Lomax » February 19th, 2018, 2:40 pm wrote:Asparagus » February 19th, 2018, 6:23 pm wrote:By "does not form a totality," was he saying that R doesn't exist? We're talking about it. We can ask questions about it. We can be either wrong or right in our assessment of it. It has all the hallmarks of an abstract object.

That's what I take him to mean - if "totality" doesn't mean "set" then I cannot parse the meaning of his statement. We can ask questions about "square circles", or about "nonexistent unicorns", but it doesn't mean they exist.

The issue is that set theory leads to a contradiction. R is one example of it. I think Russell was saying that the contradiction is the result of the mistake of treating a collection of classes as one class. But isn't that pretty close to what set theory is doing with natural numbers? I think Russell was questioning the basic assumptions of set theory, not saying that set theory is fine except R can't exist. But I'm totally open to being corrected about that.

But consider the attitude that R can't exist because it's contradictory. Would it follow from that that logic reliably guides us in understanding the world?