Thursday, April 14, 2005

eloquence and the law of the excluded middle

The law of the excluded middle started out as:

No 2 contrasting propositions can be true. One of them is false and there is no third or middle judgment

Hegel qualified this subsequently, stating that

No 2 contrasting propositions can be true if one of them has sufficient ground (emphasis mine). One of them is false and there is no third or middle judgment.

I came to realise last night that his qualification was, in strict logic terms, superfluous. A proposition (in logic, as opposed to in layman English) must have sufficient ground. A proposition must be what lawyers might call “sufficient in itself” or “legally perfect”. But Hegel was dealing primarily with psychology in explaining philosophy, perhaps that is why he was motivated to add the qualification so as to bring it to the attention of the uninititated

Consider the following propositions (which I was discussing with shing last night):

A is more eloquent than B.
B is more eloquent than A.

Shing said, correctly, that on the face both of this are true. That is because “eloquence” has many connotations. For example, it could be said that Winston Churchill was an eloquent speaker. This is understood to have its meaning in the context of the language of the speaker (English). Similiarly, no one would dispute the notion that Jiang Jieshi was an eloquent Chinese speaker.

So if I say that Winston Churchill more eloquent than Jiang Jieshi, this is true regarding in English.
If she says Jiang is more eloquent than Churchill in Chinese, that is true regarding Chinese.

So shing said, the law would only hold if we qualify that statement. Which by implication means the law doesn’t hold if we don’t.

This is correct on the surface.

But it needn’t be. This is because the propositions themselves are not really propositions at all – they undoubtedly do not pass the Hegelian “sufficient grounds” test.

However, one can argue that the “sufficient grounds” test is passed by impliedly, or constructively. Generally people understand eloquence to be measured by the medium of conveyance of that eloquence i.e. the language spoken by the speaker.

Which means the above propositions aren’t really contrasting in that sense. They are simply propositions made in different contexts. Without providing that context i.e. qualifying the statement (explicitly or impliedly) they are not really propositions at all.

Tada! The law still holds. wicked

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