<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Context is essential in virtually all human activities. Yet some logical notions seem to be context-free. For example, the nature of the universal quantifier, the very meaning of “all”, seems to be independent of the context. At the same time, there are many quantifier expressions, and some are context-independent, while others are not. Similarly, purely logical consequence seems to be context-independent. Yet often we encounter strong inferences, good enough for practical purposes, but not valid. The two types of examples suggest a general problem: how to characterise the context-free logical concepts in their natural environment, that is, in the field of their context-dependent associates. A general Thesis on Quantifiers is formulated: among all quantifiers, the context-free ones are just those definable by the universal quantifier. The issue of inferences is treated following the approach introduced by Richard L. Epstein: valid ones are an extreme case, the result of the disappearance of context-dependence. This idea can be applied to an analysis of a form of abduction, called “reductive inference” in Polish literature on logic. A tentative Thesis on Inferences identifies the validity of a strong inference that is context-independent.</p>
</abstract>

Context is essential in virtually all human activities. Yet some logical notions seem to be context-free. For example, the nature of the universal quantifier, the very meaning of “all”, seems to be independent of the context. At the same time, there are many quantifier expressions, and some are context-independent, while others are not. Similarly, purely logical consequence seems to be context-independent. Yet often we encounter strong inferences, good enough for practical purposes, but not valid. The two types of examples suggest a general problem: how to characterise the context-free logical concepts in their natural environment, that is, in the field of their context-dependent associates. A general Thesis on Quantifiers is formulated: among all quantifiers, the context-free ones are just those definable by the universal quantifier. The issue of inferences is treated following the approach introduced by Richard L. Epstein: valid ones are an extreme case, the result of the disappearance of context-dependence. This idea can be applied to an analysis of a form of abduction, called “reductive inference” in Polish literature on logic. A tentative Thesis on Inferences identifies the validity of a strong inference that is context-independent.

Characterising Context-Independent Quantifiers and Inferences

Studia Humana

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"Characterising Context-Independent Quantifiers and Inferences"}

Context is essential in virtually all human activities. Yet some logical notions seem to be context-free. For example, the nature of the universal quantifier,...

Characterising Context-Independent Quantifiers and Inferences

Published Online: Apr 28, 2024

Page range: 1 - 8

DOI: https://doi.org/10.2478/sh-2024-0007

Keywords
philosophical logic, context-independence, context-dependence, quantifier, generalised quantifier, inference, validity, abduction

© 2024 Stanisław Krajewski, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Characterising Context-Independent Quantifiers and Inferences

Published Online: Apr 28, 2024

Page range: 1 - 8

DOI: https://doi.org/10.2478/sh-2024-0007

Keywordsphilosophical logic, context-independence, context-dependence, quantifier, generalised quantifier, inference, validity, abduction

© 2024 Stanisław Krajewski, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
philosophical logic, context-independence, context-dependence, quantifier, generalised quantifier, inference, validity, abduction