Arguments Whose Strength Depends on Continuous Variation

Both the traditional Aristotelian and modern symbolic approaches to logic have seen logic in terms of discrete symbol processing. Yet there are several kinds of argument whose validity depends on some topological notion of continuous variation, which is not well captured by discrete symbols. Examples include extrapolation and slippery slope arguments, sorites, fuzzy logic, and those involving closeness of possible worlds. It is argued that the natural first attempts to analyze these notions and explain their relation to reasoning fail, so that ignorance of their nature is profound

Examples of Artificial Perceptions in Optical Character Recognition and Iris Recognition

This paper assumes the hypothesis that human learning is perception based, and consequently, the learning process and perceptions should not be represented and investigated independently or modeled in different simulation spaces. In order to keep the analogy between the artificial and human learning, the former is assumed here as being based on the artificial perception. Hence, instead of choosing to apply or develop a Computational Theory of (human) Perceptions, we choose to mirror the human perceptions in a numeric (computational) space as artificial perceptions and to analyze the interdependence between artificial learning and artificial perception in the same numeric space, using one of the simplest tools of Artificial Intelligence and Soft Computing, namely the perceptrons. As practical applications, we choose to work around two examples: Optical Character Recognition and Iris Recognition. In both cases a simple Turing test shows that artificial perceptions of the difference between two characters and between two irides are fuzzy, whereas the corresponding human perceptions are, in fact, crisp.Comment: 5th Int. Conf. on Soft Computing and Applications (Szeged, HU), 22-24 Aug 201

Induction, complexity, and economic methodology

This paper focuses on induction, because the supposed weaknesses of that process are the main reason for favouring falsificationism, which plays an important part in scientific methodology generally; the paper is part of a wider study of economic methodology. The standard objections to, and paradoxes of, induction are reviewed, and this leads to the conclusion that the supposed ‘problem’ or ‘riddle’ of induction is a false one. It is an artefact of two assumptions: that the classic two-valued logic (CL) is appropriate for the contexts in which induction is relevant; and that it is the touchstone of rational thought. The status accorded to CL is the result of historical and cultural factors. The material we need to reason about falls into four distinct domains; these are explored in turn, while progressively relaxing the restrictions that are essential to the valid application of CL. The restrictions include the requirement for a pre-existing, independently-guaranteed classification, into which we can fit all new cases with certainty; and non-ambiguous relationships between antecedents and consequents. Natural kinds, determined by the existence of complex entities whose characteristics cannot be unbundled and altered in a piecemeal, arbitrary fashion, play an important part in the review; so also does fuzzy logic (FL). These are used to resolve two famous paradoxes about induction (the grue and raven paradoxes); and the case for believing that conventional logic is a subset of fuzzy logic is outlined. The latter disposes of all questions of justifying induction deductively. The concept of problem structure is used as the basis for a structured concept of rationality that is appropriate to all four of the domains mentioned above. The rehabilitation of induction supports an alternative definition of science: that it is the business of developing networks of contrastive, constitutive explanations of reproducible, inter-subjective (‘objective’) data. Social and psychological obstacles ensure the progress of science is slow and convoluted; however, the relativist arguments against such a project are rejected.induction; economics; methodology; complexity

The Laws of Thought

The Laws of Thought is an exploration of the deductive and inductive foundations of rational thought. The author here clarifies and defends Aristotle’s Three Laws of Thought, called the Laws of Identity, Non-contradiction and Exclusion of the Middle – and introduces two more, which are implicit in and crucial to them: the Fourth Law of Thought, called the Principle of Induction, and the Fifth Law of Thought, called the Principle of Deduction. This book is a thematic compilation drawn from past works by the author over a period of twenty-three years (1990-2013)

On the Resilience of Superstition

The concept of “belief” has always been taken seriously by anthropologists and philosophers; nevertheless, it has led to a long series of perplexities. To the contrary, the concept of “superstition” has simply been discarded as ethnocentric. The first has been pushed aside for its logical uncertainty; the second for its ethical uncertainty. Yet, the two concepts seem to be surprisingly resilient in face of the continued exercise of anthropological questioning. Furthermore, their capacity for survival appears to be connected precisely to that which connects them: superstition is unfounded belief but the issue of the foundation of belief is at the centre of the anthropological and philosophical perplexities that have haunted the concept of belief. In this paper I examine two examples – one of them a short story by Joseph Conrad – in order to show that today we can look differently at what superstition may be

Contextuality: A Philosophical Paradigm, with Applications to Philosophy of Cognitive Science

We develop on the idea that everything is related, inside, and therefore determined by a context. This stance, which at first might seem obvious, has several important consequences. This paper first presents ideas on Contextuality, for then applying them to problems in philosophy of cognitive science. Because of space limitations, for the second part we will assume that the reader is familiar with the literature of philosophy of cognitive science, but if this is not the case, it would not be a limitation for understanding the main ideas of this paper. We do not argue that Contextuality is a panaceic answer for explaining everything, but we do argue that everything is inside a context. And because this is always, we sometimes ignore it, but we believe that many problems are dissolved with a contextual approach, noticing things we ignore because of their obviousity. We first give a notion of context. We present the idea that errors are just incongruencies inside a context. We also present previous ideas of absolute being, relative being, and lessincompleteness. We state that all logics, and also truth judgements, are contextdependent, and we develop a “Context-dependant Logic”. We apply ideas of Contextuality to problems in semantics, the problem of “where is the mind”, and the study of consciousness

Introduction

There has been little overt discussion of the experimental philosophy of logic or mathematics. So it may be tempting to assume that application of the methods of experimental philosophy to these areas is impractical or unavailing. This assumption is undercut by three trends in recent research: a renewed interest in historical antecedents of experimental philosophy in philosophical logic; a “practice turn” in the philosophies of mathematics and logic; and philosophical interest in a substantial body of work in adjacent disciplines, such as the psychology of reasoning and mathematics education. This introduction offers a snapshot of each trend and addresses how they intersect with some of the standard criticisms of experimental philosophy. It also briefly summarizes the specific contribution of the other chapters of this book