To make sure that you are sufficiently bored while reading, I also have to talk a little about paradoxes. The (im)point of it is that you have to strip away prejudices when you think about it. And prejudices include snap judgements. Overall, I find it generally helpful in life to approach many things without prejudice. This is especially true, by the way, when it comes to betting and gambling.
So a little excursion into the world of paradoxes can’t hurt at all.
Softening thought structures can only be helpful.
By the way, it is mathematically, logically, not quite easy to find a correct answer to the question: “What is paradox?” Examples exist, then it becomes clear to you. “That’s paradoxical.” It is also paradoxical that one can find examples but then no definition. There must be something in common, even among the examples, that makes a definition possible.
I therefore try my hand at defining: Paradox is a statement whose truth is indeterminable. So it is not true, it is not false. But that would give us a third form of truth content. A statement that is neither true nor false is paradoxical. That is the truth content.
There is also this example in pure mathematics. What is the root of -1? Surely you can’t find a number that squares to -1? Minus times minus is plus, plus times plus is also plus. So it doesn’t work. Impossible, paradoxical. The mathematician has solved the problem simply. He says: The root of -1 is i. And i is a complex number. It is simply defined.
And complex it really is, I almost said: i, is that complex. But we’ll just look at…
1) Among Indians
It happened at a time when palefaces and Indians lived in deep enmity. A white man was captured by an Indian tribe. And the tribal chief pronounced the devastating verdict: the death sentence. However, according to tribal custom, the prisoner still had influence over the manner of death in that he was allowed to say one last sentence. Death by pyre, burning, or at the stake. The medicine man would then check the truth of this sentence. If he deemed the statement true, the man would go to the fire; if he deemed the statement false, the man would be put to the stake. The man, of course, said the following sentence, and this after careful consideration: “You will put me to the stake.”
Now it was up to the medicine man to think. Was what the good man had said true or false? He briefly considered whether the statement could be true. If it was true, the man would be burned at the stake. No, then it would have been false. So it is false. He must go to the stake. No, then it would be true.
And all the wisdom of this medicine man was not enough to give this statement any truth. The man had to be set free.
The polite Indians bowed before so much wisdom. But the tribal chief was a little angry and asked the medicine man to find a solution to this problem in order to avoid further unpleasantness. And he wanted to stick to the tribal custom at all costs. The medicine man found a solution and the tribal chief was reassured.
So it happened that some time later another white (and even wiser) man fell into captivity. The same verdict. The chief confronted the prisoner with his options: “You may say one more sentence. If the statement is true, you will be burned. If the statement is false, you will be put to the stake. And if you say something that is paradoxical, we will kill you with bow and arrow. “
The wise(ish) man thought and spoke the same sentence as his predecessor, he had to do something. “You will put me to the stake.”
The medicine man was prepared for such and immediately ordered the bow and arrow to be put on. The bow and arrow were put on. The man tried one last, desperate cry for help, appealing to reasoning powers (because dead is dead, logic or not) and said, “If you shoot me now with bow and arrow, then my statement would have been false after all and you should have put me to the stake.”
Now even the medicine man could not ignore this inexorable logic. The man was finally released.
The medicine man, however, capitulated, asked his tribe to be relieved of his office and to turn the arrows on himself….
For me, the question now is: How paradoxical is paradox?
2) I am Father Christmas
One more very simple example. I will prove to you in two sentences that I am Father Christmas, okay? This is how it works: I write down two sentences. And we check their truth value.
1) One of these two sentences is false.
2) I am not Father Christmas.
Okay, so one of these two sentences is false. Let’s say the first sentence is false. Then the opposite of the statement would be true. That’s how false is defined. So the opposite of “One of these two sentences is false.” True. The opposite is that both sentences are true. That’s a contradiction to the statement, one of these two sentences is false. So 1) is not false. Accordingly, the 2nd sentence is false. And the converse of the statement, “I am not Father Christmas.” Is the statement, “I am Father Christmas.”
Have I convinced you? Because it really is true…
3) The Barber of Seville
Curiously, when something is particularly old(-famous), people always say that it has such a beard, and here it’s really true or not; personally, I’m still puzzling over what the good man is doing.
The story, yawn, goes that the Barber of Seville made the following fateful statement: “I shave all people who don’t shave themselves.” Well, that sounds perfectly logical at first. It would be nonsense to shave the people who shave themselves, because they already are. And those who either don’t have the ability or don’t feel the urge to shave, they just shave. What and how else?
But at some point the question arises, what does he do with himself? All I can think of is that he must commit suicide immediately. He no longer has a choice. He has, so to speak, pronounced his death sentence. As soon as he asks himself whether he should shave or not, he finds himself in an irresolvable, actually tragic contradiction. He is not allowed to shave himself and at the same time he has to shave himself. The situation is hopeless and hopeless.
If he shaves himself, he belongs to the group of people who shave themselves, and he doesn’t shave them. If he doesn’t, he belongs to the category of people who don’t shave themselves and those same people, he says, he now has to shave again. He can’t do anything anymore. Do you feel it too? Oh, one more solution comes to mind: Right now, time stands still…
3) A Cretan says, all Cretans lie
This “paradox” simply has to go in here. And before you now want to strike out of sheer boredom and not get any more bored, I make the following statement: This is not a paradox at all. Did you know that? Well, so much the better.
I’ll explain it anyway. So, a resident of Crete, a Cretan, said a sentence: “All Cretans lie.” Our task is to assign a truth value to this statement. There are, as we have seen, actually three truth values: True, False and Paradoxical.
So we start with the test: Is this sentence possibly true? Well, if it were true, then this man would at least be capable of a true statement. And, let us again improve the original sentence in the direction in which it is taken. It is understood as saying, “All Cretans always lie.” And if a man always lies, then every statement he makes is false. So his statement just made, “All Cretans always lie,” cannot be true at all. It is a contradiction to the assumption. The man did not speak the truth.
Then we next examine whether his statement is possibly false, whether he has simply lied to us. We assume that the sentence “All Kreataer lie (always)” is false. And this is where the argumentation gets a bit curious. I experienced this first hand. I was undergoing retraining to become an IT specialist. The conditions for admission were, firstly, that I had completed my studies (I was the only exception) and, secondly, an intelligence test in which I had to achieve a certain minimum result.
I found myself among academics, so to speak. And I dared to go to the blackboard and explain that the Cretan’s statement was wrong. I could hardly finish my argument and was already booed off the blackboard. In this respect, I have now tried the proverbial patience of the paper to “get the thought processes across” to the attentive reader. And I have also asked the reader(s) to do the same:
The logical principle behind it is quite simple. We also encounter this form of logic every day. Purely descriptively, it becomes understandable in the way it is used: The following vivid little story I say to Someone: “There are only red balls back there in the box.” He goes to the box, takes out a ball. This ball is white. He says, “It’s not true what you said. There are not only red balls in the box. Look here, I have a white one in my hand.” Now it wouldn’t do me much good to say, “Yes, there are, all the other balls are guaranteed to be red.” He doesn’t even look at it any more. What’s the point? My statement was wrong. A sample that is a refutation of the basic statement is enough to show that the overall statement is false.
So it was here with the Cretan. He said, “All Cretans lie (always).” The statement cannot possibly be true, as shown above. Is it false? If it were false, then the opposite of the statement would be true. The opposite of the statement: “All Cretans lie (always).” But is the statement, “There is one who also, at least occasionally, tells the truth.” And that is quite possible. True, we cannot check it directly now, since the only available statement by a Cretan whose truthfulness we can determine is, of all things, false, as we have just seen. But there is at least guaranteed to be no contradiction to be discovered. On the contrary: just because we have just caught a person of a certain people lying (and we have!) surely does not allow the conclusion that all the others lie too, and always and regularly. That would be pure nonsense.
So: the man lied. That is supposed to happen. And nothing about the statement is paradoxical. What other Kreataers do when they testify to something, we continue to lack any judgement about.
As I said, the outrage was huge. I was literally booed off the board. From then on, I was persona non grata. I first had to painstakingly rebuild my status as “although crazy and mentally disturbed, he is halfway harmless and in other areas he is relatively adept at concealing his lack of competence”.
I still owe you this proof? All right, but I’m working on it and really trying.
4) White elephants
As a child, the very first thing I encountered was this really tiny little paradox. My mother used to say, like a children’s joke, “Don’t think about a white elephant.” And what do you do right at that moment, almost inevitably? And you would like to indignantly rebel, “I wasn’t even thinking about it, and it never would have occurred to me if you weren’t at that very moment …” But it doesn’t help you to be honest.
4) James Bond
Yes, why James Bond? Well, the film title. “Never say never.” You should never say never. At this very moment, you already have. It’s a rule that contradicts itself. If you should never say it, you shouldn’t say it now. Or, if you want to make the rule and follow it, you have to say it yes. Still, it’s remarkable: somehow there’s some truth to it, isn’t there?
It is even astonishing that it is a rule, one could also say a principle. And a rule, a principle, gives a permanent rule of conduct. But the content of this rule is that one should not have rules, principles. “I never go bowling. I don’t enjoy it.” “Don’t say you never do it. Maybe one day you will. And then what about your rule? You’d better not even set it.” That’s right, before you contradict yourself, don’t make a rule in the first place. That’s the tip, the substance of the proverb.
Now I have thought about how one would have to formulate the rule so that it is not contradictory, not paradoxical, but the undoubtedly existing truth content remains? According to my interpretation, I have succeeded, and in this way. The sentence should read: Apart from this one rule, there are none. Or the religious version: You shall have no rules besides me. Short version: There is only this one rule.
“I know that I know nothing.”
Even if, as I have just gathered from studying on the internet, the correct translation would have been: “I know that I do not know” one hears this sentence often enough and after all, once uttered, even misquoted, can give one the pleasure of reflecting on the meaning. Nor do I share the view that the sentence would not be paradoxical if translated correctly.
When I hear such a sentence, it always gives me enormous pleasure to think about it. Why is that? First of all, that although paradoxical, somehow a kind of statement becomes recognisable. Helplessness, helplessness, but at the same time a deep understanding. One is small and insignificant. Perhaps you have learned a few things, only to realise that the gaps are getting bigger and bigger. “The more I know, the more I know that I actually know nothing.” One could also put it this way.
But now we have the sentence, “I know that I know nothing.” And it is paradoxical. Because, even if it was just this little detail that you knew, it would still be something. So the statement simply cannot be true. It refutes itself. In that case, the question “is the statement perhaps false?” is idle, even impossible. What would be the counter-statement that would have to be investigated? I don’t know that I know something? Doesn’t change much, does it?
Following on from so much philosophy, I am then concerned with how the statement could be made right, as in the example before. And that’s where it gets really curious. So I want to express that I don’t know anything (you say: I’ve already succeeded? Oh no… meanness!). And that I am aware of it. Unfortunately, then, I know a single, tiny detail. Socrates got it wrong. Apart from this tiny detail, I know nothing at all. So I would have to rephrase: “Except for the fact hereby described, I actually know nothing.”
6) If it weren’t for the little word if….
Gradually, I’m moving more towards the really purely joking parts of the term “paradox”. Although this nursery rhyme (would your father have been a millionaire too?) contains a whole lot of beautiful truth. It is even surprising that it describes a law of mathematics. This law comes from what is called “logic”. The sentence that is logically proven is like this: “From a false premise you can infer anything. The overall statement remains true.”
So if the premise equals the conclusion, then it rains. No, now that was just a stupid play on words because I happened to start the sentence with “if” as well.
So the premise is wrong. There is the word “if”. And if it didn’t exist, there would be some other word that describes the same thing (think of foreign languages in this context! If…). And since the premise is false, any statement can stand behind it. The total issue remains true. Consequently, there is nothing paradoxical about it. One would have no chance to refute what my father would be if this little word did not exist. So the statement is true. However, this does not make any father a millionaire….
7) Einem Street
This street exists in Berlin. And every time I drive along it, I think of this totally stupid question: How do you spell it? I give myself the answer: “You fool, you could have remembered that. With an m, of course!” “Oh yes,” the dialogue (which only split personalities carry on; for the others: monologue!) then continues. “That’s why she’s called that.” Think about it: otherwise it would (have to) be called “Zweiemmstraße”? But that is not enough for me as an answer. I then raise the philosophical question: If the name didn’t exist, the problem wouldn’t exist either. And vice versa. What came first? Chicken or egg? Problem or name? And especially with this name, you can go on like this. There’s nothing to laugh about. How about “Dreiemmmstrasse”? It’s only getting really funny now, and I’ll tell you another trick right away: Vieremmmmstrasse! The trick? When I fell under the table laughing, I simply took the keyboard with me and continue typing here below.
As I discovered, it works well with m even up to 999,999. Because in our number system, up to and including this number, there is not a single m! I notice that the reader is thinking and checking. Respect, keep it up. The only time there is a slight danger is always when a 7 comes. “Siehm…” At least the lips only touch at all numbers where a 7 occurs. And saying “m” without touching lips is impossible. “M” is more or less the “lip touching sound”, you also say “hmmmm” and there is a word with four “m”, you can see….
It’s only funny because I would like to explain the problem and its solution to other people. And except for today’s reader, I haven’t managed it yet. You look for other examples. Like this one: DoppelPstrasse. And that’s really totally stupid. Think about it. It’s also not right in the front and back, just in the middle. It’s like “Pfeiffer”, which is also spelled with three f’s. DoppelPstrasse has three p’s. And if I were to call it “DreiPstrasse”, it wouldn’t even be right in the middle. Let alone VierP… Well, that’s enough now.
Let’s stay like this: I’m waiting for you to send me more examples?
Please believe me when I say that I am convinced that the creator of this street name intended to give motorists something to think about, and not only them… And black ice again. I laid it myself.
Otto gave his version of the Petrus letters. One of them was: “Peter wrote to the Iroquois: ‘I’m not writing anything to you, learn to read first.'” Quite short, quite paradoxical. In this case, too, I begin by considering all the versions of the absurdity. Firstly, he did write something to them at that very moment, so it’s contradictory enough anyway. But secondly, it would be good advice to follow, if one could interpret it, as an Iroquois. But this would obviously require grasping the content of the text. This requires a certain basic prerequisite: reading itself. But if one could read it, then the sentence would be wrong, nonsensical, which demands this basic prerequisite. Since it is given, he could have written something to them under the circumstances. But that is what he did. But unfortunately, under the circumstances, he wrote something senseless or even wrong.
Should I start again from the beginning?
My father, my father, always my father. When we sons wanted to repair bicycles, he would always give us an encouraging: “Oh, are you making a broken thing out of three whole things again?” And, I just can’t help it, I always have to keep it in mind exactly how it looks then. I also know that I’m pretty lonely in the world with the ramshackle fad (ouch, ouch, kalau) of wanting to polish up the jokes by doing this. Nevertheless, in my mind’s eye I see three whole, beautiful, new bicycles in front of me. Now three boys come and start screwing. And after a few hours, their work is done: they now have exactly one, but broken, bicycle. Then I try to imagine this bicycle, to look at it and inspect it, because sitting on it should be impossible. What does the reader see at this moment? By the way, this “damage” can be repaired relatively easily. By simply exchanging words, it becomes a bicycle! You simply make a whole out of three broken parts. On the other hand, it would border on witchcraft to make three whole ones out of one broken one…
Remember the Scotsman who finds some corn plasters and buys a pair of shoes that are too tight.
How would one describe his behaviour? Kind of a precursor to paradox, isn’t it?
My father also used to sing the beautiful song “Dideldadeldideldadeldidada, this song has no meaning, Dideldadeldideldadeldidada because it also needs no meaning…” ad infinitum… Why does this song exist? And this chapter?
I told my aunt that I was writing a chapter on paradoxes. She immediately knew what a paradox was: “A paradox is when an uncle looks steadfastly at his niece.”
I can assure you, however, that the only thing that sounds paradoxical is when you fight the emptiness in your brain by teaching. For that would not even be paradoxical if one were to replace “teaching” with “emptiness”. Both forms of teaching would have the identical effect. “Waiter, air out” is just one way to illustrate this. Or: try dumping out a vacuum. Notice: When the emptiness empties, the fullness fills.
I quickly move out of reach before concluding with the words of the famous philosopher and logician, the (lowly) esteemed book author, Horacio Neumann: “Whoever read that was stupid…”.
If, after studying it, one comes to the conclusion that the emphasis should correctly be on was, I would have achieved a partial goal…