On 02/25/2024 04:42 AM, immibis wrote:
> On 24/02/24 18:46, Ross Finlayson wrote:
>> On 02/24/2024 12:22 AM, immibis wrote:
>>> On 19/02/24 17:27, olcott wrote:
>>>> On 2/19/2024 10:17 AM, Ross Finlayson wrote:
>>>>> On 02/19/2024 06:50 AM, Andy Walker wrote:
>>>>>> On 19/02/2024 11:28, Ben Bacarisse wrote:
>>>>>> [HP proofs:]
>>>>>>> Conversely, the classical proof by contradiction seems to lead a
>>>>>>> lot of
>>>>>>> non-mathematical students astray. I think they tend to assume
>>>>>>> that if
>>>>>>> you can specify it, you can implement it, and /assuming/ that there
>>>>>>> is a
>>>>>>> program that does something just makes that worse! This is why I
>>>>>>> once
>>>>>>> tried setting Post's correspondence problem as a background
>>>>>>> exercise,
>>>>>>> just as if it were any other programming problem.
>>>>>>
>>>>>> Moral: Don't try to teach such things to non-mathematicians?
>>>>>> In my time as a student, there were no CS/IT [first] degrees, and few
>>>>>> computing courses of any sort other than for mathematicians, which no
>>>>>> doubt coloured what went into them.
>>>>>>
>>>>>>> If you were teaching this material, how would you approach the
>>>>>>> halting
>>>>>>> theorem? Would you give a more intuitive proof or stick with a
>>>>>>> formal
>>>>>>> one? What model would you use? I was taught it using Minsky
>>>>>>> machines,
>>>>>>> and that has the advantage (for lectures) that it's very visual with
>>>>>>> lots of diagrams. That's almost impossible to present on Usenet,
>>>>>>> but
>>>>>>> then I'm not suggesting you actually post your favourite proof, only
>>>>>>> that you describe it.
>>>>>> When I did teach this stuff, I pretty-much followed the Minsky
>>>>>> route -- if H is a halt decider then [blah, blah], contradiction. My
>>>>>> lecture notes are on the web at
>>>>>>
>>>>>> http://http://www.cuboid.me.uk/anw/G12FCO/lect17.html
>>>>>>
>>>>>> [a reference I've given before], see about two-thirds down the page.
>>>>>> The following lecture and indeed the whole module are also relevant;
>>>>>> they are linked from the bottom of that page. In the light of what
>>>>>> has happened in this group, I might now, nearly 30 years later, be
>>>>>> tempted to do it via Busy Beaver, but both that and the Linz-style
>>>>>> proofs via languages seem to me a bit much for non-mathematicians.
>>>>>> So I would probably start not from "H is a halt decider" but rather
>>>>>> from "Let H be any program" [doing an abstract computation], then
>>>>>> "here is a construction" [usual hat stuff] showing that H is not a
>>>>>> halt decider. So there are no [perfect] halt deciders, QED. I think
>>>>>> that can be made more non-mathematician friendly. IOW, I think that
>>>>>> "So H is not a HD" is more friendly than "H /is/ a HD leads to a
>>>>>> contradiction".
>>>>>>
>>>>>> There is still the problem that showing that something has
>>>>>> /a/ counter-example is not satisfying; it suggests that if only we
>>>>>> could tweak the problem slightly to avoid that one case, all would
>>>>>> be well. Lecture 18 from the above module addresses this in some
>>>>>> detail, inc the use of emulation; but I think this is the area in
>>>>>> which some contributors here get misled.
>>>>>>
>>>>>> Meanwhile, I note from the above lecture notes:
>>>>>>
>>>>>> " If you understand this proof at first glance, you are too clever
>>>>>> " to be doing this module, and should probably have been giving
>>>>>> it.
>>>>>> " If you think you understand this proof at first glance, you
>>>>>> " probably don't. If you think you will /never/ understand this
>>>>>> " proof, please just run through it again, enlightenment will
>>>>>> " eventually dawn. "
>>>>>>
>>>>>> How that relates to contributors here, I leave to the imagination.
>>>>>>
>>>>>
>>>>> It's a difficult enough concept "random access memory"
>>>>> and "0-based or 1-based address offset computation"
>>>>> and these kinds of things, figuring that students
>>>>> know algebra and geometry at all.
>>>>>
>>>>> You figure they're going to need "order theory", for
>>>>> ordinals, about set theory, then the presentation of
>>>>> set theory's trans-finites, is sort of necessary to
>>>>> "put zero and infinity on the same page".
>>>>>
>>>>> Then that the Halting problem and Church and Rice and
