If
a and b have all their properties in common, then they
are one and the same thing.
In symbols:
(x)
(y) (F) ((F) x ≡ F (y) ⊃.
x = y)
The
basic question is:
Imagine
two steel balls which have all their properties in common. Could they
still be two?
Intuitively,
most people (I think) would say 'yes'. It doesn't seem inconceivable
prior to modal philosophising.
For
a start, wouldn’t the balls still be spatially or temporally
separate? If that is the case, then surely they wouldn't have all
their properties in common. (That's if you accept spatial and
temporal properties, which many philosophers do.)
Now
we go deeper into this thought experiment.
One
could say (I suppose) that if the balls were suddenly frozen in
space, then their positions would be different. Hence they'd have
different spatial properties. However, what if the balls will never
be frozen in space and never have been frozen in space? (Is that a
hypothetical scenario about a hypothetical scenario?)
As
they are now, and in five minutes, etc., the balls are constantly on
the move relative to one another. Thus they have all their spatial
(as well as temporal) properties in common. And because they're both
in an empty world, there can be no relational properties (care-of
other objects, conditions, events, etc.). Any relational properties a
has relative to b, b has relative to a. Thus
they have all their properties in common.
This,
then, appears to break Leibniz’s law in that the balls are
indiscernible; though not identical!
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