Madness: Not of sound mental capacity; mentally ill; not capable of sound thinking or of moral self-restraint.
There is such a thing as mental illness, just as there is such a thing as bodily illness, and in both cases some sort of organic malfunctioning is involved. Since in fact rather less is known about the brain than about most other bodily organs, there are few good causal scientific explanations of what constitutes mental illness. Even so, there is considerable agreement about many of the details and the diagnosis of quite a few mental diseases, like depression or schizophrenia.
1. There are at least three reasons to outline the above and insist that there are some real mental illnesses.
One is that there have been some psychiatrists - Laing, Szasz - who have denied that all or most mental illnesses exist, or who have insisted that mental illness is merely a kind of non-conformism with or deviance from the current social and moral ideals and practices, or indeed a liberation or mental growing of a special kind.
Another is that there have been some governments - Russian, Chinese - that found it very convenient to classify their opponents as 'insane', and lock them up in asylums, and maltreat them in various ways, e.g. with the purpose of making them really insane.
A third is that there have been some philosophers - Foucault, postmodernists in general - who have insisted that mental illness and mental health are merely relativistic ideological notions without any factual or objective basis.
The psychiatric notion - somewhat popular in the sixties and seventies of the 20th Century - that mental illness does not really exist or is some sort of liberation or non-conformism since has been mostly left behind as misguided romanticism, that unfairly and falsely denies the very real mental suffering, confusions and difficulties of people who really are mentally ill, and that also makes it more difficult to help them properly.
The governmental abuse of psychiatry also has lessened for the moment, at least in the sense that it has become less fashionable in totalitarian states to lock up dissidents on the pretext that who opposes the government must be insane.
The philosophical interpretation of mental illness as a mere social classification of deviance also has become less popular as postmodernism grew less popular, and as it became fairly to very obvious that some kinds of mental suffering, such as ordinary depression, have become quite amenable to scientific medical treatment by modern anti-depressives.
2. There is a relation between madness and philosophy that is in part indicated by Seneca's saying "There is no genius without a mixture of madness" and in part caused by the fact that the least that great philosophers are is unconventional and non-conformist, which are both characteristics that easily may cause more ordinary folks to impute madness.
Sometimes these imputations of madness are totally unjustified and based on lack of understanding, but at other times, for example in the cases of Rousseau and Nietzsche, such imputations may well be true to some extent. (Rousseau certainly was a paranoiac in later life, and Nietzsche eventually became insane. What this implies about their published philosophical texts is a moot question.)