• Re: A different perspective on undecidability --- incorrect question

    From Richard Damon@21:1/5 to olcott on Mon Oct 21 22:48:41 2024
    On 10/21/24 10:04 PM, olcott wrote:
    On 10/16/2024 11:37 AM, Mikko wrote:
    On 2024-10-16 14:27:09 +0000, olcott said:

    The whole notion of undecidability is anchored in ignoring the fact that >>> some expressions of language are simply not truth bearers.

    A formal theory is undecidable if there is no Turing machine that
    determines whether a formula of that theory is a theorem of that
    theory or not. Whether an expression is a truth bearer is not
    relevant. Either there is a valid proof of that formula or there
    is not. No third possibility.


    After being continually interrupted by emergencies
    interrupting other emergencies...

    If the answer to the question: Is X a formula of theory Y
    cannot be determined to be yes or no then the question
    itself is somehow incorrect.

    Only if "can not be determined" means that there isn't an actual answer
    to it,

    Not that we don't know the answer to it.

    For instance, the Twin Primes conjecture is either True, or it is False,
    it can't be a non-truth-bearer, as either there is or there isn't a
    highest pair of primes that differs by two.

    The fact we don't know, and maybe can never know, doesn't make the
    question incorrect.

    Some truth is just unknowable.


    An incorrect question is an expression of language that
    is not a truth bearer translated into question form.

    Right, and a question that we don't know (or maybe can't know) but is
    either true or false, is not an incorrect question.


    When "X a formula of theory Y" is neither true nor false
    then "X a formula of theory Y" is not a truth bearer.




    Does D halt, is not an incorrect question, as it will halt or not.

    That the H that it was built from won't give the right answer is irrelevent.

    You just don't understand what the terms mean, because you CHOSE to make youself ignorant, and thus INTENTIONALY made yourself into a pathetic
    ignorant pathological lying idiot.

    Sorry, but that is the facts.

    --- SoupGate-Win32 v1.05
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  • From Mikko@21:1/5 to olcott on Tue Oct 22 10:39:52 2024
    On 2024-10-22 02:04:14 +0000, olcott said:

    On 10/16/2024 11:37 AM, Mikko wrote:
    On 2024-10-16 14:27:09 +0000, olcott said:

    The whole notion of undecidability is anchored in ignoring the fact that >>> some expressions of language are simply not truth bearers.

    A formal theory is undecidable if there is no Turing machine that
    determines whether a formula of that theory is a theorem of that
    theory or not. Whether an expression is a truth bearer is not
    relevant. Either there is a valid proof of that formula or there
    is not. No third possibility.


    After being continually interrupted by emergencies
    interrupting other emergencies...

    If the answer to the question: Is X a formula of theory Y
    cannot be determined to be yes or no then the question
    itself is somehow incorrect.

    There are several possibilities.

    A theory may be intentionally incomplete. For example, group theory
    leaves several important question unanswered. There are infinitely
    may different groups and group axioms must be true in every group.

    Another possibility is that a theory is poorly constructed: the
    author just failed to include an important postulate.

    Then there is the possibility that the purpose of the theory is
    incompatible with decidability, for example arithmetic.

    An incorrect question is an expression of language that
    is not a truth bearer translated into question form.

    When "X a formula of theory Y" is neither true nor false
    then "X a formula of theory Y" is not a truth bearer.

    Whether AB = BA is not answered by group theory but is alwasy
    true or false about specific A and B and universally true in
    some groups but not all.

    --
    Mikko

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Damon@21:1/5 to olcott on Tue Oct 22 07:22:42 2024
    On 10/21/24 11:17 PM, olcott wrote:
    On 10/21/2024 9:48 PM, Richard Damon wrote:
    On 10/21/24 10:04 PM, olcott wrote:
    On 10/16/2024 11:37 AM, Mikko wrote:
    On 2024-10-16 14:27:09 +0000, olcott said:

    The whole notion of undecidability is anchored in ignoring the fact
    that
    some expressions of language are simply not truth bearers.

    A formal theory is undecidable if there is no Turing machine that
    determines whether a formula of that theory is a theorem of that
    theory or not. Whether an expression is a truth bearer is not
    relevant. Either there is a valid proof of that formula or there
    is not. No third possibility.


    After being continually interrupted by emergencies
    interrupting other emergencies...

    If the answer to the question: Is X a formula of theory Y
    cannot be determined to be yes or no then the question
    itself is somehow incorrect.

    Only if "can not be determined" means that there isn't an actual
    answer to it,

    Not that we don't know the answer to it.

    For instance, the Twin Primes conjecture is either True, or it is
    False, it can't be a non-truth-bearer, as either there is or there
    isn't a highest pair of primes that differs by two.


    Sure.

    So, you agree your definition is wrong


    The fact we don't know, and maybe can never know, doesn't make the
    question incorrect.

    Some truth is just unknowable.


    Sure.

    And again.


    An incorrect question is an expression of language that
    is not a truth bearer translated into question form.

    Right, and a question that we don't know (or maybe can't know) but is
    either true or false, is not an incorrect question.


    Sure.

    So you argee again that you proposition is wrong.



    When "X a formula of theory Y" is neither true nor false
    then "X a formula of theory Y" is not a truth bearer.




    Does D halt, is not an incorrect question, as it will halt or not.


    Tarski is a simpler example for this case.
    His theory rightfully cannot determine whether
    the following sentence is true or false:
    "This sentence is not true".
    Because that sentence is not a truth bearer.

    No, that isn't his statement, but of course your problem is you can't understand his actual statement so need to paraphrase it, and that loses
    some critical properties.


    That does not mean that True(L,x) cannot be defined.
    It only means that some expression ore not truth bearers.

    His proof does, the fact that you don't undetstand what he is talking
    about doesn't make him wrong.

    You asserting he is wrong becuase you don't understand his proof makes
    you wrong, and STUPID.


    That the H that it was built from won't give the right answer is
    irrelevent.

    You just don't understand what the terms mean, because you CHOSE to
    make youself ignorant, and thus INTENTIONALY made yourself into a
    pathetic ignorant pathological lying idiot.

    Sorry, but that is the facts.






