Axiomatic theory approach

A considerable advantage of the axiomatic approach is its universality (for instance, the author previously succeeded in developing the kinetic statistic theory of molecular weight distributions of polymers formulated according to the model for the axiomatic theory [6]). Moreover, in the initial stage of the... 

The use of formal metliods mandates a scientific approach. One possible approach is to formalise specification knowledge as an axiomatic system. Tlie CREATIV toolset uses a new model and a new definition of the specification process, together with an axiomatic theory to support specification knowledge. All operations in tlie system are provable and traceable we have built the reasoning component of tlie CREATIV toolset on the basis of this theory. 

Finally, reductionism is closely tied to the so-called syntactic approach to theories, an approach which treats theories as axiomatic systems expressed in natural or artificial languages. Indeed, closely tied may be an understatement, since deduction is a syntactic affair, and is a necessary component of reduction. Once philosophers of science began to take the semantic approach to theories seriously, the very possibility of reduction became moot. For the semantic approach treats theories as families of models, and models as implicit definitions, about which the only empirical question is whether they are applicable to phenomena. For reduction to be obtained among models semantically characterized requires an entirely different conception of reduction, and whether such a conception would capture anything of interest about inter-theoretical relations is questionable. 

Parallel with the phenomenological development, an alternative point of view has developed toward thermodynamics, a statistical-mechanical approach. Its philosophy is more axiomatic and deductive than phenomenological. The kinetic theory of gases naturally led to attempts to derive equations describing the behavior of matter in bulk from the laws of mechanics (first classic, then quanmm) applied to molecular particles. As the number of molecules is so great, a detailed treatment of the mechanical problem presents insurmountable mathematical difficulties, and statistical methods are used to derive average properties of the assembly of molecules and of the system as a whole. 

A new qualitative quantum-chemical concept of the elementary act of addition polymerization has been proposed as the development of the polymerization theory. An extensive set of various data on the kinetics and the mechanism of polymer structure controlling has been found to have a new explanation from an uniform viewpoint. This concept is developed in the framework of the axiomatic approach to the general polymerization theory and is based on five postulates, namely the principle of the intermediate, the principle of intermediate cyclicity, the principle of correspond-... 

The axiomatic approach to the development of the theory of addition polymerization presented here is the first consequent attempt to interpret as many various experimental facts as possible on the basis of as few assumptions as possible. It should be noted that at present this concept has neither a wide recognition nor has been the subject of profound criticism.. However, the author hopes that this is due to the fact that these concepts are not very well known. In this connection, the author should like to draw the attention of the reader to the following points ... 

If specification is to be a rigorous discipline, tlien tliere must be a proper scientific approach to tlie subject. We suggest a new approach to specification, in which all specification knowledge is embedded within an axiomatic or rule-based theory, though this theory is nonnally concealed from users. This requires ... 

The Molecular Theory of Solutions , by Prigogine, includes thermodynamic considerations, and Zemansky s book is a later edition of the book mentioned earlier. Wilson s volume is of a fairly advanced level and requires a fairly high standard of mathematical ability. It is mainly designed for the use of physicists. Chapters include accounts of partial differentiation, and the book approaches entropy through Carnot cycles but also describes Caratheodory s axiomatic approach. Superconductivity and solutions are considered thermodynamically. Caldin s introduction is designed for chemistry undergraduates. A student who has mastered the text should be well prepared to go on to more advanced work. Chisholm and de Borde s book develops the equations for Bose-Einstein, Fermi-Dirac, and classical statistics by unusual routes and then applies the... 

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