"The poet only asks to get his head into the heavens. It is the logician who seeks to get the heavens into his head. And it is his head that splits." G.K. Chesterton

Saturday, April 20, 2013

Much Ado About Nothing

Suppose we have two physical vessels of varying size, U and u, and suppose further that they're both empty (in the usual sense - we've run out of wine). Should we consider the degree of their emptiness as the same (i.e. even talk of such degrees is nonsense!), or can we say in a meaningful way that their degrees of emptiness differ?

Consider two urns in a marble shop. The shopkeeper labelled them in the following way - urn 1 holds only (and can only hold) white marbles, whereas urn 2 can hold both white and black marbles.

Now consider a new assistant that has just been offered an apprenticeship in the shop of his dreams (he loves playing marbles), and is not as yet familiar with the arcana of the labeling system, i.e. he hasn't as yet been told by the shopkeeper what the restrictions on the contents of the urns are.

Now consider the statements 'urn 1 contains no white marbles' and 'urn 2 contains no white marbles' - they entail different things, depending who is exposed to that information - the shopkeeper or the assistant. In particular, to the shopkeeper it means that 'urn 1 is empty'.

On a more technical side, we can substitute the terms 'has no white marbles' and 'is empty' interchangeably salva veritate 
in the context of urn 1 (charity permitted, for naturally one could generate oddly sounding sentences). This cannot however be done in the context of urn 2.

The above argument, and exercise in intuition do not exactly express the same ideas, but overlap on what is essentially the general idea.

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