Willem Remmelt De Jong

The Classical Model of Science: a millennia-old model of scientific rationality

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. In this paper we will do two things. First of all, we will propose a general and systematized account of the Classical Model of Science. Secondly, we will offer an analysis of the philosophical significance of this model at different historical junctures by giving an overview of the connections it has had with a number of important topics. The latter include the analytic-synthetic distinction, the axiomatic method, the hierarchical order of sciences and the status of logic as a science. Our claim is that particularly fruitful insights are gained by seeing themes such as these against the background of the Classical Model of Science. In an appendix we deal with the historiographical background of this model by considering the systematizations of Aristotle’s theory of science offered by Heinrich Scholz, and in his footsteps by Evert W. Beth.

The analytic-synthetic distinction and the classical model of science: Kant, Bolzano and Frege

This paper concentrates on some aspects of the history of the analytic-synthetic distinction from Kant to Bolzano and Frege. This history evinces considerable continuity but also some important discontinuities. The analytic-synthetic distinction has to be seen in the first place in relation to a science, i.e. an ordered system of cognition. Looking especially to the place and role of logic it will be argued that Kant, Bolzano and Frege each developed the analytic-synthetic distinction within the same conception of scientific rationality, that is, within the Classical Model of Science: scientific knowledge as cognitio ex principiis. But as we will see, the way the distinction between analytic and synthetic judgments or propositions functions within this model turns out to differ considerably between them.

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 ClassicalModel of Science I: Amillennia-oldmodel 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 Schroder, 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):

Theories of the Copula

Until now terms have occupied the place of central importance in this study. Certain semantic structures have been shown to be constitutive for Mill’s theory of denotation and connotation; in particular, the insight that all general (concrete) terms possess a twofold signification has been observed to be of great importance (see Table VIII).

The Classification of Names in a System of Logic

The central concern of this opening chapter is the classification of names in the second chapter of the first book of A System of Logic. Mill entitled that chapter ‘Of Names.’ In order to provide a satisfactory introduction to the terminological and conceptual frameworks that are constitutive for the present monograph, I have found it necessary to analyze Mill’s view of names precisely. In this first chapter I explore what Mill means by a name — typical logical distinctions become apparent even here — and I discuss the kinds of names he distinguishes. I deal in turn with the distinctions general—individual, concrete—abstract, connotative—non-connotative, positive—negative, and relative—non-relative. I leave the opposition universal—equivocal, which Mill injects, aside, since this distinction is of little interest here. As Mill himself states, it has no connection with names; it applies rather to “modes of employing names” (SL, p. 44).

Semantics and Metaphysics

John Stuart Mill is usually perceived — by no means incorrectly — as a pronounced adherent of later British empiricism. Yet, in the preceding chapters it became clear that this empiricism had almost no effect on his semantics; rather, he seems even consciously to have barred the door to specifically empiricist conceptions. The central part of Mill’s semantics could, in a manner of speaking, also have been formulated by a thinker from an entirely different philosophical tradition. In this chapter I attempt to throw some light on the backgrounds and causes of this state of affairs.

Themes from the History of Logic

In the course of the discussion in Chapter 1 of the various distinctions of names, I alluded several times to the insights of the older logicians, thereby revealing something of the historical backgrounds of Mill’s classification of names. Mill himself repeatedly bore witness to his awareness of standing upon the shoulders of his predecessors when handling terms and propositions. The motto, borrowed from Condorcet, of the first book of A System of Logic points in this direction: “Scholasticism, which produced in logic … a subtlety, a precision of ideas, the habit of which was unknown to the ancients, has contributed more than one can believe to the progress of good philosophy” (see SL, p. 18). Mill, as one agreeing with this assessment, appeals a number of times in connection with his classification of names to the “schoolmen.”

Thinking in Intension and Extension

In Chapter 2 I discussed the ontological backgrounds that are constitutive for du Trieu’s interpretation of connotative terms. In this chapter I intend to show, among other things, that the treatment of connotative and non-connotative terms in A System of Logic deviates from that of du Trieu and others precisely because the ontological square is no longer acceptable to a thinker like Mill. For Mill’s classification of names is based on an opposition of substance (thing-2) and attribute (thing-3).

The Semantics of Propositions

I want to turn now to the discussion of Mill’s view of the semantic status of S-P propositions. Following the survey of the theories of the copula presented in Chapter 5, this is a reasonably easy task. The way in which the copula connects subject and predicate to each other in concrete propositions is the central topic of the first four sections of this chapter. Abstract propositions come up only in 6.7.

From Predicables to Real Kinds

Following the general surveys of Chapters 2 and 3, I turn now once again to Mill’s own insights. Here I deal with a number of questions concerning the semantics of terms — questions that are related in one way or another to the development of Mill’s thought.