Earlier quoted context omitted.
Okay, I'm all ears (or, technically, eyes, since I'm reading this). How does a 400,000 year old ice core show anything about conditions 4 million years ago? Please be specific.
Now I see mention of an 800,000 year old core in that article. That's still not 4 million, or anything like it.
I don't know enough to evaluate his methods, but Mark Pagani at Yale seems to have published a number of papers that give estimates going back 40 million years: http://people.earth.yale.edu/cenozoic-evolution-carbon-dioxi...
And this paper 2005 paper by Dana Royer provides an overview of a few hundred estimates going back 500 million years: http://droyer.web.wesleyan.edu/PhanCO2(GCA).pdf