    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Damon@21:1/5 to olcott on Tue Oct 22 23:02:23 2024
    On 10/22/24 10:56 AM, olcott wrote:
    On 10/22/2024 6:22 AM, Richard Damon wrote:
    On 10/21/24 11:17 PM, olcott wrote:
    On 10/21/2024 9:48 PM, Richard Damon wrote:
    On 10/21/24 10:04 PM, olcott wrote:
    On 10/16/2024 11:37 AM, Mikko wrote:
    On 2024-10-16 14:27:09 +0000, olcott said:

    The whole notion of undecidability is anchored in ignoring the
    fact that
    some expressions of language are simply not truth bearers.

    A formal theory is undecidable if there is no Turing machine that
    determines whether a formula of that theory is a theorem of that
    theory or not. Whether an expression is a truth bearer is not
    relevant. Either there is a valid proof of that formula or there
    is not. No third possibility.


    After being continually interrupted by emergencies
    interrupting other emergencies...

    If the answer to the question: Is X a formula of theory Y
    cannot be determined to be yes or no then the question
    itself is somehow incorrect.

    Only if "can not be determined" means that there isn't an actual
    answer to it,

    Not that we don't know the answer to it.

    For instance, the Twin Primes conjecture is either True, or it is
    False, it can't be a non-truth-bearer, as either there is or there
    isn't a highest pair of primes that differs by two.


    Sure.

    So, you agree your definition is wrong


    The fact we don't know, and maybe can never know, doesn't make the
    question incorrect.

    Some truth is just unknowable.


    Sure.

    And again.


    An incorrect question is an expression of language that
    is not a truth bearer translated into question form.

    Right, and a question that we don't know (or maybe can't know) but
    is either true or false, is not an incorrect question.


    Sure.

    So you argee again that you proposition is wrong.



    When "X a formula of theory Y" is neither true nor false
    then "X a formula of theory Y" is not a truth bearer.




    Does D halt, is not an incorrect question, as it will halt or not.


    Tarski is a simpler example for this case.
    His theory rightfully cannot determine whether
    the following sentence is true or false:
    "This sentence is not true".
    Because that sentence is not a truth bearer.

    No, that isn't his statement, but of course your problem is you can't
    understand his actual statement so need to paraphrase it, and that
    loses some critical properties.



    Haskell Curry species expressions of theory {T} that are
    stipulated to be true:

       Thus, given {T}, an elementary theorem is an
       elementary statement which is true. https://www.liarparadox.org/Haskell_Curry_45.pdf

    When we start with the foundation that True(L,x) is defined
    as applying a set of truth preserving operations to a set
    of expressions of language stipulated to be true Tarski's
    proof fails.

    We overcome Tarski Undefinability the same way that ZFC
    overcame Russell's Paradox. We replace the prior foundation
    with a new one.

    https://liarparadox.org/Tarski_275_276.pdf

    So, DO THAT then, and show what you get.

    So, just as Z and F did, and went through ALL the logical proofs to show
    what you could do with there rules, write up your complete set of rules
    and then show what can be done with it.

    You have been told this for years, but don't seem to understand, perhaps because you don't understand the basics well enough to actually do that.

    Note, it isn't just the summary you will find on the informal sites that
    you need to do, but the FORMAL PROOF that is in their academic papers.

    Papers you probably can't understand.

    And not, that since you are moving to a more basic level, of changing
    the fundamental rules of the logic, you can't just assume any of the
    existing logic principles still work.

    This may well be the sort of thing where it takes 20 pages to show that
    2 + 3 = 5 at the fundamental level of defining what + means.



    That does not mean that True(L,x) cannot be defined.
    It only means that some expression ore not truth bearers.

    His proof does, the fact that you don't undetstand what he is talking
    about doesn't make him wrong.

    You asserting he is wrong becuase you don't understand his proof makes
    you wrong, and STUPID.


    That the H that it was built from won't give the right answer is
    irrelevent.

    You just don't understand what the terms mean, because you CHOSE to
    make youself ignorant, and thus INTENTIONALY made yourself into a
    pathetic ignorant pathological lying idiot.

    Sorry, but that is the facts.









    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Mikko@21:1/5 to olcott on Thu Oct 24 17:06:08 2024
    On 2024-10-22 15:04:37 +0000, olcott said:

    On 10/22/2024 2:39 AM, Mikko wrote:
    On 2024-10-22 02:04:14 +0000, olcott said:

    On 10/16/2024 11:37 AM, Mikko wrote:
    On 2024-10-16 14:27:09 +0000, olcott said:

    The whole notion of undecidability is anchored in ignoring the fact that >>>>> some expressions of language are simply not truth bearers.

    A formal theory is undecidable if there is no Turing machine that
    determines whether a formula of that theory is a theorem of that
    theory or not. Whether an expression is a truth bearer is not
    relevant. Either there is a valid proof of that formula or there
    is not. No third possibility.


    After being continually interrupted by emergencies
    interrupting other emergencies...

    If the answer to the question: Is X a formula of theory Y
    cannot be determined to be yes or no then the question
    itself is somehow incorrect.

    There are several possibilities.

    A theory may be intentionally incomplete. For example, group theory
    leaves several important question unanswered. There are infinitely
    may different groups and group axioms must be true in every group.

    Another possibility is that a theory is poorly constructed: the
    author just failed to include an important postulate.

    Then there is the possibility that the purpose of the theory is
    incompatible with decidability, for example arithmetic.

    An incorrect question is an expression of language that
    is not a truth bearer translated into question form.

    When "X a formula of theory Y" is neither true nor false
    then "X a formula of theory Y" is not a truth bearer.

    Whether AB = BA is not answered by group theory but is alwasy
    true or false about specific A and B and universally true in
    some groups but not all.

    See my most recent reply to Richard it sums up
    my position most succinctly.

    We already know that your position is uninteresting.

    --
    Mikko

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Damon@21:1/5 to olcott on Thu Oct 24 19:46:42 2024
    On 10/24/24 12:07 PM, olcott wrote:
    On 10/24/2024 9:06 AM, Mikko wrote:
    On 2024-10-22 15:04:37 +0000, olcott said:

    On 10/22/2024 2:39 AM, Mikko wrote:
    On 2024-10-22 02:04:14 +0000, olcott said:

    On 10/16/2024 11:37 AM, Mikko wrote:
    On 2024-10-16 14:27:09 +0000, olcott said:

    The whole notion of undecidability is anchored in ignoring the
    fact that
    some expressions of language are simply not truth bearers.

