Such science possesses, first, a set of reports: what has been measured, recorded, or otherwise perceived. We might term these ‘observation statements.’
A long catalogue of observation statements, however, does not by itself constitute a science. A science possesses, second, a conceptual framework which organizes, sorts, or explains these observations.
We can understand, then, what is not a science. A data-base, a massive amount of recorded measurements, is by itself not a science: it lacks a conceptual structure.
Conversely, an a priori conceptual framework, a structure of ideas without any sense-data or empirical observations connected to it, is also not a natural science (or an empirical science, or an observational science), although it might be some other type of science.
Paul Davidson Reynolds proposes a taxonomy of scientific structures, categorizing the possible types of conceptual frameworks which one might add to data in order to generate a science:
Scientific knowledge is basically a collection of abstract theoretical statements. At present, there seem to be three different conceptions of how sets of statements should be organized so as to constitute a “theory”: (1) set-of-laws, (2) axiomatic, and (3) causal process.
We might acknowledge two aspects to scientific knowledge. One aspect is concrete observations, ultimately the product of sense-data, which are measurable and quantifiable. Another aspect is theoretical: the systematic organization of these empirical perceptions.
A simple example might be seen on a Cartesian plane: individual observations are represented by dots (x,y); theory is represented by a “best-fit line” or “best-fit curve.”
It is significant that more than one theory can be paired with a set of observations: data can underdetermine the choice of theory. How does one choose between two competing theories, both of which correspond to the measurements? Or must one choose?
To extend our example, image a set of dots on the Cartesian plane, a set for which there might be more than one “best-fit curve,” where both curves have an equal degree of correspondence to the points.
Multiple best-fit curves can result either from the location of the points, or from competing methods of generating the best-fit curve. It would be necessary to distinguish between trivial non-trivial cases of sets with more than one best-fit curve.
Three conceptions of theory have been discussed: the set-of-laws form, or the view that scientific knowledge should be a set of theoretical statements with overwhelming empirical support; the axiomatic form, or set of theoretical statements, divided into axioms and propositions, those statements that can be derived from the axioms; the causal process form, or sets of statements organized in such a fashion that the causal mechanism between two or more concepts is made as explicit as possible. It may be possible to present the statements of some axiomatic theories in causal process form.
Most interesting are the theories which, as Paul Davidson Reynolds notes above, might simultaneously satisfy the conditions for more than one of the three conceptions of theory.
Richer and more complex theories, rather than the simple example of a best-fit curve, offer examples of each of the three conceptions of theory.
