[FOM] Davis's reply to Ord re hypercomputation

[Neil Tennant]

On Thu, 11 Mar 2004, Martin Davis wrote:

> because we can not expect to 
> observe more than finitely many outputs, assuring  ourselves that an 
> alleged "hypercomputer" really is one, would be in the nature of things 
> fraught with difficulty.

"Fraught with difficulty" might be something of an understatement here.
Why not rather say that the truth in such a matter, if it obtains, must be
knowable? So, if a proposition of the form "This device is a
hypercomputer" is not knowable (i.e. knowably true), then there is NO FACT
OF THE MATTER as to whether the device in question is a hypercomputer.

Of course, there might be some other epistemic route to the conclusion
"This device is a hypercomputer" (or its negation), involving a priori
reasoning from general principles plus (at least some, perhaps all)
relevant contingent truths (about the design of the device and its
behavior) that we are in a position to observe. What we would need then,
from the hypercomputationalist, is some general account of what such an
argument could possibly be like.

Failing that, the anti-realist response that "there is no fact of the
matter"---expressed more carefully in the form of a refusal to assert the
proposition "This device is a hypercomputer", along with a refusal to deny
it---seems to be the most sensible.

Neil Tennant