    A formal theory is undecidable if there is no Turing machine that
    determines whether a formula of that theory is a theorem of that
    theory or not. Whether an expression is a truth bearer is not
    relevant. Either there is a valid proof of that formula or there
    is not. No third possibility.


    After being continually interrupted by emergencies
    interrupting other emergencies...

    If the answer to the question: Is X a formula of theory Y
    cannot be determined to be yes or no then the question
    itself is somehow incorrect.

    There are several possibilities.

    A theory may be intentionally incomplete. For example, group theory
    leaves several important question unanswered. There are infinitely
    may different groups and group axioms must be true in every group.

    Another possibility is that a theory is poorly constructed: the
    author just failed to include an important postulate.

    Then there is the possibility that the purpose of the theory is
    incompatible with decidability, for example arithmetic.

    An incorrect question is an expression of language that
    is not a truth bearer translated into question form.

    When "X a formula of theory Y" is neither true nor false
    then "X a formula of theory Y" is not a truth bearer.

    Whether AB = BA is not answered by group theory but is alwasy
    true or false about specific A and B and universally true in
    some groups but not all.

    See my most recent reply to Richard it sums up
    my position most succinctly.

    We already know that your position is uninteresting.


    Don't want to bother to look at it (AKA uninteresting) is not at
    all the same thing as the corrected foundation to computability
    does not eliminate undecidability. It does eliminate undecidability
    and not bothering to look at it is no actual rebuttal.


    So, you admit that you haven't actually rebutted any of the errors
    pointed out in your logic, as saying they are not interesting isn't
    actually a rebuttal.

    Thus you admit that nothing you have said has any useful basis.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Mikko@21:1/5 to olcott on Fri Oct 25 11:14:42 2024
    On 2024-10-24 16:07:03 +0000, olcott said:

    On 10/24/2024 9:06 AM, Mikko wrote:
    On 2024-10-22 15:04:37 +0000, olcott said:

    On 10/22/2024 2:39 AM, Mikko wrote:
    On 2024-10-22 02:04:14 +0000, olcott said:

    On 10/16/2024 11:37 AM, Mikko wrote:
    On 2024-10-16 14:27:09 +0000, olcott said:

    The whole notion of undecidability is anchored in ignoring the fact that
    some expressions of language are simply not truth bearers.

    A formal theory is undecidable if there is no Turing machine that
    determines whether a formula of that theory is a theorem of that
    theory or not. Whether an expression is a truth bearer is not
    relevant. Either there is a valid proof of that formula or there
    is not. No third possibility.


    After being continually interrupted by emergencies
    interrupting other emergencies...

    If the answer to the question: Is X a formula of theory Y
    cannot be determined to be yes or no then the question
    itself is somehow incorrect.

    There are several possibilities.

    A theory may be intentionally incomplete. For example, group theory
    leaves several important question unanswered. There are infinitely
    may different groups and group axioms must be true in every group.

    Another possibility is that a theory is poorly constructed: the
    author just failed to include an important postulate.

    Then there is the possibility that the purpose of the theory is
    incompatible with decidability, for example arithmetic.

    An incorrect question is an expression of language that
    is not a truth bearer translated into question form.

    When "X a formula of theory Y" is neither true nor false
    then "X a formula of theory Y" is not a truth bearer.

    Whether AB = BA is not answered by group theory but is alwasy
    true or false about specific A and B and universally true in
    some groups but not all.

    See my most recent reply to Richard it sums up
    my position most succinctly.

    We already know that your position is uninteresting.


    Don't want to bother to look at it (AKA uninteresting) is not at
    all the same thing as the corrected foundation to computability
    does not eliminate undecidability.

    No, but we already know that you don't offer anything interesting
    about foundations to computability or undecidabilty. Ae also know
    that a good foundation to computability does not eliminate
    undecidablility but proves it, and also proves uncomputablility
    of various functions.

    Whether some foundation can be correct or what it would mean to
    call it so is a different problem.

    It does eliminate undecidability
    and not bothering to look at it is no actual rebuttal.

    You may say so but you don't offer any good argument to support
    that claim. Instead you offer various indications that you will
    never present a good argument about anything.

    --
    Mikko

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Damon@21:1/5 to olcott on Fri Oct 25 12:01:02 2024
    On 10/25/24 10:37 AM, olcott wrote:
    On 10/25/2024 3:14 AM, Mikko wrote:
    On 2024-10-24 16:07:03 +0000, olcott said:

    On 10/24/2024 9:06 AM, Mikko wrote:
    On 2024-10-22 15:04:37 +0000, olcott said:

    On 10/22/2024 2:39 AM, Mikko wrote:
    On 2024-10-22 02:04:14 +0000, olcott said:

    On 10/16/2024 11:37 AM, Mikko wrote:
    On 2024-10-16 14:27:09 +0000, olcott said:

    The whole notion of undecidability is anchored in ignoring the >>>>>>>>> fact that
    some expressions of language are simply not truth bearers.

    A formal theory is undecidable if there is no Turing machine that >>>>>>>> determines whether a formula of that theory is a theorem of that >>>>>>>> theory or not. Whether an expression is a truth bearer is not
    relevant. Either there is a valid proof of that formula or there >>>>>>>> is not. No third possibility.


    After being continually interrupted by emergencies
    interrupting other emergencies...

    If the answer to the question: Is X a formula of theory Y
    cannot be determined to be yes or no then the question
    itself is somehow incorrect.

    There are several possibilities.

    A theory may be intentionally incomplete. For example, group theory >>>>>> leaves several important question unanswered. There are infinitely >>>>>> may different groups and group axioms must be true in every group. >>>>>>
    Another possibility is that a theory is poorly constructed: the
    author just failed to include an important postulate.

    Then there is the possibility that the purpose of the theory is
    incompatible with decidability, for example arithmetic.

    An incorrect question is an expression of language that
    is not a truth bearer translated into question form.

