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Brouwer’s Notion of ‘Egoicity’

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Abstract

According to Brouwer’s ‘theory of the exodus of consciousness’, our experience includes ‘egoicity’, a distinct kind of feeling. In this paper, we (i) describe his phenomenology in order to (ii) explore and elaborate on the notion of egoic sensations. In the world of perception formed from sensations, some of them are, Brouwer claims, not completely separated or ‘estranged’ from the subject, which is to say they have a certain degree of egoicity. We claim this phenomenon can be explained in terms of the primordial state of consciousness from where the ‘exodus’ starts. Having undertaken the analysis and interpretation of Brouwer’s descriptions and examples of egoic sensations, we (iii) provide a formal account of egoicity based on Brouwer’s definition of its relation to estrangement, desire and fear. We show that the four terms can be modeled by a classical and a graded logical hexagon, giving the corresponding axiomatizations.

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Notes

  1. An account which can be traced to an essay he wrote at the age of 17 (Brouwer 1990a).

  2. The exodus of consciousness can be compared to Kant’s (1998) role of the productive imagination (B152), if we understand Brouwer’s ‘categories’ to be the new ways of arranging sensations acquired in every phase: object, causality, things, cooperation. Productive imagination pertains to the synthetic unity of apperception, where manifold is given in a single intuition. It also includes spontaneity, where the synthesis happens “in accordance with the categories” (B152) and is in that case “an effect of the understanding on sensibility and its first application [...] to objects of the intuition that is possible for us” (B152).

    Moreover, concerning the important separation between the subject and the object marking the exodus, Brouwer’s account is similar to Kant’s in as much as the latter regards the synthetic unity of apperception as the condition that the united representations can be said to belong to one and the same subject—“only because I can comprehend their manifold in a consciousness do I call them all together my representations” (B134). The concept of an object is also generated by the synthetic unity, since this unity is “something under which every intuition must stand in order to become an object for me” (B138). We thank an anonymous reviewer for pointing to Kant’s productive imagination.

  3. To our knowledge, Brouwer does not distinguish between ‘intellect’ and ‘mind’. The latter we find in (the translations of) his later works.

  4. van Dalen (1998) offers an interpretation of egoicity in a mathematical context, applying the notion to intuitionistic choice sequences. We do not find, however, any textual support for the assumption that Brouwer used the term ‘egoic’ in describing mathematical constructions.

  5. The reader should take into account that the section about immanent truth from Life, Art, and Mysticism contains some highly questionable remarks about women. Brouwer seems to have believed that experiencing immanent and transcendent truth, as well as turning-into-oneself, is an exclusively male privilege and possibility, where woman is a “Siren luring him away from his path” (1905/1996, p. 407). He provides a number of (supposed) examples from art and literature. We strongly disagree with Brouwer on this.

  6. In this paper, we use the term ‘model’ for the structures of opposition in a wider sense, to mean a (diagrammatic) representation of semantic relations. It includes and presupposes an interpretation (and a relational structure) one finds in a ‘model’ meant in the technical, narrow, sense.

  7. See Dufatanye (2012, pp. 54–56) for its English translation and analysis.

  8. The axiom is the same, expressing the implication between the A and the I corner (as we will show shortly in Fig. 2). Since we use a language of propositional logic augmented with four operators (which allows for internal negation), we need only three definitions, while Kalinowski uses four. In such language, two of Kalinowski’s definitions become derivable in our sytem, but we need to add Df1\(^c\), the counterpart of which is not present (or expressible) in Kalinowski’s account.

  9. Possibility theory was introduced by Zadeh (1978). It utilizes his fuzzy logic (Zadeh 1975) based on his fuzzy sets (Zadeh 1965), a logic which uses Łukasiewicz’ continuum-valued interpretation of logical connectives. So, the graded logical hexagon could also be called ‘fuzzy’.

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Acknowledgements

We thank an anonymous reviewer and professor Srećko Kovač for their helpful comments and suggestions.

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  1. Institute of Philosophy, a public research institute of the Republic of Croatia, Ulica grada Vukovara 54 (4th Floor), Zagreb, Croatia

    Ivan Restović

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Restović, I. Brouwer’s Notion of ‘Egoicity’. Axiomathes 32, 83–100 (2022). https://doi.org/10.1007/s10516-020-09509-4

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