Hannes Leitgeb

Ludwig-Maximilians-Universität München, Faculty of Philosophy, Philosophy of Science and Religious Studies, Faculty Member

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Papers by Hannes Leitgeb

Vindicating the verifiability criterion

Philosophical Studies, Dec 17, 2023

The aim of this paper is to argue for a revised and precisified version of the infamous Verifiabi... more The aim of this paper is to argue for a revised and precisified version of the infamous Verifiability Criterion for the meaningfulness of declarative sentences. The argument is based on independently plausible premises concerning probabilistic confirmation and meaning as context-change potential, it is shown to be logically valid, and its ramifications for potential applications of the criterion are being discussed. Although the paper is not historical but systematic, the criterion thus vindicated will resemble the original one(s) in some important ways. At the same time, it will also be more modest insofar as meaningfulness will turn out to be relativized linguistically and probabilistically, and different choices of the linguistic and probabilistic parameters may lead to different verdicts on meaningfulness.

Action, Assertability, Acceptance

Oxford University Press eBooks, Mar 30, 2017

Timothy Williamson, Knowledge and its Limits, Oxford: Oxford University Press, 2000, xi+340pp

Grazer Philosophische Studien, Aug 12, 2002

... Book Reviews Timothy Williamson. Knowledge and Its Limits. Oxford: Oxford University Press, 2... more

Neural Network Models of Conditionals

Springer undergraduate texts in philosophy, 2018

This chapter explains how artificial neural networks may be used as models for reasoning, conditi... more This chapter explains how artificial neural networks may be used as models for reasoning, conditionals, and conditional logic. It starts with the historical overlap between neural network research and logic, it discusses connectionism as a paradigm in cognitive science that opposes the traditional paradigm of symbolic computationalism, it mentions some recent accounts of how logic and neural networks may be combined, and it ends with a couple of open questions concerning the future of this area of research.

Preferential Interpreted Inhibition Net Agents and the System P

Springer eBooks, 2004

In the subsequent chapters we will state and prove representations theorems of a similar kind as ... more

Logical Closure and the Lockean Thesis

Oxford University Press eBooks, Mar 30, 2017

Stability and Epistemic Decision Theory

Oxford University Press eBooks, Mar 30, 2017

Intensionality, Lecture Notes in Logic

Logic and Philosophy. A Reconstruction

Preprint. Printed version forthcoming in: Oxford Handbook of Philosophy of Logic, ed. by E. Brendel, M. Carrara, F. Ferrari, O. Hjortland, G. Sagi, G. Sher, F. Steinberger, Oxford: Oxford University Press.

The article recapitulates what logic is about traditionally and works out two roles it has been p... more The article recapitulates what logic is about traditionally and works out two roles it has been playing in philosophy: the role of an instrument and of a philosophical discipline in its own right. Using Tarski’s philosophical-logical work as case study, it develops a logical reconstructionist methodology of philosophical logic that extends and refines Rudolf Carnap’s account of explication and rational reconstruction. The methodology overlaps with, but also partially diverges from, contemporary anti-exceptionalism about logic.

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Logic and Philosophy. A Reconstruction

The article recapitulates what logic is about traditionally and works out two roles it has been p... more The article recapitulates what logic is about traditionally and works out two roles it has been playing in philosophy: the role of an instrument and of a philosophical discipline in its own right. Using Tarski's philosophical-logical work as case study, it develops a logical reconstructionist methodology of philosophical logic that extends and refines Rudolf Carnap's account of explication and rational reconstruction. The methodology overlaps with, but also partially diverges from, contemporary anti-exceptionalism about logic.

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New Results on the Network Semantics for Cumulative Systems of Nonmonotonic Reasoning

Inference on the Low Level

Applied logic series, 2004

No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form ... more No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Contents 25 Cumulative Interpreted Inhibition Net Agents and the System C 361 25.

