giovedì 28 novembre 2013

The Continuum Hypothesis

On semantic indeterminacy and its consequences, an argument has been advanced. We shall call it the continuum hypothesis, and this is how it goes:

Continuum Hypothesis: any two terms' reference is indeterminate with respect to each other, insofar as you can always imagine a continuous transformation of the one reference into the other, with no neat line between the point where the two references switch.

An example: take "table" and "chair". One thinks: that's two very different types of objects, and the terms refer to different things. The continuum hypothesis tells us: look, you can imagine a discontinuous (there may be holes opening or closing) transformation from each table into every chair. Where does the division line lie?
One who accepts this argument would be led perhaps to a "meaning = use" theory: a table is a table as far as it is used as a table, so no wonder, there may be a table who is also a chair, and the continuum hypothesis is no threat.

Now, take "human" and "toothpick". There's no human who can be `used' as a toothpick, as far as I know, even if of course you may get another human to clean your teeth with their nails, for example, but I don't think it's the same thing. Similarly, there's no toothpick who can be `used' as human, whatever this means. There may be some delusional who takes care of his speaking toothpick as if it were a child, but I don't think it's the same thing.
Here the theory of meaning as use tells us nothing about the two extremes of this continuum. They seem to be totally apart.
Can we imagine a continuous transformation of a tootpick into a human, and vice versa? Well, at a purely graphical level of course we can. But there's a whole line in between where the `thing' we have is neither a toothpick, as it would be too big and not woody enough, and neither a human, for it would be too woody and not alive (or human) enough. While in the chair-table continuum we have a blurry line where the object is both a table and a chair, or at least may play the role of both in ordinary discourse, here we have none.
There's no continuous transformation here; there's a neat cut at least on the human side, but most likely also on the toothpick side of the deformation line; and, we may argue, that cut is very close to the extremes of the line.

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