Issues in the foundations of science, I: Languages, structures, and models

Abstract
In this first paper of a series of works on the foundations of science, we examine the significance of logical and mathematical frameworks used in foundational studies. In particular, we emphasize the distinction between the order of a language and the order of a structure to prevent confusing models of scientific theories (as set-theoretical structures) with first-order structures (called here order-1 structures), and which are studied in standard (first-order) model theory. All of us are, of course, bound to make abuses of language even in putatively precise contexts. This is not a problem—in fact, it is part of scientific and philosophical practice. But it is important to be sensitive to the dierent uses that structure, model, and language have. In this paper, we examine these topics in the context of classical logic; only in the last section we touch upon briefly on non-classical ones
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