Arianna Betti

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.

Modelling the History of Ideas

We propose a new method for the history of ideas that has none of the shortcomings so often ascribed to this approach. We call this method the model approach to the history of ideas. We argue that any adequately developed and implementable method to trace (dis)continuities in the history of human thought, or concept drift, will require that historians use explicit interpretive conceptual frameworks. We call these frameworks models. We argue that models enhance the comprehensibility of historical texts, and provide historians of ideas with a method that, unlike existing approaches, is susceptible neither to common holistic criticisms nor to Skinners objections that the history of ideas yields arbitrary and biased reconstructions. To illustrate our proposal, we discuss the so-called Classical Model of Science and draw upon work in computer science and cognitive psychology.

Lesniewski's Early Liar, Tarski and Natural Language

Abstract This paper is a contribution to the reconstruction of Tarskis semantic background in the light of the ideas of his master, Stanislaw Leśniewski. Although in his 1933 monograph Tarski credits Leśniewski with crucial negative results on the semantics of natural language, the conceptual relationship between the two logicians has never been investigated in a thorough manner. This paper shows that it was not Tarski, but Leśniewski who first avowed the impossibility of giving a satisfactory theory of truth for ordinary language, and the necessity of sanitation of the latter for scientific purposes. In an early article (1913) Leśniewski gave an interesting solution to the Liar Paradox, which, although different from Tarskis in detail, is nevertheless important to Tarskis semantic background. To illustrate this I give an analysis of Leśniewskis solution and of some related aspects of Leśniewskis later thought.

The Road from Vienna to Lvov. Twardowski's Theory of Judgement between 1894 and 1897

In several manuscripts, written between 1894 and 1897, Twardowski developed a new theory of judgement with two types of judgement: existential and relational judgements. In Zur Lehre he tried to stay within a Brentanian framework, although he introduced the distinction between content and object in the theory of judgement. The introduction of this distinction forced Twardowski to revise further Brentanos theory. His changes concerned judgements about relations and about non-present objects. The latter are considered special cases of relational judgements. The existential judgements are analysed in a Brentanian way; whereas relational judgements are analysed in a Brentanian way only as far as the act is concerned, but not when it comes to the object: the object of a relational judgement is a relationship. With this notion of relationship Twardowski comes close to introducing a concept of state of affairs for the object of (relational) judgements.

On Tarski’s Foundations of the Geometry of Solids

The paper (Tarski:Lesfondementsdelageometriedescorps,AnnalesdelaSoci´´ Polonaise de Math´ ematiques, pp. 29-34, 1929) is in many ways remarkable. We address three historico-philosophical issues that force themselves upon the reader. First we argue that in this paper Tarski did not live up to his own methodological ideals, but displayed instead a much more pragmatic approach. Second we show that Lephilosophy and systems do not play the significant role that one may be tempted to assign to them at first glance. Especially the role of background logic must be at least partially allocated to Russells systems of Principia mathematica. This analysis leads us, third, to a threefold distinction of the technical ways in which the domain of discourse comes to be embodied in a theory. Having all of this in place, we discuss why we have to reject the argument in (Gruszczyand Pietruszczak: Full development of Tarskis Geometry of Solids, The Bulletin of Symbolic Logic, vol. 4 (2008), no. 4, pp. 481-540) according to which Tarski has made a certain mistake.

Leśniewski’s characteristica universalis

Leśniewski’s systems deviate greatly from standard logic in some basic features. The deviant aspects are rather well known, and often cited among the reasons why Leśniewski’s work enjoys little recognition. This paper is an attempt to explain why those aspects should be there at all. Leśniewski built his systems inspired by a dream close to Leibniz’s characteristica universalis: a perfect system of deductive theories encoding our knowledge of the world, based on a perfect language. My main claim is that Leśniewski built his characteristica universalis following the conditions of de Jong and Betti’s Classical Model of Science (2008) to an astounding degree. While showing this I give an overview of the architecture of Leśniewski’s systems and of their fundamental characteristics. I suggest among others that the aesthetic constraints Leśniewski put on axioms and primitive terms have epistemological relevance.

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):

Propositions et états de choses chez Twardowski

Twardowskis On the Content and Object of Presentations (1894) is one of the most influential works that Austrian philosophy has left to posterity. The manuscript Logik (1894-1895) supplements that work and allows us to reconstruct Twardowskis theory of judgement. These texts raise several issues, in particular whether Twardowski accepts propositions and states of affairs in his theory of judge- ment and whether his theory is acceptable. This article presents Twardowskis theory, shows that he accepts states of affairs, that he has a notion of proposition, and that his theory is interesting and sophisticated.

The Naming of Facts and the Methodology of Language-Based Metaphysics

According to Mulligan and Correia’s entry on facts in the Stanford Encyclopedia of Philosophy, ‘any philosophy of facts owes us an account of the form of such expressions as “the fact that Sam is sad”’. They also suggest that expressions of the form ‘the fact that p’ have the form of definite descriptions, and that one possible account of such expressions as definite descriptions is the one given by Hochberg. According to Hochberg, ‘the fact that p’ is analysed as ‘the fact that contains a as a term and F as an attribute and that is of the form φx exists’. Why should we ask that any philosophy of facts be equipped with names for facts (or, more neutrally, with ways to refer to facts)? A descriptive metaphysician accepting facts might care about the naming of facts; but I do not see why a revisionary metaphysician should: I do not see whether a revisionary metaphysician accepting facts should care even as to whether it is at all possible to name them. A fortiori, for a revisionary metaphysician, there does not seem to be any need for the expression ‘the fact that p’ to come out as a definite description. So, it seems that the only philosophers for whom Hochberg’s analysis is relevant are those who think that linguistic analyses of that kind can be used in support of a philosophy of facts independently of theoretical considerations. But this, I argue, is misguided: Since it presupposes a specific philosophy of facts from the start, Hochberg’s analysis cannot be used in support of that very philosophy or of any other philosophy of facts.

1.3. Contro i fatti

This paper argues that the hypothesis that there are facts is ungrounded. I first introduce a series of important theoretical distinctions to say what facts are not – and to avoid misunderstandings as to what I take to be facts, states of affairs and relations. Then I present the so-called problem of the glue, which is linked to Bradley’s regress. Finally, I propose a stronger version of the problem of the glue, which I call the problem of directional glue, with the aim of giving additional evidence that the problem of the glue is not solvable by the theories of facts which fall prey to it.