Mancosu - Philosophy of Mathematical Practice (Oxford, 2008).pdf

132 kenneth mandersarticulating the properties of the resulting linear configuration is as an actionnot usefully separable into parts addressing justificational and non-justificationalconcerns. It furthers overall intellectual control, and only as such is it properlyunderstood. If we restrict our perspective on what virtues probing serves, weget into blind alleys in which the role of probing in the practice becomesunintelligible.Acknowledgments. I would like to thank Fabrizio Cariani for converting mytext into LaTex and producing the diagrams.BibliographyApollonius of Perga, On cutting off a ratio [De sectione rationis.] E. M. Macierowski(trans.), Robert H. Schmidt (ed.) (Fairfield, Conn.: Golden Hind Press).Arnold, Vladimir(1992), Catastrophe Theory, 3rd rev. and expanded edn (Berlin, NewYork: Springer).Ayer, Alfred,J.(1936), Language Truth and Logic (London: Dover).Dubnov, Y.(1963), Mistakes in Geometric Proofs A. Henn and O. Titelbaum, (trans.)(Boston: Heath).Euclid, Elements, publishedasEuclid’s Elements: all Thirteen Books Complete in OneVolume T. Heath (trans.), D. Densmore (ed.) (New York: Dover Books, 1959).Fowler, David (1987), The Mathematics of Plato’s Academy (Oxford: Oxford UniversityPress).Hahn, Hans(1980), ‘The Crisis in Intuition’, in Empiricism, Logic and Mathematics:Philosophical Papers (Dordrecht: Reidel), 73–102.Hilbert, David (1899/1902), Foundations of Geometry (La Salle: Open Court).Hjelmslev, Johannes (1923) Die natürliche Geometrie. Mathematischen Seminars derHamburgischen Universität.Klein, Felix (1939), Elementary Mathematics From an Advanced Standpoint E. R. Hedrickand C. A. Noble (trans. of 3rd German edn) (New York: Dover).Knorr, Wilbur(1975), The Evolution of the Euclidean Elements: a Study of the Theory ofIncommensurable Magnitudes and its Significance for Early Greek Geometry (Dordrecht,Boston: Reidel).(1980), ‘On the Early History of Axiomatics: The Interaction of Mathematics andphilosophy in Greek antiquity’, Proceedings of the 1978 Pisa Conference (Dordrecht,Boston: Reidel).(1986), The Ancient Tradition of Geometric Problems (Boston: Birkhäuser).(1989) Textual Studies in Ancient and Medieval Geometry (Boston: Birkhäuser).Loemker, Leroy(1970), Leibniz: Philosophical Papers and Letters. A selection. 2nd edn(Dordrecht: Reidel).Maxwell,E.(1961), Fallacies in Mathematics (Cambridge: Cambridge University Press).