The data back to 1860 are also sufficient to establish the current warming trend

Only if you assume that there are no significant cyclic effects on longer time scales.

Climate science as a discipline does not hinge on knowing exactly how warm it was 250 years ago within +/- 0.5C.

It does if you're claiming, as the IPCC does based on the input of climate scientists, that temperatures now are warmer than they have been in at least several thousand years.

There's no postulated mechanism for how this could be the case - where is the extra energy or heat retention coming from and managing to come into play so suddenly since the 1970s?

Whereas, if one accounts for anthropogenic CO2, it explains it superbly.

I'm implying no such thing. Consider an analogy: I look at the temperature trend from February through May and conclude that I have enough data to show a significant warming trend. I therefore predict that by November, the planet will be dangerously overheated.

Obviously I have ignored a cyclic effect on a longer timescale. Is it "highly exponential" as you describe?

long periods of no warming, and then sudden periods of rapid warming

This is not what the data shows; at least, not if you look at all the data, not just a few selected temperature reconstructions that are questionable (at best) anyway. The data in full, looking at a number of different fields, shows a cycle with a period of about 800 to 1000 years; the last iteration of the cycle consisted of the Medieval Warm Period and the Little Ice Age, and we are nearing the next maximum of the cycle now.

This is not to say that human activities (of which CO2 emissions are only one component: why is it that nobody talks about land use?) have had no effect on the climate. (Arguably, humans terraforming the planet has been a significant factor in keeping another Ice Age from starting.) But if you're using the wrong baseline, it's tough to separate the human effects from the other effects.

That's what anthropogenic climate change is - since the only effect that suitably explains warming is increased eCO2 in the atmosphere.

Absent (effective)CO2 increases, you can't explain the warming trend. There shouldn't be one as pronounced.

If you're going to say "well what if there's a long cycle" - then well, what is it exactly? Where is all this additional heat retention in the atmosphere coming from? There are no multi-decadal phenomena on Earth which can explain the temperature record.

EDIT: The data for example, does not show a 1000 year cycle. You're inferring there's a cycle, by doing what you accuse others of - pointing to a graph, and declaring that because it looks "roughly" cyclical it is.

I understand that that is the "official" view of climate science, but that doesn't mean it's right. I don't think we're going to resolve that sort of dispute here, but if your only argument is from authority--"climate science says so"--then that's not enough for me. I don't think climate science as a field has exercised sufficient care to be just taken at their word.

If you're going to say "well what if there's a long cycle" - then well, what is it exactly?

Nobody knows for sure; we don't understand how the climate works well enough for that. But the fact that we don't have a theory that explains the cycle doesn't mean there isn't one.

Where is all this additional heat retention in the atmosphere coming from?

Actually, the amount of heat being retained in the atmosphere is miniscule on a planetary scale. The significant heat sink is the oceans. You have to be careful distinguishing between heat and temperature.

As for where it's coming from, as above, we don't understand all the causal factors at work; the fact that we have studied one intensively (CO2) does not mean that one must be the only significant one. (The IPCC report itself lists a number of significant causal factors as having a "low" level of scientific understanding.)

The data for example, does not show a 1000 year cycle.

Whose data? I understand that the "Hockey Stick" does not show a 1000 year cycle, but the "Hockey Stick" is not data; it's a (questionable at best) reconstruction of temperatures from data. We do not have direct temperature data from 1000 years ago, and as far as indirect data, there is plenty to indicate that there was indeed a Medieval Warm Period and a Little Ice Age, as I said.

We know about cyclical effects on longer time scales like Milankovich cycles, we understand solar variation and volcanic effects. We know about the Younger Dryas and Daansgard-Oeschger cycles. We know about shorter term oscillations like the AMO and PDO.

You apparently know nothing of any of this, and have never heard of Muller's BEST study even though it was splattered all over the New York Times a few years back. Yet, you feel competent enough to make statements about how climatology isn't a real science.

We also know about something called the Dunning-Kruger effect.

I didn't say climatology wasn't a real science. I said it's not an accurate enough science to justify making policy decisions with huge consequences. Plenty of other real sciences are in the same state; that's to be expected, since it's a phase every real science has to go through in order to become accurate enough.