The dissertation presents a theory of semantics and pragmatics for both language and vision. I focus on sentences including proper names, descriptions, and attitude report verbs, and on the Necker cube. I propose the Open Instruction Theory (OIT), according to which the linguistic meaning of a sentence and the semantic contribution of visual feature detectors are identified, not with propositions or other standard proposals, but with instructions for the construction of mental models. These instructions leave open certain aspects of interpretation, in ways precisely delineated. The process that builds mental models makes an "inference to the best interpretation"--roughly the best guess at what the world is like consistent with the instructions. What mental models represent--readily described as structured propositions--corresponds to intuitions about "what we are told" and "what we see." Applied to language, OIT dovetails with syntax, and, as I argue, better captures intuitions about asserted and presupposed content than alternatives. Applied to the Necker cube, OIT is supported by neural and psychological data, implemented as a neural model and explains puzzling phenomena as the by-product of near-optimal vision. I argue that extant theories of proper names, descriptions, and attitude report verbs conflict with language acquisition data and syntactic constraints; and that extant models of the Necker cube are neurophysiologically implausible and lack explanatory power. I present tests for "visual" and "linguistic" ambiguity and argue that attitude reports, descriptions, and the Necker cube are not ambiguous in ways traditionally supposed. Moreover, OIT eschews a quantificational treatment of descriptions and avoids making "is" ambiguous. OIT describes a crucial role of "Topicality" in both vision and language. OIT makes it possible to systematically address issues that cut across cognitive domains, such as the relationship between presupposition, questions and visual perception, as well as visual fiction. OIT also suggests tentative conclusions about the nature of language. Principles involved in utterance interpretation beyond syntax and principles resembling external merge appear common to perceptual systems. "If" any principle of language is fundamentally unique, it has to be a more powerful principle like internal merge--a principle expected if language is "optimal". [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]