You're smart enough, I'm sure you could have given the time. Sorry if it seemed like my original response came off as aggravated, it wasn't at you. Just the individuals trying to make a mountain out of a molehill and taking too long.

The

Dude, if you have one group doing something and another doing something, they are doing something. I didn't know you'd play a game that's idiotic — Gregory

Part of your reply seems to be missing.

Which of these do you disagree with?

1. The barber shaves himself because his name is James
2. The barber's name is John because he shaves himself

@PfhorrestWhat if the barber is a woman? A prerequisite for the paradox is that the barber must have a beard; only then does the paradox enter the picture. no man, no beard and no beard, no paradox.

Many if not all of you are deliberately not talking normally. I tried my best to type this on a weird wonky tablet

say what now big fudge? Many if not all? Where do I factor into this?

Thusly because you went with them in trying to force a contradiction

If logic has an inherent contradiction, and math is based on logic, than math is self refuting

If you want to find a contradiction, you'll find it. A real contradiction is Zeno's paradox. If you desire to create contradictions instead of discovering them, that is possible

Okay I misunderstood you when you talked about language games. I thought you understood my answer. I didn't realise you had a misconception of what a paradox is and were conflating logic in math for logic in human culture. Sorry.

I'm not sure what you mean but you seem nice. I always try my hardest

If you spend all your time working on shaving others, when do you have time to work on shaving yourself? Who will shave your skull?

Well, a linguistic paradox is when two ideas are thought of to be true at the same time even though their natures inherently negate each other. So if an argument has two of these sorts of ideas in them, the chances that one or both being true are diminished. One is definitely not true, one might be or might not be.

A mathematical paradox is a mathematical conclusion so unexpected that it is difficult to accept even though every step in the reasoning is valid. For example mathematical reasonings where every step is valid in an explanation of how 2+2 could possibly equal 5 is a mathematical paradox.

You're right about the logic, but you've made the mistake of treating a language game like a numbers game. The rules aren't the same. So neither is the definition of a paradox.

For example, a paradox in time, where you travel in time and encounter a past or future version of you is a mathematical paradox.

If time travel is possible in a given universe and you encounter another version of you then what should normally be 1, becomes 2. Mathematical paradox.

To explain the problem of the barber mathematically, it's just algebra.

Symbol for Barber, Symbol for everyone, Symbol for rules of culture on who gets to cut who's hair or shave who's beard.

Let me put it this way. If all Bs are a part of E and only B gets to do S, B must do S to E, because B is equal to E, B must also do S to B.

B is Barber
E is everyone
S is shave

Does that make a bit more sense? I hope I haven't made it more confusing for you.

" you spend all your time working on shaving others, when do you have time to work on shaving yourself? Who will shave your skull?"

@Gregory Did you feel threatened at all by this comment from this extremely new account? I've sent a message to the moderators and this account. If anyone said this to my face I'd probably act pre-emptively. Way too dark and not funny if it's meant as a joke either.

I didn't feel threatened, but now that's it's pointed out, it is a weird first post

I am going to have to take a break from this thread for a week or more. If there is a true paradox here, I hope to find it when my head feels cooler. You guys did a great job. Thanks for all the help on this

If logic has an inherent contradiction, and math is based on logic, than math is self refuting — Gregory

The contradiction is in claiming that there can be any such barber. There cannot. Just because you can string words together grammatically doesn't mean you're describing something that can actually be.

That's why I like framing the problem as figuring out who would be in the set of all such barbers. You find that such a set is necessarily empty because the conditions for being a member are inconsistent. You might as well define a set of all the numbers equal to 4 and equal to 5. There's no contradiction in that; you've just defined a set that's necessarily empty.

The barber (B), a philosopher (T) who doesn't shave himself, and a mathematician (M) who does.

We have all and only men who shave all and only men who don't shave themselves.

1. M is never a member of R because he shaves a man who shaves himself.
2. P can't be a member either because he doesn't shave himself, so he'd have to shave himself to be a member, but he doesn't.
3. What about B? He would have to shave P and not M. No problem. If he shaves himself, he'd be out, like M, but if he doesn't, he'd be out like P. So B can't be a member no matter what he does.

