According to Whitehead’s theory of cosmic epochs and extensive continuum, there are material conditions that drive the more general metaphysical descriptions and principles. We only can account for the factors which characterize our cosmic epoch without overstretching these results to the cosmos in toto.
Unlike many philosophers and scientists, Whitehead views time and space as contingent features of reality which could be otherwise; they are specifications of divisibility accounting for certain respective regions. The extensive continuum is “undivided, yet divisible” in its nature and accords with Whitehead’s bi-metric geometrical framework. But this continuum presupposes a notion of extensiveness or regional togetherness that is non-metrical. Essentially, space and extension are not equivalent.
So temporal and spatial cuts or divisions happen to characterize our cosmic epoch, and this implies that space-time is NOT a necessary ontological modality applicable to the entire assemblage of solar systems. In fact, the author of Principia Mathematica concludes in another epoch it may not be the case that one and one makes two.
Pop culture science continues to advance a hubris which ignores these provisions. They claim to be measuring and accounting for the experience of the universe, in itself. A more modest proposal claims that our laws and discoveries unfold according to the epochal theory of time.
So my question is: how can we apply arithmetic in its pure metaphysical sense without recognizing that the truth of its character depends on the “societies dominating the cosmic epoch in which we live”?
I believe this is not some philosopher splitting hairs but raises a pertinent concern that even mathematics (especially the sciences) in its basic solutions should be open to the pragmatic method of indefinite revisions.
Appreciate your feedback and suggestions—thank you!