The axiomatic method, the order of concepts and the hierarchy of sciences: an introduction

This special issue of Synthese 'The Classical Model of Science II: The axiomatic method, the order of concepts and the hierarchy of sciences' follows up on the previous 'The Classical Model of Science I: A millennia-old model of scientific rationality'. Both issues centre on the role, the significance and the impact of the axiomatic ideal of scientific knowledge in the history of philosophy. The first issue focuses on the relation between axiomatics and a number of issues in the development of logic, mathematics, and methodology and philosophy of science in Aristotle, Proclus, the seventeenth century, Kant, Bolzano, Frege and Leśniewski. The papers collected in this second issue on the one hand continue to investigate that relation in Kant and Bolzano, stretching it further on to our days, via mathematicians such as Schröder, Dedekind, and Birkhoff, and on the other hand they extend that investigation to related and current issues concerning the empirical sciences, in a systematic evaluation of modern (formal) axiomatic conceptions of science. The contributions in both issues take their cue from the axiomatic ideal in question as captured in the 'Classical Model (or Ideal) of Science' (de Jong and Betti 2008): (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). 1 Actual beings......Page 1 3 Invariance......Page 5 2 Theory-talk vs. experiment-talk......Page 2 6 Axiomatization and the notion of analyticity......Page 10 5 The sea of stories......Page 12 5 Conclusion......Page 19 References......Page 20 2 The model revolution at Stanford......Page 3 4 Measurement......Page 6 7 Constructive mathematical foundations......Page 9 4.5 Birkhoff's consolidation of lattice theory......Page 17 References......Page 18 2 Axiomatization as a metatheoretical method......Page 4 5 Computations......Page 7 References......Page 11 4.2 Bennett's explication of a commonality of axiom systems......Page 13 9 Is axiomatization epistemologically motivated?......Page 14 6 Concepts and propositions at bay......Page 15 References......Page 16 3 Aristotelian ideals......Page 8 7 Towards completion......Page 22 8 Exitum: scientific representation......Page 24 References......Page 27