I had a chat with my 10 yo daughter yesterday. We started with discussing philosophy in general and ended up with me breaking it to my daughter, not so gently: We are serfs:
Remember that I’m all new to Austrianism and libertarianism, so if you spot inconsistencies, please tell me.
Your daughter is sharp as a whip! By the way, the Barber’s Paradox isn’t a paradox, just fancy wordplay.
Indeed. She’s much sharper than I am. And so is my wife. I have to be on my toes all the time! =)
I beg to differ.
This is a good one to discuss with kids, because it gets to the heart of some of the tricks language can play. The Barber Paradox, like many things thought to be paradoxes, only looks like one because of the time structure ambiguity inherent in language.
In English - and many other languages I suppose - the habitual form is the same as the present tense: “It rains” can mean either “It rains from time to time” or “It’s raining right now.” In the so-called Barber Paradox keep in mind that “He shaves himself” is using the habitual form, so there is no contradiction in saying that a man who shaves himself (every morning) also “does not shave himself” tonight (for instance). So we are left with a grammatical ambiguity wherein we can say both “He shaves himself” and “He does not shave himself” with no contradiction, because the former can be taken in the habitual sense and the latter can be taken in the one-time action sense (I don’t know the correct grammatical term for this, but I hope the meaning is clear).
That’s just a heads up, not the actual explanation of why it’s not a paradox. Here’s the actual explanation, starting with the statement of the apparent paradox as given in Wikipedia (there may indeed be a version that actually is a paradox, but this is the only one I’m aware of - please point me to an actually paradoxical version if there is one):
To see more clearly that there is no paradox, define clearly what “shaves himself” [in the habitual sense] means. Say for example that for a man to “shave himself” means that he shaves every morning. But this is still ambiguous: how many mornings in a row will he have to shave in order for him to satisfy the condition of “shaving every morning”? Yesterday only? Two days? Every morning for the past week week? To make it simple we can say a man “shaves himself” [in the habitual sense] if and only if he shaved himself the previous morning. (There are a number of other reasonable definitions we could choose, but the argument is similar for each of them.)
The barber had to start obeying “the rule” from some time t (could be when he was born, even). Let’s say t is 5pm on a given day. Before t, he had either shaved himself or he hadn’t. If he had, then in keeping with the rule that he does not shave “men who shave themselves” [in the habitual sense], he does not shave himself [in the one-time action sense] the next morning. Now, since “shaves himself” is defined to mean that he shaved himself the previous morning, there is no logical necessity that he shave himself on that day. The premises don’t dictate his actions until the following morning, when he will either shave himself or not.
Come next morning, he will now - by definition - be a man who does not shave himself [in the habitual sense], so he will proceed to shave himself [in the one-time action sense]. Naturally, he then refrains from shaving the morning after that, then resumes, refrains, resumes, etc.
Alternatively, if he hadn’t been shaving himself before t, then the next morning he does shave himself [one-time action], the following morning he refrains, shaves, refrains, shaves, refrains, etc.
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Now all that said, we can make a real “paradox” (actually just an uncompliable rule) by altering the scenario slightly:
Rule: He MUST ALWAYS BE SHAVING all men, and only those men, who aren’t shaving themselves (with his octopus arms!)
Question: Is he shaving himself now?
The answer is then, “There is no way to know.” The rule is impossible to comply with, so he obviously isn’t complying with it now, hence there is no particular reason to expect he is either shaving himself now or not.
If Sweden is free or not kinda depends on your perspective.
I had a t-shirt with a quite that implies tax is theft and a friend from Iran noticed it. He just laughed at the notion of complaining about Swedish taxes and said in his country the government had stolen literally everything and was murdering people in the streets. I had to admit that here freedom it is more of an intellectual exercise then a pressing real concern…
I’d say you are making it to a word game. How about a web page that links to all pages that do not link to themselves?
Russels paradox for AJ.
The male barber is the man that, by the end of the day which we are considering, will have been the one and only person whom all the men who have not shaved themselves during that day, will have been shaved by.
That’s just an impossibility, which you can call a “paradox” because it seems as if it should be possible - but only for that reason. In principle, it’s no different than saying, “How about a square circle?”
Right, so there can be no such man. If by “paradox” we simply mean that this result is surprising, because the idea of a barber shaving everyone who doesn’t shave themselves seems “reasonable,” then I agree - it’s surprising for a while. But it’s not surprising once you realize that there can be no such man.
By that definition there can be no paradoxes, can there? I tend to agree. Once there’s a paradox, check your premises. Which is what happened when Russel’s Paradox was formulated. It had big impact on mathematic and logic science. Set theory had before then allowed for sets to be able to include themselves. That premise had to be checked! Far from “simply” a word game, I would say.
