  In this two-part essay, we distinguish several senses in which general
relativity has been regarded as "locally special relativistic". Here, in Part
1, we focus on senses in which a relativistic spacetime has been said to be
"locally (approximately) Minkowskian". After critiquing several proposals in
the literature, we present a result capturing a substantive sense in which
every relativistic spacetime is locally approximately Minkowskian. We then show
that Minkowski spacetime is not distinguished in this result: every
relativistic spacetime is locally approximately every other spacetime in the
same sense. In Part 2, we will consider "locally specially relativistic" matter
theories.