>>>>> Goedel's and most all that is "the antidiagonal argument",
>>>>> otherwise has for "recursion theory" maybe it's better
>>>>> to have them get into "Concrete Mathematics" so that
>>>>> they already have the usual notions of boundedness
>>>>> and unboundedness, relating it to their geometry
>>>>> and their algebra and their pre-calculus and calculus.
>>>>>
>>>>> The "recurrence relations" are tougher than long division.
>>>>>
>>>>> Of course they should know about Buridan's donkey, and
>>>>> about the Heap/Sorites, and about Zeno, all the,
>>>>> "paradoxes", of logic, before getting into,
>>>>> "non-constructivist results after the trans-finite
>>>>> in asymptotics in recursion theory".
>>>>>
>>>>> I'm glad that when I learned logic it was De Morgan
>>>>> and modus ponens and modus tollens and all that,
>>>>> if it'd been "quasi-modal after ex falso quodlibet"
>>>>> and I didn't already know "dividing by zero can just
>>>>> lead to wrong results" I'd hope that I'd've rejected
>>>>> it and said "there's the door, Monty Haul".
>>>>>
>>>>> (I mostly learned "logic" from "logic puzzles".)
>>>>>
>>>>> (I'm a "full-stack all-phases dev eng ops in the
>>>>> enterprise corp" type that happens to have a copy
>>>>> of Boolos and also have read into Forster, about
>>>>> "set theories with universes" and such.)
>>>>>
>>>>> Maybe try sticking with constructivism, related
>>>>> rates, and asymptotics, and what, analysis,
>>>>> instead of like "here's a quick reason to give up".
>>>>>
>>>>>
>>>>> Of course formal automata and formal methods are great,
>>>>> accepter/rejector, automata like the right linear,
>>>>> they can help a lot for introductory, fundamental,
>>>>> coding and information theory and signal theory,
>>>>> that will be true everywhere and constructive.
>>>>>
>>>>> The Entscheidungs though is kind of like,
>>>>> well, there are various law(s) of large numbers, ....
>>>>>
>>>>> Formal languages, ....
>>>>>
>>>>> I don't know any results of Linz.
>>>>>
>>>>>
>>>>
>>>> The issue is not that I do not know enough computer science
>>>> the issue that that technical people are utterly clueless
>>>> about analytical truthmaker theory. They have been indoctrinated
>>>> to believe that:
>>>>
>>>> ...14 Every epistemological antinomy can likewise be used for a similar
>>>> undecidability proof...(Gödel 1931:43)
>>>> is not nonsense.
>>>>
>>>> Analytical truthmaker theory knows that it <is> nonsense.
>>>>
>>>
>>> I have never read this sentence, it sounds like something he made up,
>>> and I definitely haven't been indoctrinated to believe it. Nonetheless
>>> the halting problem is obviously unsolvable.
>>
>> Consider a source-book like "approximation algorithms for NP-hard
>> problems". Now, NP-hard problems would require NP resources,
>> which for example, in the resource of time, might not exist.
>> Yet, approximation algorithms both get a bunch of results,
>> and, asymptotically solve the thing.
>>
>> So, is it solvable? Or maybe intractable?
>>
>> Now, there are some crossed wires in Olcott's approach it seems,
>> but some here like maybe "an AI mind that thinks as well as
>> anybody", might be thoroughly having excluded "ex falso quodlibet",
>> and have arrived at various reasons why "almost all" programs
>> can have computed "Halts".
>>
>> Otherwise, how about framing the entire thing, "Not-Halts"?
>>
>> This is just to encourage you to not "give up" when things
>> are practically intractable, when for example practicality
>> is more that "it must be tracted" than "it's not tractable".
>>
>> Leafing through "Lecture 17", I would suggest that there
>> is a class of computing algorithms from analog computing,
>> "quantum" computing these days, or what results "surface
>> acoustic wave transducer" or these sorts notions of the
>> analog computer or quantum computer or as what results
>> from various notions of the free-form 3-D IC, that I would
>> suggest, that the free-form 3-D IC, offers a class of models
>> of computing indeed _beyond_, the Universal Turing Machine.
>>
>
> Of course there are many useful approximations to the halting problem.
> However, if you think the entire argument with Peter Olcott is about
> whether approximate solutions can be useful, you must be very new to the
> group. He believes it has not been proven unsolvable.
>

