In describing the origin of the universe, standard cosmology ascribes to the initial singularity a set of core properties: "infinitely small volume," "infinite density," "infinite curvature," and "infinitely high temperature." This paper demonstrates that these descriptions stand in irreconcilable logical conflict with the very premise upon which they rest—namely, that there was an absence of spacetime before the singularity. The act of physical measurement is fundamentally tethered to the framework of spacetime: volume requires space as the stage of extension, density requires space as the container of distribution, and curvature requires the geometry of spacetime as the substrate that bends. Once the spacetime framework is removed, all these properties immediately forfeit their physical meaning. This paper does not attack the mathematical derivation of general relativity, nor does it deny the legitimacy of the Friedmann model in the classical limit. Rather, it scrutinizes a widely neglected definitional rupture: while claiming the absence of spacetime, the standard narrative systematically deploys descriptive language that is meaningful only within a spatiotemporal framework. This rupture is present not only in popular science communication but can be traced back to the authoritative expositions of the very provers of the singularity theorems and to peer-reviewed academic literature. This paper argues that the contradiction is not a casual misstatement; it is the logical price the standard singularity narrative pays for simultaneously satisfying two conflicting demands—"sealing off inquiries into the origin" and "constructing an evolutionary narrative." It constitutes a structural collapse caused by a self-laceration in definitions.
Zhijun Li (Fri,) studied this question.