"PART II

Clarification of the Origin of the Modern Opposition between Physicalistic Objectivism and Transcendental Subjectivism

§8. The origin of the new idea of the reshaping of mathematics."

Hopfully you've at least skimmed over Part I and The Vienna Lecture before coming here. Part II includes at first a look at Galileo and the continues with Decartes, and mentions of Locke, Hume, Berkeley and Kant.

"The reshaping begins with prominent special sciences inherited from the ancients: Euclidean geometry and the rest of Greek mathematics, and then Greek natural science. In our eyes these are fragments, beginnings of our developed sciences. But one must not overlook here the immense change of meaning whereby universal tasks were set, primarily for mathematics (as geometry and as formal-abstract theory of numbers and magnitudes) - tasks of a style which was new in principle, unknown to the ancients. Of course the ancients, guided by the Platonic doctrine of ideas, had already idealised empirical numbers, units of measurment, empirical figures in space, points, lines, surfaces, bodies; ...

But Euclidean geometry, and ancient mathematics in general, knows only finite tasks, a finitely closed a priori. Aristootelian syllogistics belongs here also, as an a priori which takes precedence over all others. Antiquity goes this far, but never far enough to grasp the possibility of the infinite task which, for us, is linked as a matter of course with the concept of geometrical space and with the concept of geometry as the science belonging to it. ...

... Our apodictic thinking, proceeding stepwise to infinity through concepts, propositions, inferences, proofs, only "discovers" what is already there, what in itself already exists in truth.

... creates for it the completely new idea of mathematical natural science - Galilean science, as it was rightly called for a long time. As soon as the latter begins to move toward successful realization, the idea of philosophy in general (as science of the universe, of all that is) is transformed."

I admit maybe my select quotes are a little clumsy above

"§9. Galileo's mathematization of nature.

For Platonism, the real*..." Slight pause here ...

*trans. note. "das Reale. I have used "real" almost exclusively for the German real and its derivatives. For Husserl this term refers to the spatiotemporal world as conceived by physics (or to the psychic when it is mistakenly conceived on the model of the physical). The more general Wirklichkeit has usually been translated by etymologically correct term "actuality"."

I am fairly sure that Husserl covers this in his Cartasian Meditations, and if you wish you can google "reall" or "hyle", or even "noema". My honest opinion is that it is easier not to get bogged down, as it appears many scholar of Husserl have, in trying to cross-reference every word he wrote when his ideas from the first instance have developed beyond their origin. Just take the term "das reale" as meaning something like how we've come to refer to what is real as what is physically real. This may sound a little pedantic, but it is a worthy and subtle distinction that should not be dismissed.

"For Platonism, the real had a more or less perfect methexis in the ideal. This afforded ancient geometry possibilities of a primitive application to reality. [But] through Galileo's mathematization of nature, nature itsel is idealized under the guidance of the new mathematics; nature itself becomes - to express it in a modern way - a mathematical manifold [Mannigfaltigkeit.

What is the meaning of this mathematization of nature? How do we reconstruct the train of thought which motivated it?

Prescientifically, in everyday sense-experience, the world is given in a subjectively relative way. Each of us has his own appearances; and for each of us they count as [gelten als] that which actually is. In dealing with one another, we have long since become aware of this discrepancy between our various ontic validities*."

*trans. note. "Seinsgeltungen. Geltung is a very important word for Husserl, especially in this text. It derives from gelten, which is best translated "to count (as such and such) (for me)," as in the previous sentence, or "to be accepted (as, etc.)" or "to have validity (of such and such) (for me)." Gültigkeit is the more common substantive but is less current in Husserl. Thus "validity" ("our validities," etc.) seems as appropriate shortcut for such more exact but too cumbersome expressions as "that which counts (as)," "those things which we except (as)," etc., in this case, "those things that we accept as existing." I have used "ontic" when Husserl compounds Sein with this and other words, e.g., Seinssinn, Seinsgewissheit."

Ignore this if you wish:

In my opinion it is in these subtleties that Heidegger, and possibly Derrida, take a hermeneutic line of inquiry into "phenomenology" by way of hermeneutic linguistics. It seems to me that where Hussel critics the "reality" of the "phsyicalist" position, Derrida attempts to critic the linguistic representation of "reality". I personally see Husserl as being aware of this problem yet understanding a flaw in taking on this problem with language as language can only be talked about with language ... I will stop there before I go off on some impossibly long ramble that does little more than confuse (as is part and parcel of what I mean being the "problem"!).

"... But we do not think that, because of this, there are many worlds. Necessarily, we believe in the world, whose things only appear to us differently but are the same. [Now] have we nothing more than the empty, necessary idea of things which exist objectively in themselves? Is there not in the appearances themselves a content we must ascribe to true nature? Surely this includes everything which pure geometry, and in general the mathematics of the pure form of space-time, teaches us, with the self-evidence of absolute, universal validity, about the pure shapes it can construct idealiter - and here I am describing, without taking a position, what was "obvious"* ..."

*trans. note. "Selbstverständlichkeit is another very important word in this text. It refers to what is unquestioned but not necessarily unquestionable. "Obvious" works when the word is placed in quotation marks, as it is here. In other cases I have used various forms of the expression "taken for granted."

"... "obvious" to Galileo and motivated his thinking.

We should devote a careful exposition to what was invloved in this "obviousness" for Galileo and to whatever else was taken for granted by him in order to motivate the idea of a mathematical knowledge of nature in his new sense. We note that he, the philosopher of nature and "trail-blazer" of physics, was not yet a physicist in the full present-day sense; that his thinking did not, like that of our mathematicians and mathematical physicists, move in the sphere of symbolism, far removed from intuition; and that we must not attribute to him what, through him and the further historical development, has become "obvious" to us."

Personally I think this brief introduction to Husserl's look at Galileo shows very well how Husserl approaches every subject of investigation. What I often hear people protest against is the "obtuse" language, or ambiguous nature of his writing. I don't see this. I see a very careful and clinically unprecise language employed that is to be understood as questioning the "obviousness". The irony, so it seems to me, is that by looking in depth at our own subjective being we actually have a better way to present an objectivity! The objective essentially being nothing other than a suprasubjectivity in the first place led under the necesaary assumptions of an objective world unknowable directly in an immediate sense. It is here I find so many people protesting at his words as "fantasy" or solipsistic.

Anyway, §9 continues for around 35 pages under these subheadings which I will try and sum up in future posts:

a. "Pure geometry."

b. The basic notion of Galilean physics: nature as a mathematical universe.

c. The problem of the mathematizability of the "plena."

d. The motivation of Galileo's conception of nature.

e. The verificational character of natural science's fundamental hypothesis.

f. The problem of the sense of natural-scientific "formulae."

g. The emptying of the meaning of mathematical natural science through "technization."

h. The life-world as the forgotten meaning-fundament of natural science.

i. Portentous misunderstandings resulting from lack of clarity about the meaning of mathematization.

(note: there is no "j" in German enumeration!)

k. Fundamental significance of the problem of the origin of mathematical natural science.

l. Characterization of the method of our exposition.

I hope one or more of these subheadings intrigue someone. I will try and give a reasonable summation of each bit. If one of these sparks your interest PM me and I'll jump straight onto that one first and foremost.