Husserl: Part II Crisis §8-9 (Galileo)

[BadgerJelly]

"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.

[BadgerJelly]

a. "Pure geometry"

Not a great deal to say here other than Husserl goes over the "pure" geometry of shapes being applied to "pure" bodies. Outlining how Galileo brings them together into how physics uses mathematical ideals (with obvious success).

[BadgerJelly]

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

Here Husserl points out that Galileo's attitude toward geometry was "pregiven". Meaning its origin was never in question. For Galileo he never saw any need to look at where geometry came from and whether or not to question its application to the world. Ideals were used to express the sensible world.

What Husserl points out is the "univocal" nature of mathematics. Mathematics is truly Objective. We cannot have opinion about the answer of the sum 1+1= x, I cannot say I am of the opinion that the answer is 3. To hold an opinion in a rigidly Objective field would be utterly ridiculous.

What is generally the theme of Husserl's work is bringing to light, bringing us to ask questions of, what this "idealization" (mathematics) means and how it can and cannot be applied to our world.

This I feel is an important section toward the end of part b :

"- The things of the intuited surrounding world (always taken as they are intuitively there for us in everyday life and count as actual) have, so to speak, their "habits" - they behave similarly under typically similar circumstances. If we take intuitable world as a whole, in the flowing present in which it is straightforwardly there for us, it has even as a whole its "habit," i.e., that of continuing habitually as it has up to now. Thus our empirically intuited surrounding world has an empirical over-all style. ..."

"... Precisely in this way we see that, universally, things and their occurrences do not arbitrarily appear and run their course but are bound a priori by this style, by the invariant form of the intuitable world. In othe rwords, through a universal causal regulation, all that is together in the world has a universal immediate or mediate way of belonging together; through this the world is not merely a totality [Allheit] but an all-encompassing unity [Alleinheit], a whole (even though it is infinite). This is self-evident a priori, no matter how little is actually experienced of the particular causal dependencies, no matter how little of this is known from past experience or is prefigured about future experience."

tbc ...

Note: We are seeing the general approach of Husserl beginning to form. What I find most telling is how we take non-univocular terms in language and give them a weight "as if" they are univocular. Within mathematical language we are well within our rights to use mathematical terms and symbols as univocular because they are ideals.