Just Curious

Recent readings

I have been reading avidly these days, not having much else to do (except working out and lifting weights with my buddy Albert P. Kim, who had received some previous training in the ranger school of the US Army.)

I read another book by Prof. Chun-I T'ang (in Chinese), mainly on the realities in a humanistic world. It is interesting since towards the end of the book Prof. Tang wrote a long poem. It took the form of a series of cantos of songs sung by great sages and philosophers, from time immemorial to the modern ages. Among the singers we have Nietzsche, Marx, Schoepenhauer, Spinoza, Kant, Schiller and Plato. The ultimate bedrocks of Christian, Indian and Chinese worldviews, namely, the Buddha, Confucius and Jesus were represented by Bodhisattva Nagarjuna, Tzu Ssu and St. Augustine respectively. It is a very interesting experience reading these.

Another philosophical essay I read was by the Rev. Fr. Bernhard Bolzano (1781-1848), a Czech educator, theologian, analytic philosopher and most importantly mathematician. As a mathematician he proved the Bolzano theorem, made important discoveries that eventually led to the Bolzano-Weierstrass theorem in real analysis, and constructed the famous Bolzano function (a function that is continuous but nowhere differentiable.) A Catholic priest and professor of the philosophy of religion at Charles University of Prague, Fr. Bolzano was a vocal supporter of liberal education and political reform. For these, he was dismissed from his university post, and was subjected to a 4-year long ecclesiastical trial which fortunately ended in his acquittal.

The essay itself was called "On the Mathematical Method," and was (I suspect)among the first papers published on metamathematics and the philosophy of language. In the first half of the book Bolzano wrote very clearly on his notions of "ideas," "intuitions," "concepts," "propositions," "explications," "objects" etc. and the relationships that could hold between them, such as "contradictory to," "contrary to," "compatible" and "incompatible." In the second half he addressed issues of what constitutes an axiom, an "explication," a definition and how a mathematician should present forth his propositions and ideas (how he should arrage the order of theorems to be presented, etc.) His notions of the axiomatics are by far more sophisticated than earlier logicians from Euclid to Kant. His essay is the kind of writing that is so precise, terse and rigorous that it almost hurts the eye to read! It was only 40 page long but it took me two days to finish reading it.

posted by James Chang @ 1:29 PM