Abstract
What is a “mathematical proposition”, a “mathematical proof”, a “mathematical theory”, a “mathematical discipline”? A general theory of propositional systems as it underlies all mathematical disciplines is the subject of the following considerations outlined briefly here. A mathematical “proposition” makes sense and has a meaning only within a mathematical system, a theory or a (comprehensive) discipline as, e.g., “Euclidean geometry” or the “arithmetic of real numbers”. But what are the characteristic features, what are the general basic laws of logic common to all “mathematical systems”?
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© 2010 Springer-Verlag Berlin Heidelberg
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(2010). Zermelo 1932b. In: Ebbinghaus, HD., Fraser, C., Kanamori, A. (eds) Ernst Zermelo - Collected Works/Gesammelte Werke. Schriften der Mathematisch-naturwissenschaftlichen Klasse der Heidelberger Akademie der Wissenschaften, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79384-7_30
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DOI: https://doi.org/10.1007/978-3-540-79384-7_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79383-0
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