I can't find anything in your post I'd agree with. Certainly not the "amused pity" or the treatment of Russell's argument as an artifact.

Anyone with a Analytical Philosophy course completed, upon being asked "who shaves Russell's Barber" out of context, will simply look the interlocutor with amused pity. — Akanthinos

And you claim you are not an elitist. . . .

I can't find anything in your post I'd agree with. Certainly not the "amused pity" or the treatment of Russell's argument as an artifact. — Srap Tasmaner

Then you should reread your early Analytical history, starting by the Grundlagen... Russell's barber is an historical/theoritical artefact. It is not a riddle. Treating it as such simply devalues the discipline.

devalues the discipline. — Akanthinos

:brow:

The vast majority of my work colleagues did not believe or know that there were such a thing as logic classes taught at University (or anywhere actually). To them, what philosophers do is pelleter des nuages, literally shoveling clouds.

When you present these little problems as riddles, this is what you do, shovel clouds. If philosophy reduced itself to this, then the layman's opinion would be correct ; we'd be stupidly useless. Its fine to be unproductive and timewasting, but at least realize that you are being so.

I disagree.

The Russell set is manifestly pathological. That it is, I could know even without knowing its role in the history of philosophy, but the converse does not hold: I have to understand what it is to understand why it played the role it did.

The more interesting question might be why it is pathological, and that could be a matter of historical context. If, in the fullness of time, dialetheism wins out, the Russell set might no longer seem pathological.

As things stand, we have a predicate composed of simple, well-behaved elements to all appearances assembled in an acceptable way, and yet this predicate cannot possibly be predicated of anything. If we could say why this abomination is no predicate at all, we could regain the Paradise in which predicates always pick out classes.

Its fine to be unproductive and timewasting, — Akanthinos

Your entire argument boils down to a child throwing a fit because the neighbor kid is playing with his/her toys.

The Russell set is manifestly pathological. That it is, I could know even without knowing its role in the history of philosophy, — Srap Tasmaner

Yeah, and by doing so you'd end up, like in the Zenon's thread, talking about Planck's constant and other otiose elements.

As things stand, we have a predicate composed of simple, well-behaved elements to all appearances assembled in an acceptable way — Srap Tasmaner

Well, by the same account P & -P is a proposition composed of simple, well-behaved elements to all appearences assembled in an acceptable way.

Your entire argument boils down to a child throwing a fit because the neighbor kid is playing with his/her toys. — Jeremiah

And you have no arguments. Only a ridiculous attachment to the meaningfulness of these threads. Its telling that you chose a playground metaphor ; that is basically what you are doing, being a child pretending at having authority.

As things stand, we have a predicate composed of simple, well-behaved elements to all appearances assembled in an acceptable way, and yet this predicate cannot possibly be predicated of anything. If we could say why this abomination is no predicate at all, we could regain the Paradise in which predicates always pick out classes. — Srap Tasmaner

The Russell predicate $x \notin x$ most definitely picks out a class: the class of all things that are not members of themselves. This class just doesn't happen to be a set. It simply turns out to be the case that some collections defined by predicates are sets; and others are not. Those collections that aren't sets are called proper classes.

In ZFC, there are no official proper classes, so we use the phrase informally. We say, "The collection of all things not members of themselves is a proper class," by which we mean that it's not a set. Or as we sometimes say colloquially, it's "too big" to be a set.

On the other hand there are set theories such as Gödel-Bernays set theory, or NBG, in which the concept of proper class is officially formalized.

A 17 years old reads thus spoke Zarathoustra, figures he likes philosophy, then starts asking random religious people if God can create a boulder so heavy that he can't lift it.

The 17 years old may feel like he has hit gold, so to speak, but he is wasting time. Until he starts reading the history of debates, proof and counter proofs, until he can actually develop a critical opinion on these, he is just masturbating intellectually.

Replace theology by logic, existential proofs by logicism, and we have the same situation here.

I never read any Nietzsche, and I am likely much older than you think.

The Russell predicate $\small x \notin x$ most definitely picks out a class: the class of all things that are not members of themselves. This class just doesn't happen to be a set. It simply turns out to be the case that some collections defined by predicates are sets; and others are not. — fishfry

Yeah, that's a good point. I had forgotten about the proper class stuff and was reaching for "class" as the generic term. (I guess here we have to use "collection" for a generic term?) Not an overly satisfying distinction, this, but it is what it is.

Wikipedia has the quote from Russell's letter:

there is no class (as a totality) of those classes which, each taken as a totality, do not belong to themselves. From this I conclude that under certain circumstances a definable collection [Menge] does not form a totality

It's interesting how unlike something like $\small \{x \mid Fx \land \neg Fx \}$ Russell's set is. If it were "the set of sets that contain themselves and don't contain themselves", it would not be so peculiar. Instead it's simply "the set of sets (that are sets) and don't contain themselves". All you have to do to get into trouble is take the collection as itself an object, something that could be the value of $\small x$.

You can almost hear the other sense of "totality" in our English-language descriptions: there's no problem defining a set that contains only sets that don't contain themselves; you just can't define a set that contains all and only sets that don't contain themselves. You can tell a barber to shave only men who don't shave themselves, just not all of them.***

Pages back I mentioned the word "heterological" but got no takers, Right before the quote above, Russell says this:

Let w be the predicate: to be a predicate that cannot be predicated of itself. Can w be predicated of itself? From each answer its opposite follows. Therefore we must conclude that w is not a predicate.

"... is heterological" sure looks like a predicate, and this time there's no use saying it picks out a "proper class" instead of a "set". In Russell's opinion it's not a predicate at all. What's up with that?

*** ADDED: Nah, it works the other way around too, "all" but not "only".

that is basically what you are doing, being a child pretending at having authority. — Akanthinos

What is truly childish is pretending these paradoxes belong only in select conversation.

What we have is something that clearly works, but we haven't got the vocabulary to express it mathematically. That's a mental state familiar to everyone who's ever had to construct a proof. We get to the point where we can SEE what's going on, but we can't mathematically SAY what's going on. That's where Newton and the mathematicians of the 18th and 19th century got stuck till they finally worked out a proper formalization. — fishfry

We need only go back to 1696 to see that yes, a formal contradiction was provable. The only way, as far as I can see, to say it was just an inability to formalize is to say that it was understood but couldn't be made explicit. From Analyse des Infiniment Petits (with some modern fixes in notation and such)

I don't know how to do that Math notation stuff on this forum, but the paper "Handling Inconsistencies in the Early Calculus" (use Sci-hub to download the paper) goes over the example I had in mind when trying to find a tangent to a curve. When calculating the differenial, in the early calculus dy had to be unequal to zero, yet once the fraction had been simplified it needed to be equal to zero. Prior to limits being formalized, this was contradictory. Dy's value was necessarily non-zero at one step and then zero afterwards.