Leibniz’s Two Universe Experiment

In Letter 3: §5 of Leibniz’s correspondence with Clarke, the German philosopher gives the example of two universes which are equal in every fashion but one: spatio-temporal location.  Universe B is the reflection of Universe A around the y-axis such that all that was “east” in A is “west” in B.  If relationalism is true, then these two universes are “absolutely indiscernible” (completely equal) because space is, by definition, the span of the actual and possible relationships between objects, and the reflection did not affect these relationships.  So, any potential universe C which retains A’s relationships (C = A shifted five miles north, C = A ten years farther back, etc.) is the same as A.  Indeed, it is silly to think of C in relation to A because that would require an absolute “coordinate axis” for comparison, and that is impossible.  All spatio-temporal positions are relative.

According to absolutism, space and time exist independently of all objects and all possible relationships among objects.  Spatio-temporal positions are absolute, not relative.  Since Object 1 occupies position (5, 0) in Universe A and (-5, 0) in Universe B, the two universes are separate and distinct.

Leibniz believes that absolutism is “chimerical,” or fanciful, because it violates the principle of sufficient reason (PSR).  This principle postulates that all physical phenomena have causes, and any choice that an individual makes has a reason behind it.  Even God must have a reason for everything which He does.  PSR is metaphysical, not epistemic; the cause of an event may be impossible for us to discern, but there is one nonetheless.  This principle requires the principle of the identity of indiscernibles (PII), which postulates that there cannot be two objects which are absolutely identical.  If there were, God would not have had a reason to place the two objects in their respective positions, and thus He would have violated the PSR.  PII is a metaphysical, not an epistemological claim, because the two objects could differ in a way that our senses cannot discern.  Differences in spatio-temporal location are trivial.  If Object 1, which performs function f, is in position x during time s, and Object 2, which also performs function f, is in position y during time t, they are different in name only.  God would have no reason to switch them and indeed had no reason to put them in their respective positions in the first place.  These objects are indiscernible and violate PSR.

If PSR and PII are true, then there is no difference between the Universes A and B from the first paragraph.  Since the two universes perform the exact same functions, God has no reason to choose one or the other; if he did so, he would violate PSR.  God must have chosen a particular universe, however, because we exist.  Therefore, absolutism is false.  It imagines an impossible set of circumstances.  God could only choose between possible worlds which are qualitatively distinct from one another.

Leibniz’s refutation of absolutism holds true within the constructs of both relationalism and absolutism because he has disproved that the basic principle of absolutism – that objective positions in space and time have meaning.  Clarke thus has to tweak the PSR and say that God’s will is reason enough for His actions.  (Leibniz would respond that God would never coast on his reputation in this manner.)  One could also deny the PSR or deny that God plays an active role in the world.  The implications of this argument, however, must have been too unpleasant for Clarke to consider.

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