According to Husserl, what was “obvious” to Galileo was a long tradition of the relation and application of ancient geometry in a Platonistic guise such that the empirical world could be mathematized with a certain intuitiveness — but only to a point. Partial measurements and correspondences were known from antiquity (and revived in the [20] Renaissance). Thus, without further specifying origins, proportions between lengths of strings and sounds (harmonics) and between selected shapes (triangles, etc.not initially rough or complex shapes) and their elaboration in plane geometry could be taken for granted. But a new type of universalization, a new perspective, is taken by Galileo, a perspective which only much later can become so taken-for-granted that it becomes intuitive.
The problem revolves around sensory perception. Shapes, already closely subsumed under ancient geometry, are only a part of the sensory world. In addition, there are what Husserl calls plenary or specific-sense qualities (colors will do for an example). These do not easily fall under the geometric praxis: “The difficulty here lies in the fact that material plena — the specific sense-qualities — which concretely fill out the spatio-temporal shape-aspects of the world of bodies cannot, in their own gradations, be directly treated as are the shapes themselves.”
Some means must be devised, then, to account for these plenary qualities, or else one must realize that the geometrical method is only a special and limited praxis related to one aspect of the world. Galileo’s invention, Husserl claims, is the development of an indirect means of mathematizing the plena. Galileo must find a means to translate plenary phenomena into spatial ones in order for them to become available for geometrical analysis. And that is what he does.
Conceptually, this move, well known in both Galileo and Descartes, first denies to the objects their plenary qualities in the doctrine of primary and secondary qualities. Put baldly, the object-in-itself is purely a geometrical entity, a res extensa; its plenary qualities are located not in the object but in the subject. Colors are “subjective.” But now, since we see a thing as both extended and colored, there must be some way to subsume color into geometrical analysis. And it is here that the indirect geometrization begins to take shape. There must be some index of regularity which, while not directly spatial, can be related to some “spatial” measurement, directly or through a process of translation.
Now with regard to the “indirect” mathematization of that aspect of the world which in itself has no mathematizable world-form, such mathematization is thinkable only in the sense that the specifically sensible qualities (“plena”) that can be experienced in the intuited bodies are closely related in a quite peculiar and regulated way with the shapes that belong essentially to them.
In this perspective, not yet intuitive, Galileo dramatically paves the way for Modern physics such that, today, second thoughts are rarely given to the procedure:
[21] What we experienced in prescientific life, as colors, tones, warmth, and weight belonging to the things themselves and experienced causally as a body’s radiation of warmth which makes adjacent bodies warm, and the like, indicates in terms of physics, of course, tone-vibrations, warmth-vibrations, i.e., pure events in the world of shapes. [Italics mine]
So much of this is taken for granted that undergraduates can even say that they “see” wave lengths.
This is to say that once gestalted, the Galilean perspective becomes a kind of macroperception which can be taken for granted with new modifications possible. But it is precisely here that the ambiguity in Husserl reaches its own apex. For if the new means of understanding phenomena becomes a genuine cultural acquisition as the investigation into the origins by means of a praxis become transparent, it overlooks the contrast with the fundamental lifeworld.
But now we must note something of the highest importance that occurred even as early as Galileo the surreptitious substitution of the mathematically substructed world of idealities for the only real world, the one that is actually given through perception, that is ever experienced and experience — able — our everyday lifeworld. This substitution was promptly passed on to his successors, the physicists of all the succeeding centuries.
Husserl seems to be saying that the lifeworld is, and must be, the sensory lifeworld, based in the relations between actional humans and the concrete, material world of things and beings, which are bodily. And these are intuitively, perceptually available to everyone. Then a second type of intuitability also occurs, such as that exemplified in the Galilean revolution, in which certain combinations of praxically attained perspectives can make possible another intuitable attainment, a cultural acquisition, like a science.
However, such an acquisition is also ambiguous. Because what is gained by the very means of mathematization, Husserl argues, loses an essential sense of concreteness by overlooking the fundamental lifeworld.
Galileo, the discoverer… of physics, or physical nature is at once a discovering and a concealing genius. He discovers mathematical nature, the methodical idea, he blazes the trail for the infinite number of physical discoveries and discoverers. [But] immediately with Galileo, then, begins the surreptitious substitution of idealized nature for prescientifically intuited nature.
The acquisition of the new paradigm conceals the fundament of the ordinary dimension of the lifeworld.
In this context, however, two remarks are called for: First, it [22] should now be obvious that Husserl clearly developed something similar to the notion of a paradigm shift. This is, in essence, his interpretation of Galileo. Galileo “sees” the world differently, and once this perspective is established, it can itself become a tradition which persists. Here is normal science, a way of seeing and interpreting phenomena which contrasts with the world of ordinary activity and seeing. In this sense, and specifically by means of an experiential analysis, Husserl anticipates the new philosophy of science.
For Husserl, praxis and perception are the focal basis of the lifeworld. The lifeworld is that structure of experience which is both perceptual and historical. It contains sediments and traditions and what Husserl proposed in his reexamination of the rise of Modern Science.