On 2/19/2024 10:21 PM, Ross Finlayson wrote:
> On 02/19/2024 04:15 PM, Ben Bacarisse wrote:
>> Ross Finlayson <ross.a.finlayson@gmail.com> writes:
>>
>>> What about if M_0(n) is a Turing machine of finite bound n,
>>
>> Care to define what that you mean?
>>
>>> then there exists M_1(m) where m > n or m >> n,
>>> that is a halt decider for M_0(n).
>>
>> I'm not sure what role the subscripts 0 and 1 are playing here.  Also,
>> I'd urge you to be careful about terms like "X is a ..." when I think
>> you mean "X is any one of the class of ...".  It's OK provided everyone
>> is on board, but when things are new, extra care is sometimes needed.
>>
>>> How about that?
>>
>> With appropriate definitions, I feel sure sure one can do something like
>> that.
>>
>> Why are interested in such results?  Do they lead to some interesting
>> theory?
>>
>
> I think it's good the concept that the halting problem
> makes for an argument that "static analysis always halts".
>
> What I mean by that is relating it to something like Zeno,
> you show it doesn't go through, so show it never gets anywhere.
>
> So, showing completeness results first, then makes
> for that the student doesn't get left with the idea
> of "give up", instead "get over it", or "get through it".
>
> I.e. the idea is to make sure that there's completeness first,
> then, to forestall the feeling locked in with absence of
> free will or the conscious about it, instead, that incompleteness
> is sort of framed as about "there's asymptotic freedom",
> in a sense.
>
> Either way it's sort of liberating "my Turing machine can compute"
> or "the Turing machine can't compute me".  Here the idea is to
> make sure there's that "my Turing machine can compute", first,
> then "the Turing machine can't compute me" doesn't result
> "my Turing machine can't compute".
>
>
> Framing these kinds of things in universals and the infinite
> is sort of for "it's an open box", for the anxiety-prone of
> the claustrophobic sort, vis-a-vis the agoraphobe, fear of
> being closed in or wide-open spaces.  I.e. for not offending
> the sensibilities, is first for "here's the great part,
> it's closed, out through the unbounded, each is closed",
> you know, deterministic, then "here's the kicker:  it's open",
> so that then they can imagine it in the infinite.
>
>
>
>
> (Here the subscripts are just to indicate the generator
> and the instructions, about what populates the tape
> then what reads the tape.)
>
>
>
> (The, "epistemological antinomies" would probably relate
> to "non-logical/properly-logical paradoxes" meaning
> terms introduced above the logic, vis-a-vis "logical
> paradoxes", what are just any of the usual sorts class/set
> distinction issues like in set theory after expansion of
> comprehension into quantifier disambiguation.  Here for
> example the UTM has the monad of its state, it's sort of
> non-logical.)
>
>
> I'm only a practicing sort of corp enterprise software
> eng dev where UTM's are really academic, but formal languages
> about automata more generally like state-machines are real
> apropos, there are bounds, it's unbounded, then I usually
> sort of describe things "survey, audit, gap", in terms of
> "sensible, fungible, tractable".  Got to know your "Big O".
>
> I studied foundations for thirty years though and sort of
> have a combined approach about uncountability and logical
> paradox, though.  Like in my youtube videos or 10,000's posts
> to sci.math I demand that there are at least three continuous
> domains in mathematics, including line-reals [0,1], the
> complete ordered field as field-reals, and signal-reals,
> about the analytic construction, and their doubling/halving spaces.
> So, I would probably explore that first, ..., Zeno you know.
> Yet, that's my opinion.
>
> Like "today we're going to talk Halting Problem or Entscheidungs,
> Branching Problem.  Does anybody not know Zeno?  Has everybody
> got that Goedel has complete arithmetic then incomplete arithmetic?
> Cantor's Uncountability and the Diagonal or Anti-Diagonal?
> Alright, since we already have bounded-tape Turing machines,
> Halting Problem is about same as Goedel incompleteness."
>
> Otherwise I'd just kind of leave that out.  It's enrichment,
> vis-a-vis formal languages, accepter/rejector, automata,
> states, open/closed items, in time, these kinds of things.
>
> I'd make such notions more part of a survey in foundations
> or formal systems than formal languages and formal automata
> (defined, deterministic, and closed).
>
>
> Russell's Antinomy, Goedel's Incompleteness, the Halting Problem,
> Cantor's Paradox (the universe would be its own powerset),
> these sort of go together in "a survey of confounding results".

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.

*The halting problem <is> an instance of self-reference paradox*
*that a ZFC like solution will cure*

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

On 2/19/2024 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.

