No; of course not. You can’t calculate the natural rate outside the market process. You can’t know the price of bread outside the market process. And wether or not you are an Austrian (economists), doesn’t have any influence what so ever.
And obviously; there is no contradiction. It’s perfectly consistent.
looking at any price in history (set by government) you can’t know wether it’s too high or too low, just by looking at the price. One can understand (verstehen) that it’s too or too high low, based on an interpretation of the facts of the historical circumstance. But that’s a different ballgame.
The same price can be too high in one period of time and too low in another. Especially with something like the interestrate: because interestrates (in the real world) aren’t just based on originary interest; but on risk-assessment as well.
When the Austrian talk about the interest rate being ‘too low’; one isn’t saying: ‘ah, look: it’s 4%, but the average long term trend in economics, is 6%; so it must be too low’ and vice versa. When an Austrian is saying ‘the interestrate is too low’, he means that, given the situation, it should be higher. Signs that give you a clear view that the interestrate is too low are, for example, the monetary base expanding enormously or the interestrate being zero. They are counterfactual concepts.
Like saying: ‘I think this food has been in the microwave for too long’. You can’t say that based on the time it was in the microwave, because you can’t know how long it had to be in there. (Maybe it was deep frozen, so it had to be 7 minutes, or it wasn’t, and than it’s only 4.) But you can know it from deducing it from comprehending that food shouldn’t be like this (all burned up and all). I don’t want to overstretch the analogy, but that sort of grasps the concept.
What Friedman does, is looking at the time it was in the microwave, without looking at the food before it got in, nor at the food when it came out and saying ‘well, if food is in it longer then 5 minutes, it’s bound to be in there too long and it’s less then 5 minutes, it’s bound to be too short’. But that, obviously, doesn’t make any sense.
I really don’t get how you can say ‘in order for you to avoid contradiction, you must mean the austrian can calculate the natural rate unproblematically’. It’s not just that you are interpreting it wrong. It’s really: I have literally no idea how you can interpret it like that.