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PostPosted: Wed May 07, 2003 1:29 pm 
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Sgt Fluffy
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hey i was wondering if anyone has any descent paradoxes, i was searching for some but couldn't find any good ones.

just ones that make you think?

thanks

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PostPosted: Wed May 07, 2003 9:54 pm 
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Hi Greekboy,

Here is a couple you might find interesting.

The tragedy of life is what dies inside a man while he lives. ~ Albert Schweitzer

All men die; few men ever really live. William Wallace (Braveheart)

" Lionheart
~


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PostPosted: Thu May 08, 2003 5:10 am 
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Sgt Fluffy
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hmmmm yes there good, but arent they more like "ambigious". when i say paradox i mean like this one:

"a barber shaves all the people in the town who do not shave themselves,

he does not shave the people that do shave themselves.

Is the barber shaved or does he have a bear?"

thanx anyway though

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It pays to be obvious, especially if you have a reputation for subtlety.
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PostPosted: Thu May 08, 2003 7:32 am 
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Perhaps he had a dancing bear!

Henry


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PostPosted: Thu May 08, 2003 8:32 am 
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Sgt Fluffy
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ahhhh sorry, its ment to be "is he shaved or does he have a beard"
sory bout that

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PostPosted: Fri May 09, 2003 3:30 am 
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Russell's paradox is the most famous of the logical or set-theoretical paradoxes. The paradox arises within naive set theory by considering the set of all sets that are not members of themselves. Such a set appears to be a member of itself if and only if it is not a member of itself, hence the paradox.

Some sets, such as the set of all teacups, are not members of themselves. Other sets, such as the set of all non-teacups, are members of themselves. Call the set of all sets that are not members of themselves "R." If R is a member of itself, then by definition it must not be a member of itself. Similarly, if R is not a member of itself, then by definition it must be a member of itself.

Discovered by Bertrand Russell in 1901, the paradox has prompted much work in logic, set theory and the philosophy and foundations of mathematics.

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The significance of Russell's paradox can be seen once it is realized that, using classical logic, all sentences follow from a contradiction. For example, assuming both P and ~P, any arbitrary proposition, Q, can be proved as follows: from P we obtain P Q by the rule of Addition; then from P Q and ~P we obtain Q by the rule of Disjunctive Syllogism. Because of this, and because set theory underlies all branches of mathematics, many people began to worry that, if set theory was inconsistent, no mathematical proof could be trusted completely.

Russell's paradox ultimately stems from the idea that any coherent condition may be used to determine a set. As a result, most attempts at resolving the paradox have concentrated on various ways of restricting the principles governing set existence found within naive set theory, particularly the so-called Comprehension (or Abstraction) axiom. This axiom in effect states that any propositional function, P(x), containing x as a free variable can be used to determine a set. In other words, corresponding to every propositional function, P(x), there will exist a set whose members are exactly those things, x, that have property P. It is now generally, although not universally, agreed that such an axiom must either be abandoned or modified

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PostPosted: Fri May 09, 2003 3:31 am 
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Sgt Fluffy
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The sorites paradox is the name given to a class of paradoxical arguments, also known as little-by-little arguments, which arise as a result of the indeterminacy surrounding limits of application of the predicates involved. For example the concept of a heap appears to lack sharp boundaries and, as a consequence of the subsequent indeterminacy surrounding the extension of the predicate ‘is a heap’, no one grain of wheat can be identified as making the difference between being a heap and not being a heap. Given then that one grain of wheat does not make a heap, it would seem to follow that two do not, thus three do not, and so on. In the end it would appear that no amount of wheat can make a heap. We are faced with paradox since from apparently true premises by seemingly uncontroversial reasoning we arrive at an apparently false conclusion.
This phenomenon at the heart of the paradoxes is now recognised as the phenomenon of vagueness. Once identified, vagueness can be seen to be a feature of syntactic categories other than predicates, nonetheless one speaks primarily of the soriticality of predicates. Names, adjectives, adverbs and so on are only susceptible to paradoxical sorites reasoning in a derivative sense.

Sorites arguments of the paradoxical form are to be distinguished from multi-premise syllogisms (polysyllogisms) which are sometimes also referred to as sorites arguments. Whilst both polysyllogisms and sorites paradoxes are chain-arguments, the former need not be paradoxical in nature and the latter need not be syllogistic in form.


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PostPosted: Fri May 09, 2003 9:35 am 
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Greekboy,

Whoa…did you write this treatise on paradoxes?

