I can see your point, and it’s the one most people implicitly accept. Observations are predictable, therefore there is a shared reality out there generating those observations. It works most of the time. But in the edge cases (or “extremely fine details”) this implicit assumption breaks down. Like in the case of “objective mathematical facts waiting to be discovered”, such as the 98,765th of π before you measure it. So why insist on applying this assumption outside of its realm of applicability? Isn’t it sort of like insisting that if you shoot a bullet from a ship moving with nearly the speed of light, it will travel faster than light?
You seem to be saying that “external shared reality” is an approximation in the same way that Newtonian mechanics is an approximation for Einsteinian relativity. That’s fine. So what is “external shared reality” an approximation of? Just what exactly is out there generating inputs to my senses, and by what mechanism does it remain in sync with everyone else (approximately)?
Just what exactly is out there generating inputs to my senses, and by what mechanism does it remain in sync with everyone else (approximately)?
Sometimes the “out there” can be modeled as a shared reality, sure. The key word is “modeled”. Sometimes this model is not a good one. If you insist on privileging one model over all others to be the true objective external reality valid everywhere, you pay the price where it fails. Like in the OP’s case.
Having read through the above discussion, I don’t think you have distinguished between the claim that there are mathematical entities, and the claim that there are mathematical facts. The latter can mean nothing more than different mathematicians will find the same solutions to a given problem, which you accept. Call the second claim epistemological realism, and the first metaphysical realism. To argue that convergence on a set of facts can only be, or be explained by, form of metaphysical realism is to give to much credence to realism. Metaphysical realism about mathematical entities , Platonism, is much more controversial than realism about physical bodies.
By “good” I mean (as always) “fitting the available observations and producing accurate predictions”. In the OP’s case of the 98,765th digit of π, the model is that “A randomly picked digit is uniformly distributed” and it is a “good” (i.e. accurate) one.
There’s a puzzle about how probability theory would apply would apply to something that’s basically determinate, but the question of how randomly selected digits of pi are distributed isn’t it, because the process of picking a digit randomly bring indeterminacy in.
People pose the problem with a specific digit to make the problem determinate, and focus on the paradoxical aspect.
The paradox only arises if you ignore the view I’ve been presenting. The 98,765th digit of π is a random digit in the same way that a 98,765th reading of rand() is. Until you do some work to measure it, it’s not determined.
It is determined in the sense of having only one possible value. The same applies to a call to rand() ,so long as it is a deterministic PRNG. We don’t know what the answer is , until we have done some work, in either case, but that doesn’t mean anything indeterministic is going on. Determinism is defined in terms of inevitability, ie. lack of possible alternatives. We do not regard the future as undeterminedjust because it has not happened yet.
Determinism is defined in terms of inevitability, ie. lack of possible alternatives. We do not regard the future as undetermined just because it has not happened yet.
I don’t argue with that, in fact, the statement above makes my point: there is no difference between an as-yet-unknown to you (but predetermined) digit of pi and anything else that is not yet known to you, like the way a coin lands when you flip it.
It doens’t make your point, since I don’t agree with it.
Given any degree of realism, you can differentiate between determined but unknown things and undetermined things.
Well, you’re an anti realist. But that doesn’t give you the right to interpret what other people, if there are any other people, are saying in anti-realist terms.
I can see your point, and it’s the one most people implicitly accept. Observations are predictable, therefore there is a shared reality out there generating those observations. It works most of the time. But in the edge cases (or “extremely fine details”) this implicit assumption breaks down. Like in the case of “objective mathematical facts waiting to be discovered”, such as the 98,765th of π before you measure it. So why insist on applying this assumption outside of its realm of applicability? Isn’t it sort of like insisting that if you shoot a bullet from a ship moving with nearly the speed of light, it will travel faster than light?
You seem to be saying that “external shared reality” is an approximation in the same way that Newtonian mechanics is an approximation for Einsteinian relativity. That’s fine. So what is “external shared reality” an approximation of? Just what exactly is out there generating inputs to my senses, and by what mechanism does it remain in sync with everyone else (approximately)?
Sometimes the “out there” can be modeled as a shared reality, sure. The key word is “modeled”. Sometimes this model is not a good one. If you insist on privileging one model over all others to be the true objective external reality valid everywhere, you pay the price where it fails. Like in the OP’s case.
Having read through the above discussion, I don’t think you have distinguished between the claim that there are mathematical entities, and the claim that there are mathematical facts. The latter can mean nothing more than different mathematicians will find the same solutions to a given problem, which you accept. Call the second claim epistemological realism, and the first metaphysical realism. To argue that convergence on a set of facts can only be, or be explained by, form of metaphysical realism is to give to much credence to realism. Metaphysical realism about mathematical entities , Platonism, is much more controversial than realism about physical bodies.
“Sometimes this model is not a good one.”
What do you mean by “good” here? And, given some definitiin of good, what alternative model is better in that sort of situation?
By “good” I mean (as always) “fitting the available observations and producing accurate predictions”. In the OP’s case of the 98,765th digit of π, the model is that “A randomly picked digit is uniformly distributed” and it is a “good” (i.e. accurate) one.
..isn’t a random digit, it’s the 98,765th digit.
There’s a puzzle about how probability theory would apply would apply to something that’s basically determinate, but the question of how randomly selected digits of pi are distributed isn’t it, because the process of picking a digit randomly bring indeterminacy in.
People pose the problem with a specific digit to make the problem determinate, and focus on the paradoxical aspect.
The paradox only arises if you ignore the view I’ve been presenting. The 98,765th digit of π is a random digit in the same way that a 98,765th reading of rand() is. Until you do some work to measure it, it’s not determined.
It is determined in the sense of having only one possible value. The same applies to a call to rand() ,so long as it is a deterministic PRNG. We don’t know what the answer is , until we have done some work, in either case, but that doesn’t mean anything indeterministic is going on. Determinism is defined in terms of inevitability, ie. lack of possible alternatives. We do not regard the future as undeterminedjust because it has not happened yet.
I don’t argue with that, in fact, the statement above makes my point: there is no difference between an as-yet-unknown to you (but predetermined) digit of pi and anything else that is not yet known to you, like the way a coin lands when you flip it.
It doens’t make your point, since I don’t agree with it.
Given any degree of realism, you can differentiate between determined but unknown things and undetermined things.
Well, you’re an anti realist. But that doesn’t give you the right to interpret what other people, if there are any other people, are saying in anti-realist terms.
Right, never mind, for a moment what your discourse style is. Disengaging.