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

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 Turing machine tape is defined to contain any sequence of symbols. You
want to change it so that a Turing machine tape contains any sequence of
symbols except for one that represents the input of a program to itself?

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.

>
> A Turing machine tape is defined to contain any sequence of symbols. You
> want to change it so that a Turing machine tape contains any sequence of
> symbols except for one that represents the input of a program to itself?

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

On 2/19/24 11:31 PM, olcott wrote:
> On 2/19/2024 10:21 PM, Ross Finlayson wrote:
>> On 02/19/2024 04:15 PM, Ben Bacarisse wrote:
>>> Ross Finlayson <ross.a.finlayson@gmail.com> writes:
>>>
>>>> What about if M_0(n) is a Turing machine of finite bound n,
>>>
>>> Care to define what that you mean?
>>>
>>>> then there exists M_1(m) where m > n or m >> n,
>>>> that is a halt decider for M_0(n).
>>>
>>> I'm not sure what role the subscripts 0 and 1 are playing here.  Also,
>>> I'd urge you to be careful about terms like "X is a ..." when I think
>>> you mean "X is any one of the class of ...".  It's OK provided everyone
>>> is on board, but when things are new, extra care is sometimes needed.
>>>
>>>> How about that?
>>>
>>> With appropriate definitions, I feel sure sure one can do something like
>>> that.
>>>
>>> Why are interested in such results?  Do they lead to some interesting
>>> theory?
>>>
>>
>> I think it's good the concept that the halting problem
>> makes for an argument that "static analysis always halts".
>>
>> What I mean by that is relating it to something like Zeno,
>> you show it doesn't go through, so show it never gets anywhere.
>>
>> So, showing completeness results first, then makes
>> for that the student doesn't get left with the idea
>> of "give up", instead "get over it", or "get through it".
>>
>> I.e. the idea is to make sure that there's completeness first,
>> then, to forestall the feeling locked in with absence of
>> free will or the conscious about it, instead, that incompleteness
>> is sort of framed as about "there's asymptotic freedom",
>> in a sense.
>>
>> Either way it's sort of liberating "my Turing machine can compute"
>> or "the Turing machine can't compute me".  Here the idea is to
>> make sure there's that "my Turing machine can compute", first,
>> then "the Turing machine can't compute me" doesn't result
>> "my Turing machine can't compute".
>>
>>
>> Framing these kinds of things in universals and the infinite
>> is sort of for "it's an open box", for the anxiety-prone of
>> the claustrophobic sort, vis-a-vis the agoraphobe, fear of
>> being closed in or wide-open spaces.  I.e. for not offending
>> the sensibilities, is first for "here's the great part,
>> it's closed, out through the unbounded, each is closed",
>> you know, deterministic, then "here's the kicker:  it's open",
>> so that then they can imagine it in the infinite.
>>
>>
>>
>>
>> (Here the subscripts are just to indicate the generator
>> and the instructions, about what populates the tape
>> then what reads the tape.)
>>
>>
>>
>> (The, "epistemological antinomies" would probably relate
>> to "non-logical/properly-logical paradoxes" meaning
>> terms introduced above the logic, vis-a-vis "logical
>> paradoxes", what are just any of the usual sorts class/set
>> distinction issues like in set theory after expansion of
>> comprehension into quantifier disambiguation.  Here for
>> example the UTM has the monad of its state, it's sort of
>> non-logical.)
>>
>>
>> I'm only a practicing sort of corp enterprise software
>> eng dev where UTM's are really academic, but formal languages
>> about automata more generally like state-machines are real
>> apropos, there are bounds, it's unbounded, then I usually
>> sort of describe things "survey, audit, gap", in terms of
>> "sensible, fungible, tractable".  Got to know your "Big O".
>>
>> I studied foundations for thirty years though and sort of
>> have a combined approach about uncountability and logical
>> paradox, though.  Like in my youtube videos or 10,000's posts
>> to sci.math I demand that there are at least three continuous
>> domains in mathematics, including line-reals [0,1], the
>> complete ordered field as field-reals, and signal-reals,
>> about the analytic construction, and their doubling/halving spaces.
>> So, I would probably explore that first, ..., Zeno you know.
>> Yet, that's my opinion.
>>
>> Like "today we're going to talk Halting Problem or Entscheidungs,
>> Branching Problem.  Does anybody not know Zeno?  Has everybody
>> got that Goedel has complete arithmetic then incomplete arithmetic?
>> Cantor's Uncountability and the Diagonal or Anti-Diagonal?
>> Alright, since we already have bounded-tape Turing machines,
>> Halting Problem is about same as Goedel incompleteness."
>>
>> Otherwise I'd just kind of leave that out.  It's enrichment,
>> vis-a-vis formal languages, accepter/rejector, automata,
>> states, open/closed items, in time, these kinds of things.
>>
>> I'd make such notions more part of a survey in foundations
>> or formal systems than formal languages and formal automata
>> (defined, deterministic, and closed).
>>
>>
>> Russell's Antinomy, Goedel's Incompleteness, the Halting Problem,
>> Cantor's Paradox (the universe would be its own powerset),
>> these sort of go together in "a survey of confounding results".
>
> 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.
>
> *The halting problem <is> an instance of self-reference paradox*
> *that a ZFC like solution will cure*
>

