The length of a pencil is measured in a straight line from tip to end. This is equal to the length of the region of space occupied by the pencil. The length of a rope is measured along the rope, so that the length does not change much when the rope is coiled or uncoiled, and so unless the rope is straightened out, the length of the rope is not equal to any dimension of the region of space occupied by the rope. The length of a bow is (typically) the length of the string plus three inches. On the other hand, the length of a computer program is something quite different, not measured in length-dimensions, but in units like lines or lines-of-code or characters.
Similar points apply to almost all other predicates. These are a matter of decision rather than discovery. When we extend our language to start talking about pencils, ropes, bows and programs, we also need to decide how all the many predicates that could apply to them are to be extended. Quantifier pluralism requires predicate pluralism.
Working definitions of "quantifier pluralism" and "predicate pluralism"?
ReplyDeleteSimilar points apply when the predicates are applied to fully real things like porcupines (in what state of needles do you measure its dimensions).
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