Set Theory and Foundations of Mathematics

Post by spacehome » Fri, Jul 31, 2015, 9:13 PM UTC

gver wrote: post #50

If you follow the link to his page "I'm upset...Here is why", you can see that this person has a significant degree of "crankiness". These people through their perhaps not deliberate obfuscation, often manage to trick the mathematically naive into thinking there is substance there - "it is so hard and confusing, it must be real math." It is a disservice to have links like this on Hacker News.

Post by [deleted] » Fri, Jul 31, 2015, 9:29 PM UTC

spacehome wrote: post #51

gver wrote: post #50

If you follow the link to his page "I'm upset...Here is why", you can see that this person has a significant degree of "crankiness". These people through their perhaps not deliberate obfuscation, often manage to trick the mathematically naive into thinking there is substance there - "it is so hard and confusing, it must be real math." It is a disservice to have links like this on Hacker News.

I tried, but I don't think I have it in me to read that wall of text. What specifically made you think he was cranky?

Post by SerpentJoe » Fri, Jul 31, 2015, 9:38 PM UTC

gver wrote: post #50

If you follow the link to his page "I'm upset...Here is why", you can see that this person has a significant degree of "crankiness". These people through their perhaps not deliberate obfuscation, often manage to trick the mathematically naive into thinking there is substance there - "it is so hard and confusing, it must be real math." It is a disservice to have links like this on Hacker News.

Post by GeneTT » Sat, Aug 01, 2015, 12:30 AM UTC

pjungwir wrote: post #33

vowelless wrote: post #5

Earlier quoted context omitted.

> I have a sneaky suspicion the answer to a great many philosophical questions are hidden in there. Godel's incompleteness theorem had a profound affect on me that I find hard to quantify. I grew up starry eyed, thinking that our minds have virtually limitless capabilities and that mathematics could answer everything (naive, I know). Then I came across Russell's paradox and the incompleteness theorems and for the fir…

I felt similar amazement at Gödel's proof, and even suspect that Penrose must be on to something when he says the mind must therefore not be computable. . . . But the book Gödel's Theorem: An Incomplete Guide to its Use and Abuse by Törkel Franzén is very good at explaining that the conclusions we should draw are fairly limited, e.g. that the proof doesn't apply to anything other than arithmetic. I'm not sure I'm tot…

Post by mafribe » Sat, Aug 01, 2015, 7:32 AM UTC

dvt wrote: post #44

mafribe wrote: post #43

Earlier quoted context omitted.

Having a universal set is a sufficient condition for Russel's paradox. That's not true. There are set-theories, e.g. Quine's NF [1] which allow universal sets, and other things like the set of all ordinals, that are forbidden in ZF-style set-theories. The problem in ZF is caused by unlimited comprehension. NF circumvents this by restricting comprehension. Tom Forster [2] has written a great deal about set theories wi…

True, I was mostly referring to ZF-style set theories (which is what the thread is mainly about). Your point could even be extended by saying that there are proofs for a paraconsistent ZF with a universal set. Your [3] link doesn't work by the way, I'm interested in reading Forster!