// Linz Turing machine Ĥ applied to ⟨Ĥ⟩ its own TM description
// States with an "H" are the Linz hypothetical halt decider
// --- Does Ĥ halt on ⟨Ĥ⟩ its own machine description?
Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn // Ĥ applied to ⟨Ĥ⟩ does not halt

Richard finally agrees with the idea that I have been promoting
in these forums for several years.

On 2/23/2024 9:22 PM, Richard Damon wrote:
> Yes, Epistemological antinomies, when given to a True Predicate, get
> "rejected" in a sense, the predicate returns FALSE.
>
> That doesn't mean the statement is false, just that it isn't true.
>
> It also doesn't mean the predicate doesn't answer.

Thus a halt decidability decider returns TRUE for inputs that it
correctly determines will halt and FALSE for everything else
including epistemological antinomies such as Ĥ applied to ⟨Ĥ⟩.
A mere recognizer would simply loop in these cases.

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 2/26/24 8:38 PM, olcott wrote:
> // Linz Turing machine Ĥ applied to ⟨Ĥ⟩ its own TM description
> // States with an "H" are the Linz hypothetical halt decider
> // --- Does  Ĥ halt on ⟨Ĥ⟩ its own machine description?
> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn   // Ĥ applied to ⟨Ĥ⟩ does not halt
>
> Richard finally agrees with the idea that I have been promoting
> in these forums for several years.
>
> On 2/23/2024 9:22 PM, Richard Damon wrote:
> > Yes, Epistemological antinomies, when given to a True Predicate, get
> > "rejected" in a sense, the predicate returns FALSE.
> >
> > That doesn't mean the statement is false, just that it isn't true.
> >
> > It also doesn't mean the predicate doesn't answer.
>
> Thus a halt decidability decider returns TRUE for inputs that it
> correctly determines will halt and FALSE for everything else
> including epistemological antinomies such as Ĥ applied to ⟨Ĥ⟩.
> A mere recognizer would simply loop in these cases.
>
>

But a "Halt Decidability Decider" isn't what we are asking about.

And actually, what a "Halt Decidability Decider" SHOULD do is decide if
an input can be decided by ANY decider, which is True.

A Halt Decider needs to answer TRUE for all input that will halt,
regardless of the "ability" of the decider.

Otherwise, we could just make a "correct" Halt Decider that just
answered False to all inputs, as it didn't determine that it would halt.

Or simulate of a fixed number of steps, and then say non-halting.

Also, NO Turing Machine is an "Epistemological Antinomy" as they are
different types of things, so you are making a stupid category error.

On 2/26/24 8:38 PM, olcott wrote:
> // Linz Turing machine Ĥ applied to ⟨Ĥ⟩ its own TM description
> // States with an "H" are the Linz hypothetical halt decider
> // --- Does  Ĥ halt on ⟨Ĥ⟩ its own machine description?
> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn   // Ĥ applied to ⟨Ĥ⟩ does not halt
>
> Richard finally agrees with the idea that I have been promoting
> in these forums for several years.
>
> On 2/23/2024 9:22 PM, Richard Damon wrote:
> > Yes, Epistemological antinomies, when given to a True Predicate, get
> > "rejected" in a sense, the predicate returns FALSE.
> >
> > That doesn't mean the statement is false, just that it isn't true.
> >
> > It also doesn't mean the predicate doesn't answer.
>
> Thus a halt decidability decider returns TRUE for inputs that it
> correctly determines will halt and FALSE for everything else
> including epistemological antinomies such as Ĥ applied to ⟨Ĥ⟩.
> A mere recognizer would simply loop in these cases.
>
>

But a "Halt Decidability Decider" isn't what we are asking about.

And actually, what a "Halt Decidability Decider" SHOULD do is decide if
an input can be decided by ANY decider, which is True.

A Halt Decider needs to answer TRUE for all input that will halt,
regardless of the "ability" of the decider.

Otherwise, we could just make a "correct" Halt Decider that just
answered False to all inputs, as it didn't determine that it would halt.

Or simulate of a fixed number of steps, and then say non-halting.

Also, NO Turing Machine is an "Epistemological Antinomy" as they are
different types of things, so you are making a stupid category error.

