“We have a finite environment—the planet. Anyone who thinks that you can have infinite growth in a finite environment is either a madman or an economist.”
The slogan “you can’t have infinite growth on a finite planet” or “with finite resources” is a catchy one that sums up a concern about the planet’s limited resources very neatly; it is popular and Sir David Attenborough is only one of many to voice it. As a rallying cry it seems great. As an actual argument it is less good, though.
First, the pedant’s point: infinite growth would require that the Earth itself literally exist forever. It seems doubtful that Sir David Attenborough believes that; our best science presently suggests the sun itself will eventually ‘die’, taking Earth with it in the process. It also seems likely that economists tend to know this. This makes “infinite growth” seem like a bit of a straw man.
So, really, the argument needs to be re-phrased as something more like: “we can’t have much more growth, given the finite resources of the planet”.
This, more accurate, rendition of the argument makes clear that there is not some kind of logical argument here (something ‘infinite is impossible given finite’), but just an empirical claim. In contrast to a logical truth (which is necessarily true), an empirical claim is a claim about the world that could be true or false, and we need evidence from the world to know which it is. We can’t just determine its truth or falsity through reason alone.
So, when the straw man aspect is taken away, there isn’t really an argument here at all, just a claim.
And whether that claim is true, is far from clear: Economic growth can, in principle, be driven by new technologies that reduce consumption and save resources, so it all depends on the details.