The neo-Fisherian view does not consider a negative interest rate gap a prerequisite for boosting inflation. Instead, a negative interest rate gap is said to lower inflation. We discuss this counterintuitive response - known as the Fisher paradox - in a prototypical new-Keynesian model. We draw the following conclusions. First, with a temporarily pegged nominal rate during a liquidity trap (given an otherwise standard Taylor rule) the model generally produces multiple equilibrium paths: some of these paths are consistent with the neo-Fisherian view, others are not. Second, the unique optimal monetary policy at the lower bound on interest rates, which can be implemented in the model with interest rate rules and state-contingent forward guidance, does not result in a paradox. Third, if the assumption of perfect foresight or rational expectations is relaxed, the model produces an equilibrium that is not consistent with the neo-Fisherian view.