The intellectual iconoclast,
, has engaged in disciplined thoughts and in disciplined experiments which led him to conclude that probability does not exist.If it doesn’t exist, then it is not a thing in the world, but only a tool of cognition.
An example of something that does not exist as a thing, but is still useful as a tool of cognition is the imaginary number, i, such that i-squared is equal to -1. No real number, once multiplied by itself, ever gives -1 though.
Only imaginary (made up) ones do.
The basic question now becomes:
Is probability more like imaginary numbers, useful for certain mental acts of cognition?
Or is probability more like Karl Popper’s “propensity theory”?
I’m in the propensity camp, but Briggs argues against probability being an inherent propensity for a thing to turn out a certain way. Briggs argues that too many unspoken assumptions will affect outcomes, so that even a flipped coin will not “have” a probability.
He even created a machine that makes coin flips all come out heads.
In the comments to that post by Briggs (who doesn’t believe in the “inherent existence” of probability) which I linked to above, I wrote this:
But let me change gears: What about a true existence of a relationship between probabilities?
A single coin is flipped two thousand times. The first thousand outcomes are compared with the second thousand outcomes. The probability of the first thousand outcomes having more than 51% heads (~0.25 with a fair coin) is compared with the probability of the second thousand outcomes having less than 41% heads (~0.000000007 with a fair coin).
With a fair coin, the first outcome is 36 million times more likely to occur. Even when the coin is only close to being fair, there will be a stable relationship between the probabilities (one being "inherently" higher than the other).
Claim: Repeating the 2,000-flip experiment 100 trillion more times will lead to no (zero) instances where the ratio of these two probabilities "reverses" -- i.e., formerly higher one becomes lower one -- just as if the probability relationship has "true existence" in the world.
Addendum: It is assumed that a coin which warps over time, becoming one with a visible bend in it, disqualifies the test.
Reference
[uses of imaginary numbers] — https://www.mathsisfun.com/numbers/imaginary-numbers.html
[the propensity theory of probability] — https://plato.stanford.edu/entries/probability-interpret/