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Full-Text Articles in Mathematics
Rethinking Geometrical Exactness, Marco Panza
Rethinking Geometrical Exactness, Marco Panza
MPP Published Research
A crucial concern of early modern geometry was fixing appropriate norms for deciding whether some objects, procedures, or arguments should or should not be allowed into it. According to Bos, this is the exactness concern. I argue that Descartes’s way of responding to this concern was to suggest an appropriate conservative extension of Euclid’s plane geometry (EPG). In Section 2, I outline the exactness concern as, I think, it appeared to Descartes. In Section 3, I account for Descartes’s views on exactness and for his attitude towards the most common sorts of constructions in classical geometry. I also explain in …
Breathing Fresh Air Into The Philosophy Of Mathematics, Marco Panza
Breathing Fresh Air Into The Philosophy Of Mathematics, Marco Panza
MPP Published Research
A review of Paolo Mancosu (ed.): The Philosophy of Mathematical Practice.
Agnostic Science. Towards A Philosophy Of Data Analysis, Domenico Napoletani, Marco Panza, Daniele C. Struppa
Agnostic Science. Towards A Philosophy Of Data Analysis, Domenico Napoletani, Marco Panza, Daniele C. Struppa
MPP Published Research
In this paper we will offer a few examples to illustrate the orientation of contemporary research in data analysis and we will investigate the corresponding role of mathematics. We argue that the modus operandi of data analysis is implicitly based on the belief that if we have collected enough and sufficiently diverse data, we will be able to answer most relevant questions concerning the phenomenon itself. This is a methodological paradigm strongly related, but not limited to, biology, and we label it the microarray paradigm. In this new framework, mathematics provides powerful techniques and general ideas which generate new …
Is The Notion Of Mathematical Object An Historical Notion?, Marco Panza
Is The Notion Of Mathematical Object An Historical Notion?, Marco Panza
MPP Published Research
"Both historians and philosophers of mathematics frequently speak of mathematical objects. Are they speaking of the same or of similar things? Better: are they appealing to the same notion or to similar notions?"