We may be able to correct every divergence of (every level of) predicate
logic from correct reasoning by making a single change to predicate
logic.

THIS IS THE SINGLE CHANGE
Every aspect of every level of predicate logic must only derive
conclusions as a necessary consequence of its premises.

This single change by itself cancels the principle of explosion. It also
eliminates the Liar Paradox basis of the Tarski Undefinability theorem
thus cancelling his whole theorem.

It also eliminates the possibility of mathematical incompleteness
because the lack of a provability connection from the premises to the
conclusion simply means the argument is invalid.

We take modern predicate logic (including HOL) and get rid of every
unsound aspect on the basis that every conclusion must be a necessary
consequence of its premises or the argument is invalid.

That one single change may correct every divergence of predicate logic
from correct reasoning.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 8/4/23 8:46 PM, olcott wrote:
> We may be able to correct every divergence of (every level of) predicate
> logic from correct reasoning by making a single change to predicate
> logic.
>
> THIS IS THE SINGLE CHANGE
> Every aspect of every level of predicate logic must only derive
> conclusions as a necessary consequence of its premises.
>
> This single change by itself cancels the principle of explosion. It also
> eliminates the Liar Paradox basis of the Tarski Undefinability theorem
> thus cancelling his whole theorem.
>
> It also eliminates the possibility of mathematical incompleteness
> because the lack of a provability connection from the premises to the
> conclusion simply means the argument is invalid.
>
> We take modern predicate logic (including HOL) and get rid of every
> unsound aspect on the basis that every conclusion must be a necessary
> consequence of its premises or the argument is invalid.
>
> That one single change may correct every divergence of predicate logic
> from correct reasoning.
>

So, have you done ANY work to show what this fundamental change in logic
actually does.

How do you ACTUALLY DEFINE that statement?

You seem to have a problem with the statement that if we have proven
that if A or B being true proves that C is true, and if we can prove
that C is true and A can be proven false, that B must be true.

(I.E, your "Rules of Logic" don't seem to be able to handle abstract
concepts)

What can your logic system actually derive?

We can correct every divergence of (every level of) predicate logic
from correct reasoning by making a single change to predicate logic.

*THIS IS THE SINGLE CHANGE*
Valid arguments only include conclusions as a necessary consequence of
their premises.

This brings predicate logic back in line with the syllogism.

This single change by itself cancels the principle of explosion. It also
eliminates the Liar Paradox basis of the Tarski Undefinability theorem
thus cancelling his whole theorem.

It also eliminates the possibility of mathematical incompleteness
because the lack of a provability connection from the premises to the
conclusion simply means the argument is invalid.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 8/8/23 5:44 PM, olcott wrote:
> We can correct every divergence of (every level of) predicate logic
> from correct reasoning by making a single change to predicate logic.
>
> *THIS IS THE SINGLE CHANGE*
> Valid arguments only include conclusions as a necessary consequence of
> their premises.
>
> This brings predicate logic back in line with the syllogism.
>
> This single change by itself cancels the principle of explosion. It also
> eliminates the Liar Paradox basis of the Tarski Undefinability theorem
> thus cancelling his whole theorem.
>
> It also eliminates the possibility of mathematical incompleteness
> because the lack of a provability connection from the premises to the
> conclusion simply means the argument is invalid.
>
>
>
> And what exactly do you mean by that?

Can your idea handle "abstract" concepts?

If we have established that if A is True, or if B is True, then by
necessity C is True; and if then we can show that A it True, can we
establish that C is actually true?

If we have established that if A is True, or if B is True, then by
necessity that C is true; and if then we can show that C actually is
True, but A can not be, can we then state that B must be true?

Do you even understand what you are claiming?

If you deny any of the above, can your logic system actually prove
anything useful, or is it just a "toy"?

On 8/8/2023 9:40 PM, Dan Christensen wrote:
> On Tuesday, August 8, 2023 at 5:44:12 PM UTC-4, olcott wrote:
>> We can correct every divergence of (every level of) predicate logic
>> from correct reasoning by making a single change to predicate logic.
>> *THIS IS THE SINGLE CHANGE*
>> Valid arguments only include conclusions as a necessary consequence of
>> their premises.
>>
>> This brings predicate logic back in line with the syllogism.
>> This single change by itself cancels the principle of explosion. It also
>> eliminates the Liar Paradox basis of the Tarski Undefinability theorem
>> thus cancelling his whole theorem.
>>
>> It also eliminates the possibility of mathematical incompleteness
>> because the lack of a provability connection from the premises to the
>> conclusion simply means the argument is invalid.
>
> You said this 4 days ago and got nowhere.
>
> Dan

I revised it. I simplified the unifying criterion measure.
It is not that I got nowhere. It only seems that way on
the basis of not understanding what I am saying.

