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File: ec515060cc09d01⋯.png (307.76 KB,795x323,795:323,phpJRHxNo.png)

7ede90 No.6366

What is the ontological status of non measurable functions (particularly over a probability space)? Would their existence mean that the form of determinism which claims predictability of all existing behavior is false?

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f096a6 No.6369

What is an "ontological status"?

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f096a6 No.6370

And why do you think that you might hit upon an argument against determinism this way? Because it's a rather roundabout way, because when you're dealing with probabilities you're already somewhat removed from a purely deterministic domain.

But anyway, I'm merely acquainted with those things you've mentioned, but if the issue is that you either can't associate probabilities to certain events, or that you can't predict higher or lower order moments of their probability function, or that if we insist on associating probabilities with such events they don't work out the way they were supposed to, that doesn't immediately lead to some argument against determinism unless this unpredictability can be proven to be a real property of the things in question. This might be the "ontological status" you're looking for, I dunno.

But I don't think there's any determinist or sympathizer which believes that everything everywhere must be predictable to everyone, otherwise they might as well worry about e.g. non-computable functions, but I don't see anyone sweating those either. Any issues relating to all those things: non-computability, non-measurability and unpredictability are more likely to chucked all into the same basket, labelled "mathematical nonsense abstractions".

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3e4fb9 No.6374

>>6370

>But I don't think there's any determinist or sympathizer which believes that everything everywhere must be predictable to everyone

I disagree. I think there are lots of people who claim that all natural phenomena are inherently predictable/computable.

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5ead51 No.6403

If something is non-measureable, it's either:

>not-yet-measured

Something which is complely possible to measure, but we either dont have the means, or simply haven't bothered to measure it. Irrelevant to the question in hand.

>relatively unmeasurable

Something which is apparently unmeasureable due to the limitation of human perception, but can be indirectly measured due to it's relation with other, measurable, objects. A simple example of this in the field of physics would be radiation.

>absolutely unmeasurable

Something which is completely impossible to be comprehended by the human perception. Now, here we fall into the dillema you proposed: Are absolutely unmeasurable formally unmeasurable (ontologically, by essence) or materially unmeasurable(impossible to be measured simply by the limitation of human perception)? Well, due to the inherent nature of the object of this question, it's impossible to determine weather it's material or formal, thus making this discussion irrelevant.

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eae079 No.6411

>>6366

What is the ontological status of a set, its elements, and functions defined on them?

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