This means either our math is fundamentally wrong or it is incomplete. — Jeremiah
I understand that some feel the axiom schema of specification resolves the paradox, I was speaking generally to the notion that if it is nonsense we can ignore it. As that argument seems to repeat itself in each of my threads. Mainly I just wanted a thoughtful reply instead of just a brush off and a straw-man. We can't just dismiss mathematical paradoxes as nonsense, that is not a valid solution. — Jeremiah
In the analysis given above, R was not the Russell set, but the set of all Russell sets, and it has been shown to be empty. It does not contain any set that contains all and only sets that do not contain themselves, because there can be no such set.
Therefore if you present the paradox by beginning, "Let S be the set of all sets that do not contain themselves as members," then I will deny the premise. No set can be formed in this way, which is exactly Russell's point. — Srap Tasmaner
I think you are making a mistake. A direct contradiction that doesn't result from a compelling argument (e.g. some bachelor is married) is not the same as a paradox, which does show up as the conclusion of a compelling argument. Even if you reject the paradox, it is not of a kind with any old contradiction. — MindForged
There are two cardinal sins from which all others spring: impatience and laziness. Because of impatience we were driven out of Paradise, because of laziness we cannot return. Perhaps, however, there is only one cardinal sin: impatience. Because of impatience we were driven out, because of impatience we cannot return. — Kafka
Ah, but a man's reach should exceed his grasp,
Or what's a heaven for? — Browning
The Russell set is not what anybody had in mind when they first had the idea of sorting the world into classes. The Liar is not what anybody had in mind when they first had the idea of communicating a fact about the world to another person. What you're both missing is how perverse the paradoxical cases are — Srap Tasmaner
The layperson will not understand it if you tell them there are different sizes of infinity but we know it's true in math, but we don't take that as evidence against Cantor's work on infinity. — MindForged
As I've said elsewhere, the reaction of the average layperson will almost certainly be, "Oh, it's a trick." In my part of the world it might be worse: "I always figured math was bullshit -- guess I was right." — Srap Tasmaner
The bachelor statement is not a direct contradiction. One has to deduce the contradiction by a series of steps, so the only difference between that and the assertion of the existence of a Russell set is the length of the deduction by which one arrives at a contradiction from the statement.A direct contradiction that doesn't result from a compelling argument (e.g. some bachelor is married) is not the same as a paradox, which does show up as the conclusion of a compelling argument. — MindForged
I shared this paradox with lots of people, non-math people, not a single one of them reacted that way. I share every paradox I post here with friends and co-workers, it acts as a short conversation piece sometimes; some find them interesting, most don't really care. — Jeremiah
No, rather, you have been missing the context ever since you started this thread. You cannot ask (at least, meaningfully) someone to resolve Russell's Barber if that person hasn't shown an acceptation of unrestricted comprehension. — Akanthinos
I am fairly sure I did, so clearly I can. — Jeremiah
Btw, do you know what ad hominem is? — Jeremiah
I study math, and I pay very little attention as to where it came from. — Jeremiah
You should. Context is important — Akanthinos
I mean, some of us will have had around 40+ hours of courses — Akanthinos
I dont care if the approach is realistic for you or not, there are departments dedicated to carrying out this very research : Philosophy departments. If you dont have the time to develop a semi-complete opinion on an academic subject, then you really shouldnt present whatever you have to say with the authority you adopt. — Akanthinos
it's just a fact that the early calculus was inconsistent. — MindForged
I was replying exclusively to him. — Akanthinos
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