Quantification in the interpretational theory of validity
Bibliographic Data
| ID | 10814092 |
|---|---|
| Authors | Miriam Grossi (0000-0002-8680-2412, University of Oxford, corresponding author) |
| Year | 2023 |
| Volume | 202 |
| Issue | 3 |
| Publication date | 2023-08-29 |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Synthese (JOURNAL) |
| Journal identifiers | ISSN: 0039-7857 • E-ISSN: 1573-0964 |
| Publisher | Springer Science and Business Media LLC (PUBLISHER) |
| DOI | 10.1007/s11229-023-04302-3 |
| OpenAlex | W4386255901 |
| Language | EN |
| References cited | 20 |
According to the interpretational theory of logical validity (IR), logical validity is preservation of truth in all interpretations compatible with the intended meaning of logical expressions. IR suffers from a seemingly defeating objection, the so-called cardinality problem: any instance of the statement ‘There are n things’ is true under all interpretations, since it can be written down using only logical expressions that are not to be reinterpreted; yet ‘There are n things’ is not logically true. I argue that the cardinality problem is indeed a serious problem for IR, when understood in terms of ‘asymmetry of information’. I then argue that IR can be rehabilitated by making quantifiers context-sensitive: what we do not reinterpret is the Kaplanian character of a quantifier, rather than its content. ‘There are n things’ is false in a context where fewer than n things are relevant, so it is not logically true in IR. I finally discuss some objections and ramifications of my account: I discuss how to make space for the possibility of an explicitly absolutely general quantifier in my framework, how terms can be logical even though context-sensitive, and how to recapture classical logic within my framework
Algorithm · Cardinality (data modeling) · Character (mathematics) · Context (archaeology) · Epistemology · Meaning (existential) · Metaphysics · Philosophy of language · Philosophy of science · Quantifier (linguistics) · Statement (logic) · Truth table · Computer Science · Epistemology, Ethics, and Metaphysics · Logic, Reasoning, and Knowledge · Mathematics · Philosophy · Philosophy and Theoretical Science
On Quantifier Domain Restriction
The Boundary Stones of Thought
Semantic Paradoxes and Abductive Methodology
Philosophy of Logic
Elusive knowledge
Everything
The Concept of Logical Consequence
The Formal-Structural View of Logical Consequence
Logical Constants, or How to use Invariance in Order to Complete the Explication of Logical Consequence
The concept of logical consequence
| Highly cited | No |
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