI can be successful. 
A Bradford Book

Cognitive Carpentry: A Blueprint for How to Build a Person

This paper is concerned with the question of the truth conditions of nomological statements. My fundamental thesis is that it is possible to set out an acceptable, non Circular account of the truth conditions of laws and nomological statements if and only if relations among universals — that is, among properties and relations, construed realistically — are taken as the truth-makers for such statements.
 My discussion will be restricted to strictly universal, nonstatistical laws. The reason for this limitation is not that I feel there is anything dubious about the concept of a statistical law, nor that I feel that basic laws cannot be statistical. The reason is methodological. The case of strictly universal, nonstatistical laws would seem to be the simplest case. If the problem of the truth conditions of laws can be solved for this simple subcase, one can then investigate whether the solution can be extended to the more complex cases. I believe that the solution I propose here does have that property, though I shall not pursue that question here.

The Nature of Laws

Prospection (Gilbert & Wilson, 2007), the representation of possible futures, is a ubiquitous feature of the human mind. Much psychological theory and practice, in contrast, has understood human action as determined by the past and viewed any such teleology (selection of action in light of goals) as a violation of natural law because the future cannot act on the present. Prospection involves no backward causation; rather, it is guidance not by the future itself but by present, evaluative representations of possible future states. These representations can be understood minimally as “If X, then Y” conditionals, and the process of prospection can be understood as the generation and evaluation of these conditionals. We review the history of the attempt to cast teleology out of science, culminating in the failures of behaviorism and psychoanalysis to account adequately for action without teleology. A wide range of evidence suggests that prospection is a central organizing feature of perception, cognition, affect, memory, motivation, and action. The authors speculate that prospection casts new light on why subjectivity is part of consciousness, what is “free” and “willing” in “free will,” and on mental disorders and their treatment. Viewing behavior as driven by the past was a powerful framework that helped create scientific psychology, but accumulating evidence in a wide range of areas of research suggests a shift in framework, in which navigation into the future is seen as a core organizing principle of animal and human behavior.

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The Logical Foundations of Probability

Citations

A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory

Précis of Bayesian Rationality: The Probabilistic Approach to Human Reasoning

Cognitive Carpentry: A Blueprint for How to Build a Person

The Nature of Laws

Navigating Into the Future or Driven by the Past

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