Way beyond most of the readership, but this is a blog post I wish I'd read 3 years ago:
Magic maths and money - why mathematics has not been effective in economics.
Suffice to say, modern mathematical economic models try to generate synthetic a priori knowledge (like the relation between A and B).
But if you have some philosophy background, and maybe also know a bit about how math works at the differential equations level and above, then you know that's impossible.
Slapping together a bunch of axioms can't create one whit of knowledge, unless you also know how those axioms work with each other, which (if you're trying to build a model that corresponds in any way with the real world) requires empirical (not synthetic) knowledge.
E.g., a macroeconomic model does these things:
1. assume you can model a labour market in isolation, assume it has certain characteristics, and assume an equation modeling how it works;
2. assume you can model a firm's production in isolation, assume it has certain characteristics, and assume an equation modeling how it works;
3. assume you can model an asset market in isolation, assume its characteristics, and assume an equation modeling how it works;
4. assume there are actors, assume how homogeneous they are, assume different homogeneity doesn't change the results, assume they act a certain way, assume how homogeneous their way of acting is, and assume an equation modeling how they behave;
5. assume you haven't missed anything that changes how this network of countable infinite equations works;
6. assume that none of the above assumptions, if changed, sends the solution off in a completely different direction;
7. if you like, also assume productivity magically increases over time with something we call "A", which is completely exogenous and don't ask us what "A" really is.
Each of those assumptions is wrong, thus the model is prima facie wrong according to any mathematician or philosopher out there. All you're doing, essentially, is modeling a battle between an army of orcs and Chuck Norris. Thus every math prof shits himself laughing whenever he reads an economics paper.
So why do this?:
The answer is rooted in the observation that the 'mathematical' approach is powerful rhetorically: you can use it to convince everyone of almost anything, providing you can make the chain of arguments tricky enough to follow. From a philosophical perspective, Kant distinguished the ‘lower faculties’, such as mathematics, that would consider matters of pure reason independently of the concerns of the state from the ‘higher faculties’, engineering, jurisprudence, medicine and theology, were concerned with matters of authority and would be regulated and monitored by the state. If economics is mathematical it should inform the state, not be directed by the state, if it is not then it will have the same status (and funding) as theology (and, one would suppose, other modern social and human sciences).Exactly. Economics is meant to order politicians around. That's the whole point of neoliberalism: the death of state sovereignty and the rise of the kleptocratic elite back to their traditional position of absolute power.
It's easier to boss politicians and the government around by using math than by using data, history, and informed judgment.