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

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

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

However, the lifeworld stands revealed as the forgotten ground of meaning in natural science.

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

The geometry Galileo inherited was already far removed from intuition, yet it still retained intuitive constructions and an intuitive mode of representation.

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

This poses a problem:

Human beings who live in this world—including the natural scientist—can only ever situate their 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 the world we inhabit, in accordance with our mode of being—that is, in the full concreteness of our being. And yet, here we find no geometrical idealities: neither geometrical space nor mathematical time ⁵.

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

The lifeworld asserts itself with a force, a persistence, and a kind of truth that is at once unique and inescapable. This world is not altered simply because we have devised a particular method—the geometric and Galilean method, known as physics.

Yet, we cover the lifeworld 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, merely a 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 distortion that Galilean mathematisation imposes on the meaning of nature leads to the well-known Galilean doctrine of the pure subjectivity of sensible qualities.

This doctrine was taken further 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, present there merely as causal consequences of processes occurring in true nature—processes which themselves 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 lawfulness of nature, though itself mathematical, remains accessible through experience (a posteriori). This constitutes the fundamental opposition between mathematics and the natural sciences.

Husserl describes the aim 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 it—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