Re: Minimal Logics in the 2020's: A Meteoric Rise

On 7/7/24 9:34 AM, olcott wrote:

On 7/7/2024 6:26 AM, Richard Damon wrote:

On 7/6/24 11:42 PM, olcott wrote:

On 7/6/2024 10:12 PM, Richard Damon wrote:

On 7/6/24 10:51 PM, olcott wrote:

On 7/6/2024 9:16 PM, Richard Damon wrote:

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So if x is defined in L as ~True(L, x)
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what value does True(L, x) have?
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then True(L,x) evaluates to false ultimately meaning
that x is incorrect.

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But doesn't ~false evaluate to True?
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No. ~false evaluates to true or incorrect.

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So, "incorrect" is an ACTUAL logic state, not just "sort of" and ~~P doesn't necessarily have the same value as P.
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 It is something like tri-valued logic.

It needs to either BE tri-valued, or be bi-valued, or be whatever number of values it is.

 Every other formal system would try to force "a fish" into
true or false and if that didn't work determine that the
formal system is incomplete.

Nope, most formal system just don't define "a fish" as a statement in their langauge.

 

IF you do mean this, then you first need to fully define how "incorrect" works in ALL the logical operators.
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 (~True(L,x) ∧ ~True(L,~x)) ≡ ~Proposition(L,x)
Every variable is screened this way before any other
operations can be performed upon it.
x = "a fish" rejects every expression referencing x.

Logic doesn't work that way.
Sorry, you are just totally ignorant of how formal logic works.

 

It also means you need to figure out what you logic system supports, and can't just rely on the large base of work on normal binary logic.
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 That every expression of language that is {true on the basis of
its meaning expressed using language} must have a connection by
truth preserving operations to its {meaning expressed using language}
is a tautology. The accurate model of the actual world is expressed
using formal language and formalized natural language.

Nope, doesm't work that way. The problem is that most formal systems don't express them selves with "Natural Language".
And an "accurate model of the actual world" isn't available, so you are hypothocating on a non-existant thing.

 

Thare is a good aount of work on non-binary systems, and perhaps you can find one that is close enough to try to use, but YOU need to do that work.
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 In other words it is too difficult for you to understand
that "a fish" is not a proposition?

Nope, YOU are the one that says it is one, and needs to be handled.
What formal logic system do you think you are working in?

 

And realize that you system isn't applicable to any theorem based on a binary logic system, since your system is not one.
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 All of the current systems of logic inherit their notion of
True(L,x) on the above basis.
(~True(PA,g) ∧ ~True(PA,~g)) ≡ ~Proposition(PA,g)
Mathematical incompleteness goes away.
 

Nope, you just made your system inconsistant if it was powerful enough to express as a proposition in it that x in PA is ~True(PA, x).
Tarski shows a set of commonly held conditions that are sufficent to allow that expression to be a proposition in PA.
Just as Godel does in a different manner by constructing his Primative Recursive Relationship that detects a proof of his statement G.

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We can't know for sure that x is incorrect until
we see that True(L,~x) also evaluates to false.
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And thus you system just blew up in a mass of flaming inconsistancy.
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Is "a fish" true, false or not a proposition.

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Since there is no requirement to check True(L, ~x) and it can't affect the value of ~True(L, x) you logic just doesn't work.
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When x is defined to mean = ~True(L,x) in L
then True(L,x) is false and True(L,~x) is false
proving that x is not a proposition.

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But, since ~false isn't true, your system leaks information like crazy.
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Not at all
(~True(L,x) ∧ True(L,~x)) ≡ Conventional_False(L,x)
(True(L,x) ~Proposition(L,x) ~True(L,~x)) ≡ Conventional_True(L,x)
 Once all of the variables have been screened out for
~Proposition(L,x) then all of the conventional operations
that are truth preserving can be applied to them.
Expressions such as (x ∧ ~x) are reduced to false.
 

But you don't get to "screen out" statments like that.
You just don't understand the structure of logic.

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Is it really that hard to see that "a fish" is
not a proposition?
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You need to go back and study how logic works, but my guess is you have wasted too much time on your other projects to do anything with this, and you have poisioned you reputation with all you lies so no one is going to look at this.
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Try and show how "a fish" is true or false.
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Pity, if you spent the last 20 year looking at this and seeing if you can work out the problems, it might have made an viable alternate form of logic, but we will never know since you killed it by lying about halting and incompleteness and Tarski.

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I did and it really seems that you are flat out lying about it.
It seems that you are trying to say that "a fish" must be true or false.
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Nope, but in Tarski's logic, which is BINARY (so doesn't apply to your TRINARY system you need to complete your definition of) True(L, "a fish) would be false.
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 Tarski simply stupidly fails to reject erroneous propositions.
He falsely imagines that they don't exist. If "a fish" could
be encoded in his Tarski theory he would stupidly conclude that
this proves that a True(L,x) predicate cannot exist.
 

Nope, he showed that this "erroneous proposition" is one that MUST be a valid proposition given a few basic requirements on the logic system, and the existance of the Predicate True(L, x) that returned true for all x that are true, and false for all x that are false or non-truth-bearing.