No, a decision procedure doesn’t have an output if you don’t run it. There is something that would be the output if you ran it.
I’m not sure that is a particularly useful way to carve reality. At best it means that we need another word for the thing that Coscott is referring to as ‘output’ that we can use instead of the word output. The thing Coscott is talking about is a much more useful thing when analysing decision procedures than the thing you have defined ‘output’ to mean.
“What would happen if hypothetically X were done” is one of the most common targets in statistical inference. That’s a huge chunk of what Fisher/Neyman had done (originally in the context of agriculture: “what if we had given this fertilizer to this plot of land?”) This is almost a hundred years ago.
I’m not sure that is a particularly useful way to carve reality. At best it means that we need another word for the thing that Coscott is referring to as ‘output’ that we can use instead of the word output. The thing Coscott is talking about is a much more useful thing when analysing decision procedures than the thing you have defined ‘output’ to mean.
That’s just a potential outcome, pretty standard stuff:
http://www.stat.cmu.edu/~fienberg/Rubin/Rubin-JASA-05.pdf
“What would happen if hypothetically X were done” is one of the most common targets in statistical inference. That’s a huge chunk of what Fisher/Neyman had done (originally in the context of agriculture: “what if we had given this fertilizer to this plot of land?”) This is almost a hundred years ago.