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QM could be right.
Relativity and QM contradict
The situation (our current understanding which has value) looks nothing like we'll end up keeping one and rejecting the other.
I don't see how these statements can be consistent.
...if relativity and QM contradict, and QM turns out to be right, I'd expect us to reject relativity. Do you agree?
As far as partly right theories that have value: if we know quantum theory is not completely right, then we've ruled out the hypothesis 'quantum theory' and are now dealing with the hypothesis space of theories that share some parts with quantum theory.
T in this case is not atomic; it is itself a conjunction of a lot of statements. So I agree that I theory known to be inaccurate in some cases can be useful, in that it may contain some true components as well as some untrue ones. But this is rather different than how we treated it when we thought it could be true in its own right.
In general, I agree that there are certain ideas in science that aren't propositions in Bayesian sense, and that treating them as if they were is a serious mistake. I don't think that this means that there's something wrong with the probability probability calculus, however.
Relativity and QM contradict but we don't know which is mistaken or why. Either one, individually, could be true in its own right.
The situation (our current understanding which has value) looks nothing like we'll end up keeping one and rejecting the other.
I don't see how these two statements can be consistent. If either one, individually, could be true in its own right, then why wouldn't we won't end up keeping one? If they contradict, then why wouldn't we reject the other?
By the way, is there an explanation of the current status of LessWrong and LessWrong2.0, and could some one give me the link? I've found a few mentions of it, but am still slightly confused.
He's saying we use them both, and that has value, even though we know there must be some mistake somewhere. Saying "or" misrepresents the current situation. Both of them seem to be partly right. The situation (our current understanding which has value) looks nothing like we'll end up keeping one and rejecting the other.
I haven't much knowledge of physics, and though that he was discussing the idea of two mutually exclusive theories which we use both of. From what you're saying, it sounds more like the crucial point is that they are presumably false, but still useful. Is that a good description of the situation?
As far as partly right theories that have value: if we know quantum theory is not completely right, then we've ruled out the hypothesis 'quantum mechanics' and are now dealing with the hypothesis space of theories relevantly similar to quantum theory. So I agree that I theory known to be inaccurate in some cases can be useful, but by treating it as a piece of evidence towards the truth, which is rather different than how we treated it when we thought it could be true in its own right.
(Epistemic status: sufficiently abstract that I can't be very confident without more familiarity with the topic)
(1) the objective of science is, or should be, to increase our ‘credence’ for true theories
I would suggest that it should also decrease our credence in false theories, and allow us to correctly estimate the likelyhood of conjectures not yet proven or disproved.
However, if T is an explanatory theory (e.g. ‘the sun is powered by nuclear fusion’), then its negation ~T (‘the sun is not powered by nuclear fusion’) is not an explanation at all.
Well, no - it's a set of explanations. A very large set, consisting of every explanation other than ‘the sun is powered by nuclear fusion’, but smaller than T | ~T, and therefore somewhat useful, however slightly.
Therefore, suppose (implausibly, for the sake of argument) that one could quantify ‘the property that science strives to maximise’.
Per the first line, we are supposing this property to be 'our credence in true theories'
If T had an amount q of that, then ~T would have none at all, not 1-q as the probability calculus would require if q were a probability.
All else being equal, if we come to believe T, our credence in true theories will be higher by 1 - p, where p is our previous credence in T. If we come to believe ~T, our credence in true theories will be lower than if we were uncertain by p.
I'm not sure that it makes sense in this context to assign a value of ‘the property that science strives to maximise’ to a statement. It's not a property of statements alone but of our belief in them.
If you want to assign a value of q to near-absolute confidence in T, I would say that it's 1 - ϵ. Thus, the ~t has near-zero value as far as the objective of science is concerned, and also has 1-q + ϵ = 0 + ϵ as the laws of probability demand.
Also, the conjunction (T₁ & T₂) of two mutually inconsistent explanatory theories T₁ and T₂ (such as quantum theory and relativity) is provably false, and therefore has zero probability. Yet it embodies some understanding of the world and is definitely better than nothing.
(Assuming for the sake of example that quantum theory and relativity mutually inconsistent, but both likely,) T1 & T2 is provably false, and indeed idea that quantum theory and relativity are both true is nonsense. T1 | T2, on the other hand, embodies some understanding of the world and is definitely better than nothing.
Is it acceptable to cross-post on threads like this? I’ve recently been wanting to post the same thing here and on the SSC Discord and perhaps in a few other places, since all of these communities are small enough that I don’t always expect to get much response, and while there’s a lot of overlap, it’s far from complete.
Also, actually writing up what I want to say sometimes presents a large barrier; if I re-use what is for me the hardest part, namely starting a conversation, I’d be more likely to start actively participating.