I hear the rate of change argument a lot, but I haven’t been able to comfortably arrive at how the comparison is made. Historic temperatures (pre-nineteenth century) have to be inferred from proxies—ice formations, fossilized tree rings, et cetera. Those, in turn, must be put into a date range based on some form of (I assume) radiometric dating. Carbon dating can get you +- 80 years. The other common techniques have even less precision. Uranium-lead dating can peg down a 2 million year window, for example.
How can researchers say that the rate of change is so much greater now when, not even counting propagation of error, the granularity of measurements pre-nineteenth century is, at best, of the same order-of-magnitude as the WHOLE of the era of modern precision measurements?
EDIT: I realize my question is inconvenient, but downvoting without meaningful response is no way to counter skepticism. This topic gets more religious as time goes on.