AshvinP wrote: ↑Tue Mar 23, 2021 4:28 pm
I don't know what you are reading...
This:
https://en.wikipedia.org/wiki/Pragmatism
I know nothing of William James. Wiki is not very trustworthy, it reflects biases of writers and editing process, but still, a starting point for trying to get some sense of a meaning of a term.
So I think we are now on the same page with regards to why I do not see any major problem with Cantor's set theory math - because pragmatically, it is not untrue. We are not comparing it to an 'objective' state of reality out there, but to other conceptual systems which are tools in pursuit of various human aims. You seemed to be on board with the pragmatic perspective on truth until the segment on Peirce, which implied a subject-object division. I agree that is a problem and that aspect of pragmaticism, to the extent that Wiki is accurate and it actually exists, should be discarded.
Not so fast. Your claim is that instrumentalism of physicalism and it's applied math should reflect back to domintate metaphysics, where foundational thinking in pure mathematics belongs. Seems I read the "core tenets" of pragmatism too superficially. Does the argument boil down to Coherence theory of
truth vs. Coherence theory of
justification? This seems a promising avenue of investigation, but first, let's note:
Robert Fogelin claims to detect a suspicious resemblance between the theories of justification and Agrippa's five modes leading to the suspension of belief. He concludes that the modern proponents have made no significant progress in responding to the ancient modes of Pyrrhonian skepticism.[3]
https://en.wikipedia.org/wiki/Justifica ... stemology)
In terms of empirism, both introspective (intuition) and extrospective (Zeno's paradoxes, IRL Achilleus beats the turtle), as well as logic, postulation of 'completed infinity' is not a
coherent theory of truth on the foundational level of mathematics. As a speculative thought experiment which does not claim any truth value, different story. Agreed so far?
So, what is left is the question, how coherent is the pragmatic justification, which is ethical discussion about our aims and purposes.
1) Does calculus in it's current form, and as long as there are no better alternatives available for the
specific technical aims that it serves, justify subjecting pure mathematics as a whole to the applied mathematics of calculus, do the instrumental aims justify violating the coherence theory of truth on the foundational level of pure mathematics, so that mathematics needs to be founded on Cantor's paradise/joke?
In my view not, but you are free to disagree. If you disagree, the discussion moves onto next level:
2) How do the justifications derived from aims of calculus relate to other human aims? Do instrumentalist justifications lead to the fragmentation of the post-modern condition, so that anything can be derived from any and all aims, or is there necessity for some some sort and level of coherence when we compare different aims and their implications? If it works, as Dawkins justifies physicalism and it's cornerstone of calculus,
should it work to make us Dawkins' bitches?
Okey, using Dawkins as an example is a rhetorical stunt, not a steelman argument. Please make your own best argument, what aim of calculus could be so high and noble, that it would justify polluting pure mathematics, to justify violating coherence theory of truth as well as many other competing justifications, with Cantor's paradise/joke?
If you don't mind, I offer my own best steelman attempt for justification. The aim of targeting a big space rock so accurately, that we can prevent a big fiery rock falling from sky and wiping away much or most of life. That is a very noble aim!
On some subconscious, archetypal level, it is not unplausible that the essence, the manifest destiny of Western spirit has been exactly that: cultural level possession to serve that aim and develop for Mother Earth an antidote against big fiery rocks falling from the sky. A madness inflicted by Mother Earth on some of her children, for a justified cause for a creative process and all the collateral damage the process has splashed out. This steelman argument would entail that Western civilization has not been using, it has been used in a way that is not without its cruelty of being possessed by the justified madness.
Here's my counterargument from metamodern zeitgeist of reconciliation with modernism. Maybe we have now become on some level mature enough to liberate Western civilization from it's noble aim, to delegate and distribute the aim more evenly between other civilizations and their space technologies, so that we can further develop and maintain the technological ability to defend Mother Earth, to create conditions for more smooth and less violent evolution both biologically and spiritually. Advances in computation theory and pure mathematics are bringing better alternatives to old calculus. There are no more strong enough reasons to hold pure mathematics captive to the technological teleology, and we can liberate pure mathematics and its spiritual implications to other purposes, perhaps even more magnificent and noble.