Timeline for What if Current Foundations of Mathematics are Inconsistent?
Current License: CC BY-SA 2.5
8 events
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| Mar 13, 2017 at 3:27 | comment | added | Nathan BeDell | @wojowu He's probably refering to Gentzen's proof. I really don't like the term "finitism", as I think at face value you could interpret that a number of different ways, but I think at least under one interpretation it would be reasonable to call Gentzen's proof "finitist" (Though this is not the sense in which Hilbert used the term). | |
| May 22, 2016 at 18:12 | comment | added | Wojowu | @Anixx (sorry to bring up such an old thread, but you've got me curious) To second Joël's question, what proof of consistency of PA do you refer to? Your earlier explanation suggests that "finitistic" means that one only works with finite structures, and I find it hard to believe there is a proof of PA like that. | |
| Nov 22, 2011 at 17:11 | comment | added | Joël | What of you mean by "the proof that PA is consistent exists, and is finitist?". To what proof are you referring to? | |
| Feb 20, 2011 at 12:54 | comment | added | Anixx | To sum it up: 1) the proof that PA is consistent exists, and is finitist. 2) People who disagree are ultrafinitists 3) all mathematical paradoxes so far were discovered outside of finitist realm. | |
| Feb 20, 2011 at 12:49 | comment | added | Anixx | And the group about you said does not accept the proof not because it requires extra assumptions, but because they reject the existence of infinite set of natural numbers (i.e. they just DISAGREE with usefulness of one of the axioms). The proof itself finitistic. | |
| Feb 20, 2011 at 12:43 | comment | added | Anixx | Peano arithmetic is not finite arithmetic. It includes axiom of potential infinity. If an arithmetic is built over a finite set of numbers, it is consistent. | |
| Feb 20, 2011 at 10:30 | comment | added | David Roberts♦ | PA has only been shown to be consistent using infinite ordinals (whose existence is an extra assumption). In fact there are a (small) number of people who think that PA might be inconsistent. | |
| Feb 20, 2011 at 8:52 | history | answered | Anixx | CC BY-SA 2.5 |