Definition of mental illness should be up to the individual, something that they decide they are suffering from when they don't feel well and think they need to do something about it, like seek help/a solution.
And even then their behaviour should be treated as anti-social/self-destructive/dangerous/difficult etc, or not, in the same way as everybody's behaviour is.
Mental illness should be recognised as subjective.
While we are talking "shoulds", people committing crimes who argue that they are mentally ill should not be excused prison but be offered exclusion diets, meditation, medication if they ask for it, and other therapies to attempt to change their state while living out the usual sentence.
In fact I think prisons should put all prisoners on sugar, gluten, dairy, and corn exclusion diets automatically.
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Special diets to reform our criminals? Why not include acupuncture and aromatherapy, as well? Why not turn our prisons into luxury spas?