On 7/2/2026 5:59 PM, dbush wrote:The halting problem doesn't actually have self reference, as algorithms can be copied as in the below example of algorithm D:On 7/2/2026 6:53 PM, olcott wrote:Russell's Paradox is the exact same issue as theOn 7/2/2026 5:47 PM, dbush wrote:>On 7/2/2026 6:35 PM, olcott wrote:>On 7/2/2026 5:32 PM, dbush wrote:>On 7/2/2026 6:13 PM, olcott wrote:>On 7/2/2026 4:59 PM, dbush wrote:>On 7/2/2026 5:40 PM, olcott wrote:>On 7/2/2026 4:23 PM, dbush wrote:>On 7/2/2026 5:12 PM, olcott wrote:>The confusing part is how an intelligent person canStates that both a statement and its negation are true. And if a formal system can reach a contradiction through a series of truth preserving operations from its axioms, that means both statements are proven true.
accept POE as correct for more than sixty seconds.
>
Every average third grader knows that a contradiction
>
Every third grader knows that it must have fucked up somewhere.
Your intuition fails you. It just means that the axioms of the system in question are inconsistent. And the principle of explosion can be used to show that an inconsistent system is useless.
>
It makes more sense to use the ordinary meaning
of contradiction:
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When-so-ever two sentences contradict each other
at least one of them is false.
Whatever you call it, if the axioms of a formal system can prove both X and ~X, then the principle of explosion can be used to show that system is useless.
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X & ~X proves FALSE.
How can anyone that is not nuts possibly think otherwise?
Assuming that X & ~X has been proven from the axioms of a formal system,
Stipulating the ordinary English meaning of contradiction
Is not the stipulated meaning used in logic and is therefore irrelevant.
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If you want an example, naive set theory is an inconsistent system. It is able to prove both X = "set R contains itself" and ~X = "set R does not contain itself". So X & ~X is proven TRUE in naive set theory. The principle of explosion can then be used to show that naive set theory is useless.
pathological self reference (PSR) of the Halting
Problem. I have studied PSR as a primary focus
for 28 years.
void D(ptr *I)
{
// algorithm D; input: I
ptr *X = D;
ptr *Y = I;
int result;
{
// algorithm H; inputs: X,Y
result = 0;
}
if (result == 1) {
while (1);
}
}
Which is the counter example input to algorithm H:
int H(ptr *X, ptr *Y)
{
int result;
{
// algorithm H; inputs: X,Y
result = 0;
}
return result;
}
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