    When "X a formula of theory Y" is neither true nor false
    then "X a formula of theory Y" is not a truth bearer.

    Whether AB = BA is not answered by group theory but is alwasy
    true or false about specific A and B and universally true in
    some groups but not all.

    See my most recent reply to Richard it sums up
    my position most succinctly.

    We already know that your position is uninteresting.


    Don't want to bother to look at it (AKA uninteresting) is not at
    all the same thing as the corrected foundation to computability
    does not eliminate undecidability.

    No, but we already know that you don't offer anything interesting
    about foundations to computability or undecidabilty.

    In the same way that ZFC eliminated RP True_Olcott(L,x)
    eliminates undecidability. Not bothering to pay attention
    is less than no rebuttal what-so-ever.


    Then you plan to do the work to show this?

    Or do you think ZF only wrote down there rules and said to everyone,
    just believe us, this fixes everything.

    Of course, my guess is you have on idea how to do that, as you don't
    understand how the logic works.

    I am not sure if you understand what is needed to even properly define
    your initial set of axioms to build your logic on.

    And by changing the rules of logic, you need to rederive the rules of
    logic under your system, and then show that they are at least as useful
    as the classical one.

    ZF had the advantage that it was well known that "Naive" set theory was
    broken, and so people were looking for something to replace it.

    Until you can actually demonstrate that something logictians want is
    broken, you have a major uphill battle.

    The fact that many systems are incomplete, and many problems turn out to
    be uncomputable isn't a problem in logic, as it has been shown to be a
    pretty natural proerty following from the power of the logic system to
    express more than can be actually known.

    All I can see is your logic system tries to work by limiting what can be
    talked about, to keep things under that threshold where capability to
    express grows faster than the capability to know does, which leads to
    those properties.

    I am also not sure if your ideas are really knew, as there are a number
    of theories of restricted logic, and you haven't been about to define
    yours well enough to compare them. I am not sure YOU even undertstand
    what you want well enough to actually definie it to do so.


    Ae also know
    that a good foundation to computability does not eliminate
    undecidablility but proves it, and also proves uncomputablility
    of various functions.

    Whether some foundation can be correct or what it would mean to
    call it so is a different problem.

    It does eliminate undecidability
    and not bothering to look at it is no actual rebuttal.

    You may say so but you don't offer any good argument to support
    that claim. Instead you offer various indications that you will
    never present a good argument about anything.




    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Mikko@21:1/5 to olcott on Sat Oct 26 10:52:35 2024
    On 2024-10-25 14:37:19 +0000, olcott said:

    On 10/25/2024 3:14 AM, Mikko wrote:
    On 2024-10-24 16:07:03 +0000, olcott said:

    On 10/24/2024 9:06 AM, Mikko wrote:
    On 2024-10-22 15:04:37 +0000, olcott said:

    On 10/22/2024 2:39 AM, Mikko wrote:
    On 2024-10-22 02:04:14 +0000, olcott said:

    On 10/16/2024 11:37 AM, Mikko wrote:
    On 2024-10-16 14:27:09 +0000, olcott said:

    The whole notion of undecidability is anchored in ignoring the fact that
    some expressions of language are simply not truth bearers.

    A formal theory is undecidable if there is no Turing machine that >>>>>>>> determines whether a formula of that theory is a theorem of that >>>>>>>> theory or not. Whether an expression is a truth bearer is not
    relevant. Either there is a valid proof of that formula or there >>>>>>>> is not. No third possibility.


    After being continually interrupted by emergencies
    interrupting other emergencies...

    If the answer to the question: Is X a formula of theory Y
    cannot be determined to be yes or no then the question
    itself is somehow incorrect.

    There are several possibilities.

    A theory may be intentionally incomplete. For example, group theory >>>>>> leaves several important question unanswered. There are infinitely >>>>>> may different groups and group axioms must be true in every group. >>>>>>
    Another possibility is that a theory is poorly constructed: the
    author just failed to include an important postulate.

    Then there is the possibility that the purpose of the theory is
    incompatible with decidability, for example arithmetic.

    An incorrect question is an expression of language that
    is not a truth bearer translated into question form.

    When "X a formula of theory Y" is neither true nor false
    then "X a formula of theory Y" is not a truth bearer.

    Whether AB = BA is not answered by group theory but is alwasy
    true or false about specific A and B and universally true in
    some groups but not all.

    See my most recent reply to Richard it sums up
    my position most succinctly.

    We already know that your position is uninteresting.


    Don't want to bother to look at it (AKA uninteresting) is not at
    all the same thing as the corrected foundation to computability
    does not eliminate undecidability.

    No, but we already know that you don't offer anything interesting
    about foundations to computability or undecidabilty.

    In the same way that ZFC eliminated RP True_Olcott(L,x)
    eliminates undecidability. Not bothering to pay attention
    is less than no rebuttal what-so-ever.

    No, not in the same way. ZFC is a useful set theory for many purposes.
    You don't offer any useful theory for any purpose.

    --
    Mikko

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Damon@21:1/5 to olcott on Sat Oct 26 11:48:49 2024
    On 10/26/24 8:59 AM, olcott wrote:
    On 10/26/2024 2:52 AM, Mikko wrote:
    On 2024-10-25 14:37:19 +0000, olcott said:

    On 10/25/2024 3:14 AM, Mikko wrote:
    On 2024-10-24 16:07:03 +0000, olcott said:

    On 10/24/2024 9:06 AM, Mikko wrote:
    On 2024-10-22 15:04:37 +0000, olcott said:

    On 10/22/2024 2:39 AM, Mikko wrote:
    On 2024-10-22 02:04:14 +0000, olcott said:

    On 10/16/2024 11:37 AM, Mikko wrote:
    On 2024-10-16 14:27:09 +0000, olcott said:

    The whole notion of undecidability is anchored in ignoring >>>>>>>>>>> the fact that
    some expressions of language are simply not truth bearers. >>>>>>>>>>
    A formal theory is undecidable if there is no Turing machine that >>>>>>>>>> determines whether a formula of that theory is a theorem of that >>>>>>>>>> theory or not. Whether an expression is a truth bearer is not >>>>>>>>>> relevant. Either there is a valid proof of that formula or there >>>>>>>>>> is not. No third possibility.


