A Simple Logic of Concepts

Journal of Philosophical Logic:1-26 (forthcoming)
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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.

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Author Profiles

Thomas Icard
Stanford University
Larry Moss
Indiana University

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References found in this work

The Language of Thought.J. A. Fodor - 1978 - Critica 10 (28):140-143.
The semantic conception of truth and the foundations of semantics.Alfred Tarski - 1943 - Philosophy and Phenomenological Research 4 (3):341-376.
Generalized quantifiers and natural language.John Barwise & Robin Cooper - 1981 - Linguistics and Philosophy 4 (2):159--219.
Conjoining Meanings: Semantics Without Truth Values.Paul M. Pietroski - 2018 - Oxford, United Kingdom: Oxford University Press.
A Natural History of Negation.Jon Barwise & Laurence R. Horn - 1991 - Journal of Symbolic Logic 56 (3):1103.

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