On 2/26/2024 8:07 PM, Richard Damon wrote:
> On 2/26/24 8:38 PM, olcott wrote:
>> // Linz Turing machine Ĥ applied to ⟨Ĥ⟩ its own TM description
>> // States with an "H" are the Linz hypothetical halt decider
>> // --- Does  Ĥ halt on ⟨Ĥ⟩ its own machine description?
>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn   // Ĥ applied to ⟨Ĥ⟩ does not halt
>>
>> Richard finally agrees with the idea that I have been promoting
>> in these forums for several years.
>>
>> On 2/23/2024 9:22 PM, Richard Damon wrote:
>>  > Yes, Epistemological antinomies, when given to a True Predicate, get
>>  > "rejected" in a sense, the predicate returns FALSE.
>>  >
>>  > That doesn't mean the statement is false, just that it isn't true.
>>  >
>>  > It also doesn't mean the predicate doesn't answer.
>>
>> Thus a halt decidability decider returns TRUE for inputs that it
>> correctly determines will halt and FALSE for everything else
>> including epistemological antinomies such as Ĥ applied to ⟨Ĥ⟩.
>> A mere recognizer would simply loop in these cases.
>>
>>
>
> But a "Halt Decidability Decider" isn't what we are asking about.

None-the-less it refutes Rice's theorem by correctly determining
that its own behavior cannot correctly determine the halt status
of its own Turing Machine description.

All of my ideas about all of these things: Tarski Undefinability,
Gödel 1931 Incompleteness, The halting problem proofs amount to
simply understanding that epistemological antinomies must ALWAYS
be rejected as invalid.

Even modern day philosophers do not understand that the Liar Paradox
and other epistemological antinomies are simply not bearers of truth.
To me this is like mathematics professors that find first grade
arithmetic impossibly difficult.

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 2/26/2024 8:07 PM, Richard Damon wrote:
> On 2/26/24 8:38 PM, olcott wrote:
>> // Linz Turing machine Ĥ applied to ⟨Ĥ⟩ its own TM description
>> // States with an "H" are the Linz hypothetical halt decider
>> // --- Does  Ĥ halt on ⟨Ĥ⟩ its own machine description?
>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn   // Ĥ applied to ⟨Ĥ⟩ does not halt
>>
>> Richard finally agrees with the idea that I have been promoting
>> in these forums for several years.
>>
>> On 2/23/2024 9:22 PM, Richard Damon wrote:
>>  > Yes, Epistemological antinomies, when given to a True Predicate, get
>>  > "rejected" in a sense, the predicate returns FALSE.
>>  >
>>  > That doesn't mean the statement is false, just that it isn't true.
>>  >
>>  > It also doesn't mean the predicate doesn't answer.
>>
>> Thus a halt decidability decider returns TRUE for inputs that it
>> correctly determines will halt and FALSE for everything else
>> including epistemological antinomies such as Ĥ applied to ⟨Ĥ⟩.
>> A mere recognizer would simply loop in these cases.
>>
>>
>
> But a "Halt Decidability Decider" isn't what we are asking about.
>
> And actually, what a "Halt Decidability Decider" SHOULD do is decide if
> an input can be decided by ANY decider, which is True.
>
> A Halt Decider needs to answer TRUE for all input that will halt,
> regardless of the "ability" of the decider.
>

Self-contradictory inputs must ALWAYS be rejected
Self-contradictory inputs must ALWAYS be rejected
Self-contradictory inputs must ALWAYS be rejected
Self-contradictory inputs must ALWAYS be rejected
Self-contradictory inputs must ALWAYS be rejected
Self-contradictory inputs must ALWAYS be rejected
Self-contradictory inputs must ALWAYS be rejected
Self-contradictory inputs must ALWAYS be rejected
Self-contradictory inputs must ALWAYS be rejected
Self-contradictory inputs must ALWAYS be rejected
Self-contradictory inputs must ALWAYS be rejected
Self-contradictory inputs must ALWAYS be rejected
Self-contradictory inputs must ALWAYS be rejected
Self-contradictory inputs must ALWAYS be rejected

> Otherwise, we could just make a "correct" Halt Decider that just
> answered False to all inputs, as it didn't determine that it would halt.
>
> Or simulate of a fixed number of steps, and then say non-halting.
>
>
> Also, NO Turing Machine is an "Epistemological Antinomy" as they are
> different types of things, so you are making a stupid category error.

