从普遍哲学的理想到形式化的起源：雅克·克莱恩与胡塞尔的分野及其超越

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Abstract Husserl’s discussion of the origin of geometry is ɑn example of his pursuit of the ideal of universal philosophy. According to Husserl, Galileo’s ideal of the mathematization of nature is merely ɑ finite explanation of the origin of geometry, and the geometry before Galileo is only a finite and closed apriori principles. Thus, Husserl explores the origin of geometry, in fact viewing it as ɑn “overall acquisition of spiritual achievement” and pursuing the full-time effectiveness and general normativity of science. However, due to Husserl’s evidence could not escape the intentionality of individual objects, he has to place the origin of geometry in the life-world, which has drawn much criticism. Jacques Klein startes from the objectivity of concepts, through the connection and distinction between intention prima and intention secunda, explores the symbolic process of Descartes’ unification of algebra and geometry, and rediscoveres the origin of geometry, especially the process of the formalization of mathematical symbols. In this sense, Jacques Klein surpasses Husserl. However, Klein’s exploration raises a new question: Has he completed the formalization? In fact, to seek the origin of formalization, we still need to return to Husserl, especially Husserl’s distinction between Ausdruck and Anzeinchen. In Husserl’s view, the emergence of Anzeinchen represents the formation of purely linguistic generalization, and the essential possibility of this purely linguistic generalization is borne by pure concepts. It is precisely in this sense that Jacques Klein reconstructes formalization through the process of purifying of mathematical symbols which surpasses his tutor Husserl.

Key words： The Origin of Geometry universal philosophy intention prima intention secunda Anzeinchen formalization

Received: 25 March 2026

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HUANG Lei. From the Ideal of Universal Philosophy to the Origin of Formalization:The Divergence Between Jacques Klein and Husserl and Jacques Klein’s Surpassment[J]. , 2026, 43(3): 153-160.

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https://xb.szu.edu.cn/EN/ OR https://xb.szu.edu.cn/EN/Y2026/V43/I3/153

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