Theory Change - a metalogical view

Reinhard Kahle
 (Departament of Mathematics, Coimbra University, Portugal)

In this talk we address the problem of meaning of theoretical terms in the process of theory change. In contrast to traditional approaches we adopt a strict proof-theoretic view in the determination of meaning. Our approach makes part of a general programme to analyze intensional phenomena from a proof-theoretic perspective. It belongs to the field of proof-theoretic semantics, in its broad sense.

We consider theories - physical, mathematical or whatsoever - given as axiomatic systems. The particular derivation system (Hilbert-style, Gentzen-style or natural deduction) should not be of relevance for the following. To fix a common ground we will restrict ourselves to systems over a first-order language (however, in principle, our approach should be extensible to any other kind of formal language).

Give a first-order axiom system we adopt the view that this system implicitly defines the meaning of the non-logical terms used in it.

This notion of implicit definition allow of (quite far reaching) underspecification of the meaning of the terms, in contrast to the traditional semantic view which tries to provide concrete denotations in a semantical universe. In the axiomatic approach the meaning of a term is given only by its relation to the other terms. This view is illustrated best in David Hilbert's famous note on the axiomatization of geometry saying that this axiomatization would speak also about tables, chairs and beer mugs as long as they would relate to each other as points, straight lines, and planes.

Given an axiomatic system - coming along with its implicit characterizations of the terms used in it - we can consider the following four different forms of theory change:
1) Specification: The meaning of a term is narrowed. A prime example is the addition of an axiom about the term.
2) Liberalization: The meaning of a term is widened. An example is the extension of the domain of a quantification in the axiom system.
3) Modification: The meaning of a term is modified. We consider a modification the change of one axiom about a term while the bulk of axioms stays unchanged.
4) Revolution: The meaning of several terms is altered. In this case, the whole axiom system is modified in a substantial way.

This list is not intended to be complete, it rather illustrates how the different forms of theory change can be characterized in our

As appealing as this illustration might be, the real challenge for an approach of theory change is still pending: How can a new theory be related to an old one, if the terms have different meanings.

Except of the case of revolutions we will deal with this question by single out those axioms which the old and new theory have in common. If these axioms still provide a sufficient specific implicit definition of the term in question - "sufficient specific" understood in a way that representatives of the old and new theory can agree on the meaning on this common ground - the analysis of the change can be done base on this implicit definition.

It is worth noting that this analysis of smooth changes is not necessarily transitive. Even if the change of the meaning of a term from an axiom systems A to B, and a further change from B to C can be analyzed in this way, it might be that a direct change from A to C is not analyzable since it lacks a sufficient common ground.

In a more general perspective the proof-theoretic analysis provides us with additional structure which is lost in a theory given by a raw set of propositions. It is this additional structure which provides us with extremely useful information to analyze all kind of intensional phenomena, in particular, if we take the change of axiom systems as a meta-operation in consideration.

A Model of Scientific Hypothesis Development, Reasoning and Tracking: Creation of a Virtual World in Brain for Working out Theories

Sandeep Kumar Ganji 

Department of Biomedical Engineering and Centre For Creative Technologies, University College Of Engineering (A), Osmania University, Hyderabad, Andhra Pradesh, India. Pin Code: 500 007

We know now, without a doubt that imagination and creativity are central in invention, reasoning, understanding and testing a scientific hypothesis. Novel and unique hypothesis have to be generated from within the two domains of scientific inventory; hypothesis which may be unprecedented in the previous investigations and those which go beyond the experimental data. It is clear that such capabilities are pivotal in learning and understanding the critical links of theories from recent studies of neuroscientists. To explore these details further into the realms of cognitive abilities i.e. explaining these imaginative constructs from a neural sciences way would ensure its scientific and philosophical value. Here I present a model in which it is explained how scientific hypotheses are created in the mind and then understood, tested and tracked inside brain with the help of creation of a virtual world. In this case a number of fundamentally distinct cognitive functions come together in creating this virtual world, where in the particular hypothesis is tracked, reasoned and tested. In this way we can include the long debated role of rationality, social psychology, previous knowledge of hypothesis and creative imagination into focus of philosophical studies of scientific hypothesis development. There are genuine conceptual difficulties in applying neural based cognitive theories to the philosophical systems of scientific understanding. Hypothesis for scientific theory should be generated, and theories for it constructed, these processes should be improved in the light of the evidence (reasoning, tracking and testing). Assuming modularity of the mind and its functions, the next step is to indentify the main functional elements of the cognitive skills that help in building a scientific theory. From the recent neuropsychological studies the main elements are visual and linguistic skills, but there are also other modules like memory and pre-knowledge etc. that play a central role in this process. The creation of this virtual world helps in testing the hypothesis without the need of the any practical work being done, which is a central and distinct feature in all the major scientific breakthroughs (at least theoretical) put forward. In this virtual world created, a scientific trained mind (one which follows a methodological approach to problems) will reach a logically sound conclusion (though it can’t be guaranteed that the conclusion will be scientifically correct). At first look it looks something that is contradictory and intuitively hard to accept in its naïve state, especially when applied to the philosophical views from the cognitive knowledge, but an example would make the rule clear. When we become aware that the scientific theory we are working on is blossoming unusually different, we think this is an absolute judgement based on comparisons with past, position experiences with other scientific developments and not on the validity of the theory based on anomalies of observations. Here I elucidate on the role played by each cognitive abilities on the creation of this virtual world laboratory and ultimately on the scientific reasoning and tracking. These cognitive abilities are windows into the world of human intellectual abilities.