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 2/26/24 9:44 PM, olcott wrote:
> On 2/26/2024 8:07 PM, Richard Damon wrote:
>> On 2/26/24 8:38 PM, olcott wrote:
>>> // Linz Turing machine Ĥ applied to ⟨Ĥ⟩ its own TM description
>>> // States with an "H" are the Linz hypothetical halt decider
>>> // --- Does  Ĥ halt on ⟨Ĥ⟩ its own machine description?
>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn   // Ĥ applied to ⟨Ĥ⟩ does not halt
>>>
>>> Richard finally agrees with the idea that I have been promoting
>>> in these forums for several years.
>>>
>>> On 2/23/2024 9:22 PM, Richard Damon wrote:
>>>  > Yes, Epistemological antinomies, when given to a True Predicate, get
>>>  > "rejected" in a sense, the predicate returns FALSE.
>>>  >
>>>  > That doesn't mean the statement is false, just that it isn't true.
>>>  >
>>>  > It also doesn't mean the predicate doesn't answer.
>>>
>>> Thus a halt decidability decider returns TRUE for inputs that it
>>> correctly determines will halt and FALSE for everything else
>>> including epistemological antinomies such as Ĥ applied to ⟨Ĥ⟩.
>>> A mere recognizer would simply loop in these cases.
>>>
>>>
>>
>> But a "Halt Decidability Decider" isn't what we are asking about.
>>
>> And actually, what a "Halt Decidability Decider" SHOULD do is decide
>> if an input can be decided by ANY decider, which is True.
>>
>> A Halt Decider needs to answer TRUE for all input that will halt,
>> regardless of the "ability" of the decider.
>>
>
> Self-contradictory inputs must ALWAYS be rejected
> Self-contradictory inputs must ALWAYS be rejected
> Self-contradictory inputs must ALWAYS be rejected
> Self-contradictory inputs must ALWAYS be rejected
> Self-contradictory inputs must ALWAYS be rejected
> Self-contradictory inputs must ALWAYS be rejected
> Self-contradictory inputs must ALWAYS be rejected
> Self-contradictory inputs must ALWAYS be rejected
> Self-contradictory inputs must ALWAYS be rejected
> Self-contradictory inputs must ALWAYS be rejected
> Self-contradictory inputs must ALWAYS be rejected
> Self-contradictory inputs must ALWAYS be rejected
> Self-contradictory inputs must ALWAYS be rejected
> Self-contradictory inputs must ALWAYS be rejected

And a Turing Machine can't be SELF contrdictory.

H^ is H-Contradictory, making H get the wrong answer.

You are just proving you don't know what you are talking about.

In fact, the reason your logic degrades into th e liar's paradox, is
because there is no Turing Machine H that exists to build the H^ that
you talk about.

Non-Existing Turing Machines might be self-contradictory, but you can't
actually ask a real decider about them.

You need to keep straight what type of proof you are in.

>
>> Otherwise, we could just make a "correct" Halt Decider that just
>> answered False to all inputs, as it didn't determine that it would halt.
>>
>> Or simulate of a fixed number of steps, and then say non-halting.
>>
>>
>> Also, NO Turing Machine is an "Epistemological Antinomy" as they are
>> different types of things, so you are making a stupid category error.
>

On 2/26/24 9:42 PM, olcott wrote:
> On 2/26/2024 8:07 PM, Richard Damon wrote:
>> On 2/26/24 8:38 PM, olcott wrote:
>>> // Linz Turing machine Ĥ applied to ⟨Ĥ⟩ its own TM description
>>> // States with an "H" are the Linz hypothetical halt decider
>>> // --- Does  Ĥ halt on ⟨Ĥ⟩ its own machine description?
>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn   // Ĥ applied to ⟨Ĥ⟩ does not halt
>>>
>>> Richard finally agrees with the idea that I have been promoting
>>> in these forums for several years.
>>>
>>> On 2/23/2024 9:22 PM, Richard Damon wrote:
>>>  > Yes, Epistemological antinomies, when given to a True Predicate, get
>>>  > "rejected" in a sense, the predicate returns FALSE.
>>>  >
>>>  > That doesn't mean the statement is false, just that it isn't true.
>>>  >
>>>  > It also doesn't mean the predicate doesn't answer.
>>>
>>> Thus a halt decidability decider returns TRUE for inputs that it
>>> correctly determines will halt and FALSE for everything else
>>> including epistemological antinomies such as Ĥ applied to ⟨Ĥ⟩.
>>> A mere recognizer would simply loop in these cases.
>>>
>>>
>>
>> But a "Halt Decidability Decider" isn't what we are asking about.
>
> None-the-less it refutes Rice's theorem by correctly determining
> that its own behavior cannot correctly determine the halt status
> of its own Turing Machine description.
>
> All of my ideas about all of these things: Tarski Undefinability,
> Gödel 1931 Incompleteness, The halting problem proofs amount to
> simply understanding that epistemological antinomies must ALWAYS
> be rejected as invalid.
>
> Even modern day philosophers do not understand that the Liar Paradox
> and other epistemological antinomies are simply not bearers of truth.
> To me this is like mathematics professors that find first grade
> arithmetic impossibly difficult.
>

