Galileo’s 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.

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