The most aggressive dove

"I advocated for a 50-basis-point rate cut to 1.75 percent to 2.00 percent and a commitment not to raise rates again until core inflation reaches our 2 percent target on a sustained basis. I believe an aggressive policy action such as this is required to re-anchor inflation expectations at our target."

Kashkari's logic is pretty simple: Inflation is too low, and so the Fed needs to keep on loosening monetary policy until it gets up to the target level.

• By the numbers: The Fed adopted its 2% target for core PCE inflation in 2012. The target is supposed to be symmetrical: Inflation is meant to be above 2% and below 2% roughly equally. But since the target was set, the inflation rate has been consistently below 2%, making the target seem like more of a ceiling.

The bottom line: Cutting rates with the stock market at a record high might seem odd, but it's happened before. If the market continues to rally through the next Fed meeting, it might well happen again.