Justification Of The Concept Of "quantity" In Kant's Philosophy Of Mathematics And The Metaphysics Of Natural Sciences

With the development of mathematics and natural science in the 19th and 20th century and the theory of non-Euclidean geometry,mathematical logic and relativity were successfully introduced,Kant's philosophy of mathematics and natural science were once ignored.Kant's three-dimensional concept of Euclidean geometry is regarded as a special case of high-dimensional non-Euclidean geometry.As one of the theoretical foundations of Kant's transcendental philosophy,Aristotle's logic is overtaken by the development of modern mathematical logic.Kant's philosophy of natural science is regarded as a philosophical product of outdated Newton's mechanics.However,with the deepening of research,Kant's philosophy has exerted an increasingly profound influence on the basic problems of modern mathematics and on modern natural sciences,especially physics.The above critical views on Kant's mathematical philosophy and natural science philosophy have been strongly questioned and challenged.One of the basic ideas to defend Kant's philosophy of mathematics and natural science under the background of the progress of mathematics and science is to make a strict distinction between Kant's philosophical research and mathematical research,philosophical knowledge and scientific knowledge.Kant regards mathematics and philosophy as two kinds of prior knowledge from reason,and should separate the work of mathematics and mathematics physics from the work area of Kant's proof of his philosophy.Therefore,any view of mathematical space-time based on mathematical structure and the theory of space-time in natural science cannot fundamentally touch or refute the concept of time and space in Kant's critical philosophy.On the contrary,Kant's philosophy provides a critical metaphysical philosophical foundation for modern mathematics and natural science theory.But in the present research,the investigation of Kant's mathematical philosophy is usually confined to the discussion of the transcendental aesthetic theory of "critique of Pure reason",and most of its research conclusions remain in the philosophical conclusion that Kant regards the mathematical proposition as a prior synthetically judgment.It neglects the study of the theory of category,the theory of Schema,the theory of pure intellectual principle,and the study of mathematical philosophy in the part of Kant's Transcendental dialectic theory and the discussion of its significance of the times.In addition,there is little research on Kant's "metaphysical foundation of Natural Science" and the philosophy of mathematics in his "opus postumum".The research on philosophy of natural science lacks more deeper dialogue and discussion between Kant's philosophy of mathematics and philosophy of natural science based on the understanding of classical literature of modern mathematics and natural science philosophy.The study of this paper is not a comprehensive review of Kant's philosophy of mathematics and philosophy of natural science,but is guided by the analysis of the concept of quantity.This paper examines Kant's philosophy of mathematics and natural science through the specific content perspective of the concept of quantity.Taking the division of cognitive ability in Kant's "critique of Pure reason" as the basic research framework,and discusses the "quantity"(Gro?e)belonging to the aesthetic theory,the "quantity category"belonging to the intellectual theory,and the intellectual principle theory.The philosophy of mathematics and natural science contained in the theories of "schema of quantity" and"principle of quantity" in the theory of intellectual principle;On this basis,combined with Kant's discussion of number,quantitative concept-related categories,mathematics,and natural science in his book "metaphysical foundation of Natural Science",To form an important supplement and reference to the study of philosophy of mathematics and natural science in "criticism of Pure reason";In addition,this thesis attempts to combine the concept of "measurement" on the basis of Riemann's "The Foundation of Geometrical Hypothesis",a classical literature of non-Euclidean geometry.This paper analyzes the difference between the concept of space in Riemannian geometry and Kant's spatial view,and takes it as an example to illustrate the essential difference between the concept of space in Riemannian geometry and that of modern non-Euclidean geometry.The basic conclusion of this study is that the interpretation of the concept of quantity depends to a large extent on the grasp of Kant's philosophy.In the "Critique of Pure Reason",there is a clear philosophical distinction and an important connection between the concept of quantity as a phenomenon and the concept of quantity,as well as the graph type of quantity.On the basis of priori aesthetics theory,we should pay attention to the research on the problem of number and quantity in the transcendental philosophy of intellectuality and reason.Since in "critique of Pure reason",thing-in-itself are the limits of aesthetical ability,and the space which contain material and movement is the object of Kant's study in philosophy of natural science.So the philosophical background of the application about the concept of number and quantity should not be confused in the two works.In the two works,Kant's use of the category of quantity has changed to a certain extent.The category of quantity has been transformed from intuitionistic category of "mathematics" in priori philosophy to the category of "mathematics-mechanics" as "momentum" in philosophy of natural science,and quantity is not only the object of application in "pure mathematics",but also in "mathematics-mechanics".In addition,the space in Kant's "Critique of Pure Reason" is the condition of the possibility of the phenomenon rather than the provision attached to the phenomenon.The space is independent of the concept of time and the nature of the space is philosophical.In the "metaphysical foundation of Natural Science",the study object is the space of matter movement in experience.The concept of space and time are still independent,the scale of space is defined by linearity.In Riemannian geometry,the study object is empirical space,and the concept of space is not independent of time,but a combination of the concepts of"space and time".Its scale is a mathematical concept set by curves(nonlinear),which constructed by algebraic methods.