In orthodox macro, higher interest rates -> reduced investment -> reduced demand -> reduced inflation. This is pretty much empirically proven by how central banks have been able to control inflation in the West.
The way I see it is the "search for safety", especially where negative interest rates are concerned. There are two huge concentrations of safety-seeking money in the modern economy: pension funds and oligarchs. The pension funds more or less have to buy government bonds in a certain ratio, regardless of the price. Whereas the oligarchs have hundreds of billions they need to keep anonymously in a stable economy - ie dollars, pounds, and euros.
Things like the Apple "cash" pile of $245bn represent a lot of floating wealth too.
Ultimately, if we don't get real wealth taxes, interest rates will be forced negative simply by the market and the huge volume of safety-seeking money.