The semantic view of theories was originally proposed by Patrick Suppes in “A Comparison of the Meaning and Uses of Models in Mathematics and the Empirical Sciences”[1] as a reaction against the received view of theories popular among the logical positivists.
This should be contrasted with the alternative of presenting a theory in the first instance by identifying a class of structures as its models.
In this second, semantic, approach the language used to express the theory is neither basic nor unique; the same class of structures could well be described in radically different ways, each with its own limitations.
[4]In this same book, van Fraassen, a key founder of the semantic view of theories, critiques the syntactic view in very strong terms: Perhaps the worst consequence of the syntactic approach was the way it focused attention on philosophically irrelevant technical questions.
(p. 56)The semantic view of theories has been extended to other domains, including population genetics.