On 1/24/2024 5:15 AM, Mikko wrote:
On 2024-01-23 15:14:21 +0000, olcott said:
On 1/23/2024 3:23 AM, Mikko wrote:
On 2024-01-22 18:39:44 +0000, olcott said:
On 1/22/2024 4:17 AM, Mikko wrote:
In a formal theory nothing is semantically anything.
That it the reason why formal theories get confused
and make semantic errors that are invisible to them.
As there are no semantics in a formal system there can
be no semantic errors. However, it is possible that the
intended interpretation is not a model of the system.
Then one may hope that a small change will make it useful
for its intended purpose.
Mikko
True is an inherently semantic concept,
True
thus logic systems
always have semantics.
False. Formal systems do not have the concept "true". They may
have a symbol that looks like "true" but it is just a symbol
without meaning.
*In other words you are saying that "p ∧ q → p" is not true*
On 1/25/2024 3:56 AM, Mikko wrote:
On 2024-01-24 16:22:53 +0000, olcott said:
On 1/24/2024 5:39 AM, Mikko wrote:
On 2024-01-24 03:51:39 +0000, Richard Damon said:
Remember, Prolog is limited to Prepositional logic, not even full first >>>>> order, and only for system with a finite domain.
The basic logical system of Prolog is Horn clauses. However, it also
has library predicates (like assert and not and unify_with_occurs_check) >>>> that can break the logic system if used in a wrong place.
Mikko
unify_with_occurs_check detects cycles in the evaluation of
expressions such as LP := ~True(LP)
because it can see that this specifies
~True(~True(~True(~True(~True(...)))))
Prolog rules also permit but do no require that every unification
do the same. The consequence is that true conclusions about liar's
paradox or Quine's atom are impossible to infer.
Mikko
Not at all.
The problem is that it is conventional to encode
self-reference incorrectly.
On 1/25/24 20:28, olcott wrote:
On 1/25/2024 1:22 PM, immibis wrote:
On 1/25/24 20:21, olcott wrote:
On 1/25/2024 12:17 PM, immibis wrote:
On 1/25/24 18:47, olcott wrote:
On 1/25/2024 11:29 AM, immibis wrote:Probably because self-reference is pathological.
On 1/25/24 18:23, olcott wrote:
On 1/25/2024 11:16 AM, immibis wrote:This isn't FOL and ZFC.
On 1/25/24 18:10, olcott wrote:It can only be written in Montague Grammar.
On 1/25/2024 9:52 AM, immibis wrote:
On 1/25/24 16:45, olcott wrote:
The assumption superficially seems to be that a Truth predicate exists.
The actual assumption is that a truth predicate exists that can >>>>>>>>>>>> correctly determine the truth value of an expression having no truth
value.
Every expression has a truth value.
OK then give me the truth value of this expression:
"What time is it?"
If you write this as a sentence in FOL and ZFC, I will answer it. >>>>>>>>
LP := ~True(LP)
specifies: ~True(~True(~True(~True(~True(...)))))
Is LP true or false?
To the best of my knowledge there are zero formal systems
besides MTT that encode actual self-reference correctly.
LP := ~True(LP)
G := ~Provable(PA, G)
Are both pathological and are expressed in a formal system.
Is this MTT? Then perhaps MTT is pathological.
*MTT is merely more expressive that other formal systems*
Because it allows you to express pathologies?
On 1/25/2024 9:30 AM, Alan Mackenzie wrote:
olcott <[email protected]> wrote:
On 1/25/2024 3:52 AM, Alan Mackenzie wrote:
In comp.theory olcott <[email protected]> wrote:
On 1/24/2024 3:36 PM, Alan Mackenzie wrote:
In comp.theory olcott <[email protected]> wrote:
On 1/24/2024 3:10 PM, Alan Mackenzie wrote:
olcott <[email protected]> wrote:
On 1/24/2024 2:21 PM, Alan Mackenzie wrote:
In comp.theory olcott <[email protected]> wrote:
On 1/24/2024 1:27 PM, Alan Mackenzie wrote:
[ .... ]
You're lying. You do not understand it [proof by contradiction] >>>>>>>>>>>> at all. If I'm mistaken, feel free to outline it in your reply, >>>>>>>>>>>> or give some other unambiguous indication you understand it.
