John Earman

John Earman (born 1942) is a philosopher of physics. He is currently a professor in the History and Philosophy of Science department at the University of Pittsburgh.

The Hole argument

Earman has notably contributed to debate about the "hole argument". The hole argument was invented for slightly 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 John3 (a short form for the "three Johns": John Earman, John Stachel, and John Norton).

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 spacetime substantivalism.

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 substantivalism allows the construction of holes, that the universe must, on that view, be indeterministic. Which, Earman argues, is a case against substantivalism, as the case between determinism or indeterminism should be a question of physics, not of our commitment to substantivalism.

Books Authored by Earman

*"A Primer on Determinism"
*"World Enough and Spacetime: Absolute vs. Relational Theories of Space and Time"
*"Bayes or Bust: A Critical Examination of Bayesian Confirmation Theory"
*"Bangs, Crunches, Whimpers and Shrieks: Singularities and Acausalities in Relativistic Spacetimes"
*"Hume's Abject Failure: The Argument Against Miracles"