......humans have knowledge only of things they directly experience.

And:

He developed the position that mental behaviour is governed by “custom”; our use of induction, for example, is justified only by our idea of the “constant conjunction” of causes and effects.

So, real probabilities depend on induction (which is justified by the idea of cause and effect).

Thus, knowledge of real probabilities and/or induction is humanly impossible.

Of course probability will be unreliable but there is, in theory, a probability we should assign to a major earthquake, given what we know.

A probability of a major earthquake is never exact at all and even if it is anywhere near the actuality of it occurring, it cannot tell precisely when or where it will occur and how devastating it will be.

What if what happens deviates from the real probability?

A 7 ?

So the difference between determinism and randomness is lack of knowledge

Lack of knowledge of what? Randomness still produces a deterministic result. The knowledge of the result is acquired when the die stops rolling. When, over time, this result on average yields a number 6 once every 6 rolls, we have acquired knowledge of the probability factor in this random form of determinism.

Perhaps, randomness may be called the causality and determinism the mathematical function which translates the random potentials into a result.

A probability of a major earthquake is never exact at all and even if it is anywhere near the actuality of it occurring, it cannot tell precisely when or where it will occur and how devastating it will be.

Same goes for roulette.

The point is there is a probability you should assign it depending upon your knowledge.

Lack of knowledge of what the variables are set to.

Stephen

We can never know all the variables, that would require omniscience. If we did we could predict the end of the universe to the last instant in time. We can’t even predict the result of the butterfly effect? That simple event can yield an infinity of deterministic results, most of which we could never anticipate. Some variables may be acquired at the Planck scale, an infinity of potentials which may be triggered under certain circumstances. We can only acquire knowledge of that which we can observe in reality. Even then it is a superficial knowledge at best. We might be able to acquire knowledge of universal constants from observation, but that again would only give us probabilities, never complete certainty.

Lack of knowledge of what the variables are set to.

Stephen

But variables are not set, that’s why they are called variables. When we talk about probabilities we are talking about a result of an event which has not yet happened and which produces or may be subject to dynamic variables while in process. We can never know what variables are present or will come into play. All we can do is assign a probability number.

But we do know that those complex combination of factors average out over time to cause any particular nunber to come up 1 out of 6 times.

Yes, which is why we can use probability as our guide.

But why do these complex combination of factors average out overtime?

I believe if we answer that satisfactorily we know a lot more about the universe than if we don’t.

Stephen

In answer to that question, (which may be akin to asking why is a normal distribution a bell curve or why is any discovered statistical principle or law of physics as it is or why is our universe deterministic?) it would be unsatisfying to say that’s just the way it is. Rather, I would propose that it may be that way because that is what works in a universe that we can survive in. If there were not some element of order, we would not exist. (I can probably come up with more radical ideas if that one does not suit you.)
I salute your persistence in questioning what many would simply accept as underlying assumptions.

In answer to that question, (which may be akin to asking why is a normal distribution a bell curve or why is any discovered statistical principle or law of physics as it is or why is our universe deterministic?)

I don’t think it’s akin to asking why is a law of physics the way it is. Where does the probability come from? Does it merely come from the frequency whith which things happen? Or does the frequency with which things happen come from the probability?

Probability is linked to knowledge but we want to somehow talk about it even without people with incomplete knowledge. Because we believe this is intrinsic to the universe somehow, regardless of whether there are people with some knowledge or not.

Rather, I would propose that it may be that way because that is what works in a universe that we can survive in. If there were not some element of order, we would not exist.

Yes but I think this misses how and why probability works, which I think has an answer in the way perhaps why are the laws of nature as they are doesn’t.

I salute your persistence in questioning what many would simply accept as underlying assumptions.

Lack of knowledge of what the variables are set to.

Stephen

We can never know all the variables, that would require omniscience. If we did we could predict the end of the universe to the last instant in time.

Right, so you are saying these probabilities would disappear with complete knowledge.

Stephen

No, complete knowledge would confirm the probabilities, not the actual results. Knowing that the die has six numbered sides from 1 to 6, will give us certainty that one of these numbers will come up, but not which specific number will emerge from vagueness (potentials).
What prevents us from saying that determinism may yield a variety of observable results, depending on the place and method of observation.
I am sure that the double slit experiment is deterministic in nature, but we cannot possibly observe the photons duality simultaneously. It is a probabilty wave until we observe the particle, which collapses the wave function. How can we acquire complete knowledge of a probility wave, without measurement? I doubt that the photon itself has knowledge of its own spacetime coordinates at any given moment.

No, complete knowledge would confirm the probabilities, not the actual results.

Are you saying that if I take a die and roll it there are six possible futures that can arises as a result, given the past and given the precise situation?

And that each of these are equal, so each has a probability of 1 in 6?

And I want to second Tim’s sentiments.
Stephen, you are an excellent teacher of critical thought. You even have me lie awake at nights, thinking about this…....