[Addendum] Vladimir Tasic: _The Mathematical Roots of Postmodern Thought_, translated by Cai Zhong and Dai Jianping, Fudan University Press, October 2005
Page 5: I think we can subdivide the theoretical edifice of postmodernism. First, one may regard postmodernism as influenced by Romanticism, as a revival—or, to use slightly different terminology, a reinvention—of the ideas of those mathematicians who once challenged logical inductivism; second, one may regard postmodernism as an extreme departure from Romantic humanism, a departure whose roots can in part be traced back to mathematics, and whose postmodern version has become a rather extreme form of formalism.
////——Tasic’s perspective is highly distinctive. Indeed, whenever philosophy discovers that something has gone wrong with science, it is usually philosophy, rather than science, that is forced to change. The early twentieth-century debates over the foundations of mathematics in fact had little effect on mathematics itself (the trends toward formalization and axiomatization were already there to begin with, and were not brought about by philosophy), whereas the impact of those debates on philosophy was enormous. The influence of logicism on Anglo-American philosophy is obvious; the whole of Anglo-American analytic philosophy takes logicism as its source and thread. Yet what Tasic prompts us to notice is this: not only Anglo-American philosophy, but also Continental philosophy, with its inclinations toward irrationalism, Romanticism, and so on, was profoundly influenced by the debates in mathematics.
Just as the three major schools in the foundations of mathematics had, at the outset, their “distribution zones” — logicism mainly in the Anglo-American world, intuitionism mainly among the French, and formalism mainly among the Germans — logicism shaped the entire course of Anglo-American philosophy, while intuitionism and formalism silently influenced the development of Continental philosophy, and continued to make themselves felt even in postmodernism.
Postmodernism is a complicated thing. It is also a powerful intellectual current whose influence extends across the various disciplines: first in art and literature, and then widely in narratology, history, sociology, political science, philosophy, as well as in science, religion, and so on. Its influence has been so broad because postmodernism is not only a set of distinctive views and claims about certain problems; it also puts forward new ideas about the attitude toward problems and the methods of dealing with them themselves.
Tasic reveals the common ground shared by postmodern thought, intuitionism, and formalism, and analyzes the possible channels through which these ideas may have spread. Whether intuitionist and formalist mathematical thought has a direct lineage from irrationalism and Romanticism, or from postmodernism, is not important. What matters is that we do indeed see many commonalities and connections among them. Whether these connections arise from direct inheritance, indirect inspiration, or the convergence of independent but separate paths, they are in any case worthy of close attention; a renewed appreciation of intuitionism is beneficial.
August 25, 2006
Translated from the Chinese original with AI assistance. The original text is authoritative.
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