Formation of the idea of mathematical phenomenology in Edmund Husserl’s philosophy

Philosophy

Authors

  • Yuri G. Sedov The State Institute of Economics, Finances, Law and Technologies, 5, Roshchinskaya st., Gatchina, 188300, Russia

DOI:

https://doi.org/10.17072/2078-7898/2021-4-541-549

Keywords:

phenomenology, mathematics, formal logic, E. Husserl, egological research, transcendental logic, transformation of logic, genetic constitution

Abstract

The article presents the historical prerequisites for the creation of mathematical phenomenology. Within the framework of the infinite numbers problems, the ways of their phenomenological interpretation are discussed. Using the example of cooperation between Cantor and Husserl, the idea of mathematical phenomenology is formulated, which takes into account the correlation of mathematical objects with our consciousness. In formal logic, subjective factors often affect the judgment process. The phenomenological method is valuable in that it makes it possible to conduct both objectively and subjectively oriented research in mathematics and formal logic. In such a correlative study, subjective acts and objective referents of any phenomenon should be taken into account. The main goal of correlative research is to create conditions for overcoming relativistic tendencies in mathematics and formal logic. As a result of the analysis, the question of the relationship between descriptive phenomenology and formalized constructions is raised. In the historical and philosophical context, the answer to this question is based on the theoretical developments provided in Husserl’s Formal and Transcendental Logic. Subjective-oriented logic goes back to the latent structures of theoretical reason. Here the problems of consciousness are formulated and solved in its live, actual execution with the help of egological research. In conclusion, historical examples of the subjective transformation of formal logic are provided. In the first example, an interpretation of Descartes’ conclusion cogito, ergo sumis given, showing that the existential inconsistency of «I do not exist» and the reliability of the initial position «I exist» were realized here. Another example of the transformation of logic is Husserl’s phenomenology. In order to bring logical forms to their subjective obviousness, it is necessary to change the orientation of consciousness and to consider objects as givens of consciousness.

Author Biography

Yuri G. Sedov, The State Institute of Economics, Finances, Law and Technologies, 5, Roshchinskaya st., Gatchina, 188300, Russia

Candidate of Philosophy,Associate Professor of the Departmentof Social and Economical Management

References

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References

Cajori, F. (2007). A history of mathematical notations. Vol. II. New York: Cosimo Publ., 396 p.

Cantor, G. (1885) [About the different points of view with regard to the actual infinite (From a letter from the author to Mr. G. Eneström in Stockholm on Nov. 4, 1885)]. Zeitschrift für Philosophie und philosophische Kritik [Journal of Philosophy and Philosophical Criticism]. Vol. 88, pp. 224–233.

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Hartimo, M. (ed.) (2010). Phenomenology and mathematics. Phenomenologica. Dordrecht: Springer Publ., vol. 195, 243 p. DOI: https://doi.org/10.1007/978-90-481-3729-9

Hartimo, M. (2012). Husserl’s pluralistic phenomenology of mathematics. Philosophia Mathemanica. Vol. 20, iss. 1, pp. 86–110. DOI: https://doi.org/10.1093/philmat/nkr032

Hintikka, J. (1962). Cogito, ergo sum: inference or performance? The Philosophical Review. Vol. 72, no. 1, pp. 3–32. DOI: https://doi.org/10.2307/2183678

Husserl, E. (1891). Philosophie der Arithmetik. Psychologische und logische Untersuchungen. Bd. 1 [Philosophy of arithmetic. Psychological and logical investigations. Vol. 1]. Halle-Saale: C.E.M. Pfeffer (Robert Stricker) Publ., 340 p.

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Malet, A. and Panza, M. (2015). Wallis on indivisibles. Seventeenth-century Indivisibles Revisited. Science Networks. Historical Studies. Vol. 49. Basel: Birkhäuser Publ., pp. 307–346. DOI: https://doi.org/10.1007/978-3-319-00131-9_14

Montagova, K. (2013). [Transcendental genesis of consciousness and knowledge]. Phenomenologica. Dordrecht: Springer Publ., vol. 210, 264 p.

Sedov, Yu.G. (2016). Remarks concerning the phenomenological foundations of mathematics. Logicheskie issledovaniya [Logical Investigations]. Vol. 22, no. 1, pp. 136–144. DOI: https://doi.org/10.21146/2074-1472-2016-22-1-136-144

Zermelo, E. (1904). [Proof that any amount can be well arranged (from a letter addressed to Mr. Hilbert)]. Mathematischen Annalen [Mathematical annals]. Leipzig: Teubner Publ., vol. 59, pp. 514–516. DOI: https://doi.org/10.1007/bf01445300

Published

2021-12-29

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