Dynamical Phenomena and Their Models: Truth and Empirical Correctness
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Dynamical Phenomena and Their Models: Truth and Empirical Correctness Marco Giunti1
© The Author(s) 2020
Abstract In the epistemological tradition, there are two main interpretations of the semantic relation that an empirical theory may bear to the real world. According to realism, the theoryworld relationship should be conceived as truth; according to instrumentalism, instead, it should be limited to empirical adequacy. Then, depending on how empirical theories are conceived, either syntactically as a class of sentences, or semantically as a class of models, the concepts of truth and empirical adequacy assume different and specific forms. In this paper, we review two main conceptions of truth (one sentence-based and one model-based) and two of empirical adequacy (one sentence-based and one model-based), we point out their respective difficulties, and we give a first formulation of a new general view of the theory-world relationship, which we call Methodological Constructive Realism (MCR). We then show how the content of MCR can be further specified and expressed in a definite and precise form. The bulk of the paper shows in detail how it is possible to accomplish this goal for the special case of deterministic dynamical phenomena and their correlated deterministic models. This special version of MCR is formulated as an axiomatic extension of set theory, whose specific axioms constitute a formal ontology that provides an adequate framework for analyzing the two semantic relations of truth and empirical correctness, as well as their connections. Keywords Realism · Instrumentalism · Truth · Empirical adequacy · Syntactic view of theories · Semantic view of theories
1 Introduction In this paper, by an empirical theory we mean any scientific theoretical construct, not necessarily of a linguistic type, which is expressly designed to describe or explain specific aspects of the real world. This usage of the term thus presupposes the scientific character of an empirical theory. In this acceptance, empirical theories are naturally contrasted with mathematical ones, which are taken to be all those scientific theoretical constructs that are * Marco Giunti [email protected] 1
ALOPHIS—Applied LOgic Philosophy and HIstory of Science, Dipartimento di Pedagogia Psicologia Filosofia, Università di Cagliari, via Is Mirrionis 1, 09123 Cagliari, Italy
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not empirical theories. The exact nature of the semantic relations that an empirical theory may bear to the real world then depends on how the theory and the real world itself are further conceived or analyzed. From a philosophical point of view, the relationship between an empirical theory and the real world is often understood in two opposing ways. According to realism, either theories are true representations of those aspects of reality that they are designed to describe or, even if we cannot tell whether theories are actually true or false, they may be objectively true and, in some circumstances, we may have good reasons to conjecture that t
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