Freethought & Rationalism Archive

Witt · 07-08-2003, 07:25 AM

The barber paradox is resolved by the realization that the barber so described cannot exist.

(the x such that: it shaves all and only those that do not shave themselves) does not exist.

The predicate: it shaves all and only those that do not shave themselves, is contradictory.

x shaves all people that need a shave, implies, x shaves x.
x shaves only those that do not shave themselves, implies, ~(x shaves x).

x shaves all people that need a shave, and, x shaves only those that do not shave themselves ..implies,
(x shaves x) & ~(x shaves x).

By: p -> r .& q -> ~r .->. p & q .-> r & ~r.

(x shaves x) & ~(x shaves x), is a contradiction.

That is to say, it is false that (x shaves all people that need a shave, and, x shaves only those that do not shave themselves) ..for all x's.

i.e. There is no x such that: it shaves all and only those that do not shave themselves.

If there is no x such that.. then there is no unique x such that either.

That is, the unique barber such that it shaves all and only those that do not shave themselves, does not exist.

If there is no barber such that it shaves all and only those that do not shave themselves, then, there cannot be one and only one barber either.

Whatdoyathink?

Witt

jpbrooks · 07-08-2003, 11:46 AM

Quote:

Originally posted by Witt
The barber paradox is resolved by the realization that the barber so described cannot exist. ...

Whatdoyathink?

Witt

I agree. But my usual response has been that the town in which the barber resides cannot exist. Perhaps I shouldn't blame the whole town for the barber's "shortcomings".

John Page · 07-08-2003, 11:47 AM

Hi Witt:

You are assuming the barber gets shaved. Only if this condition is true does the paradox manifest itself.

Cheers, John

Shadowy Man · 07-08-2003, 12:12 PM

I thought the Barber was a woman.

Clutch · 07-08-2003, 12:18 PM

The Barber is not regarded as a proper antinomy, for the very reason you cite.

Quote:

That is, the unique barber such that it shaves all and only those that do not shave themselves, does not exist.

Whatdoyathink?

I think you're right.

Quote:

The proper conclusion to draw is just that there is no such barber... The paradox is simply a proof that no village can contain a man who shaves all and only those men who do not shave themselves.

-- W.V.O. Quine, "Paradox" 1962 (Reprinted as "The Ways of Paradox", 1966)

It's a good thought, which is really what matters. But it's not a new thought. It's the longstanding received view.

John Page · 07-08-2003, 01:20 PM

Quote:

Originally posted by Shadowy Man
I thought the Barber was a woman.

...who shaves her legs.

Shadowy Man · 07-08-2003, 01:56 PM

Quote:

Originally posted by John Page
...who shaves her legs.

How do you know?

fried beef sandwich · 07-10-2003, 01:51 AM

Quote:

Originally posted by Shadowy Man
How do you know?

I think she waxes.

Peter Soderqvist · 07-14-2003, 01:50 AM

The Barber or the Cretan paradox, and other puzzles are paradoxes only at the semantic level, because these paradoxes doesn't exists in the real life, since both these objects known as Cretans, and Barbers are governed by physical laws, not semantics, therefore what Cretans and barbers have done up to date are consistent with physical laws, and for the same reason, the label Cretan or Barber cannot cover all the details about these objects, in the same sense that a map cannot cover all its territory! I have a good quote here from Alfred Korzybski the founder of the Institute of General Semantics, and Richard Dawkins and Albert Einstein with emphasis in bold type by me!!

Quote:

Whatever we may say something is, obviously is not the 'something' on the silent levels. Indeed, as Wittgenstein wrote, 'What can be shown, cannot be said.' In my experience I found that it is practically impossible to convey the differentiation of silent (unspeakable) levels from the verbal without having the reader or the hearer pinch with one hand the finger of the other hand. He would then realize organismally that the first-order psycho-logical direct experiences are not verbal. The simplicity of this statement is misleading, unless we become aware of its implications, as in our living reactions most of us identify in value the two entirely different levels, with often disastrous consequences. Note the sadness of the beautiful passage of Eddington on page. He seems to be unhappy that the silent levels can never be the verbal levels. Is this not an example of unjustified 'maximum expectation' ?