When we assume that X is possible and then prove that
this results in a contradiction then X is proven impossible.
So, you've got some idea. It's not "possible" and "impossible", >>>>>>>>>> it's true and false. But all the indications are that you don't >>>>>>>>>> really understand it; all the libel against mathematicians who use >>>>>>>>>> proof by contradiction, and failure to understand the basis of >>>>>>>>>> their results.
When we falsely assume that a correct and consistent truth >>>>>>>>>>> predicate must correctly determine the truth value of a non truth >>>>>>>>>>> bearer, then this false assumption derives the false conclusion >>>>>>>>>>> that correct and consistent truth predicate does not exist.
But here you go right off the wall into incoherent rambling.
In other words you don't know what the term truth-bearer
means so this seems like nonsense to you.
Where does that come from? I know full well what a truth bearer is. >>>>>>>> I can only guess what you mean by your rambling. If my guess is >>>>>>>> right, you're wrong, hopelessly wrong.
*I will make it more explicit*
The fact that this predicate:
Boolean True(Formalized_English, "What time is it?")
cannot return a correct Boolean value
DOES NOT PROVE THAT A CORRECT AND CONSISTENT
TRUTH PREDICATE DOES NOT EXIST.
No, of course it doesn't. Who other than you said it does? The >>>>>>>> truth predicate of Tarski's theorem cannot exist. This was
proven by contradiction, something you assert you understand.
But given you don't accept the result, it seems your
understanding is, at best, superficial.
THAT YOU FAIL TO COMPREHEND THAT TARSKI'S LINE (1)
ASSUMES THE LIAR PARADOX AS HIS BASIS IS NO ACTUAL
REBUTTAL WHAT-SO-EVER.
You don't understand proof by contradiction after all.
Tarski was a top rate mathematician, you are not. His work has been >>>>>> learnt, reviewed, checked, and tested by thousands, if not millions, >>>>>> of capable mathematicians. It is correct.
True(L, x) was proven to not exist on the basis of Tarski's line(1) >>>>>>> that has been adapted from the Liar Paradox.
My understanding of the theorem's proof is that it uses the liar
paradox merely as an absurdity.
Conclusively proving ....
Stop swearing! You shouldn't use words you don't understand.
.... that you never carefully studied these four pages of his proof.
https://liarparadox.org/Tarski_247_248.pdf
https://liarparadox.org/Tarski_275_276.pdf
I've never looked at his proof in my life. Unlike you, I've got other >>>> things to do. Also unlike you, were I to look at it, I could
understand it. I just can't be bothered. Further unlike you, I
understand proof by contradiction, an essential part of that proof.
The proof by contradiction begins with the false assumption
that a correct and consistent truth predicate must be able
to return a correct truth value for a non-truth bearer.
No. It begins with an assumption, and shows that this assumption leads
to that absurdity.
It begins with an absurdity and from this absurdity
derives a false conclusion.
On 1/25/2024 3:34 AM, Mikko wrote:
On 2024-01-24 17:32:45 +0000, olcott said:
On 1/24/2024 9:36 AM, Mikko wrote:
On 2024-01-24 15:03:25 +0000, olcott said:
On 1/24/2024 4:40 AM, Mikko wrote:
On 2024-01-21 20:15:54 +0000, olcott said:
On 1/21/2024 2:06 PM, Richard Damon wrote:
On 1/21/24 2:22 PM, wij wrote:
I just found an article about the Halting Problem.
https://arxiv.org/pdf/1906.05340.pdf
In the conclusion section:
The idea of a universal halting test seems reasonable, but cannot be >>>>>>>>> for-
malised as a consistent specification. It has no model and does not >>>>>>>>> exist as
a conceptual object. Assuming its conceptual existence leads to a >>>>>>>>> paradox.
The halting problem is universally used in university courses on >>>>>>>>> Computer
Science to illustrate the limits of computation. Hehner claims the >>>>>>>>> halting
problem is misconceived......
It looks like what olcott now is claiming. Am I missing something? >>>>>>>>>
I think the problem he is seeing is that the property of "Halting" can >>>>>>>> not be uniformly determined in Finite Time.
