"Not really, there has not been that much progress. Life is pretty much the same, except we have different toys to occupy our time."
No offense, but I totally disagree. Some examples of major changes that come to mind and that IMO can't simply be downplayed as "toys":
- Medicine. Not having a large chance of dying/suffering of some incurable illness is a qualitative difference, I think (sorry, don't know the numbers).
- Human rights and democracy at least in parts of the world.
- A fairly complete rational description of the world (of course, not totally complete yet). Whatever "rational" means exactly -- but I think there *has* been an essential change and it's not all relative.
"In "Incompleteness" by Rebecca Goldstein, she talks about writers in the philosophy of mind that have taken the Incompleteness Theorems to mean that the human brain computes in a fundamentally different manner than a Turing machine. After all, it's hard to even imagine how human language could fail to describe a truth condition. And of course if that's the case, human language must be something truly and completely different than formal language."
One simple counterargument against this is that all the incompleteness results are talking about infinite sets of formulas. The set of all true sentences of arithmetic with less than n symbols, where n is, say, the number of particles in the universe, is decidable (because it is finite).
So are these people are claiming that humans can decide the truth of sentences of arbitrary length? Human lifetime or number of neurons should lead to an upper bound.
(Sorry if I got something wrong technically; it has been a while since i last looked at logic/computability)
Slashdot Mirror
"Not really, there has not been that much progress. Life is pretty much the same, except we have different toys to occupy our time."
No offense, but I totally disagree.
Some examples of major changes that come to mind and that IMO can't simply be downplayed as "toys":
- Medicine. Not having a large chance of dying/suffering of some incurable illness is a qualitative difference, I think (sorry, don't know the numbers).
- Human rights and democracy at least in parts of the world.
- A fairly complete rational description of the world (of course, not totally complete yet). Whatever "rational" means exactly -- but I think there *has* been an essential change and it's not all relative.
"In "Incompleteness" by Rebecca Goldstein, she talks about writers in the philosophy of mind that have taken the Incompleteness Theorems to mean that the human brain computes in a fundamentally different manner than a Turing machine. After all, it's hard to even imagine how human language could fail to describe a truth condition. And of course if that's the case, human language must be something truly and completely different than formal language."
One simple counterargument against this is that all the incompleteness results are talking about infinite sets of formulas. The set of all true sentences of arithmetic with less than n symbols, where n is, say, the number of particles in the universe, is decidable (because it is finite).
So are these people are claiming that humans can decide the truth of sentences of arbitrary length? Human lifetime or number of neurons should lead to an upper bound.
(Sorry if I got something wrong technically; it has been a while since i last looked at logic/computability)