Logically, exactly how would one go about proving there are no deities?
It's simple. All you have to do is to know everything just like many atheists and most believers in science.
In science, we rely exclusively on the "scientific method" period!!!
No. "We" don't do anything. Individuals do everything. All knowledge, all ideas, and all understanding is individual.
There is no "scientific method" set in stone. Many people believe "Peer review" is the 7th step but the fact is there are no set number of steps and the opinion of peers and Peers is irrelevant to science and its understanding. Some people are methodical in inventing hypotheses but most use intuition or insight. Some people use induction and some deduction. Some people remember the definitions and axioms when they interpret experiment but many do not. Some people don't even want to believe Darwin had beliefs and prejudices. They don't want to believe that his axioms and definitions determined his conclusions or affected them in any way.
You want to believe you know everything. I know I know nothing. But I can recognize a good pattern when it bites me on the nose. This is what I do; seek patterns. As a metaphysician and generalist all I care about are patterns as disclosed by deduction and experiment.
Oh, so how in the world could you possibly know this?
Everyone is doing what he thinks is right and makes sense all the time. Everyone acts on his beliefs and lives in accordance with what he thinks is right. It's not so much that some "Godless" people use this as an excuse to to wrong so much as it is that when science is wrong it leads the whole world astray. Of COURSE everyone is an individual so when the whole world goes astray it's many individuals (most of whom believe in science or who purchase science as a weapon) who lead us astray.
Science has become dangerous and has been since Darwin invented Survival of the Fittest. Now with modern technology and materials it gets more dangerous. Perhaps plastic will kill us all soon enough. You do know that longevity is crashing right. This is not symptomatic of a robust and healthy science and economy. It is symptomatic of rot at every level. I predicted in 1994 that it would crash because that is when our leaders announced there were too many people (deplorables) in flyover country. Of course it's not widely understood why longevity is crashing and there are numerous obvious causes like a healthcare system in shambles and an educational system that has been dysfunctional since the late-'40's. We even have food intentionally contaminated with all manner of chemicals and biological agents as well as products intentionally designed to fail after a few years. But thew rich get richer and live longer so it's all good. If you don't want to die young you should just pick yourself up by the bootstraps and become a billionaire. Get off your fanny and go get a job dispensing pink slime at a fast food restaurant. Anyone can do it if he just rents the right congresscritter. Don't worry be happy.
Why do you think the world is imploding? There are fewer religious people than ever and they have less input than ever before. The world is being run by purchased science so things should be improving.