On 2/25/2024 12:40 PM, Ross Finlayson wrote:
> On 02/25/2024 04:42 AM, immibis wrote:
>> On 24/02/24 18:46, Ross Finlayson wrote:
>>> On 02/24/2024 12:22 AM, immibis wrote:
>>>> On 19/02/24 17:27, olcott wrote:
>>>>> On 2/19/2024 10:17 AM, Ross Finlayson wrote:
>>>>>> On 02/19/2024 06:50 AM, Andy Walker wrote:
>>>>>>> On 19/02/2024 11:28, Ben Bacarisse wrote:
>>>>>>> [HP proofs:]
>>>>>>>> Conversely, the classical proof by contradiction seems to lead a
>>>>>>>> lot of
>>>>>>>> non-mathematical students astray.  I think they tend to assume
>>>>>>>> that if
>>>>>>>> you can specify it, you can implement it, and /assuming/ that there
>>>>>>>> is a
>>>>>>>> program that does something just makes that worse!  This is why I
>>>>>>>> once
>>>>>>>> tried setting Post's correspondence problem as a background
>>>>>>>> exercise,
>>>>>>>> just as if it were any other programming problem.
>>>>>>>
>>>>>>>      Moral:  Don't try to teach such things to non-mathematicians?
>>>>>>> In my time as a student, there were no CS/IT [first] degrees, and
>>>>>>> few
>>>>>>> computing courses of any sort other than for mathematicians,
>>>>>>> which no
>>>>>>> doubt coloured what went into them.
>>>>>>>
>>>>>>>> If you were teaching this material, how would you approach the
>>>>>>>> halting
>>>>>>>> theorem?  Would you give a more intuitive proof or stick with a
>>>>>>>> formal
>>>>>>>> one?  What model would you use?  I was taught it using Minsky
>>>>>>>> machines,
>>>>>>>> and that has the advantage (for lectures) that it's very visual
>>>>>>>> with
>>>>>>>> lots of diagrams.  That's almost impossible to present on Usenet,
>>>>>>>> but
>>>>>>>> then I'm not suggesting you actually post your favourite proof,
>>>>>>>> only
>>>>>>>> that you describe it.
>>>>>>>      When I did teach this stuff, I pretty-much followed the Minsky
>>>>>>> route -- if H is a halt decider then [blah, blah],
>>>>>>> contradiction.  My
>>>>>>> lecture notes are on the web at
>>>>>>>
>>>>>>>    http://http://www.cuboid.me.uk/anw/G12FCO/lect17.html
>>>>>>>
>>>>>>> [a reference I've given before], see about two-thirds down the page.
>>>>>>> The following lecture and indeed the whole module are also relevant;
>>>>>>> they are linked from the bottom of that page.  In the light of what
>>>>>>> has happened in this group, I might now, nearly 30 years later, be
>>>>>>> tempted to do it via Busy Beaver, but both that and the Linz-style
>>>>>>> proofs via languages seem to me a bit much for non-mathematicians.
>>>>>>> So I would probably start not from "H is a halt decider" but rather
>>>>>>> from "Let H be any program" [doing an abstract computation], then
>>>>>>> "here is a construction" [usual hat stuff] showing that H is not a
>>>>>>> halt decider.  So there are no [perfect] halt deciders, QED.  I
>>>>>>> think
>>>>>>> that can be made more non-mathematician friendly.  IOW, I think that
>>>>>>> "So H is not a HD" is more friendly than "H /is/ a HD leads to a
>>>>>>> contradiction".
>>>>>>>
>>>>>>>      There is still the problem that showing that something has
>>>>>>> /a/ counter-example is not satisfying;  it suggests that if only we
>>>>>>> could tweak the problem slightly to avoid that one case, all would
>>>>>>> be well.  Lecture 18 from the above module addresses this in some
>>>>>>> detail, inc the use of emulation;  but I think this is the area in
>>>>>>> which some contributors here get misled.
>>>>>>>
>>>>>>>      Meanwhile, I note from the above lecture notes:
>>>>>>>
>>>>>>>    " If you understand this proof at first glance, you are too
>>>>>>> clever
>>>>>>>    " to be doing this module, and should probably have been giving
>>>>>>> it.
>>>>>>>    " If you think you understand this proof at first glance, you
>>>>>>>    " probably don't. If you think you will /never/ understand this
