Magnitude and Measure
Unfortunately, we often fail to draw the distinction firmly, and our usage is confused. Even Aristotle defines time as the (arithmos), positive whole number, of change when he should have said it was the (metron), measure. In ordinary usage the words ‘quantity’ and ‘magnitude’ are ambiguous. Although we sometimes use ‘quantity’ as an abstract term for ‘howmuchness’, analogous to ‘quality’ meaning ‘whatsortness’, and sometimes use ‘magnitude’ to indicate the kind of ‘How much?’ we are asking about, whether it is expense, weight, or area, etc., we often also use them as generic terms for that of which the ‘How
much?’ question is being asked. A recipe may tell us to take a quantity of flour, much as a pollster may be told to question a number of voters. Astronomers describe stars as being of a certain magnitude, and we may say it was the magnitude of the current that caused the fire. The confusion is due, in part, to the ways in which ‘How much?’ questions and answers differ from ‘How many?’ ones; and the argument of this chapter will show how our usage needs to be refined. For the present I need only to fix on generic terms, such as ‘amount’, ‘chunk’, ‘dollop’. In contrast to the discrete ‘individuals’, ‘members’ and ‘elements’ of set theory, I shall use the words ‘portion’ and ‘extension’: I shall use the word ‘portion’ generally and mereologically of anything about which, in respect of some magnitude or other, the question ‘How much?’ can be asked and some quantitative answer given, and ‘extension’ for those portions which can form unseparated wholes.