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> The big idea in 20th century science, philosophy of science, and mathematics was that the truth is fundamentally unreachable. We got quantum mechanics as the

by JadeNB 4y ago

> The big idea in 20th century science, philosophy of science, and mathematics was that the truth is fundamentally unreachable. We got quantum mechanics as the foundation of reality. We got the idea that experiments can only rule out explanations but not establish the truth. We got used to probabilistic estimates based on data. We got all those uncomfortable results about the incompleteness and undecidability of formal systems. I am not an experimental scientist or philosopher, but I am a mathematician, and I thoroughly reject the claim that the big idea of 20th-century mathematics is that the truth is fundamentally unreachable. To be sure, we found that one can speak meaningfully, and rigorously, of the limits of decidability; but only an algorithmic view of mathematics will lead one to conclude that this makes the truth unreachable. Perhaps one could advance the claim that certain truths are unreachable (I do not, and find the claim woolly), but that is quite different from saying that truth itself is unreachable.

analog31 4y ago
I'm an experimental scientist. My take would be that truth is reachable, but the Truth with a capital T is a potentially meaningless throwback to a past age of certainty. What I mean is that some theories have been corroborated to the point that they can be regarded as "truth" for all intents and purposes, and despite known limitations in some cases. Examples might include electromagnetism, quantum mechanics, gravitation, and biological evolution. Regarding those theories, we can still say that we accept them on a tentative basis, but it would not be irrational to assign a vanishingly low likelihood that any of them will be radically overturned.
- naasking 4y ago
  Radically overturned is an overstatement I think. The theories you've listed are all tautologically valid in the domains in which we've tested them. What will happen is that either they will continue to hold in new domains where they haven't yet been tested, or we will discover a more general theory that will reduce to these theories in the limit.
  - jhanschoo 4y ago
    Indeed, to illustrate; Einstein and Planck doesn't mean that for most of our lived experience and work, classical mechanics offers a far more useful model of the world.
jltsiren 4y ago
I was referring to the crisis in the early 20th century, when the paradoxes and inconsistencies in the foundations of mathematics became too troublesome to ignore. The crisis was eventually resolved, but the mathematics that arose from it was more limited in scope than what earlier mathematicians had hoped. That is usually not a major concern if you work in mathematics, but it was a significant change in the understanding of the nature of truth.

by JadeNB 4y ago

analog31 4y ago

I'm an experimental scientist. My take would be that truth is reachable, but the Truth with a capital T is a potentially meaningless throwback to a past age of certainty. What I mean is that some theories have been corroborated to the point that they can be regarded as "truth" for all intents and purposes, and despite known limitations in some cases. Examples might include electromagnetism, quantum mechanics, gravitation, and biological evolution. Regarding those theories, we can still say that we accept them on a tentative basis, but it would not be irrational to assign a vanishingly low likelihood that any of them will be radically overturned.

naasking 4y ago
Radically overturned is an overstatement I think. The theories you've listed are all tautologically valid in the domains in which we've tested them. What will happen is that either they will continue to hold in new domains where they haven't yet been tested, or we will discover a more general theory that will reduce to these theories in the limit.
- jhanschoo 4y ago
  Indeed, to illustrate; Einstein and Planck doesn't mean that for most of our lived experience and work, classical mechanics offers a far more useful model of the world.

jltsiren 4y ago

I was referring to the crisis in the early 20th century, when the paradoxes and inconsistencies in the foundations of mathematics became too troublesome to ignore. The crisis was eventually resolved, but the mathematics that arose from it was more limited in scope than what earlier mathematicians had hoped. That is usually not a major concern if you work in mathematics, but it was a significant change in the understanding of the nature of truth.