That is all that I can get from his statement of:
The idea of a universal halting test seems reasonable, but cannot be >>>>>>>> formalised as a consistent specification.
There certainly CAN be defined formal test that define Halting, the >>>>>>>> issue is that non-halting is defined by the non-existence of a number N
for the number of steps needed to reach a final state.
Some people just don't like the fact that it can be absolutely provable
what the answer is (and thus unknowable), even if we know from the >>>>>>>> definition, that it must be one or the other.
This leads us to a great divide in logics. The classical branch accepts
that some truth is only established by infinite chains of connections, >>>>>>>> and thus can not be proven with a finite proof, and thus is unknowable.
Others don't accept that, and require Truth to be only established by >>>>>>>> Finite chains. The problem then is, such logic system need to greatly >>>>>>>> limit the domain they attempt to cover, as otherwise you get into >>>>>>>> endless chains of asking if a question can be asked, at which point you
need to ask if you can even ask about asking the questions. Only when >>>>>>>> the domain is restricted in a way that the answer MUST be determinable >>>>>>>> with finite work, can we break the cycle.
For instance, if we limit ourselves to Finite State Machines (which >>>>>>>> could be Turing Machines with a fixed finite tape, or a classical >>>>>>>> program in a computer with limited memory) then we can be sure that the
answer is determinable with a finite amount of work.
Tarski did not understand that the Liar Paradox is not a truth bearer >>>>>>> thus cannot possibly be true or false.
It is a sin to lie about other people. Tarski obviously unnderstood that,
as he could see an opportunity to exloit the fact.
Mikko
If Tarski understood that self-contradictory expressions
have no truth value and did not have his truth predicate
reject such expressions as invalid then Tarski was stupid.
Tarski was discussion the problem of constructing a predicate to
determine the truth of an arthmetic sentence. The liar's paradox
is not an arithmetic sentence so it is obviously invalid for his
predicate of arithmetic truth.
Mikko
Then why did he anchor his whole proof in the Liar Paradox?
The first line of his proof began with an adapted form of
the Liar Paradox. I had to carefully study his proof hundreds
of times before I noticed this.
*Tarski anchors his whole proof in the Liar Paradox*
https://liarparadox.org/Tarski_247_248.pdf
x asserts that x is not a true sentence. page 248
What x are you talking about? Is it a sentence of arithmetic
or a metalanguage sentence about arithmetic?
https://liarparadox.org/Tarski_275_276.pdf
x asserts that x is not a true sentence. page 248
From the top of page 275
is encoded as: x ∉ True if and only if p
"where the symbol 'p' represents the whole sentence x"
On 1/27/2024 1:41 AM, Mikko wrote:
On 2024-01-26 23:04:57 +0000, olcott said:
On 1/26/2024 4:51 PM, immibis wrote:
On 1/26/24 23:00, olcott wrote:
On 1/26/2024 3:42 PM, immibis wrote:
On 1/26/24 22:17, olcott wrote:
On 1/26/2024 2:39 PM, immibis wrote:
On 1/26/24 18:54, olcott wrote:
On 10/13/2022 11:46 AM, olcott wrote:
MIT Professor Michael Sipser has agreed that the following verbatim >>>>>>>>>> paragraph is correct (he has not agreed to anything else in this paper):Professor Sipser is the best selling author of theory of
If simulating halt decider H correctly simulates its input D until H >>>>>>>>>> correctly determines that its simulated D would never stop running >>>>>>>>>> unless aborted then H can abort its simulation of D and correctly >>>>>>>>>> report that D specifies a non-halting sequence of configurations. >>>>>>>>>
computation textbooks.
P = "simulating halt decider H correctly simulates its input D >>>>>>>>> until H correctly determines that its simulated D would never >>>>>>>>> stop running unless aborted,"
Q = "H can abort its simulation of D and correctly report that D >>>>>>>>> specifies a non-halting sequence of configurations."
P → Q
Correct determination is impossible.
In other words you believe that Professor Sipser
agreed to a vacuous truth. He did not do that.
Vacuous truths are true.
Not within the conventional understanding of true.
"It is true that all of the billion ton elephants
in the middle of my living room are rainbow colored"
Is not actually true at all
Yes it is
False presuppositions are never actually true
at all, they only seem that was to people that
do not know what False presuppositions are.
