The limits of the limits of computation

I’m very pleased to have been invited to participate in an exciting international workshop being held at Sussex later this month.


My very brief contribution has the title: “The limits of the limits of computation”.  Here’s the abstract:

The limits of the limits of computation

The most salient results concerning the limits of computation have proceeded by establishing the limits of formal systems. These findings are less damning than they may appear.  First, they only tell against real-world (or “physical”) computation (i.e., what it is that my laptop does that makes it so useful) to the extent to which real-world computation is best viewed as being formal, yet (at least some forms of) real-world computation are as much embodied, world-involving, dynamics-exploiting phenomena as recent cognitive science takes mind to be.  Second, the incomputability results state that formal methods are in some sense outstripped by extra-formal reality, while themselves being formal methods attempting to capture extra-formal reality (real-world computation) — an ironic pronouncement that would make Epimenides blush.    One ignores these limits on the incomputability results at one’s peril; a good example is the diagonal argument against artificial intelligence.




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