The Lovelock formulation, which treats the stability rather than the change as the unexplained phenomenon, may be the right way round for this question.
How did the biosphere persist for so long? Are we just really really really lucky?
A variation of the anthropic principle indicates that this might well be the case: if we weren't really lucky (compared to other planets) we wouldn't evolve far enough to ask the question. That's even scarier than the Gaia hypothesis since our luck might well run out at any moment even without us rocking the boat. Both of these points of view make it unlikely that our current behavior will be benign.
(Indeed, climate models tend to be unstable; it seems to require a narrow range of parameters to get realistic behavior. The reasons for this are interesting, but can only be investigated if people relax and accept that the models themselves are worthy of certain forms of investigation. Had computers preceded the carbon spike, so that there was less controversy, I suspect we would have broader investigations about climate modeling than we do now.)
Starting from the point of view that climate change needs explaining is wrong. If we assume that it is stability that needs explaining, we are quickly left wondering at what point the stability we count on will fail, and how much pushing it needs to fail very badly.
We are left with a very silly proposition, that we establish beyond a shred of doubt what the least amount of carbon (etc.) in the atmosphere is that is absolutely certain to have vast consequences. This treats carbon as a defendant in a courtroom with intrinsic rights. But we only have one planet.
The main job we have as climatologists should be to establish beyond a shred of doubt the greatest amount of carbon absolutely certain NOT to have vast consequences.
Those who find our methods unimpressive, those who believe we contribute no information should rationally act as if any increase in concentration of radiatively active substances is extremely dangerous.
It is the fact that the 'skeptics' argue the exact opposite that convinces me they are not intellectually serious. It's not a coherent position at all. If they are serious, and really mean well, and really don't believe much that we say, they would argue for extreme caution. After all, if we don't really know at all how big or how small a change in aerosols or greenhouse gases might be enough to make the world dramatically worse, we really ought to stop doing any of that.
Update: A so-called skeptic, Patrick Frank, has an article in Skeptic magazine that (begins with the very premise) reaches a very poorly supported argument (my inaccurate summary restated per the author's request in the comments) that we know essentially nothing, and concludes from that, somehow, that we can act with impunity:
Nevertheless, those who advocate extreme policies to reduce carbon dioxide emissions inevitably base their case on GCM projections, which somehow become real predictions in publicity releases. But even if these advocates admitted the uncertainty of their predictions, they might still invoke the Precautionary Principle and call for extreme reductions “just to be safe.” This principle says, “Where there are threats of serious or irreversible damage, lack of full scientific certainty shall not be used as a reason for postponing cost-effective measures to prevent environmental degradation.”34 That is, even if we don’t fully know that CO2 is dangerously warming Earth climate, we should curtail its emission anyway, just in case. However, if the present uncertainty limit in General Circulation Models is at least ±100 degrees per century, we are left in total ignorance about the temperature effect of increasing CO2. It’s not that we, “lack … full scientific certainty,” it’s that we lack any scientific certainty. We literally don’t know whether doubling atmospheric CO2 will have any discernible effect on climate at all.
If our knowledge of future climates is zero then for all we know either suppressing CO2 emissions or increasing them may make climate better, or worse, or just have a neutral effect. The alternatives are incommensurate but in our state of ignorance either choice equally has two chances in three of causing the least harm.35 Complete ignorance makes the Precautionary Principle completely useless. There are good reasons to reduce burning fossil fuels, but climate warming isn’t one of them.
Of course, the characterization of climate models is ludicrous. I would agree in some sense that complete ignorance makes the precautionary principle useless, and I am not a big fan of absolute principles. But in the present case the stakes are vast, and we do know that we are emitting greenhouse gases and aerosols that materially affect the climate in vast quantities. Given only that knowledge and no other it strikes me that we should restrain thses activities to the greatest extent feasible.
Fortunately Tapio Schneider has an article in the same issue, with a cogent if unsurprising presentation of the conventional wisdom. The usual "sense vs nonsense" sort of balance, but better than letting the person who doesn't even understand the evidence he's cherry-picking claim the label of "skeptic" unchallenged.
Update: The author of the ill-informed article has much to say below. Essentially my critique of it doesn't add anything to Tapio Schneider's, while his adds considerably to mine. Thanks to Hank Roberts for pointing this out in an email.