As its title indicates, our work deals with two motifs which, in the end, flow together. The first has to do with the confrontation (long a subject of philosophical discussion) between the Lebenswelt and its mathematization at the hands of the sciences. Mathematics, according to Husserl, is a science whose contents – axioms, laws, geometric solids – are ideas. Idealization, as practiced by Husserl, consists in adopting and adapting Kant’s interpretation of ‘the idea’, and in designating both mathematical exactitude and the thing in its totality as ‘ideas in the Kantian sense’. The second motif examines Husserl’s attempt to identify the Lebenswelt with Plato’s ‘mere opinion’ (doxa as opposed to episteme). Husserl mounts a defense of doxa, granting it a value as high as, or even higher than, that of episteme. We want to show what this higher value of doxa consists in. Thus, we enter into the problem of measurement, a phenomenon which, beginning as an estimative, pre-geometrical operation, leads to exactitude. In this context, we propose the following thesis: measurement, thanks to the idealization of ‘the thing’ which makes it possible, is the foundation of mathematical exactitude. However, things themselves are given only in gradations, fragments, sides – in other words, they are given perspectivally. Hence, propositions about them can at first only be subjective, private opinions (in the sense of doxa).
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