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Artist: Damien Gilley

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J. McElehney, “Mirrored and Reflected Infinity”, 2004.- Siddhant Alva

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J. McElehney, “Mirrored and Reflected Infinity”, 2004.- Siddhant Alva

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The first sentence in this text is a lie. There is something odd about saying so, as has been known since ancient times. To see why, remember that all lies are untrue. Is the first sentence true? If it is, then it is a lie, and so it is not true. Conversely, suppose that it is not true. We have said it, and normally things are said with the intention of being believed. Saying something that way when it is untrue is a lie. But then, given what the sentence says, it is true after all !

People who cracked the paradox:

1. Alfred Tarski

2. Arthur Prior

3. Saul Kripke

4. Jon Barwise

5. John Etchemendy

6. Bhartrhari

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The Crocodile Dilemma - Prakruti, Aaryani, Siddhant Alva, Sankalp

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The Crocodile Dilemma - Prakruti, Aaryani, Siddhant Alva, Sankalp

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On a trip, a child is kidnapped by a crocodile who does not wish to return the child. When the mother asks the crocodile her child back, the crocodile only agrees on the condition where he promises the parent that his or her child will be returned if and only if he or she correctly predicts what the crocodile will do next.

If the parent guesses that the crocodile WILL return the child, there is no issue and the child will be returned. However, if the parent guesses that the child will not be returned, then the crocodile has to return the child as the parent had guess correctly. Following this, in the case that the crocodile decides to give back the child, he still contradicts his terms, because the parent's prediction has been falsified (returning the child when the parent guesses the opposite), so the child should not be returned.

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Proposed by Bertrand Russell in the early 1900s, the barber paradox introduces a town where every single resident must be clean-shaven. There exists a barber in this town who only shaves residents who do not shave themselves. These statements may seem simple at first, but a paradoxical proposition arises: who shaves the barber?

The ground rules of the paradox are as follows:

1.The barber is one who shaves all those, and those only, who do not shave themselves.

2.Everyone in the town must be clean-shaven

Some additional assumptions are:

1.Everyone is male.

2.The barber needs to be shaved

3.The townspeople can only shave themselves, no one else.

If the barber shaves his own face, then he shaves someone who also shaves themselves. This breaks the initial rule that the barber can only shave people who do not shave themselves. However, if the barber does not shave himself, then he breaks the second rule stating that everyone in the town must be clean-shaven. It should also be noted that the paradox does assume everyone is male.

The answer to the barber paradox is just that, the statements themselves are false. Bertrand Russell created the paradox to examine our understanding of classes and groups in logical theory. In the end, he stated that in its original form, the Barber paradox “is just noise without meaning.” In this, his intention shines through, to create logical noise that appears paradoxical but is simply impossible.

Answering this question results in a contradiction. The barber cannot shave himself as he only shaves those who do not shave themselves. Thus, if he shaves himself he ceases to be the barber. Conversely, if the barber does not shave himself, then he fits into the group of people who would be shaved by the barber, and thus, as the barber, he must shave himself.

In its original form, this paradox has no solution, as no such barber can exist. The question is a loaded question that assumes the existence of the barber, which is false. There are other non-paradoxical variations, but those are different.

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BY THEJASVI AND PRASHANT

Protagoras agreed to instruct a poor young man, Euthalos (from a working-class family) in law and rhetoric free of charge on the condition that he would pay the sophist's fee in full if, and only if, he won his first court case. Once Euthalos had completed his course of study with Protagoras he assiduously avoided taking any cases at all. Protagoras, finally out of patience with the young man, took him to court for payment and argued thusly:

If I win this case, Euthalos will have to pay me what he owes me. If I do not win this case then Euthalos will still have to pay me because, under our agreement, he will then have won his first court case. Therefore, no matter what the outcome, Euthalos will have to pay me.

Euthalos, however, contested this claim, stating:

If I win this case I will not have to pay Protagoras, as the court has declared his case invalid. If I do not win this case I still do not have to pay as I will then have not won my first court case. Therefore, no matter what, I do not have to pay.

This argument (for which no solution was ever offered in antiquity) has come to be known as the Paradox of The Court (L. Alqvist) and a resolution to the question is still debated today in law schools as a logic problem.
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=video&cd=&cad=rja&uact=8&ved=2ahUKEwid0Oy36KjzAhU0yIsBHUAbBbEQtwJ6BAgGEAM&url=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DUMH5wGL8n-Q&usg=AOvVaw34TifDN6IXll6JSSKHvm_L