I checked the term "program space" and found a few authors who used it, but it seems to be an ad-hoc definition that is not widely used. It seems to be an amalgamation of term "sample space" with the the set of all programs or something like that. Of course, the simple comprehension of the idea of, "all possible programs" is different than the pretense that all possible programs could be comprehended through some kind of strategy of evaluation of all those programs. It would be like confusing a domain from mathematics with a value or an possibly evaluable variable (that can be assigned a value from the domain). These type distinctions are necessary for logical thinking about these things. The same kind of reasoning goes for Russell's Paradox. While I can, (with some thought) comprehend the definition and understand the paradox, I cannot comprehend the set itself, that is, I cannot comprehend the evaluation of the set. Such a thing doesn't make any sense. It is odd that the set of all evaluable functions (or all programs) is an inherent paradox when you try to think of it in the terms of an evaluable function (as if writing a program that produces all possible programs was feasible). The oddness is due to the fact that there is nothing that obviously leads to a paradox, and it is not easy to prove it is a paradox (because it lacks the required definition). The only reason we can give for the seeming paradox is that it is wrong to confuse the domain of a mathematical definition with a value or values from the domain. While this barrier can be transcended in some very special cases, it very obviously cannot be ignored for the general case. Jim Bromer
------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=8660244-6e7fb59c Powered by Listbox: http://www.listbox.com
