What do we really mean by "climate response" to GHG forcing?

citizenschallenge

I've literally been struggling with trying to enunciate some things, if just for my own intellectual expectations and journey through life.  I keep thinking I'm getting somewhere and bam, back at the bottom of the hill.  Now I've put off my Bates dissection because I need to reconcile myself with Fyfe 2016.  It's a trip, among its authors are heroes of mine, people who's lectures and articles have taught me, some who have been kind enough to respond to occasional emails.  Literally among the best and brightest.  It's ludicrous to think I could question or argue with their science (I'm capable of arguing with rhetorical games, but not facts as digested by real scientists.  I know that.).  Still that paper/comment has me in dither.  I'm beginning to understand my gripe which is summed up in my working title:  "Fyfe et al. 2016 - Examining a failure to communicate - a question of perspective" but still wrestling with it.  On a related note, this morning I was reading ATTP's Catastrophe, hoax, or just “Lukewarm”? and a couple questions crystalized that I'm hoping someone might be into sharing any thoughts,

Can someone help clarify something for me –
People/politicians/scientists spend all this time talking about climate response, when it seems to me, they are actually talking about temperature response.

As though that number tells us everything. 

What does that figure actually tell us about our Earth’s biosphere’s response,
or societal response?

What about other critically important parts of this equation?

What about extreme weather response to temperature?

How about societal responses (or lack thereof) to weather driven infrastructure destruction?

Seems to me in our collective obsession over achieving ultimate accuracy we’ve lost sight of what those number really for and are giving short shrift to the more critical matter of cascading consequences.

I understand the scientist's obsession with process and accurate is a requirement - but something critical needs to be acknowledged (explained) when communicating that science to nonscientists.  I don't pretend to know solutions, but I sure as hell know that scientific communication with challenged lay people, has failed to confront deliberate frauds.  That failure has and will continue to have increasingly grave consequences.