quote:some is 'captured' by a greenhouse gas and then some of that is thrown back at the earth so adds to the energy from the sun
I understand the above, but what is thrown back has come from the earth, indeed the result should be that a little less than 50% of the captured IR comes back to the earth. However without any additional heating the earth can not remain at the same temperature since it has just emitted energy as IR upwards. This exchange of energy up to be captured then transmitted down to the earth if left alone without any further addition to the system would result in cooling, not heating. I can not see this as amplification.
I must still be missing something. Please bear with me, I will get there in the end!