Nope.

Try to show how you can define a replacement for the definition of a
"Turing Machine" that doesn't allow the formation of that same problem.

The steps used to make H^ are basic fundamental steps, that no allowing
them means you break the power of the computation system.

Then you run into the issue that even if you somehow "ban" the contrary
action, there are still other (much more complicated) problem which can
be shown not to be computable, so you haven't actually fixed your issue.
Unless you totally destroy the power of computation, there will be
clearly definable problems that are not computable.

You are just proving your ignorance.

On 2/20/2024 6:34 AM, Richard Damon wrote:
> On 2/19/24 11:31 PM, olcott wrote:
>> On 2/19/2024 10:21 PM, Ross Finlayson wrote:
>>> On 02/19/2024 04:15 PM, Ben Bacarisse wrote:
>>>> Ross Finlayson <ross.a.finlayson@gmail.com> writes:
>>>>
>>>>> What about if M_0(n) is a Turing machine of finite bound n,
>>>>
>>>> Care to define what that you mean?
>>>>
>>>>> then there exists M_1(m) where m > n or m >> n,
>>>>> that is a halt decider for M_0(n).
>>>>
>>>> I'm not sure what role the subscripts 0 and 1 are playing here.  Also,
>>>> I'd urge you to be careful about terms like "X is a ..." when I think
>>>> you mean "X is any one of the class of ...".  It's OK provided everyone
>>>> is on board, but when things are new, extra care is sometimes needed.
>>>>
>>>>> How about that?
>>>>
>>>> With appropriate definitions, I feel sure sure one can do something
>>>> like
>>>> that.
>>>>
>>>> Why are interested in such results?  Do they lead to some interesting
>>>> theory?
>>>>
>>>
>>> I think it's good the concept that the halting problem
>>> makes for an argument that "static analysis always halts".
>>>
>>> What I mean by that is relating it to something like Zeno,
>>> you show it doesn't go through, so show it never gets anywhere.
>>>
>>> So, showing completeness results first, then makes
>>> for that the student doesn't get left with the idea
>>> of "give up", instead "get over it", or "get through it".
>>>
>>> I.e. the idea is to make sure that there's completeness first,
>>> then, to forestall the feeling locked in with absence of
>>> free will or the conscious about it, instead, that incompleteness
>>> is sort of framed as about "there's asymptotic freedom",
>>> in a sense.
>>>
>>> Either way it's sort of liberating "my Turing machine can compute"
>>> or "the Turing machine can't compute me".  Here the idea is to
>>> make sure there's that "my Turing machine can compute", first,
>>> then "the Turing machine can't compute me" doesn't result
>>> "my Turing machine can't compute".
>>>
>>>
>>> Framing these kinds of things in universals and the infinite
>>> is sort of for "it's an open box", for the anxiety-prone of
>>> the claustrophobic sort, vis-a-vis the agoraphobe, fear of
>>> being closed in or wide-open spaces.  I.e. for not offending
>>> the sensibilities, is first for "here's the great part,
>>> it's closed, out through the unbounded, each is closed",
>>> you know, deterministic, then "here's the kicker:  it's open",
>>> so that then they can imagine it in the infinite.
>>>
>>>
>>>
>>>
>>> (Here the subscripts are just to indicate the generator
>>> and the instructions, about what populates the tape
>>> then what reads the tape.)
>>>
>>>
>>>
>>> (The, "epistemological antinomies" would probably relate
>>> to "non-logical/properly-logical paradoxes" meaning
>>> terms introduced above the logic, vis-a-vis "logical
>>> paradoxes", what are just any of the usual sorts class/set
>>> distinction issues like in set theory after expansion of
>>> comprehension into quantifier disambiguation.  Here for
>>> example the UTM has the monad of its state, it's sort of
>>> non-logical.)
>>>
>>>
>>> I'm only a practicing sort of corp enterprise software
>>> eng dev where UTM's are really academic, but formal languages
>>> about automata more generally like state-machines are real
>>> apropos, there are bounds, it's unbounded, then I usually
>>> sort of describe things "survey, audit, gap", in terms of
>>> "sensible, fungible, tractable".  Got to know your "Big O".
>>>
>>> I studied foundations for thirty years though and sort of
>>> have a combined approach about uncountability and logical
>>> paradox, though.  Like in my youtube videos or 10,000's posts
>>> to sci.math I demand that there are at least three continuous
>>> domains in mathematics, including line-reals [0,1], the
>>> complete ordered field as field-reals, and signal-reals,
>>> about the analytic construction, and their doubling/halving spaces.
>>> So, I would probably explore that first, ..., Zeno you know.
>>> Yet, that's my opinion.
>>>
>>> Like "today we're going to talk Halting Problem or Entscheidungs,
>>> Branching Problem.  Does anybody not know Zeno?  Has everybody
>>> got that Goedel has complete arithmetic then incomplete arithmetic?
>>> Cantor's Uncountability and the Diagonal or Anti-Diagonal?
>>> Alright, since we already have bounded-tape Turing machines,
>>> Halting Problem is about same as Goedel incompleteness."
>>>
>>> Otherwise I'd just kind of leave that out.  It's enrichment,
>>> vis-a-vis formal languages, accepter/rejector, automata,
>>> states, open/closed items, in time, these kinds of things.
>>>
>>> I'd make such notions more part of a survey in foundations
>>> or formal systems than formal languages and formal automata
>>> (defined, deterministic, and closed).
>>>
>>>
>>> Russell's Antinomy, Goedel's Incompleteness, the Halting Problem,
>>> Cantor's Paradox (the universe would be its own powerset),
>>> these sort of go together in "a survey of confounding results".
>>
>> 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.
>>
>> *The halting problem <is> an instance of self-reference paradox*
>> *that a ZFC like solution will cure*
>>
>
>
> Nope.
>
> Try to show how you can define a replacement for the definition of a
> "Turing Machine" that doesn't allow the formation of that same problem.

