Philosophy Now Forum

We derive these three universal Truth predicate axioms: (1) ∀F ∈ Formal_Systems ∀x ∈ WFF(F) (True(F, x) ↔ (F ⊢ x)) (2) ∀F ∈ Formal_Systems ∀x ∈ WFF(F) (False(F, x) ↔ (F ⊢ ~x)) (3) ∀F ∈ Formal_Systems ∀x ∈ WFF(F) (~True(F, x) ↔ ~(F ⊢ x) A "well-formed-formula" is just a syntactical convent...

The Tarski proof is the simplest. Just read this one page paper that I have re-written at least 30 times in the last 24 hours. The second page is merely Tarski quotes to prove that my understanding of what he said is correct. https://www.researchgate.net/publication/332158426_Tarski_Undefinability_...

I'm opening this thread in light of the many threads of interest here on computation, logic, and math. This may act as a reference for everyone to discuss the varying histories about the topic. I'm not interested in our differences of opinion but to express each person's understandings of any variou...

Except that the incompleteness and undefinability proofs have always been wrong. That is the ONLY thing that I add. But this is what I thought you meant. If they are wrong, either (A) there is no such possible theorem of these types, to be considered as being true universally, OR (B) that there may...

⊢ means the conventional application of rules-of-inference as specified by the logic symbols. A A → B ------- B ∴ A ⊢ B Yes. I am asking you to define the meaning of the symbol → How would a language compiler parse "→"? Give me a specification of some sort. Truth table? Example of how you...

Then you might fit in with the option of the us and reality always existing, such as between points b and c? [blue shaded region] ... As I understand it, if time exists at all as such, it is just a part of reality and as such not anything like a dimension along which reality would exist. Rather, ti...

@PeteOlcott, Why are you using distinct threads to argue the same point? Are you attempting to measure the same value of your theory/theorem as true if one of the threads gets a pass regardless of some counter-proof elsewhere? [not implying a necessary insult,...just wondering why the separate threa...

The remaining alternative, continuing from the last post of mine above, is that (B) that there may be [a true "incompleteness" formal theorem that is true of reality (ie sound)] but that the ones that have been expressed thus far are incorrect. Would you then accept this as 'possible'? Tha...

No. Truth is deduction from true premises to true conclusions as expressed as the valid use of rules-of-inference to theorem consequences. So when the input is true then the output is true and that is all there is to the essence of truth. But then you have nothing new to add value to logic that isn...

@PeteOlcott I'm trying to interpret: Because formal systems of symbolic logic inherently express and represent the deductive inference model formal proofs to theorem consequences can be understood to represent sound deductive inference to true conclusions without any need for other representations ...

@PeteOlcott I'm trying to interpret: Because formal systems of symbolic logic inherently express and represent the deductive inference model formal proofs to theorem consequences can be understood to represent sound deductive inference to true conclusions without any need for other representations s...

I reformulated my whole position to make it more clear. Tarski Undefinability Theorem Reexamined Tarski proved that the Liar Paradox: G ↔ ~(F ⊢ G) is true in his meta-theory and not provable in his theory without ever realizing that the only reason it is not provable in his theory is that it is not...

If your reference to "blocks" is what is referred to as static , this is how Einstein pictured it and I agree with. Time acts as just another static dimension where each moment is frame of 3-dimensional space, like a movie frame. The movie frames collectively create the illusion of time a...

Time is sequential change. But 'sequence' is just a linear set of things, as a line of points. "Change" may then be thought of as whatever one given point is with respect to another, like if we say started at point 0 on a number line, any other point NOT-"point 0" is a change of...

What is time? What it is which we measure with a clock. As I see it, it all comes down to our impression that natural events occur with an intrinsic regularity, first and foremost the movement of the Sun around the Earth. This leads us to assume the metaphysical construct of time. By metaphysical h...