  Supplementing earlier literature by e.g. Tipler, Clarke, & Ellis (1980),
Israel (1987), Thorne, (1994), Earman (1999), Senovilla & Garfinkle (2015),
Curiel (2019ab), and Landsman (2021ab), I provide a historical and conceptual
analysis of Penrose's path-breaking 1965 singularity (or incompleteness)
theorem. The emphasis is on the nature and historical origin of the assumptions
and definitions used in-or otherwise relevant to-the theorem, as well as on the
discrepancy between the (astro)physical goals of the theorem and its actual
content: even if its assumptions are met, the theorem fails to prove the
existence or formation of black holes.Penrose himself was well aware of this
gap, which he subsequently tried to overcome with his visionary and influential
cosmic censorship conjectures. Roughly speaking, to infer from (null) geodesic
incompleteness that there is a "black" object one needs weak cosmic censorship,
whereas in addition a "hole" exists (as opposed to a boundary of an extendible
space-time causing the incompleteness of geodesics) if strong cosmic censorship
holds.
