Your principle leads directly to a contradiction. The restriction needed to patch the problem is restricted comprehension, which would already require there to be an infinite set that's a superset of the infinite set you wish to conjure. Without the axiom of infinity, THERE IS NO SET containing all the natural numbers — fishfry
Every arithmetical statement is either true or false. There is a function that determines the truth or falsehood of every arithmetical statement. But, of course, it's not a computable function. The truth or falsehood of every arithmetical statement is determined, but there are arithmetical statements of which we could never find the determination. It's as if those statements and their determinations are "out there floating around" but I can't visualize what it means that they are true or false except that I know there is a function that determines them — TonesInDeepFreeze
I am genuinely baffled why so often in this forum you get me completely backwards. — TonesInDeepFreeze
Did not Godel and Cantor believe that once one sees Absolute Infinity he knows all (the whole story of mathematics)? — Gregory
Did not Godel and Cantor believe that once one sees Absolute Infinity he knows all (the whole story of mathematics)? — Gregory
Cantor thought the absolute infinity was God. I don't know if he ever claimed it was the whole story of mathematics.
Don't recall reading whether Gödel had an opinion on the matter. I don't think the concept of absolute infinity was relevant by Gödel's time — fishfry
I don't know what relationship you have in mind between the quote of fishfry (refuted by me) and the quote of me, especially since neither references absolute infinity — TonesInDeepFreeze
Godel had his ontological proof too — Gregory
check Chatgpt for more info — Gregory
you seemed to wonder how we can go without being able to prove mathematics as a total system. — Gregory
Only a special infinity can subsume the whole of math — Gregory
I thought fishfry was referencing the set of all sets and numbers, — Gregory
such AI bots are so often horribly wrong and fabricate regularly — TonesInDeepFreeze
Not unlike certain posters I could name! — fishfry
You're serious? You haven't caught on to the fact that such AI bots are so often horribly wrong and fabricate regularly? — TonesInDeepFreeze
Here is the argument:
D) By continuum I mean a set of distinct points without an abrupt change or gap between points — MoK
internet videos — Gregory
Yes, my definition of the continuum is not adequate. Another poster gave a definition continuum close to mine but it is correct. I can search the thread and find the definition for you if you are interested.I like your argument but I would say that the conclusion that follows is that D is an inadequate definition of a continuum. A continuum cannot be completely described with points. — keystone
Those are videos that are of the caliber of claiming that Cantor was a nutcase based on the fact that he was in sanitarium.
6h — TonesInDeepFreeze
when i pressed fishfry on Zeno, he said uh oh let's not discuss it. — Gregory
See if you can get it to provide a proof that doesn't assume what is supposed to prove. — TonesInDeepFreeze
Of course, one doesn't have to come within a million miles of a PhD just to learn basic mathematical logic. — TonesInDeepFreeze
Of course, people are different, so my personal route might not serve everyone. But I venture to say that if I had relied on chatbots to supplement the books, I would have been quite confused and misinformed. — TonesInDeepFreeze
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