They call functions of the Boolean type predicates in all orders of predicate logic. Functions of any other type are called functions. Predicate: >(5,...
Instead of a three values system with {True, False and Nonsense} I have bivalent systems of logic that derive a type mismatch error for any expression...
It is a Boolean valued system. When epistemological antinomies are involved they must be rejected as a type mismatch error because that have no Boolea...
I have found that line of reasoning ineffective so I switched. We have to resolve my prior reply before you can begin to understand my updated reasoni...
I don't think that you can find any source that ever says anything like that for bivalent systems of logic. I don't think you can find any sources tha...
Boolean values are properties of every Proposition A proposition is a central concept in the philosophy of language, semantics, logic, and related fie...
I always verify that the essential reasoning is correct. The key elements of my system come straight from me figuring them out and no one ever wrote t...
None-the-less in every bivalent system of logic we must be able to reduce every variable to a Boolean value. Your reply did not seem to understand tha...
The Variables of propositional logic and every other order of bivalent logic must have a Boolean value. Any variables that cannot possibly be true or ...
That is like saying that a dead mouse can be a type of office building. "This sentence is not true" is not a truth bearer thus not a proposition thus ...
Every increment of HOL above FOL quantifies over expressions of the next lower order. FOL quantifies over propositions, thus propositions are the grou...
The Liar Paradox written in Minimal Type Theory: LP := ~True(LP) Which says ~True(~True(~True(~True(~True(...))))) Minimal Type Theory (YACC BNF) http...
All other sources agree. Undecidability Definition: A decision problem is a problem that requires a yes or no answer. Definition: A decision problem t...
You are not paying attention. (a) If it is true that makes it untrue so it can't be true. (b) If it is false that makes it true so it can't be false. ...
"This sentence is not true" is called the strengthened Liar Paradox and is its best form. If it is true that makes it untrue if it it false that makes...
Here is where is says he includes it https://liarparadox.org/Tarski_247_248.pdf "In accordance with the first part of Th. I we can obtain the negation...
In other words the fact that he cannot prove that a lie is true he construes as proof that truth cannot be proven. When we understand that self-contra...
I agree. Not when the entire notion of undecidability depends on these things. In that case we use your first quote as the basis of True(x). From this...
...14 Every epistemological antinomy can likewise be used for a similar undecidability proof... (Gödel 1931:43-44) Basically I am saying that self-con...
Natural language cannot be accurately evaluated until it is translated into some totally precise form. An expression that is both a statement and a qu...
OK now we are getting somewhere. "This sentence is not true" cannot be true because that would make it untrue and cannot be false because that would m...
No one anywhere on any forum ever addressed the issue that: (a) Undecidability is fully met by self-contradictory expressions. (b) Self-contradictory ...
Try and show how it makes sense to base undecidability on self-contradictory expressions or acknowledge that you do not understand that Tarski Undefin...
The important point is that it self-contradictory expressions are still considered valid proof of undecidability and this proves that the entire notio...
You seem to simply ignore the main points that prove my case. ...We are therefore confronted with a proposition which asserts its own unprovability. 1...
By saying that F is incomplete when the real issue is that G is incorrect the blame for the unprovability of G is F it misallocated. The Gödel sentenc...
This G is unprovable in F because this G is nonsense in F That G is nonsense in F does not show that there is anything wrong with F the issue is ALL G...
You misquoted me. An epistemological antinomy <is> a self-contradictory expression ...14 Every epistemological antinomy can likewise be used for a sim...
Gödel specifically states that the inability to prove a self-contradictory expression DOES MAKE THE FORMAL SYSTEM INCOMPLETE. ...14 Every epistemologi...
The problem with this definition is that it proves that mathematical systems are "incomplete" when they cannot prove or refute nonsense. Self-contradi...
When (as in Prolog) True(L, x) means Provable(L, x) and (as in Prolog) False(L, x) means Provable(L, ~x) then Tarski Undefinability theorem utterly fa...
When G asserts its own unprovability in F the proof of G in F does require a sequence of inference steps in F that prove that they themselves do not e...
Tarski's proof is directly anchored in the actual Liar Paradox itself. Liar Paradox basis of proof: https://liarparadox.org/Tarski_247_248.pdf The act...
...We are therefore confronted with a proposition which asserts its own unprovability. 15 ... (Gödel 1931:43-44) The above is a direct quote from the ...
Sentences with ambiguity must be disambiguated before that can be properly analyzed. For example asking a man that has never been married: Have you st...
That is a great counter-example. It seems to me that is actually a declarative sentence that is phrased as a rhetorical question. It is comprised of t...
Gödel's Incompleteness use diagonalization that show G is not provable in F yet totally hides why it is unprovable. When reasoning is entirely hidden ...
That is the same as saying there are a whole lot of integers that are greater than five and less than three, utterly ridiculous nonsense. That logicia...
Very close. A proposition / logic sentence is defined to always be a {truth-bearer}. This means that it is either true or its negation is true. A trut...
Yes. There is expressions of language that are true on the basis of their semantic meaning and there are expressions of language that are true on the ...
That almost everyone including the greatest experts in the field do not fully understand that self-contradictory expressions are not {truth-bearers} d...
A {truth-maker} is a more difficult subject than a {truth-bearer} It took me 20 years of primary and secondary research to fully understand exactly wh...
The term {true bearer} is very widely know throughout philosophy. That declarative sentences can be {truth bearers} and questions cannot be {truth bea...
Two Dogmas of Empiricism Willard Van Orman Quine https://www.theologie.uzh.ch/dam/jcr:ffffffff-fbd6-1538-0000-000070cf64bc/Quine51.pdf Yet he wrote a ...
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