Today's reading spans pp.41-59.
This here section we’ve read for tonight restates rather longwindedly Eddington’s famous two tables lecture! Again! I can see, too, the grounds for Husserl’s criticism of Kant from the preface. I at first thought that Husserl was more or less toeing the Kantian line by broaching the subject of the universal mathesis’ dualism (UMD). He criticizes laypeople’s mistaking formula-meaning for the “true being of nature itself” (44). I suppose if I had thought more on this phrase, I would have noticed that it itself is rather non-Kantian sounding. Anyway!
The stuff about the universal mathesis being a push toward pure symbolism, and therefore a push toward mathematics becoming a “sort of technique” is rather unsurprising at this time. Since Frege, Russell et al. I had sort of assumed that no one seriously thought mathematics was anything but symbols. Husserl says (rightly) that one cannot ascertain the truth of anything rendered by the modern mathematical technique—but then that is also obvious! Kant even made that distinction, saying in the CPR that logic is more or less empty and in need of intuitions for any truth value to be established. I like Husserl’s comparison between the operational rules of mathematics and the “rules of a game” (46). But again—who confuses pure mathematics with applied mathematics?!
These days we educated people do not go around spouting, “bar bar bar!” incoherently toward one another, nor do we confuse the axioms of Euclidean geometry for a schemata of how space is. But I do rather like Husserl’s idea of the “life-world” being something about which we fit a “garb of ideas” (51). Again, up springs Kantian dualism/UMD! I suppose Euclidean geometry does facilitate our building suspension bridges and sky scrapers.
What’s with Husserl springing upon us this Platonico-mathematical quandary about our “require[ing] a systematic process in order to being to realization as knowing, i.e., as explicit mathematics, all the shapes that ‘exist’ in spatiotemporal form” in a paragraph with which terminates his question on why we can’t ever prove the axioms of an apodictic system? What I mean is that the two—the Platonic view of mathematics and our proving the consistency and completeness of our axiomatic systems from only within those systems—seem to be incompatible positions as shown by Herr Gödel.
What is the primal, historical meaning of science?
B. Michael Payne