>>>>>>>    " proof, please just run through it again, enlightenment will
>>>>>>>    " eventually dawn. "
>>>>>>>
>>>>>>> How that relates to contributors here, I leave to the imagination.
>>>>>>>
>>>>>>
>>>>>> It's a difficult enough concept "random access memory"
>>>>>> and "0-based or 1-based address offset computation"
>>>>>> and these kinds of things, figuring that students
>>>>>> know algebra and geometry at all.
>>>>>>
>>>>>> You figure they're going to need "order theory", for
>>>>>> ordinals, about set theory, then the presentation of
>>>>>> set theory's trans-finites, is sort of necessary to
>>>>>> "put zero and infinity on the same page".
>>>>>>
>>>>>> Then that the Halting problem and Church and Rice and
>>>>>> Goedel's and most all that is "the antidiagonal argument",
>>>>>> otherwise has for "recursion theory" maybe it's better
>>>>>> to have them get into "Concrete Mathematics" so that
>>>>>> they already have the usual notions of boundedness
>>>>>> and unboundedness, relating it to their geometry
>>>>>> and their algebra and their pre-calculus and calculus.
>>>>>>
>>>>>> The "recurrence relations" are tougher than long division.
>>>>>>
>>>>>> Of course they should know about Buridan's donkey, and
>>>>>> about the Heap/Sorites, and about Zeno, all the,
>>>>>> "paradoxes", of logic, before getting into,
>>>>>> "non-constructivist results after the trans-finite
>>>>>> in asymptotics in recursion theory".
>>>>>>
>>>>>> I'm glad that when I learned logic it was De Morgan
>>>>>> and modus ponens and modus tollens and all that,
>>>>>> if it'd been "quasi-modal after ex falso quodlibet"
>>>>>> and I didn't already know "dividing by zero can just
>>>>>> lead to wrong results" I'd hope that I'd've rejected
>>>>>> it and said "there's the door, Monty Haul".
>>>>>>
>>>>>> (I mostly learned "logic" from "logic puzzles".)
>>>>>>
>>>>>> (I'm a "full-stack all-phases dev eng ops in the
>>>>>> enterprise corp" type that happens to have a copy
>>>>>> of Boolos and also have read into Forster, about
>>>>>> "set theories with universes" and such.)
>>>>>>
>>>>>> Maybe try sticking with constructivism, related
>>>>>> rates, and asymptotics, and what, analysis,
>>>>>> instead of like "here's a quick reason to give up".
>>>>>>
>>>>>>
>>>>>> Of course formal automata and formal methods are great,
>>>>>> accepter/rejector, automata like the right linear,
>>>>>> they can help a lot for introductory, fundamental,
>>>>>> coding and information theory and signal theory,
>>>>>> that will be true everywhere and constructive.
>>>>>>
>>>>>> The Entscheidungs though is kind of like,
>>>>>> well, there are various law(s) of large numbers, ....
>>>>>>
>>>>>> Formal languages, ....
>>>>>>
>>>>>> I don't know any results of Linz.
>>>>>>
>>>>>>
>>>>>
>>>>> The issue is not that I do not know enough computer science
>>>>> the issue that that technical people are utterly clueless
>>>>> about analytical truthmaker theory. They have been indoctrinated
>>>>> to believe that:
>>>>>
>>>>> ...14 Every epistemological antinomy can likewise be used for a
>>>>> similar
>>>>> undecidability proof...(Gödel 1931:43)
>>>>> is not nonsense.
>>>>>
>>>>> Analytical truthmaker theory knows that it <is> nonsense.
>>>>>
>>>>
>>>> I have never read this sentence, it sounds like something he made up,
>>>> and I definitely haven't been indoctrinated to believe it. Nonetheless
>>>> the halting problem is obviously unsolvable.
>>>
>>> Consider a source-book like "approximation algorithms for NP-hard
>>> problems". Now, NP-hard problems would require NP resources,
>>> which for example, in the resource of time, might not exist.
>>> Yet, approximation algorithms both get a bunch of results,
>>> and, asymptotically solve the thing.
