XPost: sci.logic
On 20/02/24 06:43, olcott wrote:
On 2/19/2024 11:34 PM, immibis wrote:
On 20/02/24 06:23, olcott wrote:
On 2/19/2024 11:09 PM, immibis wrote:
On 20/02/24 05:31, olcott wrote:
The key difference with Russell's Paradox is that they figured out
that they were thinking about the problem incorrectly and changed
how they thought about the problem to abolish the paradox.
ZFC prevents the existence of sets containing themselves. The same
approach can be applied to all self-reference paradox. I have been
focusing on self-reference paradox for twenty years.
So how do you think the halting problem should be redefined to make
it solvable?
There are at least two ways, one of these is consistent
with the way that the rest of the self-reference paradoxes
are solved. ZFC prevents sets that are members of themselves
from coming into existence. This abolished Russell's Paradox.
The analogous halting problem solution is to reject the
self-contradictory input.
This same thing applies to solving Tarski Undefinability.
Boolean(English, "This sentence is not true.")
Simply reject the input as invalid.
So what are the ways?
A Halt decider recognizes and rejects self-contradictory inputs.
My code already does that.
And it doesn't solve the halting problem. You want to modify the halting problem so that it can be solved. How do you precisely modify the
problem to avoid the possibility of contradiction? Do you say that a
Turing machine tape can't contain a description of a "self-contradictory
Turing machine"? Do you limit the amount of memory?
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