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The liar -

Imagine someone tells you they're lying. If what they tell you is true, then they're lying, in which case what they tell you is false. On the other hand, if what they tell you is false, then they're not lying, in which case what they tell you is true.

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The liar -

This paradox is attributed to the ancient Greek seer Epimenides, an inhabitant of Crete, who famously declared that "all Cretans are liars."

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The liar -

The paradox arises for any sentence that says or implies of itself that it's false. And it's important in part because it creates difficulties for logically rigorous theories of truth.

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Zeno's paradoxes -

In the 5th century, Zeno of Elea came up with a number of paradoxes designed to show that reality is motionless and single, meaning there's only one thing, as claimed by his teacher, Parmenides.

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Zeno's paradoxes -

For the argument against plurality, suppose that reality is plural. Then the number of things there are is only as many as the number of things there are. If the number of things there are is only as many as the number of things there are, then the number of things there are is finite.

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Zeno's paradoxes -

If reality is plural, then there are at least two distinct things. Two things can be distinct only if there is a third thing between them. And so on to infinity. Therefore, if reality is plural, it's finite and not finite, infinite and not infinite—a contradiction.

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Zeno's paradoxes -

Zeno's paradoxes have posed a serious challenge to theories of space, time, and infinity for over 2,000 years. And there's still no general agreement for many of them.

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Meno's problem -

This ancient paradox is named after a character in Plato’s eponymous dialogue. In it, Socrates and Meno are having a conversation about the nature of virtue. Meno offers several suggestions, each of which Socrates shows to be inadequate.

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Meno's problem -

Socrates then confesses that he doesn't know what virtue is. Meno asks how he would recognize it, if he ever encountered it?

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Meno's problem -

How would you see that a certain answer to the question "what is virtue?" is correct, unless you already knew the correct answer?

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Meno's problem -

Basically, the argument for this paradox is: if you know what you're looking for, inquiry is unnecessary. If you don't know what you're looking for, inquiry is impossible. Therefore, inquiry is either unnecessary or impossible.

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Moore's paradox -

Imagine, you're in a windowless room. It begins to rain outside. You haven't seen a weather report, so you don't know that it's raining. Therefore, you don’t believe that it's raining.

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Moore's paradox -

Named after philosopher G. E. Moore, this paradox rests on the sense that there's a contradiction between asserting a fact (it's raining), and believing the opposite (it isn't raining). This was seen as an absurdity by Moore.

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Moore's paradox -

The term "Moore's paradox" is attributed to Ludwig Wittgenstein (pictured), who considered the paradox as Moore's most important contribution to philosophy. This paradox helped Wittgenstein's later work on the nature of knowledge and certainty.

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Moore's paradox -

In the '50s, Wittgenstein's work helped philosophers develop a new field of philosophically-inspired language study: pragmatics.

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Sorites paradox -

This is also known as the paradox of the heap, which results from a vague predicate. Imagine a single grain of rice, which isn't a heap. Adding one grain of rice to it won't create a heap. The same goes for adding one grain of rice to two grains, or three or four grains.

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Sorites paradox -

In general, the paradox states that one can never create a heap of rice from something that isn't a heap of rice by adding one grain at a time.

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Sorites paradox -

Among modern perspectives of the paradox, one states that we simply haven't gotten around to deciding exactly what a heap is. Another perspective asserts that such predicates are vague, so any attempt to define them is wrong.

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The surprise test -

A teacher announces that there'll be a surprise test sometime during the following week. The students begin to speculate about when it might happen, until one student says there's no reason to worry, because a surprise test is impossible.

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The surprise test -

The student says that the test can't be given on Friday, because by the end of the day on Thursday they must already know about it. Nor can the test be given on Thursday, because, by the end of the day on Wednesday, they would know that the test must be given the next day. And likewise for Wednesday, Tuesday, and Monday.

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The surprise test -

Having not studied for the test, the students are all surprised when it's given on Wednesday. How could this happen? With various versions of this paradox, the hangman being one of them, it concerns a condemned prisoner who is clever, but ultimately overconfident. There's virtually no agreement about how this paradox should be solved.

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The lottery -

You buy a lottery ticket, knowing that the chances of winning are at least 10 million to one. So you are rationally justified in believing that your ticket will lose.

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The lottery -

Likewise, you're justified in believing that your friend's ticket will lose, and so on for each ticket bought by anyone you know, or don’t know.

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The lottery -

But, of course, you know that one ticket will win. So you're justified in believing what you know to be false, that no ticket will win.

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The lottery -

The paradox remains interesting because it raises several issues about the foundations of knowledge representation and uncertain reasoning. For example, the relationships between fallibility, incorrigible belief, and logical consequence.

Sources: (The Independent) (Britannica) 

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