Bolzano, Bernard (1781–1848)

Bernard Bolzano was a lone forerunner both of analytical philosophy and phenomenology. Born in Prague in the year when Kant’s first Critique appeared, he became one of the most acute critics both of Kant and of German Idealism. He died in Prague in the same year in which Frege was born; Frege is philosophically closer to him than any other thinker of the nineteenth or twentieth century. Bolzano was the only outstanding proponent of utilitarianism among German-speaking philosophers, and was a creative mathematician whose name is duly remembered in the annals of this discipline. His Wissenschaftslehre (Theory of Science) of 1837 makes him the greatest logician in the period between Leibniz and Frege. The book was sadly neglected by Bolzano’s contemporaries, but rediscovered by Brentano’s pupils: Its ontology of propositions and ideas provided Husserl with much of his ammunition in his fight against psychologism and in support of phenomenology, and through Twardowski it also had an impact on the development of logical semantics in the Lwów-Warsaw School.

Have You Read …?

If you wonder why more progress has not been made in mathematics education, you should read t this article. The author is concerned with questions that he feels should he met, such as: How is mathematics related to science and reality? Why should mathematics be taught? How does a creative mathematician generate mathematical ideas? The article proceeds to discuss some of the positions taken by various people and groups who have worked on the im provement of mathematics education. The following questions were considered: Do leaders in one group tend to take over groups other than their own and thus confuse the issues? Is experimentation being defined in too many ways to make it realistic? Are too many rnathematical concepts left to intuition? Is there somewhere intuition plays little if any part? Is it necessary to re-create mathematics in order to understand it? If mathematics is tied too closely to the real world, are we endangering the attitude of inquiry for its own sake? Have we too long ignored the real goals of mathematics and have we failed to provide an interaction between content and method? I think you and your students will be interested in reading this reaction from Professor Brown.

The Young Paseal

Versatility is not inevitably the companion of genius. It is not altogether common to find a man who is at the same time a clever experimental physicist, a creative mathematician, an inventor with an eye to money-making, a gifted writer whose artistry places him among the foremost French stylists, and a religious philosopher of singular originality and ardor. Blaise Pascal was such a man. He could write an important treatise on the vacuum as well as produce those incomparable examples of controversial literature, the famous Provincial Letters. lie invented the first adding machine of practical consequence and tried (in vain) to realize a profit from its sale. In the fragment. of his projected a pology for the Christian Religion, left unfinished by his death at the early age of thirty-nine, are to be found many evidences of his mathematical genius as well as of a remarkable piety and zeal. A clear and complete picture of his early life and education would not only be of rare in terest, but it could not fail to contain many suggestions of value to the modem teacher. It is indeed a pity that such incomplete information is available. The story is soon told, but it is well worth the telling, and perhaps it holds some inspiration or lesson for our own times.