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Fascinating. How do philosophers and scientists react to Godel's incompleteness theorem w.r.t. falsification? To me, at least, it seems to suggest that falsific

Fascinating. How do philosophers and scientists react to Godel's incompleteness theorem w.r.t. falsification? To me, at least, it seems to suggest that falsification is a flashlight that for whatever reason fails to illuminate certain otherwise possible paths. (I understand that the theorem applies in the context of "consistent" formal systems, and that falsification is about the process of refining models of systems to be more consistent. It's interesting that the emergent properties of the pursuit of falsification bring about a paradoxical system in the limit.)

lutusp 14y ago
> How do philosophers and scientists react to Godel's incompleteness theorem w.r.t. falsification? I can't speak for philosophers, but as to scientists, the issue of falsification and irreducible uncertainty are separate in nearly all cases. Remember that the Incompleteness Theorems address true assertions that cannot be proven within reasonably complex axiomatic systems -- that's a fair remove from empirical science, just as mathematics is. > To me, at least, it seems to suggest that falsification is a flashlight that for whatever reason fails to illuminate certain otherwise possible paths. Not at all. Falsification is a very reliable test that can be used to eliminate theoretical assertions from any further consideration, as in the classic "black swan" example already given above. It's unambiguous. > It's interesting that the emergent properties of the pursuit of falsification bring about a paradoxical system in the limit. No, neither paradoxical nor ambiguous. A classic falsification has properties that eliminate theories from consideration, period, full stop. Examples abound -- the Ptolemaic system, the ether theory, phlogiston, and so forth.
- politician 14y ago
  Is empirical science really so far removed from complex axiomatic systems? Isn't the point to learn how all of this universe works together? Suppose we solve gravity, QM, and the rest, then we'll have a complex system of rules which nevertheless must be incomplete and therefore flawed. I think that's fascinating -- Sisyphus is Science (not that we don't discover useful and amazing results along the way!).
  - lutusp 14y ago
    > Is empirical science really so far removed from complex axiomatic systems? Yes, absolutely. Empirical science is driven by observations of nature. Axiomatic systems are much more self-referential. It is the self-referential property of axiomatic systems that lie at the heart of the Incompleteness Theorems. > Isn't the point to learn how all of this universe works together? Which universe? That of nature, or that of intellectual representations? They differ in some very basic ways. > Suppose we solve gravity, QM, and the rest, then we'll have a complex system of rules which nevertheless must be incomplete and therefore flawed. Most people who understand Gödel's work will argue that the effect of the Theorems is overstated with respect to what we can reliably know about nature. If we find a TOE (Theory of Everything), it will probably remain incomplete, not because of Gödel, but because of irreducible observational imperfections.
    - politician 14y ago
      Of nature. Although, now I'm questioning whether I've misunderstood the goal to be a TOE, when perhaps it's more incremental and unguided.

lutusp 14y ago

> How do philosophers and scientists react to Godel's incompleteness theorem w.r.t. falsification? I can't speak for philosophers, but as to scientists, the issue of falsification and irreducible uncertainty are separate in nearly all cases. Remember that the Incompleteness Theorems address true assertions that cannot be proven within reasonably complex axiomatic systems -- that's a fair remove from empirical science, just as mathematics is. > To me, at least, it seems to suggest that falsification is a flashlight that for whatever reason fails to illuminate certain otherwise possible paths. Not at all. Falsification is a very reliable test that can be used to eliminate theoretical assertions from any further consideration, as in the classic "black swan" example already given above. It's unambiguous. > It's interesting that the emergent properties of the pursuit of falsification bring about a paradoxical system in the limit. No, neither paradoxical nor ambiguous. A classic falsification has properties that eliminate theories from consideration, period, full stop. Examples abound -- the Ptolemaic system, the ether theory, phlogiston, and so forth.

politician 14y ago
Is empirical science really so far removed from complex axiomatic systems? Isn't the point to learn how all of this universe works together? Suppose we solve gravity, QM, and the rest, then we'll have a complex system of rules which nevertheless must be incomplete and therefore flawed. I think that's fascinating -- Sisyphus is Science (not that we don't discover useful and amazing results along the way!).
- lutusp 14y ago
  > Is empirical science really so far removed from complex axiomatic systems? Yes, absolutely. Empirical science is driven by observations of nature. Axiomatic systems are much more self-referential. It is the self-referential property of axiomatic systems that lie at the heart of the Incompleteness Theorems. > Isn't the point to learn how all of this universe works together? Which universe? That of nature, or that of intellectual representations? They differ in some very basic ways. > Suppose we solve gravity, QM, and the rest, then we'll have a complex system of rules which nevertheless must be incomplete and therefore flawed. Most people who understand Gödel's work will argue that the effect of the Theorems is overstated with respect to what we can reliably know about nature. If we find a TOE (Theory of Everything), it will probably remain incomplete, not because of Gödel, but because of irreducible observational imperfections.
  - politician 14y ago
    Of nature. Although, now I'm questioning whether I've misunderstood the goal to be a TOE, when perhaps it's more incremental and unguided.