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Philosophy of Mathematics: Five Questions

Der formale Kalkül SK samt Semantik

The Stability of Belief

This book develops a joint normative theory of rational all-or-nothing belief and rational numeri... more This book develops a joint normative theory of rational all-or-nothing belief and rational numerical degrees of belief. While all-or-nothing belief is studied in traditional epistemology and is usually assumed to obey logical norms, 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 such 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 she assigns a stably high degree of belief to it. The book explains what this stability thesis amounts to, how the thesis relates to other joint principles of belief and degrees of belief, such as the so-called Lockean thesis, and how the approach avoids notorious paradoxes, such as the famous Lottery Paradox. It determines the theory's consequences for learning, suppositional reasoning, decision-making, and assertion; and it justifies the theory on various grounds, including those of epistemic decision theory.

Untimely Review of: R. Carnap, Der logische Aufbau der Welt, Berlin: Weltkreis, 1928

Topoi-an International Review of Philosophy, 2009

Mengers Logik für Ethik und Moral

Poppers Wahrheitstheorie(n)

A Bridge Principle for Ranking Functions and Subjective Probability

Von Rang und Namen, 2016

Axioms for Type-Free Subjective Probability

Review of Symbolic Logic, Feb 27, 2023

We formulate and explore two basic axiomatic systems of typefree subjective probability. One of t... more We formulate and explore two basic axiomatic systems of typefree subjective probability. One of them explicates a notion of finitely additive probability. The other explicates a concept of infinitely additive probability. It is argued that the first of these systems is a suitable background theory for formally investigating controversial principles about typefree subjective probability.

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Vindicating the verifiability criterion

Philosophical Studies, Dec 17, 2023

Action, Assertability, Acceptance

Oxford University Press eBooks, Mar 30, 2017

Timothy Williamson, Knowledge and its Limits, Oxford: Oxford University Press, 2000, xi+340pp

Grazer Philosophische Studien, Aug 12, 2002

... Book Reviews Timothy Williamson. Knowledge and Its Limits. Oxford: Oxford University Press, 2... more

Neural Network Models of Conditionals

Springer undergraduate texts in philosophy, 2018

Preferential Interpreted Inhibition Net Agents and the System P

Springer eBooks, 2004

In the subsequent chapters we will state and prove representations theorems of a similar kind as ... more

Logical Closure and the Lockean Thesis

Oxford University Press eBooks, Mar 30, 2017

Stability and Epistemic Decision Theory

Oxford University Press eBooks, Mar 30, 2017

Intensionality, Lecture Notes in Logic

Logic and Philosophy. A Reconstruction

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Logic and Philosophy. A Reconstruction

The article recapitulates what logic is about traditionally and works out two roles it has been p... more The article recapitulates what logic is about traditionally and works out two roles it has been playing in philosophy: the role of an instrument and of a philosophical discipline in its own right. Using Tarski's philosophical-logical work as case study, it develops a logical reconstructionist methodology of philosophical logic that extends and refines Rudolf Carnap's account of explication and rational reconstruction. The methodology overlaps with, but also partially diverges from, contemporary anti-exceptionalism about logic.

Download

New Results on the Network Semantics for Cumulative Systems of Nonmonotonic Reasoning

Inference on the Low Level

Applied logic series, 2004

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Philosophy of Mathematics: Five Questions

Der formale Kalkül SK samt Semantik

The Stability of Belief

Untimely Review of: R. Carnap, Der logische Aufbau der Welt, Berlin: Weltkreis, 1928

Topoi-an International Review of Philosophy, 2009

Mengers Logik für Ethik und Moral

Poppers Wahrheitstheorie(n)

A Bridge Principle for Ranking Functions and Subjective Probability

Von Rang und Namen, 2016

Axioms for Type-Free Subjective Probability

Review of Symbolic Logic, Feb 27, 2023

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Humanismus im postfaktischen Zeitalter?

Eine Festrede zum 400-jährigen Bestehen des akademischen Gymnasiums Salzburg.

