Karl Popper＇s Critical Rationalism＂ Corroboration versus Confirmation＊

This paper reviews and adds to previous arguments for the thesis that Karl Popper was mistaken to have rejected hypothetico-deductive confirmation. By turning from the positive idea of verification to the negative idea of criticism, Popper believed that he had turned his back on induction. He believed he had ＂solved＂ the ＂problem of induction＂ by providing a non-inductive account of corroboration. Popper used the term ＂corroboration＂ rather than confirmation which he believed was too closely allied to the notion of the inductive or probabilistic support that a theory can receive from evidence. Wesley Salmon＇s （1967） ＂concept of confirming evidence＂ and Clark Glymour＇s （1980） ＂bootstrap conception of evidence for theory＂ both defended respectively the thesis that passed tests can be confirmed by evidence or warranted by the degree of probability. Using a sequence of symbols in logical form or analysis, I shall further defend the concept to hypothetico-deductive confirmation in order to show that the known weaknesses of Popper＇s critical rationalism are remediable, once the notion of evidence for theories is brought back into consideration.

On the Innovation of Literary Theory in China

China＇s rise has increased concerns about innovation in China＇s indigenous literary theory. How to create theories with a ＂China style＂ and global influence has become a serious challenge for the development of contemporary Chinese literary theory. Three strategies are noteworthy in meeting this challenge. First, ＂amateurism in professionalism＂ can be used to offset the constraints of increasing disciplinization and professionalization in literary theory. Second, critical rationality needs to be cultivated among researchers and in institutional forms in order to alter the present lack of rational and vigorous debate, criticism and dialogue. Third, we need to reconstruct ＂grand narratives,＂ so as to make a unique contribution to the world in terms of universal values, meanings and ethics through transforming and advancing traditional Chinese thought.

Rational maps as Schwarzian primitives

We examine when a meromorphic quadratic differential φ with prescribed poles is the Schwarzian derivative of a rational map. We give a necessary and sufficient condition: In the Laurent series of φ around each pole c, the most singular term should take the form(1- d2)/(2(z- c)2), where d is an integer, and then a certain determinant in the next d coefficients should vanish. This condition can be optimized by neglecting some information on one of the poles(i.e., by only requiring it to be a double pole). The case d = 2 was treated by Eremenko(2012). We show that a geometric interpretation of our condition is that the complex projective structure induced by φ outside the poles has a trivial holonomy group. This statement was suggested to us by Thurston in a private communication. Our work is related to the problem of finding a rational map f with a prescribed set of critical points, since the critical points of f are precisely the poles of its Schwarzian derivative.Finally, we study the pole-dependency of these Schwarzian derivatives. We show that, in the cubic case with simple critical points, an analytic dependency fails precisely when the poles are displaced at the vertices of a regular ideal tetrahedron of the hyperbolic 3-ball.