So R = { }. No one shaves all and only men who do not shave themselves, therefore the barber does not shave all and only men who do not shave themselves. The three cases are exhaustive, in fact: no one can be a member of R whether they shave themselves or not.
— Srap Tasmaner"

First things first, some things need to be clarified:

Are B, T and M each categorized/defined (for example when M is categorized as one who shaves himself), before the hypotetical shavings are done or after they are done? I'll asume first that it is after the shavings are done:

If M shaves himself, he shaves himself and can't be a member.

Does «The philosopher does not shave himself» mean: He hasn't shaved himself until know and never will? If so, by definition he can't ever shave himself, and therefore can never be a member since he can never shave someone who does not shave himself.

Since Srap says that the implication: if the philosopher shaved himself, then he would be a member is true, we'd have to say: if he shaved himself he would shave someone who does not shave himself. But if it were possible for him to shave himself, then he would in that case have shaved someone who shaves himself (since after he shaves himself, he is someone who shaves himself) and therefore he would not be a member. So the implication can't be true if P shaves himself.

However, it's impossible for him to shave himself by definition, and therefore he can never be a member. This means the implication «If he shaved himself, he would be a member» is true, since it could only be false if he both shaved himself and wasn't a member, which can never happen since the antecedent is impossible. So what Srap says up to this point appears correct if we interpret it like this.

Or does it mean: He hasn't shaved himself until know, but may shave himself in the future? If so, he would shave someone who shaves himself (since after he shaves himself, he is someone who shaves himself) and therefore not be a member. So this can't be what it means if Srap is right.

As for the barber: If he shaves himself he will shave someone who shaves himself (since after he shaves himself, he is someone who shaves himself) and therefore not be a member.

If he shaves M, if M already shaved himself before, then the barber would shave someone who shaves himself, and not be a member. If M hasn't shaved himself yet, then he would shave someone who doesn't shave himself, and be a member. So it must be the case that M already shaved himself in the past if Srap is right.

If B shaves P, then he shaves someone who doesn't shave himself, and is therefore a member of R.

This is problematic, because according to this interpretation since P does not shave himself, the barber would shave someone who does not shave himself, and therefore the barber would be a part of R, which contradicts what Srap says: that R is empty.

Nonetheless, this interpretation does show that if he shaves himself, he would not be a member of R.

Let's now assume they are caracterized *before* any of the hypotetical shavings used in the previous reasonings happen:

If M shaves himself, then if M shaved himself in the past, then he shaves someone who shaves himself and is not a member. This must be the case if Srap is right.

If he hasn't, then he shaves someone who doesn't shave himself (yet) and therefore is a member. This can't be right if Srap is right.

If P shaves himself, then he shaves someone who doesn't shave himself (yet) and therefore is a member. According to Srap, this too can't be the case.

Unless we include in the definition of P that he never will shave himself, in which case it's impossible for him to shave someone who does not shave himself, and therefore he can never be a member of R, and the implication “if P shaves himself, he would shave someone who doesn't shave himself (yet)” would once again be true because the ground/ antecedent is by definition always false. This must be right if Srap is right.

If the barber shaves himself, and if he hasn't shaved himself in the past, then he would be shaving someone who does not shave himself, since before he shaves himself he hasn't shaved himself. Therefore, he would be a member. This can't be the case if Srap is right.

If the barber shaves himself but has also shaved himself in the past, then he shaves someone who shaves himself, and is therefore not a member. This must be so, according to Srap.

If the barber shaves M, then if M shaved himself in the past, then he shaves someone who shaves himself and is not a member. This must be the case if Srap is right.

If M hasn't shaved himself in the past, then the barber would be shaving someone who does not shave himself, and therefore would be a member, which can't be the case according to Srap.

If B shaves P, then he shaves someone who doesn't shave himself, and is therefore a member of R.

And so we have the same problem as before.

So it seems that in either case R is not empty because the barber belongs to R.

Unless I made a mistake somewhere, of course.