I’m strongly uncomfortable with the “crackpot” conclusion you jump to immediately. Without being an expert and just skimming through his post(s), wouldn’t the more likely conclusion be that he’s not simply arguing generally accepted things in computer science are plain wrong, but rather would be weakened under a different set of assumptions or new generalizations? Given that this particular area of computer science is often about negative results—which are actually kind of rare if you zoom out to all areas of mathematics—there are potentially going to be more weakening(s) of such negative results.
Sort of. The basic thing I’m trying to point at is that without more assumptions, the standard tools allow you too much freedom to compute things, and thus you need to restrict the model more to ensure that only the traditional computable functions are actually computable.
I’m strongly uncomfortable with the “crackpot” conclusion you jump to immediately. Without being an expert and just skimming through his post(s), wouldn’t the more likely conclusion be that he’s not simply arguing generally accepted things in computer science are plain wrong, but rather would be weakened under a different set of assumptions or new generalizations? Given that this particular area of computer science is often about negative results—which are actually kind of rare if you zoom out to all areas of mathematics—there are potentially going to be more weakening(s) of such negative results.
Sort of. The basic thing I’m trying to point at is that without more assumptions, the standard tools allow you too much freedom to compute things, and thus you need to restrict the model more to ensure that only the traditional computable functions are actually computable.