Unity of Science against the Rational Construction of Knowledge?

Catherine Laurent
Institut National de la Recherche Agronomique (INRA),
Département de Recherches Sciences pour l'action et le Développement, France)

Most scientists are confronted daily with the heterogeneity of scientific approaches and with the need to solve increasing difficulties to combine knowledge coming from various scientific areas. But these difficulties are ignored when philosophy of science postulates the possibility of establishing a priori rational principles of a unified science. In that case, it is logically considered that the problems met to integrate scientific knowledge originating from different sources result from institutional gaps or organisational failures, or from the lack of skill of the researchers. Subsequently, the analyses of these problems are handed over to the sociology of science. Therefore the debate on the unity of science may screen the heuristic value of approaches based on an epistemological regionalism to support the rational construction of knowledge. Actually, to study the on going building of scientific knowledge, the question of the ultimate state of the science does not matter. What is important is to acknowledge that here and now
1) to deal with a similar phenomenon, theories based on distinct conceptual architectures -and sometimes contradictory hypotheses- coexist (for example Cartwright 1999);
2) social sciences, nature sciences and technical disciplines may produce knowledge with distinct properties, generating different kinds of interactions with its environment (Hacking 2001, Hottois 1996) ;
3) each research programme has its own area of demonstration and builds knowledge through specific paths (Bachelard 1949).
If these statements are to be considered seriously –and so are they by most scientists- it is no more obvious to put together different scientific areas: the integration of scientific knowledge is an epistemic situation that needs clarification. The presentation, based on specific examples in ecology and economics, will show the perspectives open by such a view point to analyse the revision of research programmes and to assess the results of research projects. By doing so, this presentation would like to contribute to stress the need for further development of internal analyses of on going science that would associate scientists and philosophers. As a matter of facts, a vision of a unified science that would ignore the difficulties resulting from the current conceptual heterogeneity of scientific approaches would partly deprive the building of rational knowledge from the support of the internalist analyses of philosophy.

Bachelard, G., 1949/1975. Le rationalisme appliqué, PUF, Paris. 215 p.
Cartwright N., 1999. The dappled world. A study of the boundaries of science, Cambridge University Press,Cambridge.247p.
Hacking, I., 2001. Leçon inaugurale au Collège de France. Chaire de philosophie et histoire des concepts scientifiques. Paris. 25 p.
Hottois, G., 1996. Entre symboles et technosciences , Champ Vallon - PUF, Paris. 268 p.

The Structure of Styles

César Lorenzano
(National University of Tres de Febrero, Buenos Aires, Argentina)

In 1913, Enrique Wölfflin publishes a book - Principles of Art History: The Problem of the Development of Style in Later Art- that from that moment became an obliged reference to the most important theoretician and historians of the art. History of art as history of stiles –Wölfflin’s proposal- was accepted by authors like E. Gombrich (1984), E. Panovsky, or A. Hausser as a presupposed knowledge to their own developments. 

In this article it will reconstruct that theory following an amended version of the structuralist conception of theories, so as to make it easier to understand for those who are not familiarized with its jargon, or with the peculiarities of the theory of models and of groups. Besides the expositive reasons, there are ontological and epistemic reason to do so.

I will begin exposing the theory of styles by means of a hypothetical narration, but not for that reason unfaithful, of the genetic method that took to their formulation, in the supposition 
When coming this way, it is introduced in a natural way the strategy of reconstructing it starting from their copies 
Finally, diagrams will be used to show the elements and relationships of their texture, leaving aside the language of the theory of models and of groups. 
Several reasons exist to analyze the theory that Wölffflin proposes, beyond its acceptance for the community of theoretical and historians of the art, and of its validity to almost a hundred years of its approach. 
In the first place, the intrinsic interest of the history of the art like field of legitimate knowledge, habitually careless for the philosophy of the science We will make notice that the history of the art is, together with the history of the science, one of the first differential histories that obtain institutional genuineness, becoming independent of what we could call "the great history", that story of the power and its sways. 
As we will verify later on, the history of the art possesses explanatory theories It is so much of a theory about the art and their stylistic texture, as of the history of the art and their evolutionary stages that it presents a narrow parallelism with theories of the history of the science. A barely noticed, given phenomenon the separation among the communities of investigators in both disciplines. 
Be possibly the first of a long family of approaches that you/they incorporate to the texture of the story the architectural properties of that that history. When we specify the theory of the styles of Wölfflin, the likeness will be noticed that possesses with Thomas' approaches Kuhn and Ludwik Fleck 

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