Those which admit of
both descriptions are both wholes and totals. These are the things
whose nature remains the same after transposition, but whose form does
not, e.g. wax or a coat; they are called both wholes and totals; for
they have both characteristics. Water and all liquids and number are
called totals, but 'the whole number' or 'the whole water' one does
not speak of, except by an extension of meaning. To things, to which
qua one the term 'total' is applied, the term 'all' is applied when
they are treated as separate; 'this total number,' 'all these units.'
27
It is not any chance quantitative thing that can be said to be
'mutilated'; it must be a whole as well as divisible. For not only
is two not 'mutilated' if one of the two ones is taken away (for the
part removed by mutilation is never equal to the remainder), but in
general no number is thus mutilated; for it is also necessary that the
essence remain; if a cup is mutilated, it must still be a cup; but the
number is no longer the same. Further, even if things consist of
unlike parts, not even these things can all be said to be mutilated,
for in a sense a number has unlike parts (e.g. two and three) as
well as like; but in general of the things to which their position
makes no difference, e.g. water or fire, none can be mutilated; to
be mutilated, things must be such as in virtue of their essence have a
certain position. Again, they must be continuous; for a musical
scale consists of unlike parts and has position, but cannot become
mutilated.
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