The Role of Kant's theory of knowledge in setting up the epistemological foundation of mathematics
MARSIGIT, Promotor Prof. Imam Barnadib, Ph.D
2007 | Disertasi | S3 Ilmu Filsafat
This research investigates the role of Kant’s theory of knowledge in setting up the epistemological foundations of mathematics. The material object of this research is epistemological foundation of mathematics and the formal object is Kant’s theory of knowledge. To support the main purpose the research for this study has also described and reflected the philosophy and foundation of mathematics as well as Kant’s Theory of Knowledge? This research has been carried out by employing literal study on Kant’s critical philosophy and on the philosophy of mathematics, developing method for collecting related references, highlighting the related important concepts, categorizing the information, implementing the similar procedure to other document, extracting some ideas, finding other or new supporting information, composing and theorizing the findings. By employing hermeneutics and phenomenology approaches the researcher has been striving to interpret the related texts of Kant’s theory of knowledge in such a way that the results have been fitted to form of a logical coherent argument involving the historical phenomena. This research describes that any version of epistemological foundationalism of mathematics consists of an element of absolutism viz. epistemological standards, such as truth, certainty, universality, objectivity, rationality, etc. Empiricists version of foundationalism believe that the mathematical truths are certain because of their causes because they presuppose that the object which the proposition is about imposes the propositions truth. On the other hand, rationalists version of foundationalism believe that mathematical knowledge is already present in human mind before any cognitive activity begins. The development of the foundation of mathematics at least has two main different positions of epistemological problems. Firstly, mathematics should be limited by the nature of perceptual faculties, it should be intuitive and be about the perceivable world; and hence, what is needed is a more sophisticated theory of perception. Secondly, mathematics are not consistent with perceptual abilities; therefore we do not limit mathematics to what is able to intuit. Mathematics is not necessarily about perceivable things; it should be governed only by abstract considerations of rigor and reasoning. This research concludes that Kant’s theory of knowledge seeks the solid ground on epistemological foundation of mathematics by establishing basic ideas and truths from which the rest of mathematical knowledge can be inferred. Kant's most significant contribution to the epistemological foundation of mathematics is the recognition that mathematical knowledge can only be established through a necessarily presupposed synthetical a priori in which apodictically valid propositions is possible. In the contemporary philosophy of mathematics, the role of Kant’s theory of knowledge can be traced from Kant’s recognition that understanding of mathematics can be supported by the nature of perceptual faculties. Accordingly, mathematics should be intuitive; and, it implies that epistemological foundation of mathematics to be more sophisticated theory of sensible intuition.
Kata Kunci : Filsafat Pengetahuan,Teori Kant's,Matematika, philosophy of mathematics, foundation of mathematics, epistemological foundation of mathematics, Kant’s theory of knowledge, Kant’s philosophy of mathematics