I’m trying to get some reddit attention to my blog post. Now whenever I say anything libertarian-ish on reddit I always seem to attract people who are somehow scared of liberty. If you’ve got some spare time I’d appreciate some help =)
Exactly.
I’ve been looking for more on Russel’s Paradox, because the Wikipedia article on it seems silly. The idea of a set that contains itself never made sense in the first place. And the notion of a “set of all non-squares” immediately raises the question, “What is the universe of discourse!?” Not covered in the article it seems.
The article also mentions this:
In 1923, Ludwig Wittgenstein proposed to “dispose” of Russell’s paradox as follows:
“The reason why a function cannot be its own argument is that the sign for a function already contains the prototype of its argument, and it cannot contain itself. For let us suppose that the function F(fx) could be its own argument: in that case there would be a proposition ‘F(F(fx))’, in which the outer function F and the inner function F must have different meanings, since the inner one has the form O(f(x)) and the outer one has the form Y(O(fx)). Only the letter ‘F’ is common to the two functions, but the letter by itself signifies nothing. This immediately becomes clear if instead of ‘F(Fu)’ we write ‘(do) : F(Ou) . Ou = Fu’. That disposes of Russell’s paradox.” (Tractatus Logico-Philosophicus, 3.333)
But does not say if or why Wittgenstein is wrong.
The Wikipedia version is just wordplay. It was only after I wrote that long post that I realized it could be salvaged by a different interpretation. I guess I should have looked in the Stanford encyclopedia of philosophy instead.
I love reddit. Threw in a comment just for kicks, but it seems you’ve got them covered.
It’s wonderful to read your comment. I’ve read it (reddit, get it?) three times now. =)
Thanks for letting me know you think I’ve got it covered. I was going to ask how I’m doing, being all new to libertarianism as I am. Though, I can see from reading your comment (I really did read it three times) that I still have a lot to learn.
Glad you liked it. I decided to write a few more.
I upvoted them all =)
That Spideynw quote:
Word.
Thanks! One of the posters actually read the essay I suggested and wrote up a cogent response:
So many points I don’t have time to respond right now, but this is a nice debate I welcome anyone else to join.
First, the Barber Paradox is weaker than Russell’s paradox itself, since one can answer it by saying that the barber is lying. On Russell’s paradox, we have to remember (with Quine) that the statement - x is a paradox - is made relative to some deductive system. What is a deductive system? It’s an attempt to model, with axioms and rules of inference, real reasoning that goes on in the real world. In particular, in setting up our metamathematical system, mathematicians (at least those who worry about this sort of thing, rather than just having at it) want to model, in a formal system (as formal as can be, anyway) what common sense tells us works in mathematics. Frege, in particular, is concerned to build all of the actually-existing mathematical system from logic - that is, he wants math without mathematical axioms. So we get the basic logical principles, the rules of inference which Frege claims model the way we actually think (or the way the world is - I’m not clear from Frege which way he sees it, but from our perspective here it doesn’t matter.) One of these is basic logical principle 5. Russell then creates a paradox, not relative to real reasoning, or to the real world, but relative to Frege’s system, in particular basic logical principle 5. The point of the paradox, as is acknowledged by everyone involved or interested - Russell, Frege, later work in set theory and foundations - is that, actually, basic logical principle 5 is not reflective of how reason works. Russell suggests a very limited form of comprehension, namely the theory of types. Later, Zermelo and Frankel suggested an axiomatic approach to foundations, in particular, they want to demand that a set come into existence not through comprehension, but only when specified to exist by the axioms. The result, ZFC, is believed by most people in the field to correctly model the way mathematicians actually view the world. Godel attempted to build another system, but it was shown that the two have equivalent theories. Currently, mathematicians are divided on the question of certain undecided questions in ZFC, such as large cardinals, CH, and, if not CH, then some questions as to the behavior of the witnesses (Martin’s Axiom.) Interestingly, choice also yields many conclusions referred to as paradoxes, yet they don’t have the structure of Russell’s paradox, in that they fail to be self-contradictory. The best known is Banach Tarski, but this is a claim about a topological object, not a basketball or glass globe (as it is commonly stated) and hence cannot really be said to contradict physical evidence. Most mathematicians, then, accept choice. (I don’t).
Thank you so much. I’ve been looking for someone knowledgeable about this. What is basic logical principle 5?
Indeed. Seems my fellow countryman and I disagree on what we think would happen should more libertarianism-ish principles be applied. Also I would like to see him reason more pro-central planning and control than against the lack thereof. No time for it now though. I’ll return later today.