This paper is concerned with two pervasive and apparently reliable theories, namely, those general accounts of the status of science and art which seem to form part of the "bedrock" of contemporary thinking. The first section discusses what are taken to be the most commonly accepted and highly legitimized general accounts of both science and art, asserting that the common understanding of science is an "ideology of scientism" and that the common understanding of art is an "ideology of the aesthetic." The second section examines some serious problems with the accounts of science and art described in the first section, suggesting that they be rejected (while being cautious and tentative about any new notions which might replace them at the present time). The last section (conclusion) points out that the ideology of scientism gives a false status to the nature of science and turns it into a religion while the ideology of the aesthetic trivializes art by making it little more than the instrument of culture's growing narcissism. Issues related to how a technological society can produce these misunderstandings of the nature of knowledge in science and art are also addressed. (JN)