 How does language inform our downstream thinking? In particular, how do humans make meaning from language—and how can we leverage a theory of linguistic meaning to build machines that think in more human-like ways? In this paper, we propose *rational meaning construction*, a computational framework for language-informed thinking that combines neural models of language with probabilistic models for rational inference. We frame linguistic meaning as a context-sensitive mapping from natural language into a *probabilistic language of thought* (PLoT)—a general-purpose symbolic substrate for probabilistic, generative world modeling. Our architecture integrates two powerful computational tools that have not previously come together: we model thinking with *probabilistic programs*, an expressive representation for flexible commonsense reasoning; and we model meaning construction with *large language models* (LLMs), which support broad-coverage translation from natural language utterances to code expressions in a probabilistic programming language. We illustrate our framework in action through examples covering four core domains from cognitive science: probabilistic reasoning, logical and relational reasoning, visual and physical reasoning, and social reasoning about agents and their plans. In each, we show that LLMs can generate context-sensitive translations that capture pragmatically-appropriate linguistic meanings, while Bayesian inference with the generated programs supports coherent and robust commonsense reasoning. We extend our framework to integrate cognitively-motivated symbolic modules (physics simulators, graphics engines, and goal-directed planning algorithms) to provide a unified commonsense thinking interface from language. Finally, we explore how language can drive the construction of world models themselves.  We hope this work will help to situate contemporary developments in LLMs within a broader cognitive picture of human language and intelligence, providing a roadmap towards AI systems that synthesize the insights of both modern and classical computational perspectives. 