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The syntactical view holds that the structure of a scientific theory can be captured by an axiomatized system of sentences. It is expressed in a metamathematical language that included predicate logic, set theory, and model theory.[[CiteRef::Winther (2015)]] In 1928 [[Rudolf Carnap ]] published his ''The Logical Structure of the World'', which put forward this view, which was central to logical empiricism.[[CiteRef::Andersen and Hepburn (2015)]] [[Hans Reichenbach]], [[Otto Neurath]], [[Carl Hempel]], and [[Herbert Feigl ]] were also major contributors. The logical empiricist answer to the question of the structure of scientific theories was a family of related ideas rather than a single approach.[[CiteRef::Mormann (2008)]] The view was so widely accepted in the early twentieth century that it is sometimes referred to as the received view.[[CiteRef::Halvorson (2012)]]

The semantic view holds that the structure of a scientific theory can be expressed as a set of mathematical models, as models were defined by [[Alfred Tarski]]. It rejects the metamathematical language of the syntactic view.[[CiteRef::Halvorson (2012)]][[CiteRef::Winther (2015)]] Some important models in science include the bag model of quark confinement, the hard ball model of a gas, the Bohr model of the atom, the Gauss chain model of a polymer, the Lorentz model of the atmosphere, and the double helix model of DNA.[[CiteRef::Frigg (2006)]] Major proponents of the semantic view include [[John Von Neumann]], who wrote on the subject in the thirties, [[Fredrick Suppe]], and [[Bas Van Fraassen]].[[CiteRef::Winther (2015)]] The semantic view emerged in the 1960’s and 1970’s and became the dominant view in subsequent decades. [[John Ladyman ]] used it in his formulation of structural realism in physics. The semantic view has played a major role in the philosophy of biology and psychology in recent decades.[[CiteRef::Halvorson (2012)]]

The pragmatic view rejects a purely formal characterization of scientific theories entirely, and supposes that a theory necessarily consists of sentences, models, problems, standards, skills, practices, including such things as analogies, metaphors, and natural kinds, with its full characterization necessarily including elements that cannot be formalized.[[CiteRef::Mormann(2008)]][[CiteRef::Winther (2015)]] Proponents of the pragmatic view include [[Nancy Cartwright]], [[Ian Hacking]], [[Phillip Kitcher]], and [[Helen Longino]].