Nope.

In fact, the proof Rice's theorem basically says that you can't decide
on "semantic properties" because you can make a machine that askes the
decider what it will decide for this input, and does the opposite.

You are just PROVING You don't know what an "Epistemological Antinomy"
is, as it CAN'T be a Turing Machine (or a description of one) and are
just making a STUPID category error.

And, since you don't understand what they are, you don't understand,
that (except for Tarski, which WAS talkig about statments) your claim
just doesn't apply to those other theories, and just proves you
misundertanding of what you are doing. And for Tarski, he DOES
understand what an Epistemological Antinomy is and shows that just
trying to reject them as "not-true" doesn't work, because a Truth
Predicate MUST be a truth-bearer, and can get caught in a contradiction
it it exists.

It is more that you are showing that you don't understand "first grade"
level logic, and are totally lost in the higher levvel stuff, but try to
claim you understand it, and prove that you are just a liar.

On 2/26/2024 8:07 PM, Richard Damon wrote:
> On 2/26/24 8:38 PM, olcott wrote:
>> // Linz Turing machine Ĥ applied to ⟨Ĥ⟩ its own TM description
>> // States with an "H" are the Linz hypothetical halt decider
>> // --- Does  Ĥ halt on ⟨Ĥ⟩ its own machine description?
>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
>> Ĥ. q0⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn   // Ĥ applied to ⟨Ĥ⟩ does not halt
>>
>> Richard finally agrees with the idea that I have been promoting
>> in these forums for several years.
>>
>> On 2/23/2024 9:22 PM, Richard Damon wrote:
>>  > Yes, Epistemological antinomies, when given to a True Predicate, get
>>  > "rejected" in a sense, the predicate returns FALSE.
>>  >
>>  > That doesn't mean the statement is false, just that it isn't true.
>>  >
>>  > It also doesn't mean the predicate doesn't answer.
>>
>> Thus a halt decidability decider returns TRUE for inputs that it
>> correctly determines will halt and FALSE for everything else
>> including epistemological antinomies such as Ĥ applied to ⟨Ĥ⟩.
>> A mere recognizer would simply loop in these cases.
>>
>>
>
> But a "Halt Decidability Decider" isn't what we are asking about.
>
> And actually, what a "Halt Decidability Decider" SHOULD do is decide if
> an input can be decided by ANY decider, which is True.
>
> A Halt Decider needs to answer TRUE for all input that will halt,
> regardless of the "ability" of the decider.
>
> Otherwise, we could just make a "correct" Halt Decider that just
> answered False to all inputs, as it didn't determine that it would halt.
>
> Or simulate of a fixed number of steps, and then say non-halting.
>

It must provide a halt status corresponding to the behavior of its
input unless every possible encoding of itself cannot possibly do
that such as every possible encoding of Ĥ applied to ⟨Ĥ⟩

> Also, NO Turing Machine is an "Epistemological Antinomy" as they are
> different types of things, so you are making a stupid category error.

*The strawman deception is your favorite fake rebuttal*
Ĥ applied to ⟨Ĥ⟩ is the epistemological antinomy for
every possible encoding of Ĥ.

Ĥ is not the epistemological antinomy.
⟨Ĥ⟩ is not the epistemological antinomy.
Ĥ applied to ⟨Ĥ⟩ is the epistemological antinomy.

