Another paper that should get wider exposure: “The Classical Model of Science: a millennia-old model of scientific rationality” by Willem R. de Jong and Arianna Betti. Synthese (2010) 174:185-203. Excerpts:
Throughout more than two millennia philosophers adhered massively to ideal standards of scientific rationality going back ultimately to Aristotle’s Analytica posteriora. These standards got progressively shaped by and adapted to new scientific needs and tendencies. Nevertheless, a core of conditions capturing the fundamentals of what a proper science should look like remained remarkably constant all along. Call this cluster of conditions the Classical Model of Science. p.185
The Classical Model of Science as an ideal of scientific explanation
In the following we will speak of a science according to the Classical Model of Science as a system S of propositions and concepts (or terms) which satisfies the following conditions:
(1) All propositions and all concepts (or terms) of S concern a specific set of objects or are about a certain domain of being(s).
(2a) There are in S a number of so-called fundamental concepts (or terms).
(2b) All other concepts (or terms) occurring in S are composed of (or are definable from) these fundamental concepts (or terms).
(3a) There are in S a number of so-called fundamental propositions.
(3b) All other propositions of S follow from or are grounded in (or are provable or demonstrable from) these fundamental propositions.
(4) All propositions of S are true.
(5) All propositions of S are universal and necessary in some sense or another.
(6) All propositions of S are known to be true. A non-fundamental proposition is known to be true through its proof in S.
(7) All concepts or terms of S are adequately known. A non-fundamental concept is adequately known through its composition (or definition). p.186
The Classical Model of Science is a recent reconstruction a posteriori of the way in which philosophers have traditionally thought about what a proper science and its methodology should be, and which is largely set up, as it were, by abduction. The cluster (1)-(7) is intended, thus, to sum up in a fairly precise way the ideal of scientific explanation philosophers must have had in mind for a very long time when thinking about science. p.186
A proper science according to this Model has the structure of a more or less strictly axiomatized system with a distinction between fundamental and non-fundamental elements. p.186
The history of the conceptualization Science knows three milestones: first of all, Aristotle’s Analytica posteriora, especially book 1; secondly, the very influential so-called Logic of Port-Royal (1662), especially part IV: ‘De la méthode’, written mainly by Antoine Arnaud and relying in many respects on Pascal and Descartes; and finally Bernard Bolzano’s Wissenschaftslehre (1837). p.187
The formulation coming closest to a systematization of the ideal of science we codify in the Model is perhaps the description of scientific method given in the Logic of Port-Royal, ‘The scientific method reduced to eight main rules’:
Eight rules of science
1. Two rules concerning definitions
1 . Leave no term even slightly obscure or equivocal without defining it.
2. In definitions use only terms that are perfectly known or have already been explained.
2. Two rules for axioms
3. In axioms require everything to be perfectly evident.
4. Accept as evident what needs only a little attention to be recognized as true.
3 . Two rules for demonstrations
5 . Prove all propositions that are even slightly obscure, using in their proofs only definitions that have preceded, axioms that have been granted, or propositions that have already been demonstrated.
6. Never exploit the equivocation in terms by failing to substitute mentally the definitions that restrict and explain them.
4. Two rules for method
7. Treat things as much as possible in their natural order, beginning with the most general and the simplest, and explaining everything belonging to the nature of the genus before proceeding to particular species.
8. Divide each genus as much as possible into all its species, each whole into all its parts, and each difficulty into all its cases. pp.187-188
… the Model is a fruitful analytical tool. Its influence lasted until recently; having persisted at least to Lesniewski, it in fact extended far beyond what one might expect at first glance. It is certain, however, that at a some point the Model was abandoned without being replaced by anything comparable. p. 196