Impossibilism is the position that free will does not exist and is simply impossible.

It seems to be the height of hubris to make such a claim, since logically "proving" that determinism exists is itself "impossible."

A "proof" of determinism is not something that can be done with logic. Determinism is a physical question or theory so it depends on experimental evidence.

But experiments can only provide statistical evidence, with an estimated probability.

Determinism in classical physics is an idealization and an approximation.

Determinism is an emergent property that shows up for large numbers of elementary particles, which as individuals or in small numbers are more accurately described with indeterministic quantum physics. All the laws of physics are statistical laws. All are the consequence of averaging over the irreducible quantum indeterminacy of the elementary particles.

This averaging over large numbers of particles is similar to the "law of large numbers" of random events in statistics and probability theory. The statistics in physical experiments are distributed in a "normal distribution" around a mean value. The larger the numbers of experiments the sharper is the distribution around the mean value. This is known as the "central limit theorem" in mathematics.

Macroscopic (phenomenological) physical laws are arbitrarily accurate in the limit of infinite numbers of microscopic particles. But it is beyond the possibility of experimental accuracy to "prove" the idea of perfect determinism. Nevertheless, in microscopic physics we can "prove" that small numbers of elementary particles exhibit indeterminate behavior, to within the highest level of experimental accuracy achieved in modern physics.

And this indeterminism or randomness can be the generator of alternative possibilities for thoughts and actions in the first stage of our two-stage model of free will. In the second stage, a much larger part of the brain/mind de-liberates and makes a decision or choice that itself is not random, but is "caused" by the agent's values, motives, and feelings. We say that the decision is "adequately" or "statistically determined" by the agent's "character."

Our thoughts and actions are not pre-determined from time before the agent begins deliberation, let alone from the earliest times of the universe, which determinists believe.

So although one cannot "prove" the idea of impossibilism, either logically or with experimental evidence, we can prove experimentally (though not logically as philosophers might prefer) that events occur that are not pre-determined. We can thus "disprove" strict determinism.

And that is our first step to explaining human freedom and moral responsibility.

Many illusionists hold a view that is close to impossibilism, including Derk Pereboom, Saul Smilansky, Galen Strawson, and Daniel Wegner.