A theory is distinct from a mere scientific explanation. Scientific explanation requires a causal explanation, which requires a law-governed explanation. Natural law describes but does not explain natural phenomena. Newton’s law of universal gravitation described, but did not explain, what caused gravitational attraction. Theories unify empirical regularities and describe the underlying process that accounts for these phenomena. Within theories are axioms, a small set of postulates, which are not proved in the axiom system but assumed to be true.
A theory goes beyond natural laws and scientific explanations in explaining the scientific explanations. A theory refers to a body of explanatory hypotheses for which there is strong support. Theories are a conjunction of axioms (of the laws of nature) and correspondence of rules specified in a formalized ideal language. This ideal language is composed of three parts: logical terms, observational terms, and theoretical terms. The logical terms were initially treated as analytic claims (particularly under the hypothetico-deductive model). Observational claims were to be unproblematic, understood as referring to incorrigible sense-data and later to publicly available physical objects. Correspondence rules were used to connect theoretical language to observational claims.
Tracing the structure of theory back to David Hume, the logical language of a theory was considered to be analytic. In the nineteenth century there was an agreement that Baconian induction was an overly restrictive method, and that the hypothetico-deductive method was superior, given that scientific certainty was being recognized as unattainable and not as certain as it once was thought. Explanations were derived from deduction. Also, the logical connection between these laws is not simply “They work together” since that would be too broad and vague, nor would it necessarily entail “logically implies.” A theory cannot be captured by the notion of logical derivation alone. Since Humean and logical positivist methodology philosophers have recognized that these strong logical connections are not as strong as they would have considered. The logical connections are merely deriving observable consequences from the set of laws that explain. According to the hypothetico-deductive model, evidence supports the hypotheses that it entails. A hypothetico-deductive argument runs the risk of yielding the absurd result that any observation supports every hypothesis, since any hypotheses is a member of a premise set that entails that observation. This is the idea that theories and hypotheses are confirmed by their observed deductive consequences.
This is different from the positive-instance criterion and the satisfaction criterion. For instance, “A is an F and A is a G,” which is a case of positive-instance of the hypothesis that all Fs are Gs, is not a deductive consequence of the hypothesis. These criteria have the idea that observations are logically consistent with a hypothesis will confirm the hypothesis. The hypothetico-deductive states that deductive consequences of a hypothesis or theory confirm the hypothesis or theory. One of the problems with the hypothetico-deductive methodology is that it suffers from the fallacy of affirming the consequent. Philosophers recognized this limitation and accepted the reality that scientific explanations and theories could not be infallible. This led to the development of different inductive and modest abductive models (i.e. I-S model). However, one of the inescapable aspects of the hypothetico-deductive model is that, like every theorem, certain terms such as axioms will not be defended by any logical method of reasoning but will be assumed to be true. (Additionally, to call a statement an axiom is not to commit to its truth, but simply to identify its role in a deductive system.) No fallacy is necessarily present in doing so—a large number of theorems are derived from axioms deductively. Also, a statement may be recognized as an axiom in one system but as a theorem in the next. Thus, the hypothetico-model shouldn’t be rejected for its deductive problems since it encompasses many theorems and axioms derived from the same methodology. What makes a theory distinct from laws is that it cannot merely consist of logical relations to one another. There has to be something more to being a theory than merely having an axiomatic structure from which theorems can be derived (i.e. the ideal gas law and the similarity to the quantity theory of money).
One of the chief components in connecting observational language with theoretical language was the causal structure of underlying processes. The problem is that an underlying causal structure may not provide the degree of illumination and explanation desired. One of the problems was Humean empiricist claims that causation may not be as incorrigible as we may think it is. Hume never denied causation; he just gave reason to suspect its prima facie appearance or supposed mechanism (or absence of mechanism). Propositional beliefs were based on perception by being derived from sense perceptions. Thus, for the Humean and Baconian empiricist, causation inevitably became habits of the mind rooted in association (or a logical reconstruction of Hume’s psychologisitic view.) This doesn’t give a sufficient reason for rejecting the correlation between observation language and theoretical language; rather, it’s a footnote reminder in this methodology. The hypothetico-deductive view, according to logical empiricists, posited that propositional beliefs are based on sense perception in that they must be tested in terms of their implications regarding sense perceptions. Adherents of the hypothetico-deductive view must posit how hypotheses are obtained and show how those hypotheses are obtained. Theories have a predictive power under this view. Theories are tested by the observational predictions deducible from the system of axioms.
The development of the kinetic theory of gas using Newton’s laws of motions as axioms gave an example of how causal structure explains observational data. The approached used was the deductive-nomological method, which later became associated with axiomatic or syntactic approach to scientific theories associated with hypothetico-deductivism. One of the axioms derived from the Newtonian system was that there were strong grounds for determinism about everything in nature.
 Alex Rosenberg, Philosophy of Science (New York: Routeledge, 2012), 117.
 Ibid., 115.
 Jessica Pfeifer and Sahotra Sarkar, The Philosophy of Science, Eds. Jessica Pfeifer and Sahotra Sarkar (New York: Routeledge, 2006), xii.
 Thomas Nickles, “Demarcation Problem,” in The Philosophy of Science, 190. Rosenberg, 122.
 Peter Lipton, “Abduction,” in The Philosophy of Science, 2. Ellery Eells, “Confirmation Theory,” Ibid., 147.
 Eells, 147.
 Nickles, 190.
 Rosenberg, 117.
 Ibid., 122.
 Ibid., 123.
 Dudley Shapere, “Observation,” in The Philosophy of Science, 524.
 Ibid., 125.