In his letter to Henri Basnage de Beauval, Leibniz uses the analogy of the two clocks to explain three different solutions to the mind-body problem, interactionism, occasionalism, and his own view, pre-established harmony.
Two clocks are in perfect synchrony. One clock represents the mind, the other the body. Leibniz suggests three ways to explain this phenomenon:
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The way of influence, representing interactionism – the mind and the body correspond through their direct effects on eachother:
“This is the way with which Mr. Huygens experimented, with results that greatly surprised him. He suspended two pendulums from the same piece of wood. The continued strokes of the pendulums transmitted similar vibrations to the particles of wood, but these vibrations could not continue in their own frequency without interfering with each other, at least when the two pendulums did not beat together. The result, by a kind of miracle, was that even when their strokes had been intentionally disturbed, they came to beat together again, somewhat like two strings tuned to each other.”
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The way of assistance, representing occasionalism – the correspondence between the mind and the body is maintained by constant divine intervention:
“The second way of making two clocks, even poor ones, agree always is to assign a skilled craftsman to them who adjusts them and constantly sets them in agreement.”
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The way of pre-established harmony, representing Leibniz' own view:
“The third way is to construct these two timepieces at the beginning with such skill and accuracy that one can be assured of their subsequent agreement.”
“God has made each of the two substances from the beginning in such a way that though each follows only its own laws which it has received with its being, each agrees throughout with the other, entirely as if they were mutually influenced or as if God were always putting forth his hand, beyond his general concurrence”
The analogy most likely originated not from Leibniz himself, but from Simon Foucher's comments on Leibniz' Système nouveau de la nature.