>>>
>>> So, is it solvable? Or maybe intractable?
>>>
>>> Now, there are some crossed wires in Olcott's approach it seems,
>>> but some here like maybe "an AI mind that thinks as well as
>>> anybody", might be thoroughly having excluded "ex falso quodlibet",
>>> and have arrived at various reasons why "almost all" programs
>>> can have computed "Halts".
>>>
>>> Otherwise, how about framing the entire thing, "Not-Halts"?
>>>
>>> This is just to encourage you to not "give up" when things
>>> are practically intractable, when for example practicality
>>> is more that "it must be tracted" than "it's not tractable".
>>>
>>> Leafing through "Lecture 17", I would suggest that there
>>> is a class of computing algorithms from analog computing,
>>> "quantum" computing these days, or what results "surface
>>> acoustic wave transducer" or these sorts notions of the
>>> analog computer or quantum computer or as what results
>>> from various notions of the free-form 3-D IC, that I would
>>> suggest, that the free-form 3-D IC, offers a class of models
>>> of computing indeed _beyond_, the Universal Turing Machine.
>>>
>>
>> Of course there are many useful approximations to the halting problem.
>> However, if you think the entire argument with Peter Olcott is about
>> whether approximate solutions can be useful, you must be very new to the
>> group. He believes it has not been proven unsolvable.
>>
>
> It seems to follow that "Olcott's Obstinance" is a situation
> where lower in his fundamentals, he picked some opinion of
> "regularity", "the ordinary", "closed", and so ultimately
> he ultimately arrives at where induction won't carry him,
> so he balks, because deduction isn't available that he
> cross the bridge, this analytical bridge, over the
> inductive impasse, where induction carried him off "forever",
> deduction (or, induction the other way...) would arrive
> as from "always", and instead of the "meeting in the middle",
> the analytically and deductively established, "middle of
> nowhere", now a center of things, that he's sort of stick
> in the middle of what is a "pons asinorum", "bridge of fools",
> i.e. "a bridge that fools can't cross", and has upset his
> cart and demands others turn around so not to observe
> the spectacle.
>
> So, "truth-values", are, where maybe Kleene and Lukasiewcz,
> is who you'd point to when "true and/or false isn't enough",
> there's introduced for "T" and "F", then "U", for unknown
> or un-evaluable, getting into, the "multi-valent", in logic,
> multivalent or multi-valent, multi-valued, vis-a-vis the
> existence only of "T" and nowhere the existence of "F",
> that all and everywhere in this constructivist's idyll,
> reason results for any abstract context that each relation
> indicates its existence either "T" or "F" then all the
> relations "F" disappear, resulting only "T".
>
> I'd like to, ..., "help", him, because it's on his own
> volition that that he tits-for-tats, which just results
> a sort of, "i-a", but he would sort of have to revise
> his "body of knowledge" to make it, "scientific", with
> regards to the philosophy of science, and, falsifiability
> of theories, and, that theories are only at best not
> falsified, vis-a-vis the ultimately strong theory of
> logic and mathematics together, the mathematical models,
> then here the mental models of mathematical models as
> a, "mental science", here with regards to theorists,
> like Tarski, Kleene, and Lukasiewicz.
>
> I.e. he seems stuck at the middle of the bridge with
> Goedel and Tarski there but he doesn't quite have
> their attention as they would confirm him along his way.
>
> Olcott, you're missing out some things, and you're not
> helping yourself. Yet, it doesn't take much, to right
> the cart.

