THOUGHT FOR TODAY

Morning bloggers Ok all you planetbrains out there, help me with this one. The other night we were all stuck in a traffic jam on the M40 and conversation turned, as it always does, to the problems of philosophical logic. The seven year old and the ten year old were savouring the paradox of the barber - you remember, the famous hairdresser in the Cretan mountain village of Agios Giorgios who shaves all the men in the village who do not shave themselves. Does the barber shave himself? the seven year old asked the ten year old. If he does, he doesn't, said the ten year old. And if he doesn't, he does! said the seven year old. Paradox! This is a variant of the set-of-all-sets-that-do-not-include-themselves paradox that - I seem to remember - sent Russell round the bend and caused him to tear up ten years of work. Then I thought of a snappier variant. "All generalisations are wrong," I announced to the car. Now is that statement true? If it is, it isn't, said the seven year old. And if it isn't, it is! said the ten year old. Paradox! Am I right?

39 thoughts on “THOUGHT FOR TODAY”

  1. “All generalisations are wrong.”

    That generalisation can be wrong, making the statement untrue… but it does not follow that because it is untrue that *no* generalisations are wrong. It could be untrue in the sense that only *some* (or even many) generalisations are wrong.

    The trick is trapping someone into thinking it the problem has to be dealt with in polar opposites.

    Kind of like US neo-cons framing debate in such a way as to suggest that the only alternative to the current massive swing to the right is an equally massive swing to the left.

    But I digress…

  2. No, it is not a paradox. Its falsehood does not mean that all generalisations are wrong – just that at least one is.

  3. Oh dear. I’ve been wandering around the web in order to procrastinate from doing the logic exercise I’ve got to hand in soon. If ever there was a sign that I ought to stop messing around and actually do it, I think this might be it.

  4. I think Russell’s Paradox actually led to Gottlob Frege abandoning years of work…

    My favourite “snappy” variant is the one I was taught at school: “Every rule has an exception”.

  5. Yes, Max, it is a paradox, of course it is.

    Though I wouldn’t agree with Boris that it is a logical paradox – a snappier version of Russell’s “set S of all sets” jobbie…
    It is quite clearly a semantic paradox concerning truth and definability – argue as you will.

    Gosh, after all this I’m never going to write a paradoxical self-referencing sentence again…I am never going to write a paradoxical self-referencing sentence again…

    Then again, “I am lying”

  6. There are ways of getting out of the paradox. If I could remember any logic I’d let you know what they are. As it stands, it is a paradox, because you can’t substitute ‘all’ for ‘some’. The two are not the same. So to say that some generalisations are wrong is to say something completely different.

    Basically yes, you are right.

  7. No, Talulah and Claire, you are mistaken – this is not a paradox, it’s just an untruth. It would only be a paradox if the statement “all generalisations are wrong” was the only generalisation – which, of course, it isn’t.

  8. If you want to really exercise your logical philosophy skills, you should investigate Godel’s Incompleteness Theorem!

  9. New theorem:

    I’m only incomplete unless I had a drink.

    A+B = fallover, drink charcol, have stomach pumped. (completeness.)

  10. To put the cart before the horse: if one starts with the theoretical premise that all
    generalisations are not wrong,( ask Boris) if there are adequate qualifications, then surely the sin/act of omission in a statement is to blame for any apparent paradox.
    Chris B . very adequately stated” There are ( nearly always)exeptions to a rule”

  11. Macarnie – I’m so glad that I was interested in the sign and the signifer rather then stright logic.

    I mean in Seneca’s letters there’s this little bit of bad logic:

    A mouse is a syllable.
    A mouse nibbles chesse.
    Therefore: a syllable nibbles chesse.

    Doh…

  12. No, John I really, truly think it is a self-referencing semantic paradox.

    To call it an untruth means we must be logically certain that at least one generalisation is ‘true’ – and although this might well be the case – I wouldn’t want to bind myself logically by saying that.
    You do have a point, but it’s all a question of semantics…hence ‘semantic paradox’ and all the pseudo-problems the little blighters bring.
    It is a paradox and (by definition) there is no “getting out of” a paradox.

    Boris is right.

  13. “All generalisations are wrong” – the paradox being derived from the fact that this in itself is a generalisation?

    I disagree (for once, I’m not on Boris’ side). If one generalisation turns out to be true, then the statement “All generalisations are wrong” is not true. It does not follow then that “All generalisations are true”, because the one Boris made isn’t, and I can probably come up with another that isn’t.

    I beleive I have heard this called an “All swans are white” argument – if I can find one black swan, the argument is false. But my one black swan does not make all the other swans black, merely because I proved “All swans are white” to be untrue.

  14. No, no, no, no.

    The statement, as it stands, is a paradox which cannot be tested empirically – no matter how many black swans you look for – and whose truth-value cannot be judged (sort of like Blair).

    It’s a semantic paradox – there’s really nothing you can do with it, except sit back and admire how pretty it is (sort of like Boris).

  15. When I was seven I was only interested in sweets; when I was ten it was the first stirrings of wanting to change the world for my benefit.

    Call in the Social workers! Boris is messing with the kids’ minds (and mine). In fact my mind is hurting just now.

    New paradox: If Boris makes my mind hurt is that a Good.Thing or a Bad.Thing?

  16. Yeah, my favourite is: “I’m a liar”

    There isn’t always an exception to a rule. All rules are generalisations, they contain assumptions. Therefore, to make the rule true the conditions on which the rule is founded need to be met. The flexibility of these conditions differ from rule to rule. Paradox?

