Gabriele Baratelli

The goal of this paper is to provide an account of the role played by logic in the context of what Husserl names the “crisis of European sciences.” Presupposing the analyses offered in the Krisis, I look at Formale und Transzendentale Logik to demonstrate that the crisis of logic stems from the deviation of its original meaning as a “theory of science” and from its restriction to a mere “theoretical technique.” Through a comparison between Aristotelian syllogistic and modern logic, I show why the modern discovery of the purely formal dimension of knowledge which makes possible such a mathematical technization is a positive achievement that hinders at the same time the disclosure of the truly philosophical nature of logic. The correct appraisal of this ambiguous phenomenon will explain why the rise of modern logic represents a decisive challenge for the success of Husserl’s late phenomenological project.

The paper is divided into two parts. In the first one, I set forth a hypothesis to explain the failure of Husserl’s project presented in the Philosophie der Arithmetik based on the principle that the entire mathematical science is grounded in the concept of cardinal number. It is argued that Husserl’s analysis of the nature of the symbols used in the decadal system forces the rejection of this principle. In the second part, I take into account Husserl’s explanation of why, albeit independent of natural numbers, the system is nonetheless correct. It is shown that its justification involves, on the one hand, a new conception of symbols and symbolic thinking, and on the other, the recognition of the question of “the formal” and formalization as pivotal to understand “the mathematical” overall.

Although the notion of the crisis of European sciences has a general meaning, Husserl mainly focuses on this phenomenon in relation to the modern establishment of a mathematical natural science. However, he does not provide a definitive clarification of how its new method is specifically involved in bringing about such a crisis. Without trying to offer a faithful exegetical contribution, this paper further elaborates on Husserl’s analyses in the Krisis to give a possible answer to this question. After defining the concept of crisis in general, I single out why algebraic thinking is the core of the method that essentially characterizes mathematical physics. Then, I compare this method to a case of pre-modern discipline (namely, Euclidean geometry) to show that the sedimentation of meaning at work in the progressive technization of algebra is exceptional and sufficient to explain the specificity of the modern character of the crisis of the exact sciences. The exclusively technical development of formal mathematics, in fact, elicits those shifts of meaning (such as objectivism) that phenomenology is required to amend to overcome the crisis and to establish an authentic form of knowledge. On the basis of these results, I conclude by suggesting a few consequences that are useful for the understanding of the project of phenomenology of the later Husserl.