"To be clear, I am an empiricist and believe that the study of systems can only come about through careful experimentation, modeling, and formal mathematics. Mathematics, in my opinion, is the only objective measure by which we can analyse systems and trends."
I think we have to be a little careful about approaching economics as a problem to be solved. Logic, math, and empiricism have their limits (even if they are the best tools we have).
For one thing, empiricism relies on being able to control the variables. But that's hard to do, because others can always refute the results by introducing other variables and factors.
And (as you point out) the possibilities explode so quickly that it's very difficult to reason purely based on logic from base principles. And there are humans involved, which makes it even more difficult (if not impossible).
I'm not criticizing logic and empiricism as tools. But I think they can very easily give a false confidence in the answers you get. You have to realize how small a piece of the problem space your logic actually covers; and how difficult it is to distill real world events into a nice clean, unbiased data set.
I would argue that mathematics can only give you false confidence if you fail to understand it completely. A sound formal mathematical definition holds all assumptions within the definition itself.
Note that I think that if you can't encode your theory in mathematics than it is non-predictive by definition. If it is non-predictive then I see no use for it in any real sense.
I hold all economic systems to the same level of critique, by the way. If your Keynesian system doesn't encode its assumptions and predictions in mathematics then it is by definition useless.
"I would argue that mathematics can only give you false confidence if you fail to understand it completely."
Yes, that's the problem. In economics, it's difficult to know what all of the relevant variables are and the basic inputs are not well-understood (like the behavior of people).
Even if you did create a perfect model, most of the assumptions would have to be nearly wild guesses, and probably even small errors in the assumptions would lead to wild errors in the result. And the resulting model would be so complex that I'm not at all sure it would even be useful for crafting policy.
Then, let's say we had a perfect and simple model that anyone could understand. Everything would be wonderful, right? No, you still have to collect all the relevant data for inputs, run the simulation, and then distribute the results to all of the relevant parties -- all before the economy plays out in real time.
So what actually happens with mathematical models is that people oversimplify, but because it has the aura of formalism they become very confident. There are always so many wild variables like wars or drought that it's easy to later dismiss any deviation from their model as "a special event" (e.g. an earthquake).
And what's the optimization target, by the way? The total number of shoes produced? Using GDP as an optimization target has a lot of known problems and embeds a lot of assumptions itself. And some people simply prefer living under a certain kind of economic system.
So, trying to approach economics from a purely mathematical standpoint is useless, in my opinion.
I think we have to be a little careful about approaching economics as a problem to be solved. Logic, math, and empiricism have their limits (even if they are the best tools we have).
For one thing, empiricism relies on being able to control the variables. But that's hard to do, because others can always refute the results by introducing other variables and factors.
And (as you point out) the possibilities explode so quickly that it's very difficult to reason purely based on logic from base principles. And there are humans involved, which makes it even more difficult (if not impossible).
I'm not criticizing logic and empiricism as tools. But I think they can very easily give a false confidence in the answers you get. You have to realize how small a piece of the problem space your logic actually covers; and how difficult it is to distill real world events into a nice clean, unbiased data set.