Das Kalenderblatt 091220
WM
the Free State in Bloemfontein, South Africa.
In Chapter II Strauss addresses various philosophical problems in
mathematics.
Mathematics is concerned with number and space, the first two
modalities. The prime issue in mathematics is how to treat infinity.
Strauss discusses three main foundational crises in the history of
mathematics: (1) the discovery of irrationals, (2) infinitesimal
calculus, and (3) modern set theory. All three involve the relation
between potential and actual infinity. Much attention is devoted to
the conflict between Cantor's treatment of actually infinite sets and
the intuitionists' rejection of actual infinity.
The Dutch mathematician L.E.J. Brouwer (1882-1966), an ardent promoter
of intuitionism, lived in Amsterdam at the same time as Dooyeweerd and
had some influence on Dooyeweerd. Dooyeweerd acknowledged only the
potential infinite; he found the idea of the actual infinite
unacceptable. {{Es gibt offenbar sehr viele Leute, die so denken. Nur
leider sorgt die moderne Zensur dafür, dass diese Leute selten zu Wort
kommen.}} Strauss, however, argues that Dooyeweerdian philosophy
actually provides grounds for both types of infinity. Strauss
distinguishes between the successive infinite and the at once
infinite. The successive infinite is associated with numbers and
determines every denumerable, endless succession of numbers (e.g., the
integers or rational numbers). The at once infinite, on the other
hand, is associated with the continuous extension of space. The latter
represents a higher order of infinity; it cannot be reduced to a
successive infinity since space cannot be reduced to number {{weshalb
überabzählbare Zahlenmengen absurd sind.}}
Review: D.F.M. Strauss, Paradigms in Mathematics, Physics and Biology:
Their Philosophical Roots, Tekskor Bk, Danhof, South Africa, (2001,
revised 2004), 177pp.
http://www.acmsonline.org/strauss%20review.pdf
Gruß, WM
Vogel
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Sinnleerer Bullshit!
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Selber denken macht klug.