Abstract
The paper’s central theme is the link between phenomenology and the notion of the mathesis universalis, a link articulated by Husserl in the third volume of the Ideas: “My way to phenomenology was essentially determined by the mathesis universalis (Bolzano did not see anything of this).” The paper suggests three interpretations of the phenomenology—mathesis universalis nexus: the first is related to the development of Husserl’s conception of the foundations of arithmetic; the second is based on the role of the theory of manifolds in Husserl’s Logical Investigations; and the third reflects the importance of the distinction between “generalization” and “formalization” for phenomenology. After examining these interpretations, the paper explores which is most helpful for understanding why Husserl distanced himself from Bolzano, arguing that the third interpretation provides the most edifying answer.
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Notes
Husserl describes this problem in his famous letter to Carl Stumpf from February 1890 (Hua XXI, pp. 244–251).
The beginning of the change can be discerned in a text from 1891 that discusses the notion of an operation (Hua XII, pp. 408–429; 2003, pp. 385–408). That this text marks a change in Husserl’s position is indicated by the fact that the distinction between authentic and symbolic numbers does not appear in it. On the importance of this text in attesting to the change in Husserl’s stance, see Gérard (2002, pp. 73–74).
Husserl presented this new characterization in lectures delivered in Gottingen in 1901/1902.
For an analysis of the different versions of Husserl’s notion of definiteness, see Centrone (2010, pp. 167–177).
On the view that the primary intent of the Logical Investigations is to present a theory of science, a project in which phenomenology plays only a secondary role, see Fisette (2003).
In “The task and significance of the Logical investigations,” Husserl states: “Now it was something historically novel that an epistemological investigation into the logico-mathematical, undertaken entirely independently of traditional empirical psychology, should press forward towards a methodical reform of psychology and should formulate anew the problem of the relation between epistemology and psychology” (Hua IX, p. 41; Husserl 1977, p. 213). This can be interpreted, as I suggest, as attesting to the existence of a close link between Husserl’s treatment of the logical and mathematical notions in terms of the theory of manifolds, and his approach to the phenomenological notions. It is, however, important to stress that in the Logical Investigations, Husserl calls for a division of labor between mathematics and philosophy. Philosophy’s role is to supply an epistemological grounding for the mathematical concepts (Hua XVIII, pp. 253–256; 2001, pp. 158–160).
Earlier discussion of the distinction appears in Husserl’s 1906–1907 lectures on logic and the theory of logic (Hua XXIV, pp. 108–109; 2008, pp. 105–106). The roots of this distinction can be traced back to Husserl’s distinction between sensuous abstraction and purely categorial abstraction in the 6th Investigation (Hua XIX, pp. 712–713; 2001, p. 307). What is special about the way the distinction is invoked in the Ideas is the salience of its role in the overall architectonics of Husserl’s approach.
On the relation between formal ontology and phenomenology in the Ideas, see Smith (2003).
In the Ideas, Husserl distinguishes clearly between mathematics, on the one hand, and phenomenology as the descriptive science of eidetic mental processes, on the other (see Hua III, pp. 148–156; 1998, pp. 160–167).
Husserl makes similar remarks in his 1913 introduction to the Logical Investigations (Hua XX/1, p. 308; Husserl 1975, p. 48).
Paola Cantu claims that the change in question is less important than it seems, see Cantu (2011).
Bolzano famously characterizes a proposition’s truth by form (with respect to some of the ideas contained in it) in terms of its maintaining the same truth-value under substitution of any other ideas for these ideas (Bolzano 1837, Sect. 147). This notion has interesting affinities with later positions, such as Tarski’s conception of consequence, and also Husserl’s own conception of extracting essences by means of permutation. Nevertheless, as has been argued in the literature, this notion of truth by form, unlike Husserl’s notion of formality, which is based on the formal notion of an object, does not provide a clear demarcation between the formal and the non-formal. On the question of whether Bolzano’s notion of the formal provides a solution to the demarcation problem, see Simons (1992). Simons answers in the negative.
This does not mean that Bolzano accepted only actual objects in his ontology. For a discussion of Bolzano’s views on non-actual objects, see Schnieder (2007).
On the relation between Kant’s transcendental logic and Bolzano’s logic, see Tolley (2012). Tolley argues that they are closely linked. I concur that there are important affinities between them, but think that the question of whether the relation to an object in general is part of logic marks an important distinction between the two conceptions of logic.
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Roubach, M. Mathesis Universalis and Husserl’s Phenomenology. Axiomathes 32, 627–637 (2022). https://doi.org/10.1007/s10516-021-09544-9
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DOI: https://doi.org/10.1007/s10516-021-09544-9