I can’t easily find the flaw in your logic, but I don’t agree with your conclusion because the randomness of my properties could be used for predictions.
For example, I could predict medium human life expectancy based on (supposedly random) my age now. My age is several decades, and human life expectancy is 2 х (several decades) with 50 percent probability (and it is true).
I could suggest many examples, where the randomness of my properties could be used to get predictions, even to measure the size of Earth based on my random distance from the equator. And in all cases that I could check, the DA-style logic works.
I can’t easily find the flaw in your logic, but I don’t agree with your conclusion because the randomness of my properties could be used for predictions.
For example, I could predict medium human life expectancy based on (supposedly random) my age now. My age is several decades, and human life expectancy is 2 х (several decades) with 50 percent probability (and it is true).
I could suggest many examples, where the randomness of my properties could be used to get predictions, even to measure the size of Earth based on my random distance from the equator. And in all cases that I could check, the DA-style logic works.