Monday, December 13, 2010

Why does English use the word "Bollocks"?

Because Philosophy was already taken.

By the end of The Trolley Problem, I was still unsure if I am too intellectually limited to appreciate my intellectual limitations, or Philosophy is single mindedly inclined to make heavy going of a smooth sea.

The latest entry,Paradoxical Truth in The Stone: a forum for contemporary philosophers on issues both timely and timeless is no help in solving that conundrum.
Professor Greene is lecturing. Down the hall, her arch-rival, Professor Browne, is also lecturing. Professor Greene is holding forth at length about how absurd Professor Browne’s ideas are. She believes Professor Browne to be lecturing in Room 33. So to emphasize her point, she writes on the blackboard the single sentence:

Everything written on the board in Room 33 is false.

But Professor Greene has made a mistake. She, herself, is in Room 33. So is what she has written on the board true or false? If it’s true, then since it itself is written on the board, it’s false. If it’s false, then since it is the only thing written on the board, it’s true. Either way, it’s both true and false.

Philosophers and logicians love paradoxes, and this is one — one of the many versions of what is usually called the Liar Paradox.
Bollocks.

This isn't a paradox, it is a false dichotomy. Stating that "either way, it is true or false" excludes a third option: the statement is meaningless.

The obvious, but unmentioned, problem is self-reference.

If Prof Greene is in Room 34, "Everything written on the board in Room 33 is false" may well be guilty of gross generalization, but it is a sensible statement amenable to a decision one way or another.

Finding herself in Room 33, though, does not a paradox, or even a mild puzzle, make. The statement has suddenly become self referential, which has no more yields a true or false than dividing by zero yields a number.

One of the comments in the thread poses this variation of the Liar's Paradox:
There is a barber in a certain town who shaves all of the men who don't shave themselves. Does he shave himself?
Yes. No. Contradiction, paradox.

According to the article, hewing to the tradition of false dichotomies, [When] you meet a paradox, you’ve got only two choices. One is to accept that the conclusion, implausible as it may seem, is actually true; the other is to reject the conclusion, and explain what has gone wrong in the argument.

Bollocks.

Take the set of all men in a certain town, which itself consists of two distinct subsets that together comprise all the elements of the superset: those who shave, and those who don't.

One of the members of those two sets -- it doesn't matter which -- is the barber. Now recast the statement, excluding the self reference, and the subsequent question:
There is a barber in a certain town who, except for himself, shaves all the men who don't shave themselves. Does he shave himself?
Without the self reference, instead of an alleged paradox, there is no answer at all, unless "dunno" counts.

So, philosophers, how is it an unanswerable question arrives at paradox through self reference?

5 Comments:

Blogger Harry Eagar said...

Well put.

Semantics do not control facts. The phrase 'I couldn't care less' and the phrase 'I could care less' mean exactly the same to most people in most situations.

'Taint a problem of philosophy.

December 14, 2010 10:20 AM  
Blogger Brit said...

I guess Philosophy just isn't for you two then!

As with the trolley problem, you either find questions of logic and semantics interesting in themselves, or you don't.

The apparent barber paradox could be resolved in a few ways - eg. the phrasing of "all the men who don't shave themselves" does not logically exclude an "and one who does"; or that he doesn't shave at all, or that he goes to another town to shave. (You could make the problem stronger with different phrasing).

The point is to make you think about language and logic...Can't really see why you need to pronounce 'Bollocks' as if these things are a personal affront to your practical good sense!

December 16, 2010 11:21 PM  
Blogger Harry Eagar said...

I took a course in philosophy up to the point where the instructor couldn't explain Zeno's paradox.

Why bother?

Behind the semantic confusion about semantics is the error of Chomsky.

Language is a convention, it does not have any deep structure. You can do anything you want with it. Don't mean a thing.

December 17, 2010 8:25 AM  
Blogger Peter said...

I'm trying to decide whether Skipper's razor-sharp mind sees genuine flaws in the musings of the sages or whether he is just starting his grumpy old man years early. On the one hand, his cantankerousness reminds me of my aging father, but on the other, Dad wouldn't have talked about paradoxes through self-reference, he would have just stomped out of the room and poured himself a drink.

December 19, 2010 4:51 AM  
Blogger Hey Skipper said...

Brit:

I find questions of logic and semantics interesting; I just don't get how this is one of them.

The apparent paradox only gets that way through insisting that a grammatically correct statement must yield a true or false.

Worse, the article completely neglected the problem of self-reference. Try it with a spreadsheet sometime: it don't compute.

As with the trolley problem, I read this thinking that there is something completely obvious they aren't getting, or I'm not.

It isn't clear to me how rephrasing a la Brit can help. If my restatement in terms of set theory is correct, it reveals the apparent paradox as neither true nor false: the paradox simply does not exist.

What am I missing?

January 03, 2011 4:33 PM  

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