1) the only way we have to value one idea over another is through predictive ability
2) there are infintely many ways that could be 'the way it is' that all give the same answers for all data we can ever collect(infintely many models which describe all the data).
3) since the only way we can come to value one model over another is through one making better predictions than another, there is no way we can choose between this infinitude of 'perfect' models
4) we cannot know 'the way it is'
5) we feel compelled to answer questions of the form 'does X exist?'
6) since we cannot know 'the way it is', we cannot answer these questions in the strong sense, all we can do is give an answer from within the currently best model we have.
7) hence, under this interpretation of 'exists', the existence of something is man-dependent.
In objection to (1), we could claim some sort of preference for 'simplicity' of the model. This may be a good practical
consideration(a mathematically simpler model is easier to work with and milk predictions from), but we are not justified
in making the leap from 'simpler models are preferable for practical reasons' to 'simpler models describe the way it is'.
A thought experiment:
Assume mankind has reached a point in history where it has 'perfect' models of the universe (where 'perfect' means something like 'makes the most accurate possible predictions'). Say we have 'perfect models' M1, M2, M3, ...
The 'particles' in M1 are infinitely divisible (that is, M1 is a 'continuous model').
The 'particles' in M2 are not (that is, M2 is a 'discrete model').
Jones asks Smith, "is the universe continuous?"
Smith believes M1, so he says "yes!"
Jones believes M2, so he says "no way!"
who is correct? there is no argument, it seems to be a matter of faith.//
We aren't there yet. Could we ever know that we were there? How could we ever know that we weren't missing some piece of
data? Perhaps 'the way it is' changes in some complicated fashion every 100,000 years or so, making our models obsolete.
We really can't know that we are done taking data. So we won't ever need to have faith in one model over another. We can
always be in the state of 'I don't know which one is better, but I am actively collecting data in hopes of finding out, or
at least refuting one of them'.
6 comments:
why not value the true model?
even if we cannot ever know what the true model is, it seems that the best model is the one that models 'the way it is'.
a valid argument in this vicinity might go as follows:
1) the best model is the right one.
2) we cannot know which model is right.
3) thus, we cannot know which model is best.
but it is probably unsound cause (2) seems false or it at least it needs some argument in its favor.
(2) is precisely what i proved there. that was the argument in its favor.
there is no "best model" (given a model i can produce infinitely many distinct models giving the same predictions). that's the point.
Your post proves my (2), i.e. that we cannot know which model is right?
seems to me that it was simply asserted in your (4): we cannot know 'the way it is'
i assume the right model is the model that models the way it is.
also my sample argument there was for a conclusion about our knowledge of the best model not about whether or not there is a best model. so even if that argument is sound, it still could be that there is a best model.
what? (4) is a conclusion from (1), (2), (3).
you mean something different by "model" than i do. it seems that you think that when i lay out two models A and B and start tallying their merits, i can say "well, A is the right one, so +1 in its favor". but we can never, ever know such a thing -- if we already know which one is the right one, then why are we tallying?
this is about what we can know (which is all that matters -- from what we know we can postulate infinitely many "ways that it is" that fits with everything we know). talking about "the true model" is just worthless (literally worthless) idle speculation. you'd be better off talking about the collection of all models that are consistent with the data we have (an infinite collection). so, you could talk about
"the true models" -- the ones that predict everything.
what about this situation:
we have two models A and B.
A is much much simpler to work with and compute with than B (not to mention much more elegant).
A and B give precisely the same predictions (that is, they are equivalent).
however, it just happens to be the case that "the way it is" corresponds to B, not to A.
you would still claim that B is the best model. i would claim that A is a better model.
Per your example, M1 and M2 are both perfect models and thus they both make the most accurate predictions possible so they must be exactly the same predictions.
If this is true, then doesn't the fact that one is continuous and the other discrete meaningless? I don't think it is a matter of faith. It seems like it is saying that 3+1 and 2+2 both predict the same result, so which is correct? Both are man made abstractions of the same result. So M1 and M2 are exactly the same model. Until they start giving different predictions that is.
you are correct that M1 and M2 make identical predictions.
the fact that one is continuous and the other is discrete is meaningless if you are working in the quotient space of models in which two models are equivalent just in case they make the same predictions. in this space, they are the same model.
i think this is where we should work and i was attempting to demonstrate this.
by saying that picking one over the other was a matter of faith, i was saying that the distinction has no bearing on anything (that is, it is meaningless).
since it seems that your notion of sameness of models is already "make the same predictions", the post was not intended to convince you of anything.
it was intended to convince people that like to ask questions of the form "does X exist?", in the strong sense.
They ask,
"do electrons exist?"
and i say "Well, perfect model A posits electrons, but perfect model B posits no particles whatsoever."
they say "well which one is the True model?".
i say "1) we can't know, so stop asking. 2) even if we could know, the knowledge would be useless."
now they don't like that one bit. they have this need to "have it all settled" (as far as i'm concerned, there is nothing to settle), so they are forced to make a choice between A and B on faith (they might call it "intuition").
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