    After being continually interrupted by emergencies
    interrupting other emergencies...

    If the answer to the question: Is X a formula of theory Y
    cannot be determined to be yes or no then the question
    itself is somehow incorrect.

    There are several possibilities.

    A theory may be intentionally incomplete. For example, group theory >>>>>>>> leaves several important question unanswered. There are infinitely >>>>>>>> may different groups and group axioms must be true in every group. >>>>>>>>
    Another possibility is that a theory is poorly constructed: the >>>>>>>> author just failed to include an important postulate.

    Then there is the possibility that the purpose of the theory is >>>>>>>> incompatible with decidability, for example arithmetic.

    An incorrect question is an expression of language that
    is not a truth bearer translated into question form.

    When "X a formula of theory Y" is neither true nor false
    then "X a formula of theory Y" is not a truth bearer.

    Whether AB = BA is not answered by group theory but is alwasy
    true or false about specific A and B and universally true in
    some groups but not all.

    See my most recent reply to Richard it sums up
    my position most succinctly.

    We already know that your position is uninteresting.


    Don't want to bother to look at it (AKA uninteresting) is not at
    all the same thing as the corrected foundation to computability
    does not eliminate undecidability.

    No, but we already know that you don't offer anything interesting
    about foundations to computability or undecidabilty.

    In the same way that ZFC eliminated RP True_Olcott(L,x)
    eliminates undecidability. Not bothering to pay attention
    is less than no rebuttal what-so-ever.

    No, not in the same way.

    Pathological self reference causes an issue in both cases.
    This issue is resolved by disallowing it in both cases.

    Nope, because is set theory, the "self-reference" was only directly
    available in the definition of a set. By disallowing the set itself to
    be in the set of things it can contain, ZF eleminated the problem.

    For computations we have the problem that BY DEFINITION they need to be
    able to handle "ANY" finite input string.

    And, since any computation can be expressed as a finite string, we can
    not exclude as the input, a string that represents the program (or
    contains which incudes the program as part of the input).

    The problem gets compounded in that there aren't just a "few" inputs
    that could repreesent the program,


    When we disallow the Liar Paradox then Tarski cannot derive
    the first state of his proof and his proof fails.

    But he shows that you can, and thus your claim fails. All you are saying
    is that if we take "all" to not mean "all" we might be able to do
    something, but since all does mean all, that can't apply.


    Tarski's Liar Paradox from page 248
       It would then be possible to reconstruct the antinomy of the liar
       in the metalanguage, by forming in the language itself a sentence
       x such that the sentence of the metalanguage which is correlated
       with x asserts that x is not a true sentence.
       https://liarparadox.org/Tarski_247_248.pdf


    By which he shows that the language itself has been shown to support the representation of the Liar's Paradox, and thus it *IS* a valid input.



    Formalized as:
    x ∉ True if and only if p
    where the symbol 'p' represents the whole sentence x https://liarparadox.org/Tarski_275_276.pdf

    adapted to become this
    x ∉ Pr if and only if p  // line 1 of the proof

    Here is the Tarski Undefinability Theorem proof
    (1) x ∉ Provable if and only if p       // assumption (see above)
    (2) x ∈ True if and only if p              // Tarski's convention T
    (3) x ∉ Provable if and only if x ∈ True. // (1) and (2) combined
    (4) either x ∉ True or x̄ ∉ True;      // axiom: ~True(x) ∨ ~True(~x)
    (5) if x ∈ Provable, then x ∈ True;  // axiom: Provable(x) → True(x) (6) if x̄ ∈ Provable, then x̄ ∈ True;  // axiom: Provable(~x) → True(~x)
    (7) x ∈ True
    (8) x ∉ Provable
    (9) x̄ ∉ Provable

    ZFC is a useful set theory for many purposes.
    You don't offer any useful theory for any purpose.


    If we had a True(L, x) that worked consistently and L
    is formalized natural language then we could refute
    all of the dangerous lies made for political gain in
    real time before they gained any traction.

    But Tarski shows that a True((L, x), defined to work on ALL x that are expressable in L, can not be defined, as there exists some x that it can
    not have a consistent value for.

    Your logic requires that ALL doesn't actually mean ALL, and thus your
    logic system is just not consistently defined.


    Because we don't have this it looks like there is a
    good chance we will be seeing the rise of the Fourth
    Reich in a few days.


    You just don't understand cause and effect it seems.

    It is YOUR type of thinking that is fueling those dangers, so consider
    yourself part of the problem.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Damon@21:1/5 to olcott on Sat Oct 26 21:04:53 2024
    On 10/26/24 5:57 PM, olcott wrote:
    On 10/26/2024 10:48 AM, Richard Damon wrote:
    On 10/26/24 8:59 AM, olcott wrote:
    On 10/26/2024 2:52 AM, Mikko wrote:
    On 2024-10-25 14:37:19 +0000, olcott said:

    On 10/25/2024 3:14 AM, Mikko wrote:
    On 2024-10-24 16:07:03 +0000, olcott said:

    On 10/24/2024 9:06 AM, Mikko wrote:
    On 2024-10-22 15:04:37 +0000, olcott said:

    On 10/22/2024 2:39 AM, Mikko wrote:
    On 2024-10-22 02:04:14 +0000, olcott said:

    On 10/16/2024 11:37 AM, Mikko wrote:
    On 2024-10-16 14:27:09 +0000, olcott said:

    The whole notion of undecidability is anchored in ignoring >>>>>>>>>>>>> the fact that
    some expressions of language are simply not truth bearers. >>>>>>>>>>>>
    A formal theory is undecidable if there is no Turing machine >>>>>>>>>>>> that
    determines whether a formula of that theory is a theorem of >>>>>>>>>>>> that
    theory or not. Whether an expression is a truth bearer is not >>>>>>>>>>>> relevant. Either there is a valid proof of that formula or >>>>>>>>>>>> there
    is not. No third possibility.


    After being continually interrupted by emergencies
    interrupting other emergencies...

    If the answer to the question: Is X a formula of theory Y >>>>>>>>>>> cannot be determined to be yes or no then the question
    itself is somehow incorrect.

    There are several possibilities.

