dart200 <user7160@newsgrouper.org.invalid> writes:
On 11/20/25 3:15 PM, Ben Bacarisse wrote:
dart200 <user7160@newsgrouper.org.invalid> writes:
On 11/19/25 3:36 PM, Ben Bacarisse wrote:Yes, I've read the paper several times. Turing was a mathematician,
dart200 <user7160@newsgrouper.org.invalid> writes:
On 11/17/25 9:29 AM, Alan Mackenzie wrote:No. Turing was working on the Entscheidungsproblem. A different
The Halting Theorem is wholly a theorem of mathematics,
and only secondarily about computer science.
the original proof as written by turing uses notions justified in turing >>>>>> machines to then support godel's result, not the other way around
problem altogether.
it is fundamentally based in computer science using turing machines as >>>>>> "axioms", which are in turn justified by our ability to mechanically >>>>>> undertake the operations, not set theoryNo. Turing machines are not "axioms" in any sense of the word; they are >>>>> entirely mathematical entities built from the axioms of set theory.
Turing was writing for an audience that would know that a "tape" was >>>>> just a convenient term for a function from Z to Gamma (the tape
alphabet), that the "head" is just an integer and "writing to the tape" >>>>> just results in a new function from Z to Gamma. The "machine
configuration" is just a tuple as is the TM itself. I.e. a TM is just a >>>>> set (though you need to know how tuples and function are just sets in >>>>> order to believe this).
literally his words:
we may compare a man in the process of computing a real number to a
machine which is only capable of a finite number of conditions q1, q2, >>>> ... qi; which will be called "m-configurations". The machine is supplied >>>> with a "tape " (the analogue of paper) running through it, and divided into
sections (called "squares") each capable of bearing a "symbol". At any >>>> moment there is just one square, say the r-th, bearing the symbol T(r)vwhich
is "in the machine". We may call this square the "scanned square ". The >>>> symbol on the scanned square may be called the " scanned symbol". The
"scanned symbol" is the only one of which the machine is, so to speak, >>>> "directly aware" [Tur36]
several times end to end???
Yes. I taught this material at a UK university for many years.
i'm smelling some bs my dude, sorry bout that, but i'm going to
have quote turing a bunch to show how ur quite mistaken about the paper.
i haven't read the paper thoroughly end to end. i've only read certain sections thoroughly and
skimmed it end to end. most of my focus has into specifically §8, and have read that *very*
thoroughly. i then skimmed the rest of the paper concentration specifically on how the results
of of §8 are used to justify conclusions in the following sections. i've mostly ignored before
§8 since he was mostly just constructing turing machines, but have a rough idea what's going
on.
And you *haven't* read it thoroughly end to end???
working under Alonzo Church on formal systems. He is describing a
mathematical object now called a Turing Machine.
idk maybe you can describe turing machines in set theory, but it's weird toHe was a mathematician working at a time when a computer was a person
claim turing just assumed they would make the connection instead of being >>>> specific about it.
who did arithmetic and sometimes symbol manipulation -- i.e. maths. He
knew (and he knew that all his reader knew) that he was describing
mathematical results about mathematical objects.
What do you think he was talking about if not mathematical theorems
about mathematical objects?
The Entscheidungsproblem is an entirely mathematical question about
formal systems. Cranks focus on Turing's work because the metaphors of >>>>> tapes and so on are easy to get one's head around (no pun intended!). >>>>> This is also why Turing gets so much credit, but Church, technically, >>>>> got there first with his proof using the lambda calculus. No crank ever >>>>> disputes this proof because they can't waffle about it (or, in most
cases, even understand it).
no one focuses the semantic paradox actually described by turing either, >>> There is no paradox.
i'm gunna say this a million times, eh???
*the halting paradox is a paradox like how the liar's paradox is a
paradox*
I know this is a modern form of proof -- just keep saying it -- but it remains false.
they work the same way: if you try to "decide" the math object into a set classifying it's
semantics, then the object will take that classification and defy the classification, making it
impossible to decide upon.
No. Every "object" in the input set can be correctly decided. It took
me years to get PO to admit the "every instance of the halting problem
has a correct yes/no answer". Even so, he then he went on to deny it
again later. Do you also deny this?
With the halting problem counter example input
where input D does the opposite of whatever
decider H reports this specific H/D is exactly
isomorphic to the Liar Paradox.
With the halting problem counter example input
where input D does the opposite of whatever
decider H reports this specific H/D is exactly
isomorphic to the Liar Paradox.
On 2025-11-22, olcott <NoOne@NoWhere.com> wrote:
With the halting problem counter example input
where input D does the opposite of whatever
decider H reports this specific H/D is exactly
isomorphic to the Liar Paradox.
No it isn't. The Liar Paradox has an indeterminate
truth value; the H/D pair does not contain any
proposition with an indeterminate truth value.
You are too incompetent to understand what a homeomorphism is and how to prove one.