I firmly believe that the consciousness of the differences between these levels of abstractions; i.e., the silent and the verbal levels, is the key and perhaps the first step for the solution of human problems. This belief is based on my own observations, and studies of the endless observations of other investigators.

There is a tremendous difference between 'thinking' in verbal terms, and 'contemplating', inwardly silent, on non-verbal levels, and then searching for the proper structure of language to fit the supposedly discovered structure of the silent processes that modern science tries to find. If we 'think' verbally, we act as biased observers and project onto the silent levels the structure of the language we use, and so remain in our rut of old orientations, making keen, unbiased, observations and creative work well-nigh impossible. In contrast, when we 'think' without words, or in pictures (which involve structure and therefore relations), we may discover new aspects and relations on silent levels, and so may produce important theoretical results in the general search for a similarity of structure between the two levels, silent and verbal. Practically all important advances are made that way. http://www.esgs.org/uk/art/ak2.htm

Richard Dawkins Charles Simonyi Professor In the Public Understanding of Science Oxford University, Oxford, England From his book The Selfish Gene, Chapter 2 the Replicators page 18: Should we then call the original replicator molecules "living"? Who cares? I might say to you " Darwin was the greatest man who has ever lived", and you might say No, Newton was, but I hope we would not prolong the argument! The point is that no conclusion of substance would be affected whichever way our argument was resolved. The facts of the lives and achievement of Newton, and Darwin remain totally unchanged whether we label them great or not.

Similarly, the story of the replicator molecules probably happened something like the way I am telling it, regardless of whether we choose to call them "living". Human suffering has been caused because too many of us cannot grasp that words are only tools for our use, and that the mere presence in the dictionary of a word like "living" does not mean, it necessarily has to refer to something definite in the real world. Whether we call the early replicators living or not, they were the ancestors of life; they were our founding fathers

Living or non-living?
Were these early self-replicating molecules living or non-living? Dawkins: that's an idle question. 'No conclusion of substance would be affected by whichever way our argument was resolved.'
http://www.mdx.ac.uk/www/psychology/...kins.htm#sect5

Quotations by Albert Einstein
These thoughts did not come in any verbal formulation. I rarely think in words at all. A thought comes, and I may try to express it in words afterward. Quoted in H Eves Mathematical Circles Adieu (Boston 1977). http://www-groups.dcs.st-and.ac.uk/~.../Einstein.html

07-08-2003, 07:25 AM	#1
Witt Banned Join Date: May 2003 Location: Toronto Canada Posts: 1,263	The Barber Paradox Resolved The barber paradox is resolved by the realization that the barber so described cannot exist. (the x such that: it shaves all and only those that do not shave themselves) does not exist. The predicate: it shaves all and only those that do not shave themselves, is contradictory. x shaves all people that need a shave, implies, x shaves x. x shaves only those that do not shave themselves, implies, ~(x shaves x). x shaves all people that need a shave, and, x shaves only those that do not shave themselves ..implies, (x shaves x) & ~(x shaves x). By: p -> r .& q -> ~r .->. p & q .-> r & ~r. (x shaves x) & ~(x shaves x), is a contradiction. That is to say, it is false that (x shaves all people that need a shave, and, x shaves only those that do not shave themselves) ..for all x's. i.e. There is no x such that: it shaves all and only those that do not shave themselves. If there is no x such that.. then there is no unique x such that either. That is, the unique barber such that it shaves all and only those that do not shave themselves, does not exist. If there is no barber such that it shaves all and only those that do not shave themselves, then, there cannot be one and only one barber either. Whatdoyathink? Witt

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07-08-2003, 11:47 AM	#3
John Page Veteran Member Join Date: May 2001 Location: US Posts: 5,495	Hi Witt: You are assuming the barber gets shaved. Only if this condition is true does the paradox manifest itself. Cheers, John

07-08-2003, 12:12 PM	#4
Shadowy Man Veteran Member Join Date: Jun 2002 Location: A Shadowy Planet Posts: 7,585	I thought the Barber was a woman.

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