    A theory may be intentionally incomplete. For example, group >>>>>>>>>> theory
    leaves several important question unanswered. There are
    infinitely
    may different groups and group axioms must be true in every >>>>>>>>>> group.

    Another possibility is that a theory is poorly constructed: the >>>>>>>>>> author just failed to include an important postulate.

    Then there is the possibility that the purpose of the theory is >>>>>>>>>> incompatible with decidability, for example arithmetic.

    An incorrect question is an expression of language that
    is not a truth bearer translated into question form.

    When "X a formula of theory Y" is neither true nor false >>>>>>>>>>> then "X a formula of theory Y" is not a truth bearer.

    Whether AB = BA is not answered by group theory but is alwasy >>>>>>>>>> true or false about specific A and B and universally true in >>>>>>>>>> some groups but not all.

    See my most recent reply to Richard it sums up
    my position most succinctly.

    We already know that your position is uninteresting.


    Don't want to bother to look at it (AKA uninteresting) is not at >>>>>>> all the same thing as the corrected foundation to computability
    does not eliminate undecidability.

    No, but we already know that you don't offer anything interesting
    about foundations to computability or undecidabilty.

    In the same way that ZFC eliminated RP True_Olcott(L,x)
    eliminates undecidability. Not bothering to pay attention
    is less than no rebuttal what-so-ever.

    No, not in the same way.

    Pathological self reference causes an issue in both cases.
    This issue is resolved by disallowing it in both cases.

    Nope, because is set theory, the "self-reference"

    does exist and is problematic in its several other instances.
    Abolishing it in each case DOES ELIMINATE THE FREAKING PROBLEM.


    Yes, IN SET THEORY, the "self-reference" can be banned, by the nature of
    the contstruction.

    In Computation Theory it can not, without making the system less than
    Turing Complete, as the structure of the Computations fundamentally
    allow for it, and in a way that is potentially undetectable.

    You don't seem to understand that fact, but the fundamental nature of
    being able to encode your processing in the same sort of strings you
    process makes this a possibility.

    Dues to the nature of its relationship to Mathematics and Logic, it
    turns out that and logic with certain minimal requirements can get into
    a similar situation.

    Your only way to remove it from these fields is to remove that source of "power" in the systems, and the cost of that is just too high for most
    people, thus you plan just fails.

    Of course, you understanding is too crude to see this issue, so it just
    goes over your head, and your claims just reveal your ignorance of the
    fields.

    Sorry, that is just the facts, that you seem to be too stupid to understand.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Mikko@21:1/5 to olcott on Sun Oct 27 10:27:02 2024
    On 2024-10-26 12:59:33 +0000, olcott said:

    On 10/26/2024 2:52 AM, Mikko wrote:
    On 2024-10-25 14:37:19 +0000, olcott said:

    On 10/25/2024 3:14 AM, Mikko wrote:
    On 2024-10-24 16:07:03 +0000, olcott said:

    On 10/24/2024 9:06 AM, Mikko wrote:
    On 2024-10-22 15:04:37 +0000, olcott said:

    On 10/22/2024 2:39 AM, Mikko wrote:
    On 2024-10-22 02:04:14 +0000, olcott said:

    On 10/16/2024 11:37 AM, Mikko wrote:
    On 2024-10-16 14:27:09 +0000, olcott said:

    The whole notion of undecidability is anchored in ignoring the fact that
    some expressions of language are simply not truth bearers. >>>>>>>>>>
    A formal theory is undecidable if there is no Turing machine that >>>>>>>>>> determines whether a formula of that theory is a theorem of that >>>>>>>>>> theory or not. Whether an expression is a truth bearer is not >>>>>>>>>> relevant. Either there is a valid proof of that formula or there >>>>>>>>>> is not. No third possibility.


    After being continually interrupted by emergencies
    interrupting other emergencies...

    If the answer to the question: Is X a formula of theory Y
    cannot be determined to be yes or no then the question
    itself is somehow incorrect.

    There are several possibilities.

    A theory may be intentionally incomplete. For example, group theory >>>>>>>> leaves several important question unanswered. There are infinitely >>>>>>>> may different groups and group axioms must be true in every group. >>>>>>>>
    Another possibility is that a theory is poorly constructed: the >>>>>>>> author just failed to include an important postulate.

    Then there is the possibility that the purpose of the theory is >>>>>>>> incompatible with decidability, for example arithmetic.

    An incorrect question is an expression of language that
    is not a truth bearer translated into question form.

    When "X a formula of theory Y" is neither true nor false
    then "X a formula of theory Y" is not a truth bearer.

    Whether AB = BA is not answered by group theory but is alwasy
    true or false about specific A and B and universally true in
    some groups but not all.

    See my most recent reply to Richard it sums up
    my position most succinctly.

    We already know that your position is uninteresting.


    Don't want to bother to look at it (AKA uninteresting) is not at
    all the same thing as the corrected foundation to computability
    does not eliminate undecidability.

    No, but we already know that you don't offer anything interesting
    about foundations to computability or undecidabilty.

    In the same way that ZFC eliminated RP True_Olcott(L,x)
    eliminates undecidability. Not bothering to pay attention
    is less than no rebuttal what-so-ever.

    No, not in the same way.

    Pathological self reference causes an issue in both cases.
    This issue is resolved by disallowing it in both cases.

    There is no self reference in a formal theory. Expressions of a formal
    theory don't refer.

    --
    Mikko

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Damon@21:1/5 to olcott on Sun Oct 27 07:38:49 2024
    On 10/26/24 9:22 PM, olcott wrote:
    On 10/26/2024 8:04 PM, Richard Damon wrote:
    On 10/26/24 5:57 PM, olcott wrote:
    On 10/26/2024 10:48 AM, Richard Damon wrote:
    On 10/26/24 8:59 AM, olcott wrote:
    On 10/26/2024 2:52 AM, Mikko wrote:
    On 2024-10-25 14:37:19 +0000, olcott said:

    On 10/25/2024 3:14 AM, Mikko wrote:
    On 2024-10-24 16:07:03 +0000, olcott said:

    On 10/24/2024 9:06 AM, Mikko wrote:
    On 2024-10-22 15:04:37 +0000, olcott said:

    On 10/22/2024 2:39 AM, Mikko wrote:
    On 2024-10-22 02:04:14 +0000, olcott said:

    On 10/16/2024 11:37 AM, Mikko wrote:
    On 2024-10-16 14:27:09 +0000, olcott said:

    The whole notion of undecidability is anchored in >>>>>>>>>>>>>>> ignoring the fact that
    some expressions of language are simply not truth bearers. >>>>>>>>>>>>>>
    A formal theory is undecidable if there is no Turing >>>>>>>>>>>>>> machine that
    determines whether a formula of that theory is a theorem >>>>>>>>>>>>>> of that
    theory or not. Whether an expression is a truth bearer is not >>>>>>>>>>>>>> relevant. Either there is a valid proof of that formula or >>>>>>>>>>>>>> there
    is not. No third possibility.


