logical objection to heavier objects falling faster
Galileo makes a logical objection to a proposition
from Aristotle’s physics: that heavier objects fall faster than lighter objects.
Galileo’s logical objection to this proposition is that it has contradictory
entailments and so cannot possibly be true.
Suppose that a heavier object, O1, is joined with a
lighter object, O2. The result is an even heavier object. So the Aristotelian
proposition entails that the combined object will fall faster than either O1 or
O2. This is one entailment. However, if one combines a heavier object with a
lighter object, the lighter object will be disposed to fall at a slower speed
than the heavier object, according to Aristotle’s physics, in which case the
lighter object should have the effect of reducing the falling speed of the
heavier object and hence of the combined object. Therefore the Aristotelian
proposition entails that the combined object will fall at a slower speed than
O1 but a faster speed than O2. This is another entailment. But these two
entailments are inconsistent.