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  • I have been asked to be the last speaker of today.

  • I know, of course, that you will all be extremely tired at this moment.

  • But the fun thing is that I'll be talking

  • about logic and creativity.

  • And you see the subtitle: "A False Opposition".

  • It will mainly be about logic.

  • But the fun thing is that you don't have to think. OK?

  • So, just let your mind go all possible ways

  • 'cause I will try to show you -- what I want to try to show you is this.

  • In western philosophy for over more than 2000 years --

  • I'm not exaggerating here, for more than 2000 years,

  • there was always the idea that

  • you have logicians on one hand,

  • and you have creative people on the other hand.

  • And the two will never meet.

  • So, you have this image of a logician,

  • which does not correspond to me,

  • namely, the kind of person with a very strict mind who follows

  • the conclusions he or she has to follow with an inevitable force,

  • whereas the creative mind can explore all the possibilities, etc.

  • Well, first of all, if you do logical analysis you get problems.

  • And, what I will do, in the time that I have at my disposal,

  • I will show you some of these problems.

  • And they are deep, deep, deep problems,

  • also extremely amusing.

  • And if you want to try to solve problems, you need creativity.

  • So, that's me being logical,

  • logical analysis needs creativity.

  • It's even better.

  • If you want to inverse the whole story,

  • if you want to be creative, you have to explore.

  • But, if you want to explore, then you need maps for exploration.

  • Such maps need logical analysis,

  • so, inevitably, creativity needs logical analysis.

  • So, right. This is the end of the talk.

  • (Laughter)

  • I have made my point, so --

  • (Applause)

  • But I still have 16 minutes. So, OK. Let's have some fun.

  • OK. I'll start with a very simple problem.

  • One of the problems that logicians think about a great deal

  • is how do we define things.

  • It's something that -- we don't do it on a daily basis.

  • Very often if somebody asks you: "What is this?"

  • Then what you do, you give it a description,

  • you try to define what it is.

  • OK, let's take one of the most famous examples

  • from the British philosopher Bertrand Russell,

  • and it goes as follows.

  • Imagine a village, and in the village is a barber,

  • and the barber is that person that shaves people.

  • Now, imagine that you give the following definition.

  • Who is the barber in the village? Well, that's that person

  • who shaves everybody who does not shave himself.

  • Sounds OK. People who don't shave themselves go to to the barber --

  • it's a very neat village, clean people, I'm not living there. (Laughter)

  • They go to the barber to get shaved.

  • And then you realize this definition is no good

  • because the only question you have to ask, "What should the poor barber do?"

  • Imagine the barber getting up in the morning.

  • He goes into the bathroom, looks in the mirror,

  • and he says: "Should I shave myself?

  • Ah, no, I can't, because I'm the person

  • who shaves everybody who does not shave himself.

  • Now, if I would shave myself, then I can't go to my barber, but that's me.

  • So, I can't shave myself."

  • But then, of course, he wonders,

  • "Should then I not shave myself?"

  • He says: "Well, that's no good, because then

  • I belong to those people who come to me to get shaved.

  • So, now, I have to shave myself."

  • So, he has to shave himself,

  • if and only if he does not have to shave himself.

  • Right. Can you get out of this?

  • Sure. There's a very easy solution.

  • Take a woman.

  • (Laughter)

  • (Applause)

  • And, since I always have clever students

  • in my college classes, one of them said,

  • "Yes, but did you take into account the woman with a beard in the circus?"

  • Okay, so that's why it's added a woman without a beard. Yeah.

  • You can of course say, "Reject the definition."

  • OK, fine, but what are you then going to do?

  • So the question you then ask --

  • and this is a question that is still an open question,

  • we have no good, decent answer to it.

  • Namely, how can we decide, when I give you a definition,

  • how can you decide that that definition is OK?

  • Well, the answer is, you can't.

  • Here's another example, one of my great favorites.

  • OK. Watch this.

  • Since time is staring at me at this very moment

  • this is a perfect example.

  • Suppose you have the following definition.

  • If you have two watches, "one" and "two",

  • then "one" is a better watch than "two"

  • if "one" gives you more often correct time.

  • That seems reasonable. No, it isn't.

  • It's a very bad idea because -- (Laughs) --

  • if you have a broken watch that gives you

  • two times a day the correct time -- Right?

  • Whereas if you have a watch that runs ahead one minute

  • it never gives you the right time.

  • So the broken watch is better than the other one.

  • OK?

  • It's of course a bad definition because it doesn't tell you

  • that you have to know when it gives you the correct time.

  • Bad definition. OK. Let's forget about definitions.

  • Let's take something more fun.

  • Truth. Ah! (Laughs)

  • I was very pleased that TED has as a subtitle,

  • "Ideas Worth Spreading".

  • Not "True Ideas Worth Spreading"

  • because otherwise I would have not been here today.

  • Because I will show you that I have no idea what truth is.

  • Why? OK. Follow me for a moment.

  • Assume the following.

  • If I say something that is meaningful

  • then it is either true or false.

  • At least in first order we can accept it,

  • I know we have plenty of occasions where we have doubts.

  • Is it raining, or not raining? It's drizzling. OK.

  • But in that case, is it drizzling, or not drizzling?

