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With the underpins the dynamics of knowledge growth, as well as with the specific body of knowledge accepted at any one time. Traditional philosophers such as Locke and Kant admit the legitimacy and indeed the necessity of genetic considerations in epistemology. So do an increasing number of modern philosophers, such as Dewey(1950), Wittgenstein (1953), Ryle (1949) Lakatos (1970), Roulmin (1972), Polanyi (1958), Kuhc (1970), and Hamlyn (1978).
Secondly, there is the distinction between mathematics as an isolated and discrete discipline, which is strictly demarcated and separated from other realms of knowledge, as opposed to a view of mathematics which is connected with, and indissolubly a part of the whole fabric of human knowledge. Absolutist views of mathematics accord it a unique status, it being (with logic) the only certain realm of knowledge, which uniquely rests on rigorous proof. These conditions , together with the associated internalist denial of the relevance of history or genetic or human contexts, serve to demarcate mathematics as an isolated and discrete discipline.
Fallibilists include much more within the ambit of the philosophy of mathematics . Since mathematics is seen as fallible, it cannot be categorically divorced from the empirical (and hence fallible ) knowledge of the physical and other sciences. Since falliblism attends to the genesis of mathematical knowledge as well as its product, mathematics is seen as embedded in history and in human practice. Therefore mathematics cannot be divorced from the humanities and the social sciences, or from a considerations of human culture in general. Thus from a fallibilist perspective mathematics is seen as connected with, and indissolubly a part of the whole fabric of human knowledge.
The third distinction can be seen as a specialisation and further development of the second. It distinguishes between views of mathematics as objective and value free, being connected only with its own inner logic, in contrast with mathematics is seen as integral part of human culture, and thus as fully imbued with human values as other realms of knowledge and endeavour. Absolutist views with their internal concerns, see mathematics as objective as absolutely free of moral and human values. The fallibilist view, on the other hand, connects mathematics with the of human knowledge through its historical and social origins. Hence it sees mathematics as value-laden, imbued with moral and social values which play a significant role in the development and applications of mathematics .
What has been proposed is thet proper concern of the philosophy of mathematics should include external questions as to the historical orgins and social context of mathematics, in addition to the internal questions concerning knowledge, existence, and their justification.
For some years there has been a parallel debate over an internalist-externalist dichotomy in the philosophy of science (Losee, 1987). As in the philosophy of mathematics there has been a split between philosophers promoting an internalist view in the philosophy of science (such as the logical empiricists and Popper) and those espousing an externalist view.
The latter include many of the most influential recent philosophers of science, such as Feyerabend, Hanson, Kuhn, Lakatos, Laudan and Toulmin. Contributions of these authors to the philosophy of science is a powerful testimony to the necessity of considering ‘extemal’ questions in the the philosophy of science. However in the philosophy of science, even philosophers espousing an internalist position, such as Popper, admit the importance of considering the development of scientific knowledge for epistemology.
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