- Epistemology, Pragmatics, Semantics, Meaning, Theories Of Truth, Philosophical Logic, and 34 morePhilosophy of Science, Philosophy Of Language, Logical Empiricism, Philosophy Of Mathematics, Cognitive Science, Artificial Neural Networks, Logic, Dynamical Systems, Probability Theory, Beliefs, Willard Van Orman Quine, Epistemic Logic, Conditionals, Accuracy, Belief Revision (Computer Science), Belief, Assertion (and other linguistic actions), Dependency, Kenneth Arrow, Truth, Structuralism (Philosophy), Philosophy of Logic, Rationality, Rudolf Carnap, Modality, Deontic Logic, Paradoxes, Chance, Modal Logic, Probability, Metaphilosophy, Inference, Induction (Philosophy), and Analytic Philosophyedit
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... 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.
Research Interests: Biochemistry, Mathematics, Paleontology, Computer Science, Philosophy, and 13 morePhilosophy Of Language, Epistemology, Pragmatism, Biology, Meaning, Philosophy of Property, Linguistics, Probability, Probabilistic Logic, Dynamic Semantics, Philosophical Studies, Bayesian Confirmation Theory, and Verifiability
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... Book Reviews Timothy Williamson. Knowledge and Its Limits. Oxford: Oxford University Press, 2000. Pp. xi + 340. Let there be no vulgar suspense. ...
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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... 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.
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In the subsequent chapters we will state and prove representations theorems of a similar kind as in chapter 16, but now for different systems of nonmonotonic logic.
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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... 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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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,... 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.
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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... 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.
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... 150 The Modal Supervenience of the Concept of Time Kasia M. Jaszczolt ... 356 Reducing Sets to Modalities Rafał Urbaniak ..... ...
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some reasonable assumptions concerning the nature of mental causation,
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Now we consider net agents based on interpreted inhibition networks which are antitone and which do not have inhibitory connections. By ‘antitone’ we mean here: the net I is such that N is antitone in I. The property of being antitone... more
Now we consider net agents based on interpreted inhibition networks which are antitone and which do not have inhibitory connections. By ‘antitone’ we mean here: the net I is such that N is antitone in I. The property of being antitone together with the lack of inhibitory connections directly entails that in such networks every excitatory connection from a node which is not the bias, to another node is superfluous. Thus, in such nets the “essential” excitatory connections lead from the bias to other nodes. A node gets excited either directly by the input or by the bias node. These networks are of course trivial but they may be used in order to complete our intended list of representation results.
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Now we consider again the (input-determined) cumulative interpreted inhibition network agents from the last chapter, but this time without inhibitory connections, i.e., where I = O.
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In this paper we argue that all-or-nothing belief may be understood as a kind of qualitative (subjective) probability. We present the basics of a joint theory of belief and degrees of belief to that effect, and we compare it with classic... more
In this paper we argue that all-or-nothing belief may be understood as a kind of qualitative (subjective) probability. We present the basics of a joint theory of belief and degrees of belief to that effect, and we compare it with classic work on qualitative probability (by de Finetti, Suppes, and others).
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We present an intensional version of a Quinean argument in favor of the indeterminacy of translation thesis.
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This "lecture notes style" article gives a brief survey of neural network models of conditionals. After short introductions into the studies of neural networks and conditionals, we turn to the notion of... more
This "lecture notes style" article gives a brief survey of neural network models of conditionals. After short introductions into the studies of neural networks and conditionals, we turn to the notion of an interpreted dynamical system as a unifying concept in the logical investigation of dynamic systems in general, and of neural networks in particular. We explain how conditionals get represented by interpreted dynamical systems, which logical systems these conditionals obey, and what the main open problems in this area are.