False presuppositions never prevent anything else from being true.
Mikko
*I just proved otherwise*
The false presupposition that the man was married makes the question:
Have you stopped beating your wife?
untrue and unfalse.
On 1/28/2024 7:12 AM, Mikko wrote:
On 2024-01-27 16:31:33 +0000, olcott said:
On 1/27/2024 6:38 AM, immibis wrote:
On 1/27/24 09:48, Mikko wrote:
On 2024-01-26 17:01:58 +0000, olcott said:
Most other sources simply say that Tarski directly applies
his Truth() predicate to the Liar Paradox itself.
It does not really matter what other sources say,
only what Tarski says.
Please stop trying to prove truth or falsehood based on a person's authority.
When we are determining whether or not Tarski is
wrong we must go by what Tarski actually said.
On the first line of his proof he contradicts
the actual correct truth predicate
It would help if you could quote the first line
of his proof. But you can't even find it. the
best you can do is a strawman and not even a
good strawman:
*The next line is the first line of his proof*
On 1/28/2024 11:56 AM, Mikko wrote:
On 2024-01-28 16:12:05 +0000, olcott said:
On 1/28/2024 7:12 AM, Mikko wrote:
On 2024-01-27 16:31:33 +0000, olcott said:
On 1/27/2024 6:38 AM, immibis wrote:
On 1/27/24 09:48, Mikko wrote:
On 2024-01-26 17:01:58 +0000, olcott said:
Most other sources simply say that Tarski directly applies
his Truth() predicate to the Liar Paradox itself.
It does not really matter what other sources say,
only what Tarski says.
Please stop trying to prove truth or falsehood based on a person's authority.
When we are determining whether or not Tarski is
wrong we must go by what Tarski actually said.
On the first line of his proof he contradicts
the actual correct truth predicate
It would help if you could quote the first line
of his proof. But you can't even find it. the
best you can do is a strawman and not even a
good strawman:
*The next line is the first line of his proof*
What does "next" mean in this context?
Mikko
*Line (1) is the next line that I referred to*
*Here is the Tarski Undefinability Theorem proof*
(1) x ∉ Provable if and only if p // assumption
On 1/28/2024 11:41 AM, Mikko wrote:
On 2024-01-27 15:31:10 +0000, olcott said:
On 1/27/2024 1:41 AM, Mikko wrote:
On 2024-01-26 23:04:57 +0000, olcott said:
On 1/26/2024 4:51 PM, immibis wrote:
On 1/26/24 23:00, olcott wrote:
On 1/26/2024 3:42 PM, immibis wrote:
On 1/26/24 22:17, olcott wrote:
On 1/26/2024 2:39 PM, immibis wrote:
On 1/26/24 18:54, olcott wrote:
On 10/13/2022 11:46 AM, olcott wrote:
MIT Professor Michael Sipser has agreed that the following verbatimProfessor Sipser is the best selling author of theory of >>>>>>>>>>> computation textbooks.
paragraph is correct (he has not agreed to anything else in this paper):
If simulating halt decider H correctly simulates its input D until H
correctly determines that its simulated D would never stop running >>>>>>>>>>>> unless aborted then H can abort its simulation of D and correctly >>>>>>>>>>>> report that D specifies a non-halting sequence of configurations. >>>>>>>>>>>
P = "simulating halt decider H correctly simulates its input D >>>>>>>>>>> until H correctly determines that its simulated D would never >>>>>>>>>>> stop running unless aborted,"
Q = "H can abort its simulation of D and correctly report that D >>>>>>>>>>> specifies a non-halting sequence of configurations."
P → Q
Correct determination is impossible.
In other words you believe that Professor Sipser
agreed to a vacuous truth. He did not do that.
Vacuous truths are true.
Not within the conventional understanding of true.
"It is true that all of the billion ton elephants
in the middle of my living room are rainbow colored"
Is not actually true at all
Yes it is
False presuppositions are never actually true
at all, they only seem that was to people that
do not know what False presuppositions are.
False presuppositions never prevent anything else from being true.
Mikko
*I just proved otherwise*
The false presupposition that the man was married makes the question:
Have you stopped beating your wife?
untrue and unfalse.