  17. The paradox

    Has anyone yet asked the question
    Why Britain is now the first choice?
    Of the terrorists seeking asylum;
    The answer is here they’ve a voice.
    It’s louder than that of the natives,
    Who daren’t let their feelings be known,
    For fear of the eye of Big Brother,
    As the High Court’s decisions have shown.
    They’re allowed to be rude to the Nation,
    Preach sedition, and promulgate hate,
    And we pay police just to guard them,
    To see that none crashes their gate.
    We fall into various manholes,
    Left open by Brown, Clarke and Blair
    We’re seen as the terrorists’ haven:
    Expel them? — We just wouldn’t dare.
    They know we’re P.C.: it’s their aegis;
    They’re safe from the wrath of the folk
    They say what they like, say it often,
    Yet we pay for their safety….. A joke
    It’s a little like Spain, they have bullfights,
    The bull is the loser, no doubt
    In place of toreros, there’s lawyers,
    Whom the Bull pays, so they’re not thrown out.

    Is that a paradox?

  18. “All generalisations are dangerous, including this one” quoth Alexandre Dumas. Would work equally well as “All generalisations are wrong, including this one” which I’ve frequently misquoted 🙂

    Russell

  19. Sorry Talulah. It’s not a paradox – as much as it pains me to say that Boris is wrong about anything (although the fact that I am right makes it slightly more bearable).

    Probably we should make some attempt to define ‘paradox’ – if we define it as a statement that looks like it ought to be true or false, but cannot be either, then this is not a paradox, as it can be false.

    Boris’ paradox is very much like Epimenides paradox – ‘All Cretans are liars’ – which strictly speaking is not, thus stated, a paradox. Whereas ‘This sentence is false’ is a paradox. For further explanations see:

    http://en.wikipedia.org/wiki/Epimenides_paradox

    http://david.tribble.com/text/liar.htm

    Quine’s “The Ways of Paradox”.

    Life would be so much simpler if people just accept that I’m right, without arguing.

  20. You are, I fear, a bit devious, Richard van der Draaij, in quoting the Epimenides paradox: you must be aware that your name ; translated from the Dutch, means, apart from turn or twist:prevarication.You start with an advantage.

  21. Dear John,

    We are not going to agree. I take your point, I understand what you are saying…however, it’s all a question of semantics (hence, semantic paradox…)
    I will retaliate by saying that the crux of the matter is that the sentence is 100% self-referencing.
    “All generalisations are wrong” is more akin to “This sentence is false” than it is to “All Cretans are liars” because “All generalisations are wrong” is itself a generalisation and therefore affected by its own truth or falsehood. “All Cretans are liars” is different because it itself is not a Cretan (even if the person saying it might be).
    I reiterate my point that it is a stand-alone statement and cannot be judged either true or false…how are you able to take the stance that there is at least one “right” generalisation??
    If you really feel you have to debate the strictness of the definition of a paradox, that’s fine – interesting and important…but a bit anal I think. The kind of a distinction that can give philosophy a bad name – even when it makes a valid point.
    If as you say, people must always accept that you are right (apart from temping me into an ad hominem attack) then I suggest you forget philosophy and go for a more clear-cut science…like politics.
    And do not feel that you are going against Boris -he never actually assigned himself a point of view. He just posed the question.

    Talulah xxx

  22. “All generalisations are wrong” can be false. No paradox. I don’t really want to argue this any further, and I can’t think of a clearer way of stating it than I already have.

    I didn’t debate the strictness of definition of paradox. I just offered a definition, in case we understood different things by the term paradox. The very fact that I am still replying is anal, but I don’t think that my offering a definition was.

    As it is you appear to be accepting my definition. In which case you are wrong.

    I didn’t say that people must accept that I am always right. I didn’t even state that I was always right (I am not). I just said life would be easier if people just accepted I was right. (Which it would: I wouldn’t need to continue this argument.) In any case, it was a joke.

    And Boris did assign a point of view. If he had not, his question ‘Am I right?’ would be meaningless.

  23. Sorry Boris, you’re not right. John’s hit the nail on the head. When your ten year old said “if it isn’t, it is!” I fear he was in error – I can think of many true mathematical generalisations, for example.

  24. The statement “This sentence is false” is self-referencing, and so is “All generalisations are wrong”. However, the first one *only* references itself, whereas “All generalisations are wrong” has to be all-encompassing, otherwise it isn’t a generalisation. This expansion into the global is what kills it as a paradox, because it is not true that if all generalisations are *not* wrong, then they are all correct – they could almost all be wrong, apart from the one that wasn’t, and the “paradoxical” one.

    The counter-statement “All generalisations are correct” would then still not be true, and the paradox is not forced – “All generalisations are wrong” can be untrue without having to be true at the same time.

  25. This is the sort of thing that put me off philosophy when I was a student lad. I’ll repeat my earlier question:

    Does any of this actually matter?

  26. I think that the statement all generalisations are wrong is probably right because whenever a generalisation is made their is bound to be proved wrong by someone, the exception to the rule. Thus,Boris was actually correct, however it isn’t a paradox.

  27. Also, the barber could be female. Although female hair cutting people (horrible term but moving on) are generally referred to as hairdressers, the term barber actually means a hairdresser who WORKS ON men (ie is not necessarily one herself)

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