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Originally Posted by lastcardcharlie
The output is fixed, but different counting programs might order the elements differently.
Sorry, I had responded before reading your updates to the language. Here's the original statement under consideration:
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In this context, it does make sense to claim that the possible outcomes of the first program can be counted.
Now, you've changed a few ideas:
* "possible outcomes" has been replaced with "partial outputs"
* "can be counted" means "[can be] listed algorithmically"
I can accept this if you assume that a "partial output" is merely the output after a finite number of steps of the program.
But now I don't understand how this works with the following claim:
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According to this view, nothing with probability zero ever happens as, unlike in the standard interpretation, there is never any final, completed infinite sequence.
Your concept of probability seems ill-defined at this point.
Let's look at your program:
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10 Flip a coin and print the outcome
20 Goto 10
What is the probability of the partial output {H}? The answer is that it depends on how long the program is allowed to run. I would say that this has probability 0 as long as the program is allowed to run three steps (because the partial output is now something else). However, I would also say that it happened.
I think you've exchanged infinity for a time-dependent concept, where you're necessarily inserting an artificial halt into a program that doesn't halt.