Quantification Quotes
Quantification, like surgery, is an excellent thing in the right place, but a very bad topic for obsession. Unless you know just what you are counting--unless you are sure that the things counted are standard units--and unless you understand what is proved by results of your counting, quantifying provide you only with the outward show of science, a mirage, never the oasis.
Mary Midgley
In summary, then, the set theoretic 'needs' of physics are surprisingly similar to the set theoretic needs of pure logic. Both disciplines need some set theory to function at all. Both disciplines can 'live' - but live badly - on the meager diet of only predicative sets. Both can live extremely happily on the rich diet of impredicative sets. Insofar, then, as the indispensability of quantification over sets is any argument for their existence - and we will discuss why it is in the next section - we may say that it is a strong argument for the existence of at least predicative sets, and a pretty strong, but not as strong, argument for the existence of impredicative sets.
Hilary Putnam
If you know a thing only qualitatively, you know it no more than vaguely. If you know it quantitatively-grasping some numerical measure that distinguishes it from an infinite number of other possibilities-you are beginning to know it deeply. You comprehend some of its beauty and you gain access to its power in the understanding it provides. Being afraid of quantification is tantamount to disenfranchising yourself, giving up on one of the most potent prospects for understanding and changing the world.
Carl Sagan
