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wedrifid comments on Bayes Slays Goodman's Grue - Less Wrong
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Comments (120)
You don't need Bayes to solve 'grue' problems. Merely reductionism.
Explain please
"Goodman's Grue" just doesn't seem to be a problem at all. It can only seem like a problem if you forget that 'grue' is a name given to a somewhat complex sequence of events (relative to a thing just being a color) and start making mistakes when manipulating the symbol. There just isn't any reason to suppose there is any 'threat to the whole of science' in the first place.
I agree, you are essentially saying that if you forget that green and blue are not simply syntactical binary predicates from first order logic – if you remember that they are semantic concepts, then it is clear that the grue problem is not at all a threat to science. But this is no trivial result, it means that there is a part to the application of Bayes, i.e., induction, which requires the acquisition of semantic concepts. If you fed evidence statements into a bayesian program, it would have to have an understanding of the semantic application of terms like green and grue. So you are right: reducing "green" and "grue" to their semantic/physical tests is the key in my proposed solution. Bayes can't be enough, obviously, since bayes is a syntactical and axiomatic system.
I guessed what seemed bayesian to me about the whole thing was the analogy to bayse's table problem, which was the main intuition pump I used to solve the problem. I'll edit the article to reflect this. Thanks
I think this is incorrect. The actual application of Bayes' theorem works the same way for each of your theories. What differs is your priors, and that difference sticks around until you have some evidence that's more likely for one theory than another. If your priors are screwy, then yes, you'll hold wrong beliefs until you're given evidence that lets you distinguish between the correct and incorrect beliefs.
Ahh, that makes sense!
The first thing that struck me was the inherently self-contradictory nature of the grue definition. For physical properties to be retroactively alterable seems to contradict fundamental principles of causality and matter.
Am I simply not understanding the topic? Or is my intuitive-conceptualization too influenced by "timeless physics"? (The notion that all moments in time can be stated to 'exist').
The most you get with statements about "grue-ness" is that some objects which we observed to be "green" were in fact green but after a specific time (T) all changed to another color. This does not change the fact that they were green in the past.
Science seems perfectly-well suited to handling things that change from one state to another. Radioactive decay, for example. If this is some extra-material transition that occurs... well, I just don't see how that's an actually available physical phenomenon. If you change the definition of the term, you are now discussing a new thing.
you are missing the point. nothing changes color. and no definitions are changed, only meanings.
... but meanings are definitions. You can't change one without changing the other. The terms are synonyms.
Time-based definitions just mean you use one definition before time T and another definition after time T. I am lost as to what the paradox here is.
defenitions point to meanings, but the meaning of a term can only be found by looking at the cognitive machines that use the term, and in that specific contxt as well.
...
definition:
A statement of the exact meaning of a word, esp. in a dictionary.An exact statement or description of the nature, scope, or meaning of something.meaning:
What is meant by a word, text, concept, or actionDefinitions are meanings. And meanings are definitions.
A ⊃ B & B ⊃ A ⊨ A = BI remain lost as to where the paradox is supposed to be.
The quotes you give suggest definitions are statements of meaning, not meanings.
Would you similarly say that "mortal" is a term with a self-contradictory definition?
wedrifid is pointing to the destination of the road that I'm going down in the comment branch over here, I think.