Paul Pietroski, Thomas Icard

Simple concepts and meanings: adequacy from below

Introduction

Simple concepts and meanings: adequacy from below. Explore a computationally simple calculus for concept composition, proposing linguistic meanings build monadic mental concepts. Achieves descriptive adequacy by extending simple models, contrasting Aristotelean/Fregean views, and connecting to FOL and modal logics.

Abstract

We offer a limited account of concept composition, formalized in terms of a calculus that has the computational complexity of propositional logic. We then show that small additions to this core system have dramatic effects, inviting an old idea that Pietroski 2018 develops: linguistic meanings are instructions for how to build concepts – symbols of a mental language – in constrained ways; more specifically, while some atomic concepts of the relevant mentalese are dyadic, all other concepts are monadic. In this respect, the posited generator is more Aristotelean than Fregean, and simpler than the lambda calculus of Church 1941. Icard & Moss (2023) make this vivid by establishing some results, which we review, about a precise version of the language Pietroski sketched. Here, we present the system in stages and stress a corresponding methodology: in providing theories of meaning, one can try to approach descriptive adequacy by modestly extending a model that undergenerates but captures some central phenomena, instead of starting with a powerful model that overgenerates (Chomsky 1957, 1959, 1965). For example, our core system doesn't generate negations of concepts or mental correlates of relative clauses. But the final product, which is still a context free procedure, delivers conceptual analogs of ‘thing that is not a cow'. Indeed, it is expressively equivalent to a monadic (one free variable) fragment of FOL. To help locate the proposed mentalese relative to more familiar models of how ideal concepts compose, we discuss some connections to modal logics and the variable-free system of Schönfinkel 1924.

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