In religion there are those who simply don't want to listen to any argument that goes against their belief and emotions because that by definition is wrong. This is very much why those against independence keep harping on about the lack of proof (the default trumping of anything and everything). But as jim360 correctly points out, there is no such thing as proof on these matters, and along venator's lines this is a question of whether you believe politicians and other leaders will competently take society forward. As with venator, not everyone will be happy with the way things go and they will continue to voice their beliefs and opinions, just as there are still people who insist it has not been proven that the earth is not flat. That is life. What is utterly beyond dispute is that the UK scores unimpressively-to-poorly on listings of societal performance (everything from infant death, life expectancy and social equality to peacefulness and happiness). The prospect of the UK catching up with the leaders on such listings has to be seen as unlikely (the UK is falling on some) and Scotland will never affect the outcome in UK governmental elections which then dictates the way the UK is run. There is no sign evident, in any of the nations that have separated from others, of any desire to rejoin those former "co-countries" (or join any other) - and that is over, say, the past century or so whether the separation was violent or democratic. On the other hand most of them are on very good terms with each other. Independence not only works but is manifestly satisfactory - nobody says there are no mistakes along the way but they are their own mistakes, and that is an important improvement (as curious as that may sound to some). Size is significant in that the best listings performers are almost always smaller nations, large size gives rise to inertia, inefficiency and inability to react quickly and well to deal with problems and all the while the problems become entrenched and less soluble.
Scotland is about to choose between running all its own affairs or leaving that up to its neighbour. It can stay at its current status or aim higher, have some hope, imagination and even some optimism. I have no doubt at all that after independence the UK and Scotland will/would be on very good terms and sort it all out swiftly and amicably, including currency, border arrangements and a wholehearted support of a seamless integration internationally. If there is a No outcome then the UK will have a lodger who continually will be thinking of what might have been.
To me this is a no-brainer.