Just like my simplification of Tarski's Undefinability Proof:
Boolean True(English, "This sentence is not true.")

When a correct and consistent truth predicate / halt decider
rejects self-contradictory inputs as invalid then as with
ZFC applied to Russell's Paradox the paradox is abolished.

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

On 2/20/24 9:05 AM, olcott wrote:
> On 2/20/2024 6:34 AM, Richard Damon wrote:
>> On 2/19/24 11:31 PM, olcott wrote:
>>> On 2/19/2024 10:21 PM, Ross Finlayson wrote:
>>>> On 02/19/2024 04:15 PM, Ben Bacarisse wrote:
>>>>> Ross Finlayson <ross.a.finlayson@gmail.com> writes:
>>>>>
>>>>>> What about if M_0(n) is a Turing machine of finite bound n,
>>>>>
>>>>> Care to define what that you mean?
>>>>>
>>>>>> then there exists M_1(m) where m > n or m >> n,
>>>>>> that is a halt decider for M_0(n).
>>>>>
>>>>> I'm not sure what role the subscripts 0 and 1 are playing here.  Also,
>>>>> I'd urge you to be careful about terms like "X is a ..." when I think
>>>>> you mean "X is any one of the class of ...".  It's OK provided
>>>>> everyone
>>>>> is on board, but when things are new, extra care is sometimes needed.
>>>>>
>>>>>> How about that?
>>>>>
>>>>> With appropriate definitions, I feel sure sure one can do something
>>>>> like
>>>>> that.
>>>>>
>>>>> Why are interested in such results?  Do they lead to some interesting
>>>>> theory?
>>>>>
>>>>
>>>> I think it's good the concept that the halting problem
>>>> makes for an argument that "static analysis always halts".
>>>>
>>>> What I mean by that is relating it to something like Zeno,
>>>> you show it doesn't go through, so show it never gets anywhere.
>>>>
>>>> So, showing completeness results first, then makes
>>>> for that the student doesn't get left with the idea
>>>> of "give up", instead "get over it", or "get through it".
>>>>
>>>> I.e. the idea is to make sure that there's completeness first,
>>>> then, to forestall the feeling locked in with absence of
>>>> free will or the conscious about it, instead, that incompleteness
>>>> is sort of framed as about "there's asymptotic freedom",
>>>> in a sense.
>>>>
>>>> Either way it's sort of liberating "my Turing machine can compute"
>>>> or "the Turing machine can't compute me".  Here the idea is to
>>>> make sure there's that "my Turing machine can compute", first,
>>>> then "the Turing machine can't compute me" doesn't result
>>>> "my Turing machine can't compute".
>>>>
>>>>
>>>> Framing these kinds of things in universals and the infinite
>>>> is sort of for "it's an open box", for the anxiety-prone of
>>>> the claustrophobic sort, vis-a-vis the agoraphobe, fear of
>>>> being closed in or wide-open spaces.  I.e. for not offending
>>>> the sensibilities, is first for "here's the great part,
>>>> it's closed, out through the unbounded, each is closed",
>>>> you know, deterministic, then "here's the kicker:  it's open",
>>>> so that then they can imagine it in the infinite.
>>>>
>>>>
>>>>
>>>>
>>>> (Here the subscripts are just to indicate the generator
>>>> and the instructions, about what populates the tape
>>>> then what reads the tape.)
>>>>
>>>>
>>>>
>>>> (The, "epistemological antinomies" would probably relate
>>>> to "non-logical/properly-logical paradoxes" meaning
>>>> terms introduced above the logic, vis-a-vis "logical
>>>> paradoxes", what are just any of the usual sorts class/set
>>>> distinction issues like in set theory after expansion of
