Abstract
In this article, we focus on the movement of constitution of the mathematical object from a phenomenological perspective. In order to tackle this task, we proceeded hermeneutically studying the First Logical Investigation of Edmund Husserl, titled Expression and Meaning, from “Investigações Lógicas: segundo volume, parte I: Investigações para a Fenomenologia e a Teoria do Conhecimento, segunda edição, 1913” (We indicate this book in Portuguese because we had our investigation studying this version). In that text, Husserl is not dealing specifically with the mathematical object, but with the object in general. Given this scope, we interrogated the text, seeking to understand nuances of the object, which, in the realm of this investigation, we thematize as the mathematical object. We made considerations in pure logic and expressed the intimate relationship among (mathematical) object, as presented, and sense, meaning, demonstrating, speaking, expressing, as well as the acts of getting signification, evidence, and to understand the essence in order to elucidate how the movement of constitution of the mathematical object is actualized. We point out that the mathematical object is understood as an idea from the perspective of apprehended evidence.
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Notes
- 1.
Psychologism is understood as the process of psychologically analyzing what is not in the field of psychology; a reduction of the object in question to psychology (Peres, 2017).
- 2.
We indicate 1901, because given the structure of the second edition of Logical Investigations, Volume 2, it is possible to access, in volume 2, the text of Logical Investigations, Volume 1, first edition. For further information, see the Portuguese translation of Logical Investigations, volume 2, Part I, Investigations for Phenomenology and Theory of Knowledge, Second Edition, 1913.
- 3.
Cited in the Introduction of the German editor Walter Biemel of “The Idea of Phenomenology”, while mentioning Edmund Husserl’s manuscripts of September, 1907, BII 1 (Husserl, 2008a).
- 4.
The Sixth Logical Investigation was published in 1921, separately from part I of the second volume.
- 5.
In order to preserve academic rigor, direct quotations were taken from the work published in English.
- 6.
In agreement with Onate, with understand physical state as “[...] is a concrete sign phenomenon” (2016, p. 91, author’s translation).
- 7.
Derrida talks about the possibility of surpassing the absence of a voice: “Mutism and deafness go together. A deaf individual can only participate in a colloquy by shaping their deeds in the form of words whose telos allows them to be heard by the speaker” (1994, p. 89, author’s translation).
- 8.
Still, the complexity of communicating to other individuals what is learned can be overcome if the interlocutors are focused on what is expressed in a pure way. “Pure,” in the sense Ales Bello (2004) points to, means that there are no external affects in the phenomenological analysis; which is performed in the phenomenological field without interference from other philosophical thoughts.
- 9.
Within the text, to refer to “apprehended evidence,” we wrote “intellectually grasped.”
- 10.
For Husserl the need to go back to “corresponding intuition,” for the clarification of the meaning represented symbolically, it occurs in cases in which the meaning of the content of a concept are fluid. In this case, the jurisdiction of illustrative intuition aims at identifying the topological limits of the differences shown with which the expressions express, and guarantee an effective judgment of the corresponding meaning.
- 11.
“The use of quotation marks in the expressions in-themselves and truths themselves is intended to mark the Husserlian detachment from meaning they enjoy in Kantian philosophy, but also, and above all, to indicate that they must be understood in a strictly phenomenological semantic context, to be gradually clarified in the sequence of Logical Investigations and other works published, as well as the other private texts currently available” (Onate, 2016, p. 101, author’s emphasis, author’s translation).
- 12.
“tend towards” is used here, in the sense of fostering, projecting, furthering; as we understand that, according to Husserl, intellectual thought cannot directly bring meaning.
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Venturin, J.A., de Souza Coelho, F. (2020). The Constitution of the Mathematical Object in Acts of Evidence, from the Perspective of Edmund Husserl’s First Logical Investigation. In: Viggiani Bicudo, M. (eds) Constitution and Production of Mathematics in the Cyberspace. Springer, Cham. https://doi.org/10.1007/978-3-030-42242-4_14
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