When we create a three-valued logic system that has these
three values: {True, False, Nonsense} https://en.wikipedia.org/wiki/Three-valued_logic
On 4/20/2024 2:54 AM, Mikko wrote:
On 2024-04-19 18:04:48 +0000, olcott said:
When we create a three-valued logic system that has these
three values: {True, False, Nonsense}
https://en.wikipedia.org/wiki/Three-valued_logic
Such three valued logic has the problem that a tautology of the
ordinary propositional logic cannot be trusted to be true. For
example, in ordinary logic A ∨ ¬A is always true. This means that
some ordinary proofs of ordinary theorems are no longer valid and
you need to accept the possibility that a theory that is complete
in ordinary logic is incomplete in your logic.
I only used three-valued logic as a teaching device. Whenever an
expression of language has the value of {Nonsense} then it is
rejected and not allowed to be used in any logical operations. It
is basically invalid input.
On 4/21/2024 2:57 AM, Mikko wrote:
On 2024-04-20 15:20:05 +0000, olcott said:
On 4/20/2024 2:54 AM, Mikko wrote:
On 2024-04-19 18:04:48 +0000, olcott said:
When we create a three-valued logic system that has these
three values: {True, False, Nonsense}
https://en.wikipedia.org/wiki/Three-valued_logic
Such three valued logic has the problem that a tautology of the
ordinary propositional logic cannot be trusted to be true. For
example, in ordinary logic A ∨ ¬A is always true. This means that
some ordinary proofs of ordinary theorems are no longer valid and
you need to accept the possibility that a theory that is complete
in ordinary logic is incomplete in your logic.
I only used three-valued logic as a teaching device. Whenever an
expression of language has the value of {Nonsense} then it is
rejected and not allowed to be used in any logical operations. It
is basically invalid input.
You cannot teach because you lack necessary skills. Therefore you
don't need any teaching device.
That is too close to ad homimen.
If you think my reasoning is incorrect then point to the error
in my reasoning. Saying that in your opinion I am a bad teacher
is too close to ad hominem because it refers to your opinion of
me and utterly bypasses any of my reasoning.
As you make the syntax of your language dependent on semantics
you lose one of the greatest advantage of formal languages:
the simplicity of determination whether a string is a well formed
formula.
Not at all. By combining them together we can simultaneously determine syntactic and semantic correctness. By keeping them separate we have misconstrued expressions that are not even propositions as propositions
that prove incompleteness and undecidability.
A proposition is a central concept in the philosophy of language,
semantics, logic, and related fields, often characterized as the primary bearer of truth or falsity. Propositions are also often characterized as being the kind of thing that declarative sentences denote. https://en.wikipedia.org/wiki/Proposition
On 4/22/2024 4:35 AM, Mikko wrote:
On 2024-04-21 14:44:37 +0000, olcott said:
On 4/21/2024 2:57 AM, Mikko wrote:
On 2024-04-20 15:20:05 +0000, olcott said:
On 4/20/2024 2:54 AM, Mikko wrote:
On 2024-04-19 18:04:48 +0000, olcott said:
When we create a three-valued logic system that has these
three values: {True, False, Nonsense}
https://en.wikipedia.org/wiki/Three-valued_logic
Such three valued logic has the problem that a tautology of the
ordinary propositional logic cannot be trusted to be true. For
example, in ordinary logic A ∨ ¬A is always true. This means that >>>>>> some ordinary proofs of ordinary theorems are no longer valid and
you need to accept the possibility that a theory that is complete
in ordinary logic is incomplete in your logic.
I only used three-valued logic as a teaching device. Whenever an
expression of language has the value of {Nonsense} then it is
rejected and not allowed to be used in any logical operations. It
is basically invalid input.
You cannot teach because you lack necessary skills. Therefore you
don't need any teaching device.
That is too close to ad homimen.
If you think my reasoning is incorrect then point to the error
in my reasoning. Saying that in your opinion I am a bad teacher
is too close to ad hominem because it refers to your opinion of
me and utterly bypasses any of my reasoning.
No, it isn't. You introduced youtself as a topic of discussion so
you are a legitimate topic of discussion.
I didn't claim that there be any reasoning, incorrect or otherwise.
If you claim I am a bad teacher you must point out what is wrong with
the lesson otherwise your claim that I am a bad teacher is essentially
an as hominem attack.
On 4/22/2024 10:27 AM, Mikko wrote:
On 2024-04-22 14:10:54 +0000, olcott said:
On 4/22/2024 4:35 AM, Mikko wrote:
On 2024-04-21 14:44:37 +0000, olcott said:
On 4/21/2024 2:57 AM, Mikko wrote:
On 2024-04-20 15:20:05 +0000, olcott said:
On 4/20/2024 2:54 AM, Mikko wrote:
On 2024-04-19 18:04:48 +0000, olcott said:
When we create a three-valued logic system that has these
three values: {True, False, Nonsense}
https://en.wikipedia.org/wiki/Three-valued_logic
Such three valued logic has the problem that a tautology of the >>>>>>>> ordinary propositional logic cannot be trusted to be true. For >>>>>>>> example, in ordinary logic A ∨ ¬A is always true. This means that >>>>>>>> some ordinary proofs of ordinary theorems are no longer valid and >>>>>>>> you need to accept the possibility that a theory that is complete >>>>>>>> in ordinary logic is incomplete in your logic.
