Earman has notably contributed to debate about the "
hole argument". The hole argument was invented for different purposes by
Albert Einstein late in 1913 as part of his quest for the
general theory of relativity (GTR). It was revived and reformulated in the modern context by John Earman,
John Stachel, and
John D. Norton. The trio of Einstein scholars have sometimes been jokingly referred to as With the GTR, the traditional debate between
absolutism and
relationalism has been shifted to whether or not
spacetime is a substance, since the GTR largely rules out the existence of, e.g., absolute positions. The "hole argument" offered by John Earman is a powerful argument against
manifold substantialism. This is a technical mathematical argument but can be paraphrased as follows: Define a function d as the identity function over all elements over the
manifold M, excepting a small neighbourhood (
topology) H belonging to M. Over H, d comes to differ from identity by a smooth function. With use of this function d we can construct two mathematical models, where the second is generated by applying d to proper elements of the first, such that the two models are identical prior to the time t=0, where t is a time function created by a
foliation of spacetime, but differ after t=0. These considerations show that, since substantialism allows the construction of holes, that the universe must, on that view, be indeterministic. Which, Earman argues, is a case against substantialism, as the case between
determinism or
indeterminism should be a question of physics, not of our commitment to substantialism. ==Bibliography==