Civilization maintains an elaborate infrastructure devoted to the maintenance of synchronized time. Governments mandate daylight saving time. Standards bodies insert leap seconds into Coordinated Universal Time. Engineers debate leap milliseconds and leap nanoseconds. The Global Positioning System applies relativistic corrections at the nanosecond level. All of these adjustments attempt to preserve an assumption: that a single global time exists and that clocks can be made to agree upon it.
This paper argues that this assumption constitutes a category mistake in the sense of Ryle (1949). We show that special and general relativity prohibit absolute simultaneity, that the one-way speed of light is conventionally defined rather than measured, and that recent experiments on indefinite causal order demonstrate nature admits correlations with no well-defined temporal sequence. We trace the consequences of this category mistake through distributed computing, where it manifests as the Forward-In-Time-Only (FITO) assumption that underlies Lamport's logical clocks (1978), the impossibility results of Fischer-Lynch-Paterson (1985), and the CAP theorem (2000). From this perspective, daylight saving time and leap seconds are not corrections to time but corrections to conventions -- they sharpen the guillotine of synchronization in preparation for executing something that does not exist.