Sunday, March 1, 2009

Cube Staircase

     Sometimes, when arguing a position, people will use a string of points, where-in each point supports the one following it, but does not end up supporting the subsequent point after that.  If you look at these arguments as a series of short “Because A, then B” statements, then each one of them as an individual is sound, but the argument as a whole is not.

    The reason it’s not sounds is because, although each points supports the one after it, it does so in such a way that doesn’t support the following points.   Here’s an example:

I’ve heard that this vacuum is powerful enough to pick up a chair; so, this vacuum sucks really hard.  If any product sucks really hard, you shouldn’t buy it.  So, you shouldn’t buy this vacuum.

    It’s true that a vacuum is powerful enough to suck up a chair, that it sucks really hard.  And it’s also true that if a product sucks really hard, that you shouldn’t buy it.  However, these aren’t true using the same sense of the phrase “sucks really hard.”  In this example, the conflation is really easy to spot, but people often sneak these into their arguments in a more subtle way.

     Here’s another way to think of it: imagine a staircase, made out of cubes.  Each cube is placed off-center from the cube below it, but in such away that its weight will still be supported and it wont fall off.


     Now imagine that a few more blocks were added on, and each block supports the block above it in the same way, and if you look specifically at any two sequential blocks, they will seem to support be supported.  However, each block will support two-or-more blocks above itself, and over-all the structure is unsound, and would fall down.

CubeStaircase2      Arguments work in the same way.  Each piece of evidence given needs to support the point which relies on it, but also every piece which relies on that one and so on. 

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