popper-logic-scientific-discovery

appendix *xi 465
motion. 2 It disproves the Aristotelian supposition that the natural
velocity of a heavier body is greater than that of a lighter body. ‘If
we take two moving bodies’, Galileo’s spokesman argues, ‘such that
their natural velocities are unequal, it is manifest that if we join them
together, the slower and the faster one, then the latter will be partly
retarded by the slower one, and the slower partly sped up by the
faster one’. Thus ‘if a big stone moves, for example, with a velocity
of eight steps and a smaller one with a velocity of four, then, after
being joined together, the composite system will move with a
velocity of less than eight steps. But the two stones joined together
make a stone bigger than the first one which moved with a velocity
of eight steps. Thus the composite body (although bigger than the first alone) will
nevertheless move more slowly than the first alone; which is contrary to your
supposition.’ 3 And since this Aristotelian supposition was the one
from which the argument started, it is now refuted: it is shown to be
absurd.
I see in Galileo’s imaginary experiment a perfect model for the best
use of imaginary experiments. It is the critical use. I do not wish to
suggest, however, that there is no other way of using them. There
is, especially, a heuristic use which is very valuable. But there are less
valuable uses also.
An old example of what I call the heuristic use of imaginary experiments
is one that forms the heuristic basis of atomism. We imagine that
we take a piece of gold, or some other substance, and cut it into smaller
and smaller parts ‘until we arrive at parts so small that they cannot be
any longer subdivided’: a thought experiment used in order to explain
‘indivisible atoms’. Heuristic imaginary experiments have become particularly
important in thermodynamics (Carnot’s cycle); and they have
lately become somewhat fashionable owing to their use in relativity
and in quantum theory. One of the best examples of this kind is
Einstein’s experiment of the accelerated lift: it illustrates the local
equivalence of acceleration and gravity, and it suggests that light rays in
2 Galileo himself proudly says of his argument (he puts the words into the mouth of
Simplicio): ‘In truth, your argument has proceeded exceedingly well.’ Cf. Dialogues Concerning
Two New Sciences, 1638, First Day, p. 109 (p. 66 of vol. xiii, 1855, of the Opere Complete;
pp. 64 and 62 of the English edition of Crew and Salvio, 1914).
3 Op. cit., p. 107 (1638); p. 65 (1855); p. 63 (1914).