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Mathematical Empiricism. A Methodological Proposal

I make a proposal for how to do philosophy: mathematical empiricism.

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Stability and the Lottery Paradox

forthcoming in: The Lottery Paradox, ed. by Igor Douven, Cambridge: Cambridge University Press, 2019

I study the Lottery Paradox from a stability point of view.

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HYPE: A System of Hyperintensional Logic (With an Application to Semantic Paradoxes). REVISED VERSION

This article introduces, studies, and applies a new system of logic which is called 'HYPE'. In HY... more This article introduces, studies, and applies a new system of logic which is called 'HYPE'. In HYPE, formulas are evaluated at states that may exhibit truth value gaps (partiality) and truth value gluts (overdeterminedness). Simple and natural semantic rules for negation and the conditional operator are formulated based on an incompatibility relation and a fusion operation on states. The semantics is worked out in formal and philosophical detail, and a sound and complete axiomatization is provided both for the propositional and the predicate logic of the system. The propositional logic of HYPE is shown to contain first-degree entailment, to have the Finite Model Property, to be decidable, to have the Disjunction Property, and to extend intuitionis-tic propositional logic conservatively when intuitionistic negation is defined appropriately by HYPE's logical connectives. Furthermore, HYPE's first-order logic is a conservative extension of intuitionistic logic with the Constant Domain Axiom, when intuitionistic negation is again defined appropriately. The system allows for simple model constructions and intuitive Euler-Venn-like diagrams, and its logical structure matches structures well-known from ordinary mathematics, such as from optimization theory, combinatorics, and graph theory. HYPE may also be used as a general logical framework in which different systems of logic can be studied, compared, and combined. In particular, HYPE is found to relate in interesting ways to classical logic and various systems of relevance and paraconsistent logic, many-valued logic, and truthmaker semantics. On the philosophical side, if used as a logic for theories of type-free truth, HYPE is shown to address semantic paradoxes such as the Liar Paradox by extending non-classical fixed-point interpretations of truth by a conditional as well-behaved as that of intuitionistic logic. Finally, HYPE may be used as a background system for modal operators that create hyperintensional contexts, though the details of this application need to be left to follow-up work.

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HYPE: A System of Hyperintensional Logic (With an Application to Semantic Paradoxes

This is the first draft of an article introducing, studying, and applying a new system of logic w... more This is the first draft of an article introducing, studying, and applying a new system of logic which is called 'HYPE'. In HYPE, formulas are evaluated at states that may be " gappy " (partial) or " glutty " (overdetermined). Simple and natural semantic rules for negation and the conditional operator are formulated based on an incompatibility relation and a fusion operation on states. The semantics is worked out in formal and philosophical detail, and a sound and complete axiomatization is provided both for the propositional and the predicate logic of the system. The propositional logic of HYPE is shown to contain first-degree entailment, to have the Finite Model Property, to be decidable, to have the Disjunction Property, and to extend intuitionistic propositional logic conservatively when intuitionistic negation is defined appropriately by HYPE's logical connectives. HYPE's first-order logic is a conservative extension of intuitionistic logic with the Constant Domain Axiom, when in-tuitionistic negation is again defined appropriately. The system allows for simple model constructions and intuitive Euler-Venn-like diagrams, and its logical structure matches structures well-known from ordinary mathematics, such as from optimization theory, combinatorics, and graph theory. HYPE may also be used as a general logical framework in which different systems of logic can be studied, compared, and combined. In particular, HYPE is found to relate in interesting ways to classical logic and various systems of relevance and paraconsistent logic, many-valued logic, and truthmaker semantics. On the philosophical side, if used as a logic for theories of type-free truth, HYPE is shown to address semantic paradoxes such as the Liar Paradox by extending non-classical fixed-point interpretations of truth by a conditional as well-behaved as that of intuitionistic logic. Finally, HYPE may be used as a background system for modal operators that create hyper-intensional contexts, though the details of this application need to be left to follow-up work.

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