Re: H(D,D) cannot even be asked about the behavior of D(D) --- Boilerplate Reply

On 6/21/2024 3:00 PM, Richard Damon wrote:

On 6/21/24 3:45 PM, olcott wrote:

On 6/21/2024 2:33 PM, Richard Damon wrote:

On 6/21/24 3:19 PM, olcott wrote:

int sum(int x, int y){ return x + y; }
When this program is asked: sum(3,4) this maps to 7.
When this program is asked: sum(5,6) this DOES NOT map to 7.

>
Right.
>

>
When H is asked H(D,D) this maps to D correctly simulated by H.
When H is asked H(D,D) this DOES NOT map to behavior that halts.
>
>

>
Nope. H(M,d) is DEFINED (if it is correct) to determine if M(d) will Halt.
>

>
If one "defines" that the input to H(D,D) maps to the behavior
of D(D) yet cannot show this because it does not actually
map to that behavior *THEN THE DEFINITION IS SIMPLY WRONG*

 But we CAN show that it maps to the behavior of D(D) (at least when the representation of D includes the H that is giving the 0 answer) by just runnig it and seeing what it does.
 

No you cannot show that the mapping for the input to
H(D,D) maps to the behavior of D(D).
That you saw Bill's identical twin brother Jack rob
a liquor store does not prove that Bill robbed
that liquor store.
Instead you simply assume that the mapping from a
non-input must equally apply.
You assume that the call to H(D,D) from D correctly
simulated by H *must return* against the verified facts
that it does not return.
The directly executed D(D) is essentially the first call
in a recursive chain where the second call is always aborted.
*these two calls are not identical*
If H(D,D) did not correctly recognize that it must abort
the simulation of its input to correctly prevent its own
non-termination the directly executed D(D) would never halt.

Thus, the actual defined mapping exist, it just isn't comutable by H.
 

Misconceptions do not count as mapping.
int sum(int x, int y) { return x + y; }
Does not map sum(5,6) to 7.
The input to H(D,D) does not map to halting.
H(D,D) is not free to simply assume that the call from
D(D) to H(D,D) will return.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer