"I learned to make my mind large, as the universe is large, so that there is room for paradoxes." -Maxine Hong Kingston, Novelist
Paradox:
-A paradox is a statement or group of statements that leads to a contradiction or a situation which defies intuition. The term is also used for an apparent contradiction that actually expresses a non-dual truth. Typically, either the statements in question do not really imply the contradiction, the puzzling result is not really a contradiction, or the premises themselves are not all really true or cannot all be true together. The word paradox is often used interchangeably with contradiction. Often, mistakenly, it is used to describe situations that are ironic. -Wikipedia
For the simple mind like all of us, a paradox would be something along the lines of:
1. a statement or proposition that seems self-contradictory or absurd but in reality expresses a possible truth.
2. paradox does not equal irony (ohh, how we love GP)
For which if I were to say I were a liar, how would I be judged?
- If I'm a liar: wouldn't I be telling the truth if I said I was a liar?
- Likewise if I was goody-two-shoes: wouldn't I be lying if I said I was a liar?
Similarly, a humble man wouldn't go around claiming that he's humble, would he? (:
Yeah, and there are some really cool paradoxes out there. Billions of them actually, but these are a few good ones.
The Sorites Paradox
Paradox of the heap
The name "Sorites" derives from the Greek word for heap. The paradox goes as follows: consider a heap of sand from which grains are individually removed. One might construct the argument, using premises, as follows:
1,000,000 grains of sand is a heap of sand (Premise 1)
A heap of sand minus one grain is still a heap. (Premise 2)
Repeated applications of Premise 2 (each time starting with one less grain), eventually forces one to accept the conclusion that a heap may be composed of just one grain of sand (and consequently, if one grain of sand is still a heap, then removing that one grain of sand to leave no grains at all still leaves a heap of sand).
On the face of it, there are some ways to avoid this conclusion. One may object to the first premise by denying 1,000,000 grains of sand makes a heap. But 1,000,000 is just an arbitrarily large number, and the argument will go through with any such number. So the response must deny outright that there are such things as heaps. (A fallacious statement?) Alternatively, one may object to the second premise by stating that it is not true for all collections of grains that removing one grain from it still makes a heap. Or one may accept the conclusion by insisting that a heap of sand can be composed of just one grain.
Interestingly, this paradox can be reconstructed for a variety of predicates, for example, with "tall", "rich", "old", "blue" and so on. Bertrand Russell argues, in his paper titled "Vagueness", that all of natural language, even logical connectives, are vague; most views do not go that far, but it is certainly an open question.
The Theaseus Paradox
According to Greek legend as reported by Plutarch,
The ship wherein Theseus and the youth of Athens returned [from Crete] had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus (not stated how long, but yeah, think loooonnng time), for they took away the old planks as they decayed, putting in new and stronger timber in their place, so much so that this ship became a standing example among the philosophers, for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same.
—Plutarch, Theseus
Plutarch thus questions whether the ship would remain the same if it were entirely replaced, piece by piece. As a corollary, one can question what happens if the replaced parts were used to build a second ship. Which, if either, is the original Ship of Theseus?
The Unexpected Hanging Paradox
A judge tells a condemned prisoner that he will be hanged at noon on one weekday in the following week but that the execution will be a surprise to the prisoner. He will not know the day of the hanging until the executioner knocks on his cell door at noon that day.
Having reflected on his sentence, the prisoner draws the conclusion that he will escape from the hanging. His reasoning is in several parts. He begins by concluding that the "surprise hanging" can't be on a Friday, as if he hasn't been hanged by Thursday, there is only one day left - and so it won't be a surprise if he's hanged on a Friday. Since the judge's sentence stipulated that the hanging would be a surprise to him, he concludes it cannot occur on Friday. He then reasons that the surprise hanging cannot be on Thursday either, because Friday has already been eliminated and if he hasn't been hanged by Wednesday night, the hanging must occur on Thursday, making a Thursday hanging not a surprise either. By similar reasoning he concludes that the hanging can also not occur on Wednesday, Tuesday or Monday. Joyfully he retires to his cell confident that the hanging will not occur at all. The next week, the executioner knocks on the prisoner's door at noon on Wednesday — which, despite all the above, will still be an utter surprise to him. Everything the judge said has come true. Was the prisoner unfairly killed?
The Prisoner's Dilema
In its classical form, the prisoner's dilemma ("PD") is presented as follows:
Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal. If one testifies (defects from the other) for the prosecution against the other and the other remains silent (cooperates with the other), the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How should the prisoners act?
The classical prisoner's dilemma can be summarized thus:
In this game, regardless of what the opponent chooses, each player always receives a higher payoff (lesser sentence) by betraying; that is to say that betraying is the strictly dominant strategy. For instance, Prisoner A can accurately say, "No matter what Prisoner B does, I personally am better off betraying than staying silent. Therefore, for my own sake, I should betray." However, if the other player acts similarly, then they both betray and both get a lower payoff than they would get by staying silent. Rational self-interested decisions result in each prisoner being worse off than if each chose to lessen the sentence of the accomplice at the cost of staying a little longer in jail himself (hence the seeming dilemma).
And for the last one (:
The Monty Hall Problem
The problem is also called the Monty Hall paradox, as it is a veridical paradox in that the result appears absurd but is demonstrably true.
The problem can be unambiguously stated as follows:
Suppose you're on a game show and you're given the choice of three doors. Behind one door is a car; behind the others, goats. The car and the goats were placed randomly behind the doors before the show. The rules of the game show are as follows: After you have chosen a door, the door remains closed for the time being. The game show host, Monty Hall, who knows what is behind the doors, now has to open one of the two remaining doors, and the door he opens mus
t have a goat behind it. If both remaining doors have goats behind them, he chooses one randomly. After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door. Imagine that you chose Door 1 and the host opens Door 3, which has a goat. He then asks you "Do you want to switch to Door Number 2?" Is it to your advantage to change your choice?
Yup, apparently it is. Great thing is, if you think its okay to stay cause it's 50%/50% that you'll get a car, many other people have the same thinking, Nobel Physicists included. :D Well, it's less favourable to stay though. Explanations rather simple.
Say there is door A, B and C. B and C contains goat, while A contains car, same throughout all 3 scenarios.:
Scenario 1: You choose A. Either of the doors are opened to reveal a goat. Switching loses.
Scenario 2: You choose B. C is opened to reveal a goat. Switching wins.
Scenario 3: You choose C. B is opened to reveal a goat. Switching wins.
Yeah, by observation, you should switch, cause you'll have a 2/3 chance of winning.
I found this rather entertaining, amusing to a certain extent. Well, if you're having a headache with all the information you've just read, hahaha, my apologies. Kinda interesting, isn't it?
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Ironic, isn't it. Just the thought of it.
I've heard this from a few people, unnervingly true it is though.
"During promos (Promotional Examinations) when you're supposed to study you'll feel like playing, and after promos, when you're not supposed to study that hard or rather play/take a break, you don't feel like playing?!"
Ah well, whats over is over, spilt milk is not worth shedding tears over. Let's hope for the best then. (:
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SCHWIMM!:))
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