Abstract
The word ‘form’ has often been used in mathematics, and still is, in various different contexts. Two relatively technical senses (as opposed to very general or passing uses) are of relevance here, and will be noted later: the content-free form of an algebra, as contrasted with its contentual ‘matter’ in a particular case; and form as a central feature of a structuralist philosophy of mathematics.
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References
Bollinger, M.: 1972, ‘Geschichtliche Entwicklung des Homologiebegriffs’, Archive for History of Exact Sciences 9, 94–166.
Boyer. C.B.: 1956, History of Analytic Geometry. New York, Scripta Mathematica.
Bucur, I. and Deleanu, A.: 1968, Categories and Functors. London, Wiley.
Cavaillès, J.: 1938, Méthode Axiomatique et Formalisme. 3 pts., Paris, Hermann.
Cournot, A.A.: 1847, De l’Origine et des Limites da la Correspondance Entre l’Algèbre et la Géométrie. Paris-Algiers, Hachette.
Crowe, M.J.: 1967, A History of Vector Analysis. Notre Dame-London, Notre Dame University Press.
Grattan-Guinness, I.: 1987, ‘What Was and What Should Be The Calculus?’, in Grattan-Guinness, ed., History in Mathematics Education. Paris, Berlin, 116–35.
Grattan-Guinness, I.: 1992, ‘Structure-Similarity as a Cornerstone of the Philosophy of Mathematics’, in Echeverria, J., Ibarra, A. and Mormann, T., eds., The Space of Mathematics. Philosophical, Epistemological, and Historical Explorations. Berlin-New York, de Gruyter, 91111.
Grattan-Guinness, I.: 1993. ‘Structure-Similarity: Between Mathematics and Philosophy’, in Czermak, J., ed., Proceedings of the 15th International Wittgenstein-Symposium, Vienna. Hölder-Pichler-Tempsky, pt. 1, 317–33.
Grattan-Guinness,I. ed., 1994, Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences,2 vols. London, Routledge.
Grattan-Guinness, I. with the collaboration of Ravetz, J.R.: 1972, Joseph Fourier 1768–1830.
Hawkins, T.W.: 1972, ‘Hypercomplex Numbers, Lie Groups, and the Creation of Group Representation Theory’, Archive for History of Exact Science, 8, 243–87.
Kempe, A.B.: 1886, ‘A Memoir on the Theory of Mathematical Form’, Philosophical Transactions of the Royal Society of London, 177, 1–70.
Hawkins, T.W.: 1975, ‘Cauchy and the Spectral Theory of Matrices’, Historia Mathematica, 2, 1–29.
Kempe, A.B.: 1894, Mathematics, Proceedings of the London Mathematical Society, (1)26, 5–15.
Klein, J.: 1968, Greek Mathematical Thought and the Origins of Algebra. Cambridge, Mass., MIT Press.
Mac Lane, S.: 1986, Mathematics, Form and Function. Berlin, Springer.
Mehrtens, H.: 1979, Die Entstehung der Verbandstheorie. Hildesheim, Gerstenberg.
Moore, E.H.: 1910 Introduction to a Form of General Analysis. New Haven, Yale University Press. Merrill, D.D.: 1990 Augustus De Morgan and the Logic of Relations. Dordrecht, Kluwer.
Panteki, M.: 1992, ‘Relationships Between Algebra, Differential Equations and Logic in England:1800–1860’, C.N.A.A. (London), doctoral dissertation.
Parshall, K.H.: 1985, ‘Joseph H.M. Wedderburn and the Structure Theory of Algebras’, Archive for History of Exact Sciences, 32, 223–349.
Roberts,D.:1973, The Existential Graphs of Charles S. Peirce. The Hague-Paris, Mouton.
Scanlan, M.: 1991, ‘Who Were the American Postulate Theorists?’, The Journal of Symbolic Logic, 56, 981–1002.
Scholz, E., ed.: 1990, Geschichte der Algebra. Eine Auführung. Mannheim, Wissenschaftsverlag. Unguru, S.: 1977, `On the Need to Rewrite the History of Greek Mathematics’, Archive for History of Exact Sciences, 15, 67–114.
van der Waerden, B.L.: 1985, A History of Algebra. Berlin, Springer.
Vercelloni, L.: 1988, Filosofia delle Strutture. Florence, La Nuova Italia.
Wussing, H.: 1984, The Genesis of the Abstract Group Concept. Cambridge Mass., MIT Press.
Zaddach, A.: 1994, Grassmanns Algebra in der Geometrie. Mannheim, Wissenschaftsverlag. Zellweger, S.: 1982, `Sign-Creation and Man-Sign Engineering’, Semiotica, 38, 17–54.
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Grattan-Guinness, I. (1999). Forms in Algebras and Their Interpretations: Some Historical and Philosophical Features. In: Albertazzi, L. (eds) Shapes of Forms. Synthese Library, vol 275. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2990-1_8
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DOI: https://doi.org/10.1007/978-94-017-2990-1_8
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