A Simple Logic of Concepts

Journal of Philosophical Logic 52 (3):705-730 (2022)
  Copy   BIBTEX

Abstract

In Pietroski ( 2018 ) a simple representation language called SMPL is introduced, construed as a hypothesis about core conceptual structure. The present work is a study of this system from a logical perspective. In addition to establishing a completeness result and a complexity characterization for reasoning in the system, we also pinpoint its expressive limits, in particular showing that the fourth corner in the square of opposition (“ Some_not ”) eludes expression. We then study a seemingly small extension, called SMPL +, which allows for a minimal predicate-binding operator. Perhaps surprisingly, the resulting system is shown to encode precisely the concepts expressible in first-order logic. However, unlike the latter class, the class of SMPL + expressions admits a simple procedural (context-free) characterization. Our contribution brings together research strands in logic—including natural logic, modal logic, description logic, and hybrid logic—with recent advances in semantics and philosophy of language.

Other Versions

No versions found

Similar books and articles

A Modal Logic For Quantification And Substitution.Yde Venema - 1994 - Logic Journal of the IGPL 2 (1):31-45.
Solovay-Type Theorems for Circular Definitions.Shawn Standefer - 2015 - Review of Symbolic Logic 8 (3):467-487.
Natural deduction for first-order hybrid logic.Torben BraÜner - 2005 - Journal of Logic, Language and Information 14 (2):173-198.
A hybrid logic for reasoning about knowledge and topology.Bernhard Heinemann - 2007 - Journal of Logic, Language and Information 17 (1):19-41.
A Logic for Aristotle's Modal Syllogistic.Clarence Lewis Protin - 2022 - History and Philosophy of Logic (3).
Logic may be simple. Logic, congruence and algebra.Jean-Yves Béziau - 1997 - Logic and Logical Philosophy 5:129-147.

Analytics

Added to PP
2022-11-23

Downloads
1,154 (#17,575)

6 months
275 (#9,218)

Historical graph of downloads
How can I increase my downloads?

Author Profiles

Thomas Icard
Stanford University
Larry Moss
Indiana University

Citations of this work

The Logic of Lexical Connectives.Giorgio Sbardolini - 2023 - Journal of Philosophical Logic 52 (5):1327-1353.

Add more citations

References found in this work

The origin of concepts.Susan Carey - 2009 - New York: Oxford University Press.
A Natural History of Negation.Laurence R. Horn - 1989 - University of Chicago Press.
The Language of Thought.J. A. Fodor - 1978 - Critica 10 (28):140-143.

View all 46 references / Add more references