Note to all genuine historians of economic thought: yes, I know. There's real history, then there's Whig history, and then there's this blog post.
Knut Wicksell said that there is one rate of interest at which desired savings equals desired investment, so that aggregate demand equals aggregate supply. This is the long run equilibrium rate of interest. He called it the "natural rate of interest". He said that if the central bank set the rate of interest permanently above the natural rate of interest, this would reduce aggregate demand for goods permanently below aggregate supply, and cause a "cumulative process" in which the price level would fall without limit. And if it set the rate of interest permanently below natural rate, this would raise aggregate demand for goods permanently above aggregate supply, and cause a "cumulative process" in which the price level would rise without limit.
Irving Fisher said that you need to distinguish between the nominal and the real rate of interest. The (expected) real rate equals the nominal rate minus (expected) inflation. Savings and investment, and hence aggregate demand, depend on the (expected) real rate of interest, and do not depend on the nominal rate. So the long run equilibrium or natural rate of interest is a real rate of interest, and is independent of the rate of inflation. If the central bank sets a nominal rate of interest, that nominal rate of interest must equal the natural rate plus the (expected) rate of inflation, if we are to be in long run equilibrium.
Milton Friedman said that actual inflation depends on expected inflation, as well as on the gap between aggregate demand and aggregate supply. So if aggregate demand exceeds aggregate supply, actual inflation will exceed expected inflation. And he said that expected inflation will eventually catch up to any constant level of actual inflation. This means that if aggregate demand permanently exceeds aggregate supply, we won't just get rising prices, as Wicksell said; we will get ever-accelerating inflation.
John Taylor added Wicksell, Fisher, and Friedman together, and came up with the Taylor Principle. The Taylor Principle is designed for central banks which set a nominal rate of interest and want to keep inflation near to its target. The Taylor Principle says that if the rate of inflation rises by 1 percentage point above target, the central bank must raise the nominal interest rate by more than 1 percentage point, otherwise inflation will rise without limit. And if the rate of inflation falls 1 percentage point below target, the central bank must lower the nominal rate of interest by more than 1 percentage point, otherwise inflation will fall without limit. Here's why:
The central bank cannot observe the natural rate of interest, and will almost always get it wrong. Suppose the central bank sets the nominal rate of interest too low -- below the natural rate plus the (expected) rate of inflation. So the real rate of interest is below the natural rate, so aggregate demand exceeds aggregate supply, and so inflation rises without limit. As inflation rises, so does expected inflation. So the (expected) real rate of interest falls still further, so aggregate demand rises still further. To make inflation stop rising, and make it fall back towards the target, the central bank needs to raise the real rate of interest, which means raising the nominal rate of interest by more than inflation has increased above target.
Anyone who recognises the validity of the Taylor Principle implicitly recognises the validity of Wicksell's insight (as well as Fisher's and Friedman's insights). The Taylor Principle is designed to stop the Wicksellian cumulative process happening. The Taylor Principle is designed to make an otherwise unstable long-run equilibrium stable. If Wicksell was wrong, then so is the Taylor Principle.