Although modern scientific and technological advances derive computational power primarily from the classical evidence-based bottom-up cognition as founded by Greek philosopher Aristotle in his philosophy of science with a bivalent logic, the classical cognition, however, has met stiff challenges during the last few decades because of uncertainty faced by many new scientific endeavors. The holistic top-down nature of nanotechnology and brain modeling are just two of many examples. This new development points to the need for a critical review of the historical origins and distinctions of both top-down and bottom-up cognitions. This paper reviews the philosophy of science as founded by Aristotle (300BC), the Platonic realism as founded by Aristotle's teacher Plato (400BC-300BC), and the YinYang philosophy as founded by the ancient Chinese philosopher Laozi (or Laotze) (600BC). It is suggested that the long-standing unsettled dispute between Aristotle and Plato features a major source of uncertainty for both logic and mathematics. The authors hence propose a number of controversial philosophical and logical issues for debate. We advocate YinYang as an inspiration and unifying force for both top-down inductive and bottom-up deductive reasoning. We attempt to use an equilibrium-based YinYang bipolar dynamic logic (BDL) to bridge the gap between Aristotle and Plato as well as between logic and mathematics. Furthermore, we present a taxonomy for YinYang scientific computing with a classification of logical and statistical models for further discussion; we suggest that YinYang can be used as a catalyst for resolving certain "terminological difficulties" regarding truth, polarity, intuitionism, para-consistency, and fuzziness for equilibrium and harmony. A number of critical points are enumerated and discussed. An open challenge is posted.
Available at: http://works.bepress.com/wen-ran_zhang/40/