As noted in Chapter 1, many words and phrases are vague in the way that 'bald' is vague. Examples include 'tall', 'orange', 'heap of sand' (i.e. we cannot draw a precise boundary between tall and not-tall, between orange and red, and cannot say exactly how many grains of sand you need to have a heap). These words pertain to a certain one-dimensional quality, such as height, region of the colour spectrum (which proceeds gradually from red through orange, yellow, green, blue and violet), or amount of sand.

These sorts of words seldom present problems for actual argument reconstruction and assessment.3 More important for critical reasoning are forms of vagueness which do not pertain simply to one-dimensional qualities like height. Indeed, many of the most rhetorically powerful or emotionally provocative words in public (and private) discourse are vague in this way. Consider:

• conservative

• sovereignty

• responsibility

As pointed out in Chapter 1, we often have the feeling that these things are bad, or that they are good, without any precise idea of what we mean by them. What they signify is typically a whole group or cluster of things which are not unified in any exact way.

Let us take 'conservative' (in the political sense) as our example. There are various attributes often associated with someone's being 'conservative':

3 But they do cause trouble for logic. Consider the term 'sand dune1. There is no exact rule for how much sand is needed to constitute a sand dune, but here is one proposition about sand dunes that seems undeniable: If X is a sand dune and one grain of sand is removed from X, then X is still a sand dune. But now suppose that X is a sand dune. If we remove one grain of sand from X, then X is still a sand dune. But then if we remove one grain of sand from this, we still have a sand dune. And so on. But then eventually we run out of sand, so we have no sand dune. So at some point, X was a sand dune consisting of n grains of sand for some number n, such that X ceased to be a sand dune, upon the removal of one grain of sand. But that seems absurd; we cannot imagine a sand dune such that removing one grain of sand destroys its status as a sand dune. So we seem to have a contradiction. This paradox - Paradox of the Heap or Sorites paradox - was puzzled over by the ancient Greeks, and there is still no consensus as to how to avoid the apparent contradiction.

The practice of argument reconstruction


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