I only used three-valued logic as a teaching device. Whenever an >>>>>>> expression of language has the value of {Nonsense} then it is
rejected and not allowed to be used in any logical operations. It >>>>>>> is basically invalid input.
You cannot teach because you lack necessary skills. Therefore you
don't need any teaching device.
That is too close to ad homimen.
If you think my reasoning is incorrect then point to the error
in my reasoning. Saying that in your opinion I am a bad teacher
is too close to ad hominem because it refers to your opinion of
me and utterly bypasses any of my reasoning.
No, it isn't. You introduced youtself as a topic of discussion so
you are a legitimate topic of discussion.
I didn't claim that there be any reasoning, incorrect or otherwise.
If you claim I am a bad teacher you must point out what is wrong with
the lesson otherwise your claim that I am a bad teacher is essentially
an as hominem attack.
You are not a teacher, bad or otherwise. That you lack skills that
happen to be necessary for teaching is obvious from you postings
here. A teacher needs to understand human psychology but you don't.
You may be correct that I am a terrible teacher.
None-the-less Mathematicians might not have very much understanding
of the link between proof theory and computability.
When I refer to rejecting an invalid input math would seem to construe
this as nonsense, where as computability theory would totally understand.
On 4/23/2024 3:21 AM, Mikko wrote:
On 2024-04-22 17:37:55 +0000, olcott said:
On 4/22/2024 10:27 AM, Mikko wrote:
On 2024-04-22 14:10:54 +0000, olcott said:
On 4/22/2024 4:35 AM, Mikko wrote:
On 2024-04-21 14:44:37 +0000, olcott said:
On 4/21/2024 2:57 AM, Mikko wrote:
On 2024-04-20 15:20:05 +0000, olcott said:
On 4/20/2024 2:54 AM, Mikko wrote:
On 2024-04-19 18:04:48 +0000, olcott said:
When we create a three-valued logic system that has these >>>>>>>>>>> three values: {True, False, Nonsense}
https://en.wikipedia.org/wiki/Three-valued_logic
Such three valued logic has the problem that a tautology of the >>>>>>>>>> ordinary propositional logic cannot be trusted to be true. For >>>>>>>>>> example, in ordinary logic A ∨ ¬A is always true. This means that >>>>>>>>>> some ordinary proofs of ordinary theorems are no longer valid and >>>>>>>>>> you need to accept the possibility that a theory that is complete >>>>>>>>>> in ordinary logic is incomplete in your logic.
I only used three-valued logic as a teaching device. Whenever an >>>>>>>>> expression of language has the value of {Nonsense} then it is >>>>>>>>> rejected and not allowed to be used in any logical operations. It >>>>>>>>> is basically invalid input.
You cannot teach because you lack necessary skills. Therefore you >>>>>>>> don't need any teaching device.
That is too close to ad homimen.
If you think my reasoning is incorrect then point to the error
in my reasoning. Saying that in your opinion I am a bad teacher
is too close to ad hominem because it refers to your opinion of
me and utterly bypasses any of my reasoning.
No, it isn't. You introduced youtself as a topic of discussion so
you are a legitimate topic of discussion.
I didn't claim that there be any reasoning, incorrect or otherwise. >>>>>>
If you claim I am a bad teacher you must point out what is wrong with >>>>> the lesson otherwise your claim that I am a bad teacher is essentially >>>>> an as hominem attack.
You are not a teacher, bad or otherwise. That you lack skills that
happen to be necessary for teaching is obvious from you postings
here. A teacher needs to understand human psychology but you don't.
You may be correct that I am a terrible teacher.
None-the-less Mathematicians might not have very much understanding
of the link between proof theory and computability.
Sume mathematicians do have very much understanding of that. But that
link is not needed for understanding and solving problems separately
in the two areas.
When I refer to rejecting an invalid input math would seem to construePeople working on computability theory do not understand "invalid input"
this as nonsense, where as computability theory would totally understand. >>
as "impossible input".
The proof then shows, for any program f that might determine whether
programs halt, that a "pathological" program g, called with some input,
can pass its own source and its input to f and then specifically do the opposite of what f predicts g will do. No f can exist that handles this
case, thus showing undecidability. https://en.wikipedia.org/wiki/Halting_problem#
So then they must believe that there exists an H that does correctly determine the halt status of every input, some inputs are simply
more difficult than others, no inputs are impossible.
They understand it as an input that must be
handled differently from ordinary input. Likewise, mathematicians do
understand that some inputs must be considered separately and differently. >> But mathematicians don't call those inputs "invalid".
It is so dead obvious that the whole world must be wired with a short
circuit in their brains. Formal bivalent mathematical systems of logic
must reject every expression that cannot possibly have a value of true
or false as a type mismatch error.
A proposition is a central concept in the philosophy of language,
semantics, logic, and related fields, often characterized as the primary bearer of truth or falsity. https://en.wikipedia.org/wiki/Proposition
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