Standards of Classical Architecture Criticism: Between Mathematics and Philosophy

On Brouwer’s Criticism of Classical Logic and Mathematics

The aim of this paper is to reconstruct Brouwer’s justification for the intuitionistic revision of logic and mathematics. It is attempted to show that pivotal premisses of his argument are supplied by his philosophy. To this end, the basic tenets of his philosophical doctrine are discussed: the concepts of mind, causal attention, intuition of two-ity and his repudiation of realism. The restrict...

Philosophy of Mathematics, Mathematics Education, and Philosophy of Mathematics Education

19th Century Logic between Philosophy and Mathematics

Doubt could be expressed that a special section on late 19th century mathematics, or, more specifically, on Victorian mathematics, was an appropriate place for a lecture on 19th century logic. Most 19th century scholars would have been of the opinion that philosophers are responsible for research on logic. On the other hand, the history of late 19th century logic indicates clearly a very dynami...

Philosophy of Mathematics and Philosophy of History

mathematical and one philosophical. In the first, Socrates leads the slave boy to correct, refine, and extend his intuition of a pair of geometrical diagrams by examining his presuppositions in the light of certain background knowledge (about arithmetic), as they solve a problem together. In the second, Socrates leads Meno to correct, refine, and extend his intuition about virtue as well as abo...

Architecture, City and Mathematics: The Lost Connection

The connection between architecture and science and sound based on mathematical relations has continued to develop[ since the rise of the Western classical civilization that originated in Ancient Greece. The mysterious Pythagorean cosmology pursued as secret esoteric knowledge was related to the search of rhythm, proportionality and harmony. Even somewhat earlier, Greek mysteries were based on ...