Ladislav Kvasz

Mathematics was considered by the members of the Vienna Circle an a priori discipline consisting of analytic propositions. The aim of the present paper is to draw attention to the experiential dimension of mathematical knowledge. Following the interpretation of physical knowledge as knowledge constituted by the use of instruments, I am trying to interpret also mathematical knowledge as knowledge based on instrumental experience. This interpretation opens a new perspective on the place of the logicist program in philosophy of mathematics. The aim of the present paper is to argue that mathematics is based on experience and that mathematical experience is instrumental. The difference between mathematics and physics is that in the case of mathematics the instruments are not measuring devices but tools of symbolic representation. In order to distinguish the mathematical experience from the physical one, I will call the instrumental experience in mathematics as symbolic experience. In analogy with the measuring devices of physics I will interpret the tools of symbolic representation as tools constituting symbolic experience.

The aim of the paper is to analyze how language affects scientific research, from planning experiments and interpreting their results, through constructing models and the testing their predictions, to building theories and justifying their principles. I try to give an overview of the potentialities of language of science. I propose to distinguish six potentialities: analytic, expressive, methodical, integrative, explanatory, and constitutive power of language. I will shortly characterize each of these potentialities and illustrate their contribution to scientific research. Although I believe that the theory is valid for a wide range of scientific disciplines, all illustrations are taken from physics.

Mathematics was considered by the members of the Vienna Circle an a priori discipline consisting of analytic propositions. The aim of the present paper is to draw attention to the experiential dimension of mathematical knowledge. Following the interpretation of physical knowledge as knowledge constituted by the use of instruments, I am trying to interpret also mathematical knowledge as knowledge based on instrumental experience. This interpretation opens a new perspective on the place of the logicist program in philosophy of mathematics. The aim of the present paper is to argue that mathematics is based on experience and that mathematical experience is instrumental. The difference between mathematics and physics is that in the case of mathematics the instruments are not measuring devices but tools of symbolic representation. In order to distinguish the mathematical experience from the physical one , I will call the instrumental experience in mathematics as symbolic experience. In analogy with the measuring devices of physics I will interpret the tools of symbolic representation as tools constituting symbolic experience

The book is a detailed and penetrating study of the relations between Bolzano’s philosophical views and his mathematical achievements. It opens with a Biographical sketch, written with a good understanding of the political situation in Central Europe at Bolzano’s times. The words of the Emperor Francis II: “I do not need scholars but obedient citizens” , and of an English visitor of Austria at those times: “These school-books are the most barren and stupid extracts which ever left the printing press.” express the problems of the intellectuals in this part of the world

This book argues that Descartes’ physics was a milestone on the road to modern mathematical physics. After Newton introduced a completely different approach to mathematical description of motion, Descartes’ physics became obsolete and even difficult to comprehend. This text follows the language of Descartes and the means of which motion can be described. It argues that Descartes achieved almost everything that later Newton was able to do—to describe the motion of interacting bodies- by different (i.e. algebraic) means. This volume completely refutes the received view according to which Descartes’ physics was merely a kind of discursive natural philosophy. To make this interpretation more plausible the book follows Descartes’ ideas from his early work in mathematics, through his invention of the analytic method towards his mature physics. It shows that Descartes followed a similar heuristic pattern. The volume appeals to students and researchers; it invites the reader equippedwith minimal understanding of college mathematics to follow Descartes on his intellectual journey through the Scientific Revolution. The reader will gain a deeper understanding of the role of mathematical language in the creation of modern physics and a glimpse into the fascinating world of Descartes’ scientific thought. Several of Descartes’ philosophical ideas can be traced back to his scientific interests and thus the book elucidates the motivation behind some of Descartes’ key positions in the area of epistemology and method. In the penultimate chapter the book presents four arguments in favor of seeing Descartes as a physicist on par with Galileo and Newton.

The aim of the present paper is to describe the fundamental epistemic ruptures, which occurred during the history of physics. Our approach is based on the reconstruction of the changes in the formal language of a particular physical discipline. We take into account aspects like the analytic, expressive or explanatory power, as well as analytic and expressive boundaries. One of the main results of our reconstruction is a new interpretation of Kant’s famous antinomies of pure reason. If we are prepared to relativise some of Kant’s antinomies, and instead of ascribing them to reason as such we relate them to the language of physics, it is possible to show, that these antinomies are relevant even for modern physics. Taking the form of a phenomenon, that we call the expressive boundaries of language are the antinomies a universal feature of all physical theories. This shows, that Kant in his antinomies pointed to a remarkable epistemological fact