All you are saying is that the situation vaguely /feels/
like it resembles the Liar Paradox, and that legitimizes
you to use a term like "isomorphism".
On 11/22/2025 12:08 AM, Kaz Kylheku wrote:
On 2025-11-22, olcott <NoOne@NoWhere.com> wrote:
With the halting problem counter example input
where input D does the opposite of whatever
decider H reports this specific H/D is exactly
isomorphic to the Liar Paradox.
No it isn't. The Liar Paradox has an indeterminate
truth value; the H/D pair does not contain any
proposition with an indeterminate truth value.
With the halting problem counter example input
where input D does the opposite of whatever decider
H reports this specific H/D pair is exactly
isomorphic to the Liar Paradox.
When the behavior of D depends on the return
value of H and D does the opposite of whatever
H returns the H/D pair itself is a yes/no question
that lacks a correct yes/no answer.
Every yes/no question that lacks a correct yes/no answer
is isomorphic to this question:
Is this sentence true or false: "This sentence is not true" ?
What correct Boolean value should H return to D?
On 2025-11-22, olcott <polcott333@gmail.com> wrote:
On 11/22/2025 12:08 AM, Kaz Kylheku wrote:
On 2025-11-22, olcott <NoOne@NoWhere.com> wrote:
With the halting problem counter example input
where input D does the opposite of whatever
decider H reports this specific H/D is exactly
isomorphic to the Liar Paradox.
No it isn't. The Liar Paradox has an indeterminate
truth value; the H/D pair does not contain any
proposition with an indeterminate truth value.
With the halting problem counter example input
where input D does the opposite of whatever decider
H reports this specific H/D pair is exactly
isomorphic to the Liar Paradox.
When the behavior of D depends on the return
value of H and D does the opposite of whatever
H returns the H/D pair itself is a yes/no question
that lacks a correct yes/no answer.
Umm, no; there has to be a self-negation in order to have a Liar
Paradox. For instance "This sentence has four words" contains a contradiction: the sentence's "behavior" of having a word count of five contradicts an assertion that is found in the same sentence. Yet there
is no paradox: the sentence readily identifies as having a false value.
Every yes/no question that lacks a correct yes/no answer
is isomorphic to this question:
The correct answer is 1 in the H/D pair in which H returns 0.
It is not lacking. Just like the correct answer is "five words"
in "This sentence has four words".
Is this sentence true or false: "This sentence is not true" ?
What correct Boolean value should H return to D?
The correct value is 1.
On 11/22/2025 10:45 AM, Kaz Kylheku wrote:
On 2025-11-22, olcott <polcott333@gmail.com> wrote:
On 11/22/2025 12:08 AM, Kaz Kylheku wrote:
On 2025-11-22, olcott <NoOne@NoWhere.com> wrote:
With the halting problem counter example input
where input D does the opposite of whatever
decider H reports this specific H/D is exactly
isomorphic to the Liar Paradox.
No it isn't. The Liar Paradox has an indeterminate
truth value; the H/D pair does not contain any
proposition with an indeterminate truth value.
With the halting problem counter example input
where input D does the opposite of whatever decider
H reports this specific H/D pair is exactly
isomorphic to the Liar Paradox.
When the behavior of D depends on the return
value of H and D does the opposite of whatever
H returns the H/D pair itself is a yes/no question
that lacks a correct yes/no answer.
Umm, no; there has to be a self-negation in order to have a Liar
Paradox. For instance "This sentence has four words" contains a
contradiction: the sentence's "behavior" of having a word count of five
contradicts an assertion that is found in the same sentence. Yet there
is no paradox: the sentence readily identifies as having a false value.
Every yes/no question that lacks a correct yes/no answer
is isomorphic to this question:
The correct answer is 1 in the H/D pair in which H returns 0.
It is not lacking. Just like the correct answer is "five words"
in "This sentence has four words".
Neither return value is correct because D does
the opposite of whatever value is returned just
like "This sentence is not true" is true if it
is not true and not true if it is true, thus
it is neither true nor false therefore not a
proposition.
Is this sentence true or false: "This sentence is not true" ?
What correct Boolean value should H return to D?
The correct value is 1.
int D()
{
int Halt_Status = H(D);
if (Halt_Status)
HERE: goto HERE;
return Halt_Status;
}
You know that you are lying about this. Does that
give you a cheap thrill?
On 11/22/2025 12:08 AM, Kaz Kylheku wrote:
On 2025-11-22, olcott <NoOne@NoWhere.com> wrote:
With the halting problem counter example input
where input D does the opposite of whatever
decider H reports this specific H/D is exactly
isomorphic to the Liar Paradox.
No it isn't. The Liar Paradox has an indeterminate
truth value; the H/D pair does not contain any
proposition with an indeterminate truth value.
With the halting problem counter example input
where input D does the opposite of whatever decider
H reports this specific H/D pair is exactly
D and H are the generic template.
DD and HHH are the physical implementation.
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