About Completed Infinities (“True Nature”)

Sunset on Clear LakeI’ve been asked to comment on “True Nature” (as in, “a person’s true nature”).

Here’s a paragraph or two from Dispute over Infinity Divides Mathematics:

Infinity has ruffled feathers in mathematics almost since the field’s beginning. The controversy arises not from the notion of potential infinity–the number line’s promise of continuing forever–but from the concept of infinity as an actual, complete, manipulable object.

Assuming actual infinity leads to unsettling consequences. Cantor proved, for instance, that the infinite set of even numbers {2,4,6,…} could be put in a “one-to-one correspondence” with all counting numbers {1,2,3,…}, indicating that there are just as many evens as there are odds-and-evens.

The mathematician Poincare sums it up nicely for me (from Wikipedia, actual infinity):

There is no actual infinity, that the Cantorians have forgotten and have been trapped by contradictions.

(H. Poincare [Les mathematiques et la logique III, Rev. metaphys. morale (1906) p. 316])

I would say that the assumption of the existence of a completed infinite, as in “True Nature”, or “Dao”, or “God”, will result in contradictions, and such an assumption isn’t really required to benefit from the positive and substantive particulars in most of the wisdom teachings of the world.

At the same time, there’s a lot of useful mathematics that relies on the notion of a completed infinity for proof, and I would guess the majority of people on this earth find terms like “True Nature” useful as a means of orientating themselves in everyday living.

I think it is possible to talk about the boundaries of the senses, and somehow to perceive things that lie beyond those boundaries, and that perception may be characterized as “infinite” (as in “the infinity of ether”, the perception of the first of the non-material meditative states–bearing in mind that the non-material states are marked by “uniformity with respect to the senses”).

At least Gautama tended to describe things in mostly positive and substantive terms, as when he described how “the infinity of ether” was “the excellence of the heart’s release” through the suffusion of the world with “a mind of compassion”:

[One] dwells, having suffused the first quarter of the world with compassion, likewise the second, likewise the third, likewise the fourth; just so above, below, across; [one] dwells having suffused the whole world everywhere, in every way, with a mind of compassion that is far-reaching, wide-spread, immeasurable, without enmity, without malevolence.

(MN I 38, Pali Text Society volume I pg 48)

That’s kind of how “people who are moving around outside” sit with me, when I sit:

When you sit, the cushion sits with you. If you wear glasses, the glasses sit with you. Clothing sits with you. House sits with you. People who are moving around outside all sit with you. They don’t take the sitting posture!

(Kobun Chino Otogawa, “Aspects of Sitting–Shikantaza”, from jikoji.org)

That’s as close to the notion of a “completed infinity” as I like to get, because of the contradictions that will otherwise inevitably arise.


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