The result of the never-clarified idea “of a formal ontology” (FTL, § 24, 76; italics in original) is the forgetting of the natural world in preference to mathematical hypotheses, leading to “The Crisis of European Sciences and Psychology.”131
GALILEO: A DISCOVERING AND A CONCEALING GENIUS
Husserl points out that this is not a fortuitous development, and he traces his historical analysis back to Galileo, “a discovering and a concealing genius.”132 In a sense, Galileo reversed tradition; until then, although no longer commonly remembered as such, geometry took as its basis intuited nature, and defined certain privileged shapes—line, point, square—as ideal shapes that could be understood by everybody. Yet nature was still understood as the basis for these ideal shapes. In answer to the Sophists, Plato’s search for the certainty of knowledge led him to base it on the model of geometry, as it was in his time. To recall Plato, if I can draw a line in the sand, I can imagine that if I do not stop, if I am not bound by the finite world of my everyday living, the line can go on and on forever. From this insight, I can imagine the idea of infinity. If I draw a triangle, none of the ones I draw are perfect, but I can imagine one that is absolutely perfect and that will become the form of a perfect triangle in which all the finite triangles thought or drawn by humans will participate. The ideal triangle will be a model that cannot ever appear in the world but that will guide our finite thinking from then on. It is then possible to show that there must be a domain that is guiding our finite human thinking: the domain that is a foundation of epistēmē, knowledge, as opposed to doxa.
The Platonic answer was still derived from the world in which he lived. His perfect “reality,” the domain of Ideas or Forms, was immaterial. Material nature participated in the immaterial Forms. By contrast, by the time this tradition reached Galileo, it was already sedimented. Geometry was refined and he simply turned it around, declaring that nature is written in triangles and circles.133 For Galileo, immaterial Forms become the matter: nature is essentially mathematical.134
Galileo “divorced” nature from geometry and posited the ideal shapes as primary: “The geometrical ideal shape [. . .] functions as a guiding pole” (Crisis, § 9b, 29). By the same token, if nature is mathematical, then our everyday intuition of cause and effect can be idealized as well. In the Galilean universe, it becomes “the law of causality, the ‘a priori form’ of the ‘true’ (idealized and mathematised) world, the ‘law of exact lawfulness’ according to which every occurrence in ‘nature’—idealized nature—must come under exact laws.”135 As Husserl declares, “The whole of infinite nature, taken as a concrete universe of causality—for this was inherent in that strange conception—became [the object of] a peculiarly applied mathematics” (Crisis, § 9c, 37; italics in original; square brackets in translation).
Thus, by the reversal of the tradition, Galileo transgressed the finite world of our lives. From then on, atoms, rocks, pendulums, and heavenly bodies are all subject to the one law—the law of causality. Transforming the idea of Aristotelian nature, Galileo’s two revolutionary ideas were the idea of the precise causality of mathematical nature, and the idea of indirect mathematization. The ancient Greeks were familiar with measuring bodies; but how can one measure, for example, smell, sound, warmth—except to say something like “more or less,” “louder,” “warmer.” But if nature is mathematical, we must be able to turn these qualities into mathematical formulae. Thus indirect mathematization overcomes this “vagueness,” inaugurating modern physics.
We are so accustomed to this way of thinking that it is difficult to imagine the revolutionary impact of this idea. We now take for granted that we can measure nearly everything by transposing the qualitative properties of objects into quantitative properties. If I “have a temperature,” I use a thermometer. A thermometer represents nothing but the alignment of warmth with a tube of mercury that expands under its influence, so that I can state, in a (nearly) precise sense, a numerical index of temperature. For us, this relation/causality between two separate domains—qualitative and quantitative—seems obvious. It is this hypothesis that allows sciences to predict and to interfere with many natural processes. For Galileo, it was not a hypothesis; he simply assumed that nature is mathematical. “For him physics was immediately almost as certain as the previous pure and applied mathematics.” As Husserl explains, through “this by no means obvious hypothesis,” Galileo connected the formerly unpredictable “factual structure of the concrete world” to mathematical reckoning (Crisis, § 9d, 39). From Newton onward, the idea of the mathematized world became understood as nature given a priori in “its way of being”; yet this being must be “unendingly hypothetical and unendingly verified” (Crisis, § 9e, 42).
The final outcome of this inversion of tradition is “the consistent development of the exact sciences in the modern period,” which would be impossible without turning the world into mathematical, hypothetical structures. This transformation of nature into symbolic equations “was a true revolution in the technical control of nature.”136
CONCLUSION: PHILOSOPHY AND THE CRISIS OF EUROPEAN HUMANITY
Merely fact-minded sciences make merely fact-minded people. (Crisis, § 2, 6)
One should note Husserl’s motive for doing philosophy. It is not primarily a theoretical motivation, but a practical one, or more precisely an ethical one—the ethical striving for a life in absolute self-responsibility.137
Despite the general feeling of skepticism of his time, Husserl strives to affirm the idea of rationality as we have inherited it from the ancient Greeks. As he points out, it is important to show that there is a domain of truth that can guide us in our search for knowledge; his commitment is to give reasons for our beliefs instead of accepting blind prejudices without thinking. For Husserl, it is this commitment to truth and knowledge that underlies our striving to confirm rational meaning in our human existence.
As he consistently shows throughout his oeuvre, if we mistakenly accept that the only truths are empirical, based on our experience only, the gate is opened to a flood of skepticism and relativism that denies the possibility of knowledge. In a certain sense, we deny the human capacity to reason. By denying the possibility of formal laws, we affirm changeable truths, deriving them from empirical laws that are part of the natural world. As already noted, empirical laws cannot be apodictic: by definition, they are only probable. They are dependent on further observations through which we can institute a further probability that might explain better or more simply the succession of experienced events. However, without the formal a priori notion of probability and the a priori idea of causality, as David Hume asserts, the meaning of empirical events and their succession is a mystery.138 Rationality is declared misplaced.
The next step is more insidious: the meanings of “probability” and “relativity” are taken as equal. The equivocation of these two different states leads, then, to the conclusion that our belief in reason is an antiquarian prejudice. By this seemingly innocuous move, the notion of “truth” is reduced to empirical truths that are changeable by definition. The “final” conclusion seems to follow without any further reflection: there is no truth; there are only particular truths, dependent on our thinking (psychologism) and our human species (anthropologism). The acceptance of this conclusion leads to relativism without any possibility of assessing different claims; without any possibility of accounting for our claims; without any possibility of invoking a rational basis for our inconsistent claims. It is to declare that doxa—that is, claims made without giving reasons for their validity—is here to stay. However, as Husserl points out, probability and relativity are different ideas. The idea of probability is one of the modalities of truth; probability cannot be equated with relativity, the idea that supposedly defines our changeable human experience (see FTL, § 35, 101n1).
After all, the only self-evident insight is knowledge expressed by formal laws that are the foundation of our empirical judgments. As Husserl shows, formal laws express only