    After being continually interrupted by emergencies
    interrupting other emergencies...

    If the answer to the question: Is X a formula of theory Y >>>>>>>>>>>>> cannot be determined to be yes or no then the question >>>>>>>>>>>>> itself is somehow incorrect.

    There are several possibilities.

    A theory may be intentionally incomplete. For example, group >>>>>>>>>>>> theory
    leaves several important question unanswered. There are >>>>>>>>>>>> infinitely
    may different groups and group axioms must be true in every >>>>>>>>>>>> group.

    Another possibility is that a theory is poorly constructed: the >>>>>>>>>>>> author just failed to include an important postulate.

    Then there is the possibility that the purpose of the theory is >>>>>>>>>>>> incompatible with decidability, for example arithmetic. >>>>>>>>>>>>
    An incorrect question is an expression of language that >>>>>>>>>>>>> is not a truth bearer translated into question form. >>>>>>>>>>>>>
    When "X a formula of theory Y" is neither true nor false >>>>>>>>>>>>> then "X a formula of theory Y" is not a truth bearer. >>>>>>>>>>>>
    Whether AB = BA is not answered by group theory but is alwasy >>>>>>>>>>>> true or false about specific A and B and universally true in >>>>>>>>>>>> some groups but not all.

    See my most recent reply to Richard it sums up
    my position most succinctly.

    We already know that your position is uninteresting.


    Don't want to bother to look at it (AKA uninteresting) is not at >>>>>>>>> all the same thing as the corrected foundation to computability >>>>>>>>> does not eliminate undecidability.

    No, but we already know that you don't offer anything interesting >>>>>>>> about foundations to computability or undecidabilty.

    In the same way that ZFC eliminated RP True_Olcott(L,x)
    eliminates undecidability. Not bothering to pay attention
    is less than no rebuttal what-so-ever.

    No, not in the same way.

    Pathological self reference causes an issue in both cases.
    This issue is resolved by disallowing it in both cases.

    Nope, because is set theory, the "self-reference"

    does exist and is problematic in its several other instances.
    Abolishing it in each case DOES ELIMINATE THE FREAKING PROBLEM.


    Yes, IN SET THEORY, the "self-reference" can be banned, by the nature
    of the contstruction.


    That seems to be the best way.

    It works for sets, but not for Computations, due to the way things are
    defined.


    In Computation Theory it can not, without making the system less than
    Turing Complete, as the structure of the Computations fundamentally
    allow for it,

    Sure.

    So, you ADMIT that your computation system you are trying to advocate is
    less than Turing Complete?

    That means that the Halting Problem isn't a problem.


    and in a way that is potentially undetectable.


    I really don't think so it only seems that way.

    Of course it is.

    The method of assigning meaning to the symbols can be done is a
    meta-system that the system doesn't know about, and thus its meaning is unknowable to the logic system.




    You don't seem to understand that fact, but the fundamental nature of
    being able to encode your processing in the same sort of strings you
    process makes this a possibility.


    It does not make these things undetectable, it merely
    allows failing to detect.

    No, it makes things undetectable, unless you allow the system to just
    reject ALL statements, even if they are not actually "self-referential"
    to be considered "bad".


    Dues to the nature of its relationship to Mathematics and Logic, it
    turns out that and logic with certain minimal requirements can get
    into a similar situation.


    I think that I can see deeper than the Curry/Howard Isomorphism.
    Computations and formal systems are in their most basic foundational
    essence finite string transformation rules.

    You don't undertstand what you see.

    Part of the problem is that while Compuation Theory and Formal Logic
    System do have large parts that are just finite string transformation
    rules, they have other parts that are not.


    Your only way to remove it from these fields is to remove that source
    of "power" in the systems, and the cost of that is just too high for
    most people, thus you plan just fails.


    Detection then rejection.

    But since detection is impossible, you can not get to rejection.

    Once you allow the creation of the statement, you can't reject it later
    and still have the claim of handling "All".


    Of course, you understanding is too crude to see this issue, so it
    just goes over your head, and your claims just reveal your ignorance
    of the fields.

    Sorry, that is just the facts, that you seem to be too stupid to
    understand.

    In other words you can correctly explain every single detail
    conclusively proving how finite string transformation rules
    are totally unrelated to either computation and formal systems.


    That isn't what I said, and just proves your stupidity.

    You mind is just too small to handle these discussions.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Richard Damon@21:1/5 to olcott on Sun Oct 27 13:49:02 2024
    On 10/27/24 9:29 AM, olcott wrote:
    On 10/27/2024 3:27 AM, Mikko wrote:
    On 2024-10-26 12:59:33 +0000, olcott said:

    On 10/26/2024 2:52 AM, Mikko wrote:
    On 2024-10-25 14:37:19 +0000, olcott said:

    On 10/25/2024 3:14 AM, Mikko wrote:
    On 2024-10-24 16:07:03 +0000, olcott said:

    On 10/24/2024 9:06 AM, Mikko wrote:
    On 2024-10-22 15:04:37 +0000, olcott said:

    On 10/22/2024 2:39 AM, Mikko wrote:
    On 2024-10-22 02:04:14 +0000, olcott said:

    On 10/16/2024 11:37 AM, Mikko wrote:
    On 2024-10-16 14:27:09 +0000, olcott said:

    The whole notion of undecidability is anchored in ignoring >>>>>>>>>>>>> the fact that
    some expressions of language are simply not truth bearers. >>>>>>>>>>>>
    A formal theory is undecidable if there is no Turing machine >>>>>>>>>>>> that
    determines whether a formula of that theory is a theorem of >>>>>>>>>>>> that
    theory or not. Whether an expression is a truth bearer is not >>>>>>>>>>>> relevant. Either there is a valid proof of that formula or >>>>>>>>>>>> there
    is not. No third possibility.


