Philosophy Now Forum

wtf wrote: ↑Tue Mar 26, 2019 3:09 am

PeteOlcott wrote: ↑Tue Mar 26, 2019 2:53 am In this thread I am only prepared to refute the Tarski Undefinability Theorem ...

AND this simplified refutation of the 1931 Incompleteness Theorem. ∃F ∈ Formal_Systems (∃G ∈ Language(F) (G ↔ ~(F ⊢ G))).

You claim to have falsified Gödel's incompleteness theorem. That theorem applies to ALL formal systems that can express elementary number theory, whether type theory or set theory or category theory or any other foundational approach. Axioms are True: The elementary statements which belong to T are...

When I asked you to comment on the obvious consequences of your claim, you changed the subject and started a new thread. I don't know the consequences of my claim. It has taken all of my time on the single-minded focus for 22 years to simply make my claim and its proof clear enough to be understood...

I understand truth to be essentially another name for whatever it is we believe. It's not the exact same thing. Belief implies say it's true. Not that it's true of reality. When you said : "truth to be essentially another name for whatever it is we believe." you didn't mean what you said....

OK, that may be something we could disagree about. I understand truth to be essentially another name for whatever it is we believe. That would logically entail that the Earth really was flat when (before Pythagoras) there was a universal consensus that the Earth was flat. No because a belief doesn'...

Previously I could never find any people interested in the philosophy of logic foundations that could begin to understand any aspect of predicate logic. Now that I finally totally understand these ideas myself I can bridge the gap between the math and plain English. I added a laymen's section to th...

My last reply seems to have gotten lost. I also agree that the principle of explosion is semantically unsound. I do not want to digress into talking about this until all of my current points are fully addressed. Relevance logic seems to address the principle of explosion quite well. My main point i...

My last reply seems to have gotten lost. I also agree that the principle of explosion is semantically unsound. I do not want to digress into talking about this until all of my current points are fully addressed. Relevance logic seems to address the principle of explosion quite well. My main point i...

More evidence for my claim that set theorists and type theorists are speaking cross-paradigms. I, myself, find it to be an uphill battle to speak to Mathematicians coming from a Computer Science background. IF you accept the consequences of the Curry-Howard isomorphism there is no difference betwee...

I have completely reformulated this making it much more clear: Tarski Undefinability Theorem Reexamined https://www.researchgate.net/publication/332158426_Tarski_Undefinability_Theorem_Reexamined The above supersedes and replaces the following, except for the way the link provided below explains how...

I have received many comments on my work over the years. I have finally (just barely) gained enough mathematical maturity that logicians are starting to take me seriously. I publish on Researchgate and PhilPapers. ResearchGate only permits members with actual published works OK, why choose this mea...

Yes. That"s what I thought reading your piece. I haven't yet looked at the details and I'm not a mathematician, but so far I agree with all your points. My pet peeve is the principle of explosion, which I find intuitively just moronic and I can't understand how gown-up mathematicians could cou...

Logik wrote: ↑Sun Mar 24, 2019 6:58 am

PeteOlcott wrote: ↑Sat Mar 23, 2019 9:15 pm Nearly all logicians maintain two separate representations to analyze semantics.

Why have you chosen set theory and not type theory for your mathematical foundation?

Minimal Type Theory (formally specified at the end of my paper) is higher order logic with types, thus a kind of type theory.

I would define set theory differently than the way it is defined. I don't want to digress into this. I have not paid very much attention to things unrelated to the decision problems that I cited. Here are the two pages of Linz that I studied off and on since 2004. http://liarparadox.org/Peter_Linz_H...

Oh, right 1936. After carefully studying the Peter Linz (simplest possible) sufficiently elaborated Halting Problem proof off and on since 2004, last December, I finally figured out the precise algorithm showing exactly how the Linz H would decide halting for the Linz (Ĥ, Ĥ) input pair. This solutio...