My attitude to money is that there is a certain amount coming in every month, a certain amount going out every month, a sum of assets that I own and a sum of debt that I owe. Much like the profit & loss and balance sheet respectively of a company. Any kind of compartmentalisation of that is purely artificial, done either from a lack of a holistic understanding of finance or out of sheer personal convenience. Either way, however, you should recognise the conceit for what it is.
I read an interesting article a while ago that argued, in quite sensible, rational manner, that you should never pay your mortgage off completely.
The argument was that if you were borrowing at a fairly low rate of interest on your mortgage, the money that you would otherwise have used to pay off your mortgage, you could invest that elsewhere and earn a higher income from those savings or investments than you'd be 'saving' if you didn't have the mortgage, iyswim.
It did actually make sense.
E.g. If your mortgage is what, 2-3 per cent, maybe 5 or 6 per cent at the moment, and you made overpayments to repay capital, you'd be 'saving' 2-6 per cent. But if, instead of sensibly choosing to overpay your mortgage, you chose to play the market, haven't some stocks gone up a lot and done fairly well over recent months? So you could potential make 10-20 per cent on your investment.
I wish I could be that daring and make money work for me, like some people seem to be able to. But my flat's paid for, I own it outright, and I've no intention of taking advantage of low mortgage rates and then gambling with the money. (Although I might end up taking out a small mortgage to get my windows and central heating done next year.)