The End of Philosophy
11/19/21 06:25 PM Filed in: Natural Theology | Philosophy
Bertrand Russell was working on his "Principia Mathematica" in an attempt to prove that mathematics was both consistent and complete. That is, it was consistent in that it contained no self-contradictory statements. It was complete, in that it could prove all true theorems.
While Russell was working on his Principa, Kurt Gödel's Incompleteness Theorems came along and proved that a self-describing system (i.e. a system that is sufficiently complex to express the basic arithmetic of the natural numbers) cannot simultaneously be consistent and complete. If it's consistent, it's not complete; if it's complete, it isn't consistent.
This ended Russell's lifelong dream. While his Principa is a tremendous intellectual achievement, it did not - and could not - achieve the goals Russell had for his work.
If nature is self-describing (as I think the posts on Natural Theology will show, once they're organized and edited for clarity), then philosophy suffers the same problem as mathematics. Empirically, the universe appears to be consistent. If we put a stake in that position, then all descriptions of nature will be incomplete. There will be no final "theory of everything."
If that's so then, observationally, there are questions for which we cannot know the answers. One such question is on the ontological nature of endlessness (infinity). Is endlessness emergent from a finite universe, or is the universe infinite and what we perceive as reality a quantization of this continuity? It's interesting that the theory of relativity is based on an infinitely continuous picture of nature. Quantum mechanics is based on a discrete picture of nature. String theory tries to split the difference by postulating tiny vibrating strings, but if nature has continuous/discontinuous duality like matter has wave/particle duality, then string theory may, like Russell's Principa, fall short of its intended goal.
Another such question is the nature of randomness. Does randomness indicate purposelessness (as the naturalists claim) or does it indicate hidden purpose (as the theists claim)? The value of 𝜋 can be computed by a deterministic formula. It can also be calculated via Monte Carlo methods (see Buffon's Needle). Therefore, the use of randomness does not preclude agency. Nor does it establish it.
Given that these questions cannot be answered, I propose "Newton's" Third Law of Metaphysics: there are some fundamental questions for which for every answer there is an equal and opposite answer. A corollary to this is that the question of the existence/non-existence of God is in this class. Certainly, the inability over thousands of years of arguing to establish a decisive conclusion is evidence of this principle. Or it may be that the right insight hasn't yet been achieved. An answer which is also evidence of this principle.
I think Gödel has done to philosophy what he did to math. Philosophy won't end, since math didn't end. But it will put limits on what philosophy can say about certain things. I said as much in the post "Epistemology and Hitchens" but that was before I think that the idea that nature is self-describing could be demonstrated from the ground up.
While Russell was working on his Principa, Kurt Gödel's Incompleteness Theorems came along and proved that a self-describing system (i.e. a system that is sufficiently complex to express the basic arithmetic of the natural numbers) cannot simultaneously be consistent and complete. If it's consistent, it's not complete; if it's complete, it isn't consistent.
This ended Russell's lifelong dream. While his Principa is a tremendous intellectual achievement, it did not - and could not - achieve the goals Russell had for his work.
If nature is self-describing (as I think the posts on Natural Theology will show, once they're organized and edited for clarity), then philosophy suffers the same problem as mathematics. Empirically, the universe appears to be consistent. If we put a stake in that position, then all descriptions of nature will be incomplete. There will be no final "theory of everything."
If that's so then, observationally, there are questions for which we cannot know the answers. One such question is on the ontological nature of endlessness (infinity). Is endlessness emergent from a finite universe, or is the universe infinite and what we perceive as reality a quantization of this continuity? It's interesting that the theory of relativity is based on an infinitely continuous picture of nature. Quantum mechanics is based on a discrete picture of nature. String theory tries to split the difference by postulating tiny vibrating strings, but if nature has continuous/discontinuous duality like matter has wave/particle duality, then string theory may, like Russell's Principa, fall short of its intended goal.
Another such question is the nature of randomness. Does randomness indicate purposelessness (as the naturalists claim) or does it indicate hidden purpose (as the theists claim)? The value of 𝜋 can be computed by a deterministic formula. It can also be calculated via Monte Carlo methods (see Buffon's Needle). Therefore, the use of randomness does not preclude agency. Nor does it establish it.
Given that these questions cannot be answered, I propose "Newton's" Third Law of Metaphysics: there are some fundamental questions for which for every answer there is an equal and opposite answer. A corollary to this is that the question of the existence/non-existence of God is in this class. Certainly, the inability over thousands of years of arguing to establish a decisive conclusion is evidence of this principle. Or it may be that the right insight hasn't yet been achieved. An answer which is also evidence of this principle.
I think Gödel has done to philosophy what he did to math. Philosophy won't end, since math didn't end. But it will put limits on what philosophy can say about certain things. I said as much in the post "Epistemology and Hitchens" but that was before I think that the idea that nature is self-describing could be demonstrated from the ground up.
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