The Logic of “Most” and “Mostly”

The Logic of “Most” and “Mostly” The paper suggests a modal predicate logic that deals with classical quantification and modalities as well as intermediate operators, like “most” and “mostly”. Following up the theory of generalized quantifiers, we will understand them as two-placed operators and call them determiners. Quantifiers as well as modal operators will be constructed from them. Besides the classical deduction, we discuss a weaker probabilistic inference “therefore, probably” defined by symmetrical probability measures in Carnap’s style. The given probabilistic inference relates intermediate quantification to singular statements: “Most S are P” does not logically entail that a particular individual S is also P, but it follows that this is probably the case, where the probability is not ascribed to the propositions but to the inference. We show how this system deals with single case expectations while predictions of statistical statements remain generally problematic. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Axiomathes Springer Journals

The Logic of “Most” and “Mostly”

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer Science+Business Media Dordrecht
Subject
Philosophy; Philosophy, general; Ontology; Linguistics, general; Cognitive Psychology; Logic
ISSN
1122-1151
eISSN
1572-8390
D.O.I.
10.1007/s10516-017-9338-2
Publisher site
See Article on Publisher Site

Abstract

The paper suggests a modal predicate logic that deals with classical quantification and modalities as well as intermediate operators, like “most” and “mostly”. Following up the theory of generalized quantifiers, we will understand them as two-placed operators and call them determiners. Quantifiers as well as modal operators will be constructed from them. Besides the classical deduction, we discuss a weaker probabilistic inference “therefore, probably” defined by symmetrical probability measures in Carnap’s style. The given probabilistic inference relates intermediate quantification to singular statements: “Most S are P” does not logically entail that a particular individual S is also P, but it follows that this is probably the case, where the probability is not ascribed to the propositions but to the inference. We show how this system deals with single case expectations while predictions of statistical statements remain generally problematic.

Journal

AxiomathesSpringer Journals

Published: Apr 28, 2017

References

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