    After being continually interrupted by emergencies
    interrupting other emergencies...

    If the answer to the question: Is X a formula of theory Y >>>>>>>>>>> cannot be determined to be yes or no then the question
    itself is somehow incorrect.

    There are several possibilities.

    A theory may be intentionally incomplete. For example, group >>>>>>>>>> theory
    leaves several important question unanswered. There are
    infinitely
    may different groups and group axioms must be true in every >>>>>>>>>> group.

    Another possibility is that a theory is poorly constructed: the >>>>>>>>>> author just failed to include an important postulate.

    Then there is the possibility that the purpose of the theory is >>>>>>>>>> incompatible with decidability, for example arithmetic.

    An incorrect question is an expression of language that
    is not a truth bearer translated into question form.

    When "X a formula of theory Y" is neither true nor false >>>>>>>>>>> then "X a formula of theory Y" is not a truth bearer.

    Whether AB = BA is not answered by group theory but is alwasy >>>>>>>>>> true or false about specific A and B and universally true in >>>>>>>>>> some groups but not all.

    See my most recent reply to Richard it sums up
    my position most succinctly.

    We already know that your position is uninteresting.


    Don't want to bother to look at it (AKA uninteresting) is not at >>>>>>> all the same thing as the corrected foundation to computability
    does not eliminate undecidability.

    No, but we already know that you don't offer anything interesting
    about foundations to computability or undecidabilty.

    In the same way that ZFC eliminated RP True_Olcott(L,x)
    eliminates undecidability. Not bothering to pay attention
    is less than no rebuttal what-so-ever.

    No, not in the same way.

    Pathological self reference causes an issue in both cases.
    This issue is resolved by disallowing it in both cases.

    There is no self reference in a formal theory. Expressions of a formal
    theory don't refer.

    Godel says otherwise.


    In Godel, the reference is "self", but a big circle that gets back to
    its start.

    He shows that Mathematics is capable of expressing that level of
    recursive referencing.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From Mikko@21:1/5 to olcott on Mon Oct 28 11:08:11 2024
    On 2024-10-27 13:29:19 +0000, olcott said:

    On 10/27/2024 3:27 AM, Mikko wrote:
    On 2024-10-26 12:59:33 +0000, olcott said:

    On 10/26/2024 2:52 AM, Mikko wrote:
    On 2024-10-25 14:37:19 +0000, olcott said:

    On 10/25/2024 3:14 AM, Mikko wrote:
    On 2024-10-24 16:07:03 +0000, olcott said:

    On 10/24/2024 9:06 AM, Mikko wrote:
    On 2024-10-22 15:04:37 +0000, olcott said:

    On 10/22/2024 2:39 AM, Mikko wrote:
    On 2024-10-22 02:04:14 +0000, olcott said:

    On 10/16/2024 11:37 AM, Mikko wrote:
    On 2024-10-16 14:27:09 +0000, olcott said:

    The whole notion of undecidability is anchored in ignoring the fact that
    some expressions of language are simply not truth bearers. >>>>>>>>>>>>
    A formal theory is undecidable if there is no Turing machine that >>>>>>>>>>>> determines whether a formula of that theory is a theorem of that >>>>>>>>>>>> theory or not. Whether an expression is a truth bearer is not >>>>>>>>>>>> relevant. Either there is a valid proof of that formula or there >>>>>>>>>>>> is not. No third possibility.


    After being continually interrupted by emergencies
    interrupting other emergencies...

    If the answer to the question: Is X a formula of theory Y >>>>>>>>>>> cannot be determined to be yes or no then the question
    itself is somehow incorrect.

    There are several possibilities.

    A theory may be intentionally incomplete. For example, group theory >>>>>>>>>> leaves several important question unanswered. There are infinitely >>>>>>>>>> may different groups and group axioms must be true in every group. >>>>>>>>>>
    Another possibility is that a theory is poorly constructed: the >>>>>>>>>> author just failed to include an important postulate.

    Then there is the possibility that the purpose of the theory is >>>>>>>>>> incompatible with decidability, for example arithmetic.

    An incorrect question is an expression of language that
    is not a truth bearer translated into question form.

    When "X a formula of theory Y" is neither true nor false >>>>>>>>>>> then "X a formula of theory Y" is not a truth bearer.

    Whether AB = BA is not answered by group theory but is alwasy >>>>>>>>>> true or false about specific A and B and universally true in >>>>>>>>>> some groups but not all.

    See my most recent reply to Richard it sums up
    my position most succinctly.

    We already know that your position is uninteresting.


    Don't want to bother to look at it (AKA uninteresting) is not at >>>>>>> all the same thing as the corrected foundation to computability
    does not eliminate undecidability.

    No, but we already know that you don't offer anything interesting
    about foundations to computability or undecidabilty.

    In the same way that ZFC eliminated RP True_Olcott(L,x)
    eliminates undecidability. Not bothering to pay attention
    is less than no rebuttal what-so-ever.

    No, not in the same way.

    Pathological self reference causes an issue in both cases.
    This issue is resolved by disallowing it in both cases.

    There is no self reference in a formal theory. Expressions of a formal
    theory don't refer.

    Godel says otherwise.

    No, he doesn't. Terms of formal system can be interpreted as references
    but an interpretation is not a part of the formal theory. The word
    "formal" means that only a form is defined but not any meaning. For
    example, the meanings of the terms are not needed in order to determine
    whether a finite sequence of finite strings is a proof.

    There is a common interpretation of the symbols of Peano arithmetic:
    the constant 0 means the empty set and the successor of the set X is
    the set X ∪ {X}, and the meanings of the other operators follow from
    that and their defining axioms; usually but not always the range of
    meanings is restricted to the smallest collection of sets that contains
    the exmpty set and the successor of every member. With this interpretation, every term refers to a set so no term refers to itself or any other term
    or any formula.

    --
    Mikko

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)