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We argue that logicism, the thesis that mathematics is reducible to logic and analytic truths, is true. We do so by (a) developing a formal framework with comprehension and abstraction principles, (b) giving reasons for thinking that this... more
We argue that logicism, the thesis that mathematics is reducible to logic and analytic truths, is true. We do so by (a) developing a formal framework with comprehension and abstraction principles, (b) giving reasons for thinking that this framework is part of logic, (c) showing how the denotations for terms and predicates of a mathematical theory can be viewed as logical objects that exist in the framework, and (d) showing how each theorem of a mathematical theory can be given a true reading in the logical framework. ∗This paper originated as a presentation that the third author prepared for the 31st Wittgenstein Symposium, in Kirchberg, Austria, August 2008. Discussions between the co-authors after this presentation led to a collaboration on, and further development of, the thesis and the technical material grounding the thesis. The authors would especially like to thank Daniel Kirchner for suggesting important refinements of the technical development. We’d also like to thank . . ....
We summarize Goodman's worries about the notion of similarity and how to overcome them.
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ABSTRACT
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Is it possible to maintain classical logic, stay close to classical semantics, and yet accept that language might be semantically indeterminate? The article gives an affirmative answer by Ramsifying classical semantics, which yields a new... more
Is it possible to maintain classical logic, stay close to classical semantics, and yet accept that language might be semantically indeterminate? The article gives an affirmative answer by Ramsifying classical semantics, which yields a new semantic theory that remains much closer to classical semantics than supervaluationism but which at the same time avoids the problematic classical presupposition of semantic determinacy. The resulting Ramsey semantics is developed in detail, it is shown to supply a classical concept of truth and to fully support the rules and metarules of classical logic, and it is applied to vague terms as well as to theoretical or open-ended terms from mathematics and science. The theory also demonstrates how diachronic or synchronic interpretational continuity across languages is compatible with semantic indeterminacy.
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I make a proposal for how to do philosophy: mathematical empiricism.
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I make a proposal for how to do philosophy: mathematical empiricism.
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A new justification of probabilism is developed that pays close attention to the structure of the underlying space of possibilities. Its central assumption is that rational numerical degrees of belief ought to be partition invariant. By... more
A new justification of probabilism is developed that pays close attention to the structure of the underlying space of possibilities. Its central assumption is that rational numerical degrees of belief ought to be partition invariant. By means of a representation theorem, one can prove that if graded belief satisfies the resulting set of postulates, rational degrees of belief may be identified with probabilities.
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A new justification of probabilism is developed that pays close attention to the structure of the underlying space of possibilities. Its central assumption is that rational numerical degrees of belief ought to be partition invariant. By... more
A new justification of probabilism is developed that pays close attention to the structure of the underlying space of possibilities. Its central assumption is that rational numerical degrees of belief ought to be partition invariant. By means of a representation theorem, one can prove that if graded belief satisfies the resulting set of postulates, rational degrees of belief may be identified with probabilities.
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This article sketches a proposal for how to interpret exact truthmaker semantics within inexact truthmaker semantics: exact truthmaking might be viewed as inexact truthmaking by minimal totality facts. While the philosophical idea is... more
This article sketches a proposal for how to interpret exact truthmaker semantics within inexact truthmaker semantics: exact truthmaking might be viewed as inexact truthmaking by minimal totality facts. While the philosophical idea is explained by reference to an example, the logical details are left to follow-up work.
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This article sketches a proposal for how to interpret exact truthmaker semantics within inexact truthmaker semantics: exact truthmaking might be viewed as inexact truthmaking by minimal totality facts. While the philosophical idea is... more
This article sketches a proposal for how to interpret exact truthmaker semantics within inexact truthmaker semantics: exact truthmaking might be viewed as inexact truthmaking by minimal totality facts. While the philosophical idea is explained by reference to an example, the logical details are left to follow-up work.
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Eine Festrede zum 400-jährigen Bestehen des akademischen Gymnasiums Salzburg.
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I make a proposal for how to do philosophy: mathematical empiricism.
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I study the Lottery Paradox from a stability point of view.
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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... 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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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... 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.