On 2/25/24 2:07 PM, olcott wrote:

> It is not that I am missing anything at all it is that logicians
> are totally missing the slightest inkling of the actual philosophical
> foundation of analytical truth.
>
> They mistake their own ignorance of the foundation of analytical
> truth for my ignorance of the rules of logic.
>
> Richard is doing better than most by reverse-engineering the
> architecture of my design of a decider that does not get stuck
> on epistemological antinomies:
>
> 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.
>
> Richard does not understand that the above architecture
> refutes the Tarski Undefinability theorem that is anchored
> in the Liar Paradox.
>

Nope, you have conceeded that you method doesn't work since you can't
tell me what Boolean True(L, x) returns when x is defines as:

In L, x := ~(Boolean True(L, x))

Until you answer that, you have conceeded that you failed.

Of course:

If Boolean True(L, x) returns true, then x is the equivalent of ~true,
or false, and thus you have that True(L, false) is true, which is wrong, or

If Boolean True(L, x) returns false, then x is the equivalent of ~false,
or true, and thus you have that True(L, true) is false, which is also wrong.

You have the problem that the existance of a Truth Predicate not only
creates an Epistemological Antinomy, but a Truth-Bearing Epistemological
Antinomy, which rather than not having a truth value, has both the
values True and False at the same time.

This breaks the logic system.

The only way to get around this is to abandon two-valued logic, which
would put you out of the reach of most of the formal proofs you dislike,
but means you need to decide which version of multi-valued logic you are
going to try to use, or try to invent your one.

On 2/25/2024 2:14 PM, Richard Damon wrote:
> On 2/25/24 2:07 PM, olcott wrote:
>
>> It is not that I am missing anything at all it is that logicians
>> are totally missing the slightest inkling of the actual philosophical
>> foundation of analytical truth.
>>
>> They mistake their own ignorance of the foundation of analytical
>> truth for my ignorance of the rules of logic.
>>
>> Richard is doing better than most by reverse-engineering the
>> architecture of my design of a decider that does not get stuck
>> on epistemological antinomies:
>>
>> 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.
>>
>> Richard does not understand that the above architecture
>> refutes the Tarski Undefinability theorem that is anchored
>> in the Liar Paradox.
>>
>
> Nope, you have conceeded that you method doesn't work since you can't
> tell me what Boolean True(L, x) returns when x is defines as:
>
> In L, x := ~(Boolean True(L, x))
>
> Until you answer that, you have conceeded that you failed.
>

I am conceding that you keep having the same syntax error.

You already know that True(L, x) rejects every epistemological
antinomy thus trying to create one that is not rejected
is defined to be fruitless.

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

On 2/25/24 3:32 PM, olcott wrote:
> On 2/25/2024 2:14 PM, Richard Damon wrote:
>> On 2/25/24 2:07 PM, olcott wrote:
>>
>>> It is not that I am missing anything at all it is that logicians
>>> are totally missing the slightest inkling of the actual philosophical
>>> foundation of analytical truth.
>>>
>>> They mistake their own ignorance of the foundation of analytical
>>> truth for my ignorance of the rules of logic.
>>>
>>> Richard is doing better than most by reverse-engineering the
>>> architecture of my design of a decider that does not get stuck
>>> on epistemological antinomies:
>>>
>>> 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.
>>>
>>> Richard does not understand that the above architecture
>>> refutes the Tarski Undefinability theorem that is anchored
>>> in the Liar Paradox.
>>>
>>
>> Nope, you have conceeded that you method doesn't work since you can't
>> tell me what Boolean True(L, x) returns when x is defines as:
>>
>> In L, x := ~(Boolean True(L, x))
>>
>> Until you answer that, you have conceeded that you failed.
>>
>
> I am conceding that you keep having the same syntax error.
>
> You already know that True(L, x) rejects every epistemological
> antinomy thus trying to create one that is not rejected
> is defined to be fruitless.
>
>
>

WHAT "Syntax Error". If your "Boolean True(L,x)" can't be used in an
expression, it isn't a Predicate, and you are proven to be a liar, and
stupid.

And, I guess you give up!! As you won't give the needed answer.

or, what value?

Remember, the Predicate MUST answer, which is the problem.

You are just proving your total ignorance of how logic system work.

And that you are too stupid to learn from being corrected on your errors.