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Topic: Solution: Epimenides paradox (Read 546 times) |
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Johan_Gunardi
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If Epimenides was liar, then the correct statement maybe, "Some of Cretans are liars." It's not a paradox anymore.
Any comment?
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towr
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Re: Solution: Epimenides paradox
« Reply #1 on: Jun 8th, 2007, 1:40pm » |
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If he said "I like pizza", it also wouldn't be a paradox anymore. (Well, maybe a temporal one, but nevermind that).
You don't solve the paradox in the statement by considering instead a different statement; that's just amounts to changing the topic.
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jollytall
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Re: Solution: Epimenides paradox
« Reply #2 on: Jun 9th, 2007, 11:09pm » |
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Johan, you do not mention the original sentence thought to be a paradox. The most common version is "All of Cretans are liars. One of them said so.".
This is only a paradox, if we know PRIOR to the statement that all of Cretans are the same, liars or truth-tellers (usually such is not true, although a very common mistake to put nations into "boxes", with sentences like All the xxxxians are ...).
If we DO NOT have the pre-information, then both the original and your statements worth the same, only mean the opposite:
The original means that the person is a Liar and there are both liars and truth-tellers on the island. (Btw, this loophole in the though-to-be paradox was identified practically at the same time, when this paradox was invented.)
Your statement means that he is a Truth-teller and there are Liars and Truth-teller(s) on the island.
If we DO HAVE this pre-information then the meaning of "Some " starts to matter, whether "Some" can mean "All" or not. With other words does or does not "Some" also mean "Some not".
If "Some" can be "All":
Because of the pre-information "Some" must mean "All", and your statement is the same as the original and IS a paradox.
If "Some" cannot be "All":
This is the only case when your statement is not a paradox, while the original is. I still do not like it, because to me "Some" can mean "All". Also somebody saying to me "Some" and thus also "Some not" on an island where we know everybody is the same, does not seem to be right. Only a liar would say it anyway.
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JiNbOtAk
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Re: Solution: Epimenides paradox
« Reply #3 on: Jun 11th, 2007, 9:37pm » |
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"All generalizations are dangerous, including this one." - Alexandre Dumas
"All generalizations are false, including this one." - Mark Twain
So, are generalizations dangerously false, or falsely dangerous ? 
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