Summary: The Crisis of European Sciences and Transcendental Phenomenology (page 5)

Mathematics becomes an Ars—that is, a mere art of obtaining results through a technique of calculation that follows technical rules: The only modes of thought and forms of evidence that come into play are those that are absolutely necessary for a technique as such. We operate with letters and symbols denoting relational operations (+, ×, =, etc.) ¹.

This was only the beginning: The process of technicisation gradually extended to all other methods intrinsic to the natural sciences ².

However, the lifeworld emerges as the forgotten foundation of meaning in natural science.

Indeed, already in Galileo, a remarkable substitution takes place: the mathematical world of idealities is taken as the only real world, supplanting our experience—the world of our everyday life.

The geometry that Galileo inherited was already far removed from intuition, yet we still find intuitive constructions and an intuitive way of imagining.

From Galileo onwards, however, the substitution of an idealised nature for the pre-scientific nature given in intuition begins ³.

This poses a problem:

The human being who lives in this world—including the natural scientist—can only situate all practical and theoretical questions within the lifeworld ⁴.

The lifeworld is the horizon of all meaningful induction. It is the world in which all known and unknown realities are encountered:

It is within it that we ourselves live, in accordance with our mode of being—that is, in the full flesh of our person. And yet, here we find nothing of geometrical idealities: neither geometrical space nor mathematical time ⁵.

We are thus witnessing the substitution of a methodically idealising activity for what is immediately given as reality ⁶.

The lifeworld imposes itself with a force, a persistence, and a truth whose nature is singular and insurmountable. This world is not altered simply because we have devised a particular method—the geometric and Galilean method, which goes by the name of physics.

Yet, we overlay the world of life with the garment of ideas ⁷: mathematics and physics. And it is this garment of ideas that leads us to take as true what is, in reality, only method ⁸.

Galileo discovered the mathematical nature of reality and the law of causality, according to which every event in nature must obey exact laws:

Nature is mathematical in itself, given in formulae, and to be interpreted only through formulae ⁹.

The consequence of the distortion of meaning that Galilean mathematisation imposes on nature is the well-known Galilean doctrine of the pure and simple subjectivity of sensible qualities.

This doctrine was logically developed by Hobbes into a theory of the subjectivity of all concrete phenomena in nature and, more broadly, of the entire world as it is given in sensible intuition. Phenomena exist only within subjects; they are present in them merely as causal consequences of processes occurring in true nature—processes which, for their part, exist only in the form of mathematical properties.

If the world given in intuition—the world we experience—is purely subjective, then all the truths of pre-scientific and extra-scientific life lose their value ¹⁰.

If nature is mathematical, then the universal legality of nature, though itself mathematical, remains accessible through experience (a posteriori). This constitutes the fundamental opposition between mathematics and natural science.

Husserl describes the goal of his inquiry as an attempt to reclaim originary intuition—that is, the pre-scientific lifeworld:

The authentic return to the naivety of life—but in a reflection that rises above this ground—is the only possible way to overcome the philosophical naivety latent in the "scientificity" of traditional objectivist philosophy ¹¹.

¹ ibid., p.54
² ibid.
³ ibid., p.56
⁴ ibid., p.58
⁵ ibid.
⁶ ibid, p.58-59
⁷ ibid., p.59
⁸ ibid., p.60
⁹ ibid.
¹⁰ ibid., p.62
¹¹ ibid.p.68-69