Fung Koo
January 7th, 2009, 02:15 PM
If we are going to select a scientific principle to apply to philosophical questions, why not Godel's Theorem which would tell us, given a goddess, there is now way we could describe the goddess because our system lacks the terms. But, we might be able to chart some consequences of the goddess existing.
Seems to me that Goedel's Theorem is pretty much just another way of saying the same thing.
I question your interpretation somewhat of "no way we could describe the goddess due to a lack of terms." The second incompleteness theorem describes the first incompleteness theorem as complete, and suggests that a second-order system is required to complete the first. It also indicates that a lower-order system cannot describe a higher order system of itself, and as such obeys the first incompleteness theorem such that any singular system is inherently incomplete.
So it's more like there are infinite terms, rather than no terms. Terms upon terms required to establish still more terms. And because it's infinite, it may as well be "no terms," but if "no terms" was the case then we'd be talking non-formal systems which, by definition, have no terms.
...ouch, that hurt. :rolleyes:
If we break that down into something a little more legibly colloquial, you might say it something like "Nothing can describe itself completely without reference to something else." If we infer the implications of the assertion to any functional material system (finite), we get interesting analogues with social interaction. Sort of like my assertion that sentience is necessarily reflective -- we aren't sentient unless we have another sentient thing to compare ourselves to. This also accords with the assertion that morality can't exist in a solitary system -- it only exists where two or more interacting systems create a reflection to define any single moral system.
Goedel's theorem isn't a loop, though. The second theorem completes the first, but the second theorem is demonstrably incomplete based on the application of the first theorem. So it's infinitely regressive and linear.
It also corresponds in that multiple systems (which we can substitute as what I keep calling "specifics," or in the philosophical term, a "logic") are required to establish the completeness of the larger system. Specifically, the theorem deals with the completeness of formal systems (logic), so essentially what we're talking here is that an infinite number of formal systems are required to complete any one finite formal system. (An infinite number of logics are required uphold any single logic -- no logic can prove itself.) In other words, the more you specify a particular quality of a thing (such a position of a particle), an infinite set of formal systems are required to support that specification. In the end, the infinite systems only prove the system, and that system's corresponding and non-exclusive specification.
Which, to me, is pretty much the exact thing that the uncertainty principle is saying. The more specifically we try to "locate" a thing, the less we know about everything other than the process/system/logic we used to locate the thing.
It also goes perfectly with the assertion that the Laws of the Universe are not Laws at all, but averages. Assuming we can define physics as a formal system, insofar as it attempts to describe the relationships between all functioning components of a more-or-less stable universe, then physics is just a formal system/logic as any other. If they were "laws" proper, then the set/system/logic would be finite and, according to Goedel's Theorem, incomplete by reference to itself. Something outside the laws would have to exist to complete the laws.
So then physics as a formal system/logic is necessarily incomplete. Indeed, any formal system/logic would be incomplete without a second order system/logic. Physics comes out of math, which Goedel has proven incomplete, so all sub-systems/logics that branch from any formal arithmetic system are just expanding second-order systems. It's incomplete without its pair, the non-formal system, or non-logic.
This is where the whole thing goes airy-fairy though, and into that bucket of impossible, non-linear, non-recursive, inductive thought. In other words, it goes to the classically feminine.
And then we get stuck in the Liar's Paradox, where we're requiring ourselves to apply rules to a thing that is, by definition, without rules and undefinable. You can't formalize the non-formal.
And we're back at God as the Ultimate Generalization.
Seems to me that Goedel's Theorem is pretty much just another way of saying the same thing.
I question your interpretation somewhat of "no way we could describe the goddess due to a lack of terms." The second incompleteness theorem describes the first incompleteness theorem as complete, and suggests that a second-order system is required to complete the first. It also indicates that a lower-order system cannot describe a higher order system of itself, and as such obeys the first incompleteness theorem such that any singular system is inherently incomplete.
So it's more like there are infinite terms, rather than no terms. Terms upon terms required to establish still more terms. And because it's infinite, it may as well be "no terms," but if "no terms" was the case then we'd be talking non-formal systems which, by definition, have no terms.
...ouch, that hurt. :rolleyes:
If we break that down into something a little more legibly colloquial, you might say it something like "Nothing can describe itself completely without reference to something else." If we infer the implications of the assertion to any functional material system (finite), we get interesting analogues with social interaction. Sort of like my assertion that sentience is necessarily reflective -- we aren't sentient unless we have another sentient thing to compare ourselves to. This also accords with the assertion that morality can't exist in a solitary system -- it only exists where two or more interacting systems create a reflection to define any single moral system.
Goedel's theorem isn't a loop, though. The second theorem completes the first, but the second theorem is demonstrably incomplete based on the application of the first theorem. So it's infinitely regressive and linear.
It also corresponds in that multiple systems (which we can substitute as what I keep calling "specifics," or in the philosophical term, a "logic") are required to establish the completeness of the larger system. Specifically, the theorem deals with the completeness of formal systems (logic), so essentially what we're talking here is that an infinite number of formal systems are required to complete any one finite formal system. (An infinite number of logics are required uphold any single logic -- no logic can prove itself.) In other words, the more you specify a particular quality of a thing (such a position of a particle), an infinite set of formal systems are required to support that specification. In the end, the infinite systems only prove the system, and that system's corresponding and non-exclusive specification.
Which, to me, is pretty much the exact thing that the uncertainty principle is saying. The more specifically we try to "locate" a thing, the less we know about everything other than the process/system/logic we used to locate the thing.
It also goes perfectly with the assertion that the Laws of the Universe are not Laws at all, but averages. Assuming we can define physics as a formal system, insofar as it attempts to describe the relationships between all functioning components of a more-or-less stable universe, then physics is just a formal system/logic as any other. If they were "laws" proper, then the set/system/logic would be finite and, according to Goedel's Theorem, incomplete by reference to itself. Something outside the laws would have to exist to complete the laws.
So then physics as a formal system/logic is necessarily incomplete. Indeed, any formal system/logic would be incomplete without a second order system/logic. Physics comes out of math, which Goedel has proven incomplete, so all sub-systems/logics that branch from any formal arithmetic system are just expanding second-order systems. It's incomplete without its pair, the non-formal system, or non-logic.
This is where the whole thing goes airy-fairy though, and into that bucket of impossible, non-linear, non-recursive, inductive thought. In other words, it goes to the classically feminine.
And then we get stuck in the Liar's Paradox, where we're requiring ourselves to apply rules to a thing that is, by definition, without rules and undefinable. You can't formalize the non-formal.
And we're back at God as the Ultimate Generalization.