the title. At least as far as I know, because they may live deceived without knowing it, that's what it is.
But I've decided to resurrect the blog to talk about me. No, no. Not this time. More or less.
not intend to spend pranks. Ah, you did not know it was today ... therefore beware, it is likely that Silvio Berlusconi raise the minimum wage several times over the next few hours.
As I was saying, what claim the title as hyperbolic. In a high school class is not difficult to guess what the teacher told us that the following was not a paradox:
- "All Cretans lie," said a Cretan. However
not told us why it was not a paradox, because he did not remember the solution, and thought it was really complicated:
"I think what was done to resolve it was ... well ... that this predicate part ... or the subject of this part do not have to ... bah, it is the same. "
For this to have some sense remember that a paradox is a proposition which, if verified, it can be deduced that verifies its negation, and vice versa, if not checked, then we can deduce that if verified. I hope I explained well ...
Why think that up there is a paradox? Because we are easily deceived. Because at school we were taught to add, to subtract, multiply and divide, but not to think, to non-injured .
To see this, suppose that the person is more hate in the world and I say "all wise men are white." If you are Caucasian like me, will think ... well yes, my parents are white. But let's assume that Kings are Melchor, Gaspar and Baltasar. Then obviously the statement "all wise men are white" is false. Why? Because "at least one of the Magi is not white." Suffice it to Balthazar, who is black. Oh, how simple it seems. Silly, is common sense ... Perfect
, then start with our seeming paradox:
- "All Cretans lie," said a Cretan.
To demonstrate that it is a paradox, we must prove that if we assume that is true we conclude that it is false, and if we assume that is untrue, we conclude that it is true.
Suppose it is true that "all Cretans lie. "Then, the Cretan who said" all Cretans lie, "was lying. Therefore, it is false that" all Cretans lie "... that is what we wanted to prove.
Suppose it is false that" all Cretans lie. "Then the Cretan who said" all Cretans lie "was telling the truth, so that" all Cretans lie "is true, that's what I wanted to try .
And already? Was a paradox, really? Why the hell I put in italics what I wrote after the last "then"? Obviously, since such a conclusion is invalid. Let's do it:
Suppose it is false that "All Cretans lie." So at least one Cretan who tells the truth. And this does not imply that all Cretans tell the truth (no lie) As with the Magi! And already there is no contradiction.
So if a Cretan says all Cretans lie, we must conclude that it is he who is lying, or is not being clear: what had trouble saying "All Cretans, but me, lie? But this has much to do.
Maybe it is that I was a bit silly, but the only trick he has the solution did not learn until the last course, a math teacher took it for granted that it was obvious that:
The opposite of "all" is "there", right?
words, " not all the wise men are white" is the same as "at least one Wise Man is not white" is not the same as saying "all Magi are not white. " It is not the same!
Note: Wikipedia entry on this subject here.
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