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 the relations of concepts, and not relations between existent things in the world and their predicates, because formal laws are free of existential content. The earlier example of swans demonstrates this difference between empirical and formal laws. Formal laws can only guide our thinking; they cannot guarantee the correctness of it. We can always be mistaken, inconsistent; our thinking can be erroneous. Formal laws are necessary not only for our account of empirical laws, but also for the constitution of meaning, as Husserl points out; they are valid all the time because of their form. They are not based on our thinking—which is an event in the world—but guide it. Formal laws express truth in itself; truth being the ideal limit that, in the empirical domain, we can approach only asymptotically.
If we deny the possibility of formal laws, which are the only laws that we can know apodictically and that are the foundation of empirical sciences, there is no possibility of knowledge. Our empirical judgments are by definition only probable. They are derived from many singular observations, from which we inductively formulate natural laws that will help us to predict other instances of similar happenings. Moreover, the formal law of induction is not based on experience, but guides it.
However, as Husserl argues, we cannot think, and by implication live, without certainty of knowledge. Yet what knowledge is cannot be reduced to the formal knowledge of sciences. His whole career was devoted to this problem. On his journey, starting from the consideration of Philosophy of Arithmetic and continuing to his last work, Crisis, Husserl realizes that once questions concerning humans as they live in the natural world are excluded from sciences, which have become the domain of technical thinking instead of responsible practice, the formal questions—the hallmark of natural science—will lead to existential crisis. As he notes, “The questions which are decisive for a genuine humanity,” that is, “questions of the meaning or meaninglessness of the whole of this human existence” (Crisis, § 2, 6), cannot be answered by formal knowledge. But neither should those questions be left to “scientists, who, in the specialized business of the positive sciences, [are] fast becoming unphilosophical experts” (Crisis, § 4, 11). As he notes in FTL, “Apriori sciences, by virtue of being apriori, always function normatively and technologically” (§ 7, 31; italics in original), yet they do so as “sciences and not technologies.” The reason is that there is a
