Math Is Fun Forum

RealEstateBroker

Member

Registered: 2006-06-01

Posts: 45

Faulty Logic?

A story was posted on another site (which I participate in under the user name "SK-B") which purported to illustrate an example of fallacious, circular reasoning. However, in reading the story, it seems to me that the logic did yield a sound and correct results, even though I can see why it is being called faulty logic.

Could faulty in this example lead to a sound conclusion? When you read it, I am sure that you will agree that the conclusion is correct even though it was derived through circular reasoning. I wonder if anyone has any insights about this?

Here is a link to the story: 
http://www.ibrattleboro.com/article.php … 9#comments produces http://www.ibrattleboro.com/article.php/20070204042418539#comments

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Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Faulty Logic?

Our natural thought process is so intuitive, that it can be actually hard to find out how we think.

First thing is the realization that the spot is somehow special.  The next question is why is it special.  What gets rid of snow?  The answers can be along the lines of: it melted, it fell there and then moved, it never fell there in the first place.  There may be other possibilities, but off hand I can't think of any.  Then one by one we can eliminate them by a process which is known as "being reasonable".  We arrive at only one valid solution, that of being a car.

But it all happens so fast we don't even realize we did it.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Re: Faulty Logic?

I think it is past experience that teaches us. I can easily imagine giving the answer to a child who would then say "oh, yeah!", and they would then know for life what causes those shapes.

But there is no circular argument, because the shape is the deciding factor. Unless you say "the shape matches a car and a car matches the shape is circular" ... !

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Dross

Member

Registered: 2006-08-24

Posts: 325

Re: Faulty Logic?

A correct conclusion is absolutely no garuntee of correct reasoning. A logical argument can be broken down into premises, and conclusions. A valid logical argument is one where the conclusions neccessarily follow from the premises, and a sound logical argument is a valid argument whose premises are true.
For a blatant example of an invalid argument with a correct conclusion, I put to you that;

1) All elephants are larger than atoms.
2) All planets in our solar system are larger than elephants.

3) Therefore my username is "Dross".

Both of the premises, as well as the conclusion, are blatantly true, though the argument is invalid.

Note that in an argument of the above form, the conclusion is derived from the premise.

A circular argument is one in which the conclusion is, indeed, derived from one or more premise, but one (or more) of those premises is derived from the conclusion. For example:

4) The sky is blue and the ocean reflects this blue light, therefore the ocean is blue.
5) The ocean is blue and the sky reflects this blue light, therefore the sky is blue.

(note this argument does not try to argue that the sky or ocean are blue - it tries to argue why they are blue)

So, looking at the argument made in the above post, the man seems to be saying:

6) There is a rectangular shape in the snow, therefore there was a car there.
7) A car was there, therefore there is a rectangular shape in the snow.

This argument is plainly circular.

However, this circularity can be resolved by simply changing the second argument to something like "I can see a hole in the snow, therefore there is a hole in the snow".

All that's happened is the good doctor has "tricked" the man into making the second statement, which he didn't really mean to - he's making the man state that the conclusion that there is a hole in the snow is derived from the fact that there was a car there, when really we don't need this knowlege (that the car was there) to derive that there is a hole in the snow.

There is, however, the fact that argument (6) above is not valid, since the shape could have been caused by, say, an oddly shaped scattering of grit/salt, or a malicious child wanting to fool someone into a circular argument

Last edited by Dross (2007-02-06 22:44:18)

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