>>>> comprehension into quantifier disambiguation.  Here for
>>>> example the UTM has the monad of its state, it's sort of
>>>> non-logical.)
>>>>
>>>>
>>>> I'm only a practicing sort of corp enterprise software
>>>> eng dev where UTM's are really academic, but formal languages
>>>> about automata more generally like state-machines are real
>>>> apropos, there are bounds, it's unbounded, then I usually
>>>> sort of describe things "survey, audit, gap", in terms of
>>>> "sensible, fungible, tractable".  Got to know your "Big O".
>>>>
>>>> I studied foundations for thirty years though and sort of
>>>> have a combined approach about uncountability and logical
>>>> paradox, though.  Like in my youtube videos or 10,000's posts
>>>> to sci.math I demand that there are at least three continuous
>>>> domains in mathematics, including line-reals [0,1], the
>>>> complete ordered field as field-reals, and signal-reals,
>>>> about the analytic construction, and their doubling/halving spaces.
>>>> So, I would probably explore that first, ..., Zeno you know.
>>>> Yet, that's my opinion.
>>>>
>>>> Like "today we're going to talk Halting Problem or Entscheidungs,
>>>> Branching Problem.  Does anybody not know Zeno?  Has everybody
>>>> got that Goedel has complete arithmetic then incomplete arithmetic?
>>>> Cantor's Uncountability and the Diagonal or Anti-Diagonal?
>>>> Alright, since we already have bounded-tape Turing machines,
>>>> Halting Problem is about same as Goedel incompleteness."
>>>>
>>>> Otherwise I'd just kind of leave that out.  It's enrichment,
>>>> vis-a-vis formal languages, accepter/rejector, automata,
>>>> states, open/closed items, in time, these kinds of things.
>>>>
>>>> I'd make such notions more part of a survey in foundations
>>>> or formal systems than formal languages and formal automata
>>>> (defined, deterministic, and closed).
>>>>
>>>>
>>>> Russell's Antinomy, Goedel's Incompleteness, the Halting Problem,
>>>> Cantor's Paradox (the universe would be its own powerset),
>>>> these sort of go together in "a survey of confounding results".
>>>
>>> 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.
>>>
>>> *The halting problem <is> an instance of self-reference paradox*
>>> *that a ZFC like solution will cure*
>>>
>>
>>
>> Nope.
>>
>> Try to show how you can define a replacement for the definition of a
>> "Turing Machine" that doesn't allow the formation of that same problem.
>
> Just like my simplification of Tarski's Undefinability Proof:
> Boolean True(English, "This sentence is not true.")

But that isn't a "simplification" of his proof, just a demonstration tha
tyou don't understand what he is talking about.

It just shows that you think "Strawmen" are valid argument forms.

>
> When a correct and consistent truth predicate / halt decider
> rejects self-contradictory inputs as invalid then as with
> ZFC applied to Russell's Paradox the paradox is abolished.
>

Nope, he shows that the mere existance of a truth predicate means that
we can prove that the "Liar" has a valid truth value.

Thus, since that can't be right, we can't have the existance of a valid
Truth Predicate.

Note, the ZFC rule can't be applied here, as the "problem" comes in via
to indirect of a path, and in effect, you would need to solve halting
(in the currect definition) to be able to reject you "invalid" inputs.

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?