The meaning of the words that I said above proves that they
are all true.

People that don't fully understand the meaning of the simple
conventional words that I use in: *THIS IS THE SINGLE CHANGE*
will not be able to verify that such a system wold get rid of
incompleteness, undefinability and the principle of explosion.

There are a lot more details that must be specified before
*THIS IS THE SINGLE CHANGE* can be fully implemented yet it
does remain a single change.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 8/8/23 11:43 PM, olcott wrote:
> On 8/8/2023 9:40 PM, Dan Christensen wrote:
>> On Tuesday, August 8, 2023 at 5:44:12 PM UTC-4, olcott wrote:
>>> We can correct every divergence of (every level of) predicate logic
>>> from correct reasoning by making a single change to predicate logic.
>>> *THIS IS THE SINGLE CHANGE*
>>> Valid arguments only include conclusions as a necessary consequence of
>>> their premises.
>>>
>>> This brings predicate logic back in line with the syllogism.
>>> This single change by itself cancels the principle of explosion. It also
>>> eliminates the Liar Paradox basis of the Tarski Undefinability theorem
>>> thus cancelling his whole theorem.
>>>
>>> It also eliminates the possibility of mathematical incompleteness
>>> because the lack of a provability connection from the premises to the
>>> conclusion simply means the argument is invalid.
>>
>> You said this 4 days ago and got nowhere.
>>
>> Dan
>
> I revised it. I simplified the unifying criterion measure.
> It is not that I got nowhere. It only seems that way on
> the basis of not understanding what I am saying.
>
> The meaning of the words that I said above proves that they
> are all true.
>
> People that don't fully understand the meaning of the simple
> conventional words that I use in: *THIS IS THE SINGLE CHANGE*
> will not be able to verify that such a system wold get rid of
> incompleteness, undefinability and the principle of explosion.
>
> There are a lot more details that must be specified before
> *THIS IS THE SINGLE CHANGE* can be fully implemented yet it
> does remain a single change.
>

No, it is an UNDEFINED change, since you can't actually define what it
means.

You haven't answered the simple questions I made about it, because if
you try to, you will reveil that it makes the logic system worthless (or
shows that it isn't actually any change at all)

You are just proving your utter stupidity.

On 8/4/23 8:46 PM, olcott wrote:
> We may be able to correct every divergence of (every level of) predicate
> logic from correct reasoning by making a single change to predicate
> logic.
>
> THIS IS THE SINGLE CHANGE
> Every aspect of every level of predicate logic must only derive
> conclusions as a necessary consequence of its premises.

Simple question, what make you think that predicat logic allows you to
derive a conclusion that isn't a "neccessary consequence" of its premises?

>
> This single change by itself cancels the principle of explosion. It also
> eliminates the Liar Paradox basis of the Tarski Undefinability theorem
> thus cancelling his whole theorem.

And what are you changing?

Remember, you can only use inferences that are either given as part of
the essential truth of the system, or that are provable in the system.

That means, that any conclusion that can be soundly and validly derived
from such an inference, is BY NECESSITY TRUE.

Your problem seems to be that you are willing to accept statements which
are not true, partially because you seem to think in natural languages,
which are inherently incomplete, and take statments ignoring their
context (which are logically part of them)

>
> It also eliminates the possibility of mathematical incompleteness
> because the lack of a provability connection from the premises to the
> conclusion simply means the argument is invalid.

But that isn't "Incompleteness". Incompleteness is that there exists
statements (not conclusions") that are True, but are NOT provable by a
finite series of logical conclusions.

Remember, a statment is "Analytically True" if there exist a chain of
reasoning (which can be infinite in length, since the chaim being finite
is NOT a requirement for truth) in the system from the basic truthmakers
of the system, to it.

Provable means that there exists a finite chain.

Incompleteness says the system has some statements that the only chains
to them are infinte in length.

You are just proving you don't understand what you are talking about.

>
> We take modern predicate logic (including HOL) and get rid of every
> unsound aspect on the basis that every conclusion must be a necessary
> consequence of its premises or the argument is invalid.
>
> That one single change may correct every divergence of predicate logic
> from correct reasoning.
>

Which just shos you don't understand what anything means.