No, it does not. A question is not true or flase anyway.
Mikko
Every yes/no question lacking a correct yes/no
answer is an incorrect question.
On 1/29/2024 3:19 AM, Mikko wrote:
On 2024-01-27 16:12:27 +0000, olcott said:
On 1/27/2024 4:20 AM, Mikko wrote:
On 2024-01-26 16:27:24 +0000, olcott said:
On 1/26/2024 6:53 AM, Mikko wrote:
On 2024-01-25 16:03:51 +0000, olcott said:
On 1/25/2024 3:08 AM, Mikko wrote:
On 2024-01-24 15:03:25 +0000, olcott said:
On 1/24/2024 4:40 AM, Mikko wrote:
On 2024-01-21 20:15:54 +0000, olcott said:
On 1/21/2024 2:06 PM, Richard Damon wrote:
On 1/21/24 2:22 PM, wij wrote:
I just found an article about the Halting Problem.
https://arxiv.org/pdf/1906.05340.pdf
In the conclusion section:
The idea of a universal halting test seems reasonable, but cannot be
for-
malised as a consistent specification. It has no model and does not
exist as
a conceptual object. Assuming its conceptual existence leads to a >>>>>>>>>>>>> paradox.
The halting problem is universally used in university courses on >>>>>>>>>>>>> Computer
Science to illustrate the limits of computation. Hehner claims the
halting
problem is misconceived......
It looks like what olcott now is claiming. Am I missing something?
I think the problem he is seeing is that the property of "Halting" can
not be uniformly determined in Finite Time.
That is all that I can get from his statement of:
The idea of a universal halting test seems reasonable, but cannot be
formalised as a consistent specification.
There certainly CAN be defined formal test that define Halting, the
issue is that non-halting is defined by the non-existence of a number N
for the number of steps needed to reach a final state. >>>>>>>>>>>>
Some people just don't like the fact that it can be absolutely provable
what the answer is (and thus unknowable), even if we know from the >>>>>>>>>>>> definition, that it must be one or the other.
This leads us to a great divide in logics. The classical branch accepts
that some truth is only established by infinite chains of connections,
and thus can not be proven with a finite proof, and thus is unknowable.
Others don't accept that, and require Truth to be only established by
Finite chains. The problem then is, such logic system need to greatly
limit the domain they attempt to cover, as otherwise you get into >>>>>>>>>>>> endless chains of asking if a question can be asked, at which point you
need to ask if you can even ask about asking the questions. Only when
the domain is restricted in a way that the answer MUST be determinable
with finite work, can we break the cycle.
For instance, if we limit ourselves to Finite State Machines (which
could be Turing Machines with a fixed finite tape, or a classical >>>>>>>>>>>> program in a computer with limited memory) then we can be sure that the
answer is determinable with a finite amount of work.
Tarski did not understand that the Liar Paradox is not a truth bearer
thus cannot possibly be true or false.
It is a sin to lie about other people. Tarski obviously unnderstood that,
as he could see an opportunity to exloit the fact.
Mikko
If Tarski understood that self-contradictory expressions
have no truth value and did not have his truth predicate
reject such expressions as invalid then Tarski was stupid.
If you could show some exmples of self-contradictory arithmetic >>>>>>>> expressions we perhaps could understand what you are trying to say. >>>>>>>>
Mikko
Tarski did not use PA in this proof:
Tarski's discussion is fairly generic. It is applicable to PA and
many other theories.
Mikko
No conventional language encodes self-reference correctly
thus No conventional language encodes the Liar Paradox
correctly. Thus No conventional language can directly
see the infinite recursive structure of the actual Liar
Paradox.
What do you mean by "conventional"? Is the l anguage of ordinary
formal first order logic "conventional"? Is ordinary Enlish
"conventional"?
Mikko
Every conventional formal language incorrectly formalizes the Liar
Paradox as something like this LP ↔ ~True(LP) rather than like this
LP := ~True(LP) thus the infinitely recursive structure of the Liar
Paradox is invisible when formalized incorrectly.
That does not actually answer the question but apparently
you mean 'convetional formal laguage' so yes about ordinary
first order longic and no about ordinary English.
Mikko
This does correctly formalize the Liar Paradox
LP := ~True(LP)
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