AWE-tisim the Living Breathing Paradox

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Wikiapedia,
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 (cf. kōan, Catuskoti). Typically, 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. It is also used to describe situations that are ironic.

Common themes in paradoxes include:
self-reference, the infinite regress, circular definitions, and confusion between different levels of abstraction.
Patrick Hughes outlines three laws of the paradox:[2]

Self reference - An example is "This statement is false", a form of the Liar paradox. The statement is referring to itself. Another example of self reference is the question of whether the barber shaves himself in the Barber paradox. One more example would be "Is the answer to this question no?" In this case, if you replied no, you would be stating that the answer is not no. If you reply yes, you are stating that it is not no, because you said yes.
Contradiction - "This statement is false"—the statement cannot be false and true at the same time.
Vicious circularity or infinite regress - "This statement is false"—if the statement is true, then the statement is false. In which case, the statement is true, which means the statement is false... Another example of vicious circularity is the following group of statements:
"The statement below is false."
"The statement above is true."
Other paradoxes involve false statements or half-truths and the resulting biased assumptions.

For example, consider a situation in which a father and his son are driving down the road. The car collides with a tree and the father is killed. The boy is rushed to the nearest hospital where he is prepared for emergency surgery. On entering the surgery suite, the surgeon says, "I can't operate on this boy. He's my son."

The apparent paradox is caused by a hasty generalization; if the surgeon is the boy's father, the statement cannot be true. The paradox is resolved if it is revealed that the surgeon is a woman, the boy's mother.

Paradoxes which are not based on a hidden error generally happen at the fringes of context or language, and require extending the context or language to lose their paradoxical quality. Paradoxes that arise from apparently intelligible uses of language are often of interest to logicians and philosophers. This sentence is false is an example of the famous liar paradox: it is a sentence which cannot be consistently interpreted as true or false, because if it is known to be false then it is known that it must be true, and if it is known to be true then it is known that it must be false. Therefore, it can be concluded that it is unknowable. Russell's paradox, which shows that the notion of the set of all those sets that do not contain themselves leads to a contradiction, was instrumental in the development of modern logic and set theory.

Thought experiments can also yield interesting paradoxes. The grandfather paradox, for example, would arise if a time traveler were to kill his own grandfather before his father was conceived, thereby preventing his own birth. This paradox can be resolved by postulating that time travel leads to parallel or bifurcating universes, or that only contradiction-free timelines are stable.

W. V. Quine (1962) distinguished between three classes of paradoxes:

A veridical paradox produces a result that appears absurd but is demonstrated to be true nevertheless. Thus, the paradox of Frederic's birthday in The Pirates of Penzance establishes the surprising fact that a twenty-one-year-old would have had only five birthdays, if he was born on a leap day. Likewise, Arrow's impossibility theorem demonstrates difficulties in mapping voting results to the will of the people.
A falsidical paradox establishes a result that not only appears false but actually is false due to a fallacy in the supposed demonstration. The various invalid mathematical proofs (e.g., that 1 = 2) are classic examples, generally relying on a hidden division by zero. Another example is the inductive form of the Horse paradox, falsely generalizes from true specific statements.
A paradox which is in neither class may be an antinomy, which reaches a self-contradictory result by properly applying accepted ways of reasoning. For example, the Grelling–Nelson paradox points out genuine problems in our understanding of the ideas of truth and description.
A fourth kind has sometimes been described since Quine's work.

A paradox which is both true and false at the same time in the same sense is called a dialetheism. In Western logics it is often assumed, following Aristotle, that no dialetheia exist, but they are sometimes accepted in Eastern traditions[which?] and in paraconsistent logics. An example might be to affirm or deny the statement "John is in the room" when John is standing precisely halfway through the doorway. It is reasonable (by human thinking) to both affirm and deny it ("well, he is, but he isn't"), and it is also reasonable to say that he is neither ("he's halfway in the room, which is neither in nor out"), despite the fact that the statement is to be exclusively proven or disproven.

My step son told me this one the other day. I heard it on "The Cosby Show" many years ago. Interestingly, my step-son's version entailed a general instead of a surgeon which indicated to me that there might have been some movement in gender stereotypes (that people might more readily guess the surgeon could be a woman/mother now than they would have many years ago, causing people to reformulate the puzzle with a general instead).




I would answer no to that question. To me this question is like asking if the room contains John (if X is in Y, then Y contains X, if Y does not contain X, then X is not in Y), and since at least some of John is not contained in the room, the answer must be no. I think it is more of a problem if John is in the room, but someone has chopped his hand off and left that in the hallway. Now is John only those parts of John still attached to the other parts of John? If so John is in the room. But if the detachment does not stop John's hand from being part of John, then John is not contained within the room. This provokes the question "what is John?".

One of my favorites is Monty Hall's Paradox. Almost nobody understands it on the first try and it can be interesting to explain the true answer to people.