4 min read

Origin of Geometry notes

Husserl's The Origin of Geometry is fairly short (24 pages) but it's also not exactly edge-of-my-seat entertainment so let's write some notes to try and keep myself awake.

I'm mainly reading this because of the Derrida connection. Derrida's first major work was an Introduction to The Origin of Geometry, and it covers very similar themes to Voice and Phenomenon... there's this quote where he calls it "the other side (recto or verso, as you wish)".

According to my timeline (glad I made this!), Geometry was an appendix to a late work of Husserl's, 1936's The Crisis of European Sciences and Transcendental Phenomenology. But it also (and Derrida points this out) has echoes of one of his earliest works, The Philosophy of Arithmetic from 1891. They're both about experiential grounding of maths, in some way, but his idea of what grounding should be has changed a lot. Arithmetic was where he got in trouble with Frege for 'psychologism', or reducing everything to individual perception, which is dubious when mathematical truths are shared by everyone. As I remember it Husserl reversed course on this pretty quickly, and that pushed him towards a kind of idealism, where our perceptions give us access to some kind of universal mathematical objects... and that seems to be on display here:

But geometric existence is not psychic existence…it has, from its primal establishment, an existence which is peculiarly super temporal and which – of this we are certain – is accessible to all men… This is, we note, an “ideal” objectivity.

So now there's the problem of how individual perceptions can become shared ideal objective knowledge:

… how does geometrical ideality … proceed from its primary intrapersonal origin, where it is a structure within the conscious space of the first inventor’s soul, to its ideal objectivity?

The same themes came up in Leszek's Husserl and the Search for Certitude so maybe I should compare my notes there.

There's a bit of a detour talking about language, which is a practical answer to how meaning is communicated between people, but doesn't really solve the problem of how to pass from perception to these annoyingly slippery ideal objects that Husserl is determined to have.

OK, and now he's talking about time-consciousness, and how perceptions fade and pass away, they aren't in the "supertemporal" realm of ideal objects.  So this really does have a lot of the same themes as Voice and Phenomenon.

It sounds like on Husserl's account the ideality is created in the following way:

  • an individual can 'reload' a faded understanding into living experience again. This is still intrapersonal, but...
  • something something intersubjectivity, so through language the first person can load this understanding into a second person, and it can light up in the lived experience of both of them in the same way:
In the unity of the community of communication among several persons the repeatedly produced structure becomes an object of consciousness, not as a likeness, but as the one structure common to all.
  • OK but this still isn't timeless ideality, it's more like a pattern of lights flickering on and off as different people briefly think about the thing and then go do something else. Husserl addresses this next (sort of?), by saying that written language can be used to mediate between people, to make communication possible even when there are times when nobody is lit up by the idea. I say 'sort of' because this addresses how we practically cope with the flickering, but doesn't get rid of it, so I'm a little confused.

Next Husserl talks about how written language allows people to just read out the words without reactivating the understanding, the lights are no longer on but you can still recite the quadratic formula or whatever and get a usable piece of knowledge. (I mean, you can do this with speech too? But it's true that it's harder to make things memorable enough.)

It sounds like Husserl thinks that scientists have a moral responsibility to keep the lights on, to make sure that every fact is reactivatable and can pass into living understanding:

This must be done by the individual scientist, and not only by the inventor but by every scientist as a member of the scientific community after he has taken over from the others what is to be taken over. This belongs, then, to the particulars of the scientific tradition within the corresponding community of scientists as a community of knowledge living in the unity of a common responsibility.

(I sort of agree? Or, well, more accurately I have complicated feelings about this... it's unworkable, but I admire something about the moral seriousness.)

Now I think we're getting on to one of the big topics of the essay, and getting a sense of why he's concerned about geometry in particular. As an ancient subject that's been investigated for millennia, there's a huge pile of bits of knowledge that all build on each other. But nobody has the whole chain of inferences loaded into their heads at any one time, people only have living experience of little pieces of it. Which leaves the questions:

In the finally immense proliferation of a science like geometry, what has become of the claim and the capacity of reactivation? When every researcher works on his part of the building, what of the vocational interruptions and time out for rest, which cannot be overlooked here? When he returns to the actual continuation of work, must he first run through the whole immense chain of groundings back to the original premises and actually reactivate the whole thing?

Presumably Husserl answers these, but I'm only half way through and this is as much Husserl as I can take in one go, so I'll stop here for now.