To mathematicians, mathematics is a happy game, to scientists a mere tool and to philosophers a Platonic mystery - or so the caricature runs. The caricature reflects the alleged 'cultural gap' between the disciplines- a gap for which there too often has been, sadly, sound historical evidence. In many minds the lack of communication between philosophy and the exact disciplines is especially prominent. Yet in the past there was no separation - exact knowledge, covering both scientists and mathemati- cians, was known as natural philosophy and the business of providing a critical view of the...
To mathematicians, mathematics is a happy game, to scientists a mere tool and to philosophers a Platonic mystery - or so the caricature runs. The cari...
The twentieth century has witnessed a striking transformation in the un- derstanding of the theories of mathematical physics. There has emerged clearly the idea that physical theories are significantly characterized by their abstract mathematical structure. This is in opposition to the tradi- tional opinion that one should look to the specific applications of a theory in order to understand it. One might with reason now espouse the view that to understand the deeper character of a theory one must know its abstract structure and understand the significance of that struc- ture, while to...
The twentieth century has witnessed a striking transformation in the un- derstanding of the theories of mathematical physics. There has emerged clearl...
In May of 1973 we organized an international research colloquium on foundations of probability, statistics, and statistical theories of science at the University of Western Ontario. During the past four decades there have been striking formal advances in our understanding of logic, semantics and algebraic structure in probabilistic and statistical theories. These advances, which include the development of the relations between semantics and metamathematics, between logics and algebras and the algebraic-geometrical foundations of statistical theories (especially in the sciences), have led to...
In May of 1973 we organized an international research colloquium on foundations of probability, statistics, and statistical theories of science at the...
The twentieth century has witnessed a striking transformation in the understanding of the theories of mathematical physics. There has emerged clearly the idea that physical theories are significantly characterized by their abstract mathematical structure. This is in opposition to the tradi- tional opinion that one should look to the specific applications of a theory in orrter to understand it. One might with reason now espouse the view that to understand the deeper character of a theory one must know its abstract structure and understand the significance of that structure, while to understand...
The twentieth century has witnessed a striking transformation in the understanding of the theories of mathematical physics. There has emerged clearly ...
The twentieth century has witnessed a striking transformation in the understanding of the theories of mathematical physics. There has emerged clearly the idea that physical theories are significantly characterized by their abstract mathematical structure. This is in opposition to the tradi- tional opinion that one should look to the specific applications of a theory in orrter to understand it. One might with reason now espouse the view that to understand the deeper character of a theory one must know its abstract structure and understand the significance of that structure, while to understand...
The twentieth century has witnessed a striking transformation in the understanding of the theories of mathematical physics. There has emerged clearly ...
In two earlier volumes, entitled The Logico-Algebraic Approach to Quan- tum Mechanics (hereafter LAA I, II), I have presented collections of research papers which trace out the historical development and contem- porary flowering of a particular approach to physical theory. One might characterise this approach as the extraction of an abstract logico-algebraic skeleton from each physical theory and the reconstruction of the physical theory as construction of mathematical and interpretive 'flesh' (e. g., measures, operators, mappings etc. ) on this skeleton. The idea is to show how the specific...
In two earlier volumes, entitled The Logico-Algebraic Approach to Quan- tum Mechanics (hereafter LAA I, II), I have presented collections of research ...
1. INTRODUCTION In the Spring of 1975 we held an international workshop on the Foundations and Application of Decision Theory at the University of Western Ontario. To help structure the workshop into ordered and manageable sessions we distri- buted the following statement of our goals to all invited participants. They in turn responded with useful revisions and suggested their own areas of interest. Since this procedure provided the eventual format of the sessions, we include it here as the most appropriate introduction to these collected papers result- ing from the workshop. The reader can...
1. INTRODUCTION In the Spring of 1975 we held an international workshop on the Foundations and Application of Decision Theory at the University of Wes...
1. INTRODUCTION In the Spring of 1975 we held an international workshop on the Foundations and Application of Decision Theory at the University of Western Ontario. To help structure the workshop into ordered and manageable sessions we distri- buted the following statement of our goals to all invited participants. They in turn responded with useful revisions and suggested their own areas of interest. Since this procedure provided the eventual format of the sessions, we include it here as the most appropriate introduction to these collected papers result- ing from the workshop. The reader can...
1. INTRODUCTION In the Spring of 1975 we held an international workshop on the Foundations and Application of Decision Theory at the University of Wes...