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 2/26/24 10:16 PM, olcott wrote:
> On 2/26/2024 8:07 PM, Richard Damon wrote:
>> On 2/26/24 8:38 PM, olcott wrote:
>>> // Linz Turing machine Ĥ applied to ⟨Ĥ⟩ its own TM description
>>> // States with an "H" are the Linz hypothetical halt decider
>>> // --- Does  Ĥ halt on ⟨Ĥ⟩ its own machine description?
>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
>>> Ĥ. q0⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn   // Ĥ applied to ⟨Ĥ⟩ does not halt
>>>
>>> Richard finally agrees with the idea that I have been promoting
>>> in these forums for several years.
>>>
>>> On 2/23/2024 9:22 PM, Richard Damon wrote:
>>>  > Yes, Epistemological antinomies, when given to a True Predicate, get
>>>  > "rejected" in a sense, the predicate returns FALSE.
>>>  >
>>>  > That doesn't mean the statement is false, just that it isn't true.
>>>  >
>>>  > It also doesn't mean the predicate doesn't answer.
>>>
>>> Thus a halt decidability decider returns TRUE for inputs that it
>>> correctly determines will halt and FALSE for everything else
>>> including epistemological antinomies such as Ĥ applied to ⟨Ĥ⟩.
>>> A mere recognizer would simply loop in these cases.
>>>
>>>
>>
>> But a "Halt Decidability Decider" isn't what we are asking about.
>>
>> And actually, what a "Halt Decidability Decider" SHOULD do is decide
>> if an input can be decided by ANY decider, which is True.
>>
>> A Halt Decider needs to answer TRUE for all input that will halt,
>> regardless of the "ability" of the decider.
>>
>> Otherwise, we could just make a "correct" Halt Decider that just
>> answered False to all inputs, as it didn't determine that it would halt.
>>
>> Or simulate of a fixed number of steps, and then say non-halting.
>>
>
> It must provide a halt status corresponding to the behavior of its
> input unless every possible encoding of itself cannot possibly do
> that such as every possible encoding of Ĥ applied to ⟨Ĥ⟩

Nope, it must provvid a halt status corresponding to the behavior of its
input. PERIOD.

It doesn't matter about the "encoding" of itself, if it exists, it has
definite behavior and thus always answers the same input with the same
output.'

You are just proving your utter ignorance of the field by your comments.

>
>> Also, NO Turing Machine is an "Epistemological Antinomy" as they are
>> different types of things, so you are making a stupid category error.
>
> *The strawman deception is your favorite fake rebuttal*
> Ĥ applied to ⟨Ĥ⟩ is the epistemological antinomy for
> every possible encoding of Ĥ.

Nope.

You don't understand what that terms means it seems.

>
> Ĥ is not the epistemological antinomy.
> ⟨Ĥ⟩ is not the epistemological antinomy.
> Ĥ applied to ⟨Ĥ⟩ is the epistemological antinomy.
>

Ĥ applied to (Ĥ) is a computation, and for a specific Ĥ it will have a
specific behavior.

The fact that this behavior violates its requirements the requirements
on Ĥ for every possible machine (not "encodings") just means that the
requirements are unsubstantiatable, and no such machine exists.

Note, "Different Encodings" all produce the same results, that is like
changing the name of a varaible from x to y EVERYWHERE in a program.

You are just proving you don't understand at all what you are talking
about, which is why you lie every time you post. You don't even know
what you are saying.

On 27/02/24 02:38, olcott wrote:
> // Linz Turing machine Ĥ applied to ⟨Ĥ⟩ its own TM description
> // States with an "H" are the Linz hypothetical halt decider
> // --- Does  Ĥ halt on ⟨Ĥ⟩ its own machine description?
> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn   // Ĥ applied to ⟨Ĥ⟩ does not halt
>
> Richard finally agrees with the idea that I have been promoting
> in these forums for several years.
>
> On 2/23/2024 9:22 PM, Richard Damon wrote:
> > Yes, Epistemological antinomies, when given to a True Predicate, get
> > "rejected" in a sense, the predicate returns FALSE.
> >
> > That doesn't mean the statement is false, just that it isn't true.
> >
> > It also doesn't mean the predicate doesn't answer.
>
> Thus a halt decidability decider returns TRUE for inputs that it
> correctly determines will halt and FALSE for everything else
> including epistemological antinomies such as Ĥ applied to ⟨Ĥ⟩.
> A mere recognizer would simply loop in these cases.

void D(ptr x) {
if (HaltDecidabilityDecider(x,x)) {
EpistemologicalAntimony();
}
}