  • OK, fine.

  • Keep the world simple for a moment.

  • Either true or false. Right?

  • Either the one or the other.

  • That seams, OK -- that's trivial.

  • And this one too. Not both of them.

  • You can't say of something that is both true and false.

  • That's excluded. Right?

  • Doesn't it sound perfectly reasonable?

  • It doesn't. (Laughs)

  • And this is the reason why.

  • The famous liar paradox. OK.

  • This sentence says, "This sentence is not true."

  • So this sentence says of itself that it is not true.

  • It is meaningful. I assume that everybody here present

  • knows what this statement says.

  • It says about itself that is not true.

  • So, we understand it. So that means

  • it must have a truth value: either true or false.

  • But now what happens?

  • If it is true, then it turns out that is not true.

  • Of course. Assume that a sentence is true.

  • Then what the sentence says must be the case.

  • What does it say?

  • That it is not true.

  • So if it is true, it is not true.

  • That's OK. That's fine. That's OK.

  • You can conclude from that that is not true.

  • So then assume that is not true.

  • What then?

  • Well, if it is not true,

  • then that is exactly what the sentence says.

  • Now, if something says exactly what is the case, then it is true.

  • So, if it's not true, false, then it is true.

  • It is true, if and only if it is false.

  • So, there you have it.

  • Ah! Then you say: "How can we get out of this?"

  • First a warning. I have to confess I'm a professor,

  • so I'm a teacher and I can't resist teaching.

  • So, here's a short moment of teaching.

  • You will learn something

  • you can embarrass logicians with. OK?

  • So I'm now working against my own Trade Union,

  • the United Force of Logicians Worldwide.

  • If you now meet the logicians you can say,

  • "Tell me, how about that problem," -- namely this problem.

  • The paradox that I've just shown you is also known

  • as the Epimenides paradox.

  • And it goes as follows.

  • All Cretans -- you are on the island of Creta,

  • and a Cretan says to you,

  • "I have to warn you, all Cretans are liars."

  • Now, what are you supposed to do here?

  • Well, very funny, first of all a bit of theology.

  • If you say logic, you say theology.

  • What would theologians be without logicians

  • to prove the existence of God -- which, of course, doesn't work.

  • Neither does the opposite, but that's another problem.

  • And that's a different talk, by the way, also.

  • Which I have, so, OK, worth spreading.

  • I told you, I'm doing the thinking for you. OK?

  • So you don't have to think.

  • Actually, the Epimenides paradox,

  • the first reference you get is in the bible.

  • It's in the Epistle of Paul to Titus.

  • Titus, being sent off with his family, yes, his family,

  • to Crete, to convert people there.

  • And Paul gives him a warning.

  • And that's chapter 1, 1-12, -- you may remain seated --

  • "One of themselves, a prophet of their own said,

  • 'Cretans are always liars, evil beasts, idle gluttons.' "

  • And then Paul makes a horrible mistake.

  • He says, "This testimony is true." (Laughs)

  • Which proves that in the early Roman-Catholic church

  • there weren't that many logicians around.

  • Because they would have said,

  • "Paul, don't write this, I mean, it's silly."

  • Because what you have it's the following situation.

  • There is no paradox.

  • So any logician will tell you,

  • "Oh, this is definitely a paradox."

  • It isn't. Why?

  • Because it is not so that all Cretans are liars.

  • Because you know it has been said by a Cretan,

  • so if what he says it would be the case,

  • then they are all liars, so he must be a liar.

  • OK. Now what is the meaning of "It is not so that all Cretans are liars"?

  • That is, that some of them are liars

  • and some of them speak the truth.

  • Now if it so happens that the Cretan that is telling you this,

  • is a liar, everything is fine.

  • It's basically a liar who has told you a lie.

  • If he had been a truth teller,

  • then you would have had a problem.

  • And that's exactly what Paul wrote.

  • I'm not going into a theological discussion here,

  • Hence this must be -- OK, what?

  • How to solve it?

  • I'll be very brief. We don't know.

  • One of the brute -- yes, well, I mean --

  • (Applause)

  • This is no exaggeration.

  • There are plenty of logicians who would say,

  • "Don't say such thing."

  • "I'm now saying a lie." "Shut up."

  • Or you could say, well, there's more than true and false.

  • You have true, you have false, and you have stuff in between.

  • That's a possibility. It's not a good possibility.

  • Or, why not -- and this is something that logicians

  • have been working on since the 1950's-60's --

  • why can't we reason with sentences,

  • statements that are both true and false?

  • If you say, "What's typical for a sentence like,

  • 'It's Saturday today?' "

  • Well, in this case it is true.

  • Tomorrow it will be false. Fine.

  • What is typical for a sentence such as,

  • "I'm rambling." Well, you have to decide.

  • And if you then ask,

  • what's typical for "This sentence is not true."

  • Answer, that is is both true and false.

  • That's the characteristic of it. Ah, lovely.

  • OK. Let's get closer to the world.

  • I'm sure you are all familiar with Zeno's paradoxes.

  • And we have a solution, that's nice.

  • We have a solution. OK.

  • You know the problem of course.

  • If I have to walk from here to there --

  • I've just done it, that's nice.

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