I’m sorry you were disenchanted with my selection of paradoxes. I’m sure I could have found some better suited ones had I not been in such a haste to retire the day. That’s what happens at 2 am, what may seem lucid in the wee hours can become a vapour at noon. However your retort did raise an eyebrow!
Actually I’m not sure what you imply by ambiguous? While a paradox may seem self-contradictory or absurd, it can also make a reflective statement, whereas an ambiguous statement will be vague or have a double meaning.
I would be interested to know what you see in these two quotes that would suggest to you that they are ambiguous?

“ Lionheart
~

The tragedy of life is what dies inside a man while he lives. ~ Albert Schweitzer

All men die; few men ever really live. William Wallace (Braveheart)


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PostPosted: Fri May 09, 2003 11:05 am 
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Sgt Fluffy
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na, i wasn't disenhearted at all, thanx for contributing them, they were interesting to hear.

Those paradoxes.... we were presented with in a small philosophy course which i partake in.... so i did some research on the net and i got myself slightly more detailed explanations. But yea i love paradoxes.

hmmmm yes i suppose amgiguous isn't the correct word to use, the word.... is more like.... hmmm, i wouldn't actually know it, its kinda like a word that has a metaphorical message....that makes sense, but the in the literal sense the word does not make sense. Sorry, i must have misread the quotations, sincere apologies. There nice quotes aswell

however, speaking of paradoxes however.... you wouldn't happen to know of any would you?

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PostPosted: Fri May 09, 2003 10:29 pm 
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Greekboy,

Thank you for the apology although none was required. I was merely trying to spark some discourse on those quotes. I think you are right when you say they are to some degree metaphorical, and yes I would agree that out of context they don’t make sense.
Nonetheless I don’t want to distract from your original intentions to find some interesting paradoxes. I must warn you it is almost 2 am once again and I’ll try a couple more which at the moment seem relevant, however I may have to eat my words tomorrow.

Great is truth, but still greater, from a practical point of view, is silence about truth.
Aldous Huxley

I believe that unarmed truth and unconditional love will have the final word in reality. That is why right, temporarily defeated, is stronger than evil triumphant.
Martin Luther King Jr.

“ Lionheart
~

Until lions have their historians, tales of the hunt shall always glorify the hunter.
African proverb


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PostPosted: Sat May 10, 2003 4:08 am 
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Sgt Fluffy
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woah, cool quotes. I like the first one, although i'm not sure that i understand it entirely. The secound ones cool aswell, i love martin luther, he has an interesting way with words, and an interesting way of conveying things to the people.

anyways i shall leave you on a paradox type quote, although i'm not entirely sure what it is

"the boy in the mirror blinked...with both eyes"

do you understand it? i find it quite interesting...made me feel stupid once i understood it.

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PostPosted: Sat May 10, 2003 7:17 am 
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what does paradox actually mean?


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PostPosted: Sat May 10, 2003 9:58 am 
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Sgt Fluffy
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aha well....

PARADOX:

1.A seemingly contradictory statement that may nonetheless be true: the paradox that standing is more tiring than walking. 2.
One exhibiting inexplicable or contradictory aspects: “The silence of midnight, to speak truly, though apparently a paradox, rung in my ears” (Mary Shelley).
3.An assertion that is essentially self-contradictory, though based on a valid deduction from acceptable premises.
4.A statement contrary to received opinion.

http://dictionary.reference.com/search?q=paradox


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PostPosted: Sat May 10, 2003 10:34 am 
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GB,

I like your quote >>"the boy in the mirror blinked...with both eyes"<<. I could be totally off the wall but does it have anything to do with his reflection in the mirror?

>> Great is truth, but still greater, from a practical point of view, is silence about truth.<<

Speaking for myself of course, I think the quote is implying that it is better to allow a certain amount of meditation on truth, and allow it to become part of ones virtue. Thus instead of just parroting truth, you will be living truth, or in other words out of your own life will flow truth.

Any thoughts?

“ Lionheart
~


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PostPosted: Sat May 10, 2003 10:36 am 
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the_day_walker

>>what does paradox actually mean?<<

I think GB had some pretty good ideas on paradoxes.
The only thing I will add to that is my personal condensed version.

Paradox = Cerebral Enigma…or perhaps a more perplexing thought,
Paradox = Cerebral Enema!

I may write more on this later…depending on the inevitable responses.

“ Lionheart
~


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