On the matter of choosing time periods:
It is possible to pick time periods which satisfy AGW as well. Would that be evidence for AGW? No, not by itself. Basically, you would have to defend your choice of time periods, if it were to be valid at all. In your case, you can't choose 2000 years divided into two parts because
- warming could have been occurring during the first 1000 (say 2 degrees)
- cooling could have been occurring during 80% of the second 1000 period (say by 1 degree), and then been reversed by our human activity at that 80% mark (say 2 degrees warmer for net 1 degrees warming in the second millennium).
- Then, someone like you could come along and dismiss that last 20% of the time, and based it on the arbitrary choice of two sequential 1000 year periods leading up to today.
The trouble with such a scenario would be that if it is 2 degrees warmer in the last 200 years, that equals the warming that happened over the first 1000 years. This SHOULD result in someone saying "Wow! we've had quite a powerful warming trend". But, if we follow your intellectual lead, we end up ignoring important information. Choosing those 1000 year periods like that is completely irrelevant, so whoever convinced you to do that should be ignored as a source of credible analysis. Such people make their followers look foolish.
The exact same problem can arise with the choosing of the 400/200 year time periods. It is less likely to occur there, but it is still possible. It is less likely because it more closely coincides with mankind's significant output of greenhouse gasses. Nevertheless, there could be a natural cooling or warming during any parts of it which could skew the matter
in favor of either viewpoint. No matter which one it favored, it really wouldn't be evidence. It is again irrelevant, and as such should make you question the source of the notion to use such analysis.
On the matter of the most recent decade:
You claimed that temperatures had decreased or stayed level during the last decade. I attempted to partly divine how you thought that was relevant to the issue, but apparently got it wrong. Nothing you have said now explains why you think it is relevant at all. But, I can tell you that it would be, again, irrelevant (by itself), so it really doesn't matter.
On the matter of what you would view as proof
I don't understand why you would think it was relevant that it would be warmer now than it ever was during 'this interglacial'. Can you think for yourself of scenarios where it might be cooler now, and yet we would still be causing warming?
Please be more specific: How should they prove that the cause of 'any warming' is the result of CO2? What would prove this to you?
You very last statement may not, again, be relevant.
If your standard of evidence is that they accurately predict how warm it will be in 100 years, and then we wait to see how accurate they are, then you are asking us to wait until warming would be even more of a problem than it might be if we acted now. If this is your requirement, then you are essentially saying that even if it is true, it is something that cannot be proven to your satisfaction, right now. Which is essentially what the guy said which started this whole conversation between you and I. "If the scientific consensus doesn't convince you, nothing will".