Research over the last 30 years has consistently shown that diagnosable mental illness does not underlie most gun violence.
http://behavioralscientist.org/myth-mental-illness-causes-mass-shootings/
(This turned into a bit of an essay, and is not really just a response to your post, so apologies
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For me, any violence or any behaviour originates within a person's thinking and consciousness, and the foundational issue with any shooting, say, is what happens within the human being, regardless of whether it's classed as a diagnosable mental illness.
Our society brings the worst out of people, and what interests me is that, when you look at the various native and ancient philosophies of the human being around the world that have not come from Western society (quite the opposite - often from places that have been invaded or where there's been colonialism from 'the white man'), such as Vedic, Buddhist, Kahuna, Sufi, etc, it starts to look like there's basically a sort of perennial philosophy, or a default philosophy that people ended up in before the influence of Western society, and the example of this I've been most taken aback by is a tribe in the Amazon called the 'Piraha tribe', whose philosophy and perspective on 'presence' is seemingly consistent with those up there. They live in the middle of absolutely nowhere, yet they have views on 'presence', 'the immediacy of experience', etc that are consistent with these other philosophies, and this sort of thing is often talked about in terms of a link to happiness, love, peace, etc, and has even cropped up sometimes in the West with people like the theosophists and the stoics:
https://en.wikipedia.org/wiki/Stoicism
"According to its teachings, as social beings, the path to happiness for humans is found in accepting this moment as it presents itself"
To bring this back to the issue of what causes violence in the world, you have a situation today where you have a society that probably causes some of the most wide-ranging variety of stress imaginable, yet there is absolutely nothing in our culture or any school curriculum that tries to get us to understand ourselves, and how to deal with all the sadness, worry, isolation, etc of the human being that can then come to cause violence, anger and madness. There's a sort of collective conscience that many people agree upon in terms of what we feel is right, what is moral, etc, but nothing in our education that aims to get us to really see any of this as self-evident. To be honest, you could maybe say our current approach is more prone to leading to moral relativism and nihilism.
With gun control, it reminds me of the political correctness issue, and how society seems to tripping over itself to cater for people who are apparently offended. You can establish laws left, right and centre telling people what they can do, what they can possess, etc, but at some point something like the above approach surely has to be embedded into our culture with the aim of preventing violence before it happens.
It's like in football how you don't need to learn how to defend as well if you can control possession and prevent the other team from really getting much of the ball in the first place. If we put more effort into developing a more controlled and happy state of awareness amongst the populace, perhaps you wouldn't need to put so much effort into defending people, and at the cost of liberty and freedom of speech.