Hannes Leitgeb

Alexander Hieke

Philosophers often have tried to either reduce "disagreeable" objects or concepts to (more) acceptable objects or concepts. Reduction is regarded attractive by those who subscribe to an ideal of ontological parsimony. But the topic is not just restricted to traditional metaphysics or ontology. In the philosophy of mathematics, abstraction principles, such as Hume's principle, have been suggested to support a reconstruction of mathematics by logical means only. In the philosophy of language and the philosophy of science, the logical analysis of language has long been regarded to be the dominating paradigm, and liberalized projects of logical reconstruction remain to be driving forces of modern philosophy. This volume collects contributions comprising all those topics, including articles by Alexander Bird, Jaakko Hintikka, James Ladyman, Rohit Parikh, Gerhard Schurz, Peter Simons, Crispin Wright and Edward N. Zalta.

Proceedings of the 31th International Ludwig Wittgenstein-Symposium in Kirchberg, 2008

Reduction - Abstraction - Analysis

In contrast to the prevailing tradition in epistemology, the focus in this book is on low-level inferences, i.e., those inferences that we are usually not consciously aware of and that we share with the cat nearby which infers that the bird which she sees picking grains from the dirt, is able to fly. Presumably, such inferences are not generated by explicit logical reasoning, but logical methods can be used to describe and analyze such inferences. Part 1 gives a purely system-theoretic explication of belief and inference. Part 2 adds a reliabilist theory of justification for inference, with a qualitative notion of reliability being employed. Part 3 recalls and extends various systems of deductive and nonmonotonic logic and thereby explains the semantics of absolute and high reliability. In Part 4 it is proven that qualitative neural networks are able to draw justified deductive and nonmonotonic inferences on the basis of distributed representations. This is derived from a soundness/completeness theorem with regard to cognitive semantics of nonmonotonic reasoning. The appendix extends the theory both logically and ontologically, and relates it to A. Goldman's reliability account of justified belief.

An Investigation into Deduction, Nonmonotonic Reasoning, and the Philosophy of Cognition

Inference on the Low Level

In everyday life we normally express our beliefs in all-or-nothing terms: I believe it is going to rain; I don't believe that my lottery ticket will win. In other cases, if possible, we resort to numerical probabilities: my degree of belief that it is going to rain is 80%; the probability that I assign to my ticket winning is one in a million. It is an open philosophical question how all-or-nothing belief and numerical belief relate to each other, and how we ought to reason with them simultaneously. The Stability of Belief develops a theory of rational belief that aims to answer this question by building new bridges between logic and probability theory, traditional and mathematical epistemology, and theoretical and practical rationality. Hannes Leitgeb develops a joint normative theory of all-or-nothing belief and numerical degrees of belief. While rational all-or-nothing belief is studied in traditional epistemology and is usually assumed to obey logical norms, rational degrees of belief constitute the subject matter of Bayesian epistemology and are normally taken to conform to probabilistic norms. One of the central open questions in formal epistemology is what beliefs and degrees of belief have to be like in order for them to cohere with each other. The answer defended in this book is a stability account of belief: a rational agent believes a proposition just in case the agent assigns a stably high degree of belief to it. Leitgeb determines this theory's consequences for, and applications to, learning, suppositional reasoning, decision-making, assertion, acceptance, conditionals, and chance. The volume builds new bridges between logic and probability theory, traditional and formal epistemology, theoretical and practical rationality, and synchronic and diachronic norms for reasoning.

Hannes Leitgeb

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