>Mainstream exists in a form it is not because Mainstream translates the Truth™, but because there are no better theories yet.

Where have I heard that before? Oh yeah, the string wars in theoretical physics.

>Newton's mechanics is worse than Einstein theory in describing celestial bodies' movements, yet the former was better than anything until the latter appeared.

In its early days, the Copernican model was no better than the mainstream Ptolemaic model at describing the motion of celestial bodies:

For his contemporaries, the ideas presented by Copernicus were not markedly easier to use than the geocentric theory and did not produce more accurate predictions of planetary positions. Copernicus was aware of this and could not present any observational "proof", relying instead on arguments about what would be a more complete and elegant system.[0]

>I have a lot to argue against neoclassical economy, especially about its view of a person as a profit-driven (rational, as they call it) degenerate

I think you're confusing a person with a firm. A person has rational preferences[1] -- another unrealistic assumption -- while a firm seeks to maximise profits.

>The problem is that no heterodox theory provides both an axiomatic basis and empirical framework to compete mainstream economic science.

The idea that an axiomatic basis is necessary for a good theory is classic physics envy[2], and ignores the fact that even physics itself does not have an axiomatic basis, because that is Hilbert's sixth problem, which remains open.[3]

I don't know why this phenomenon is called "physics" envy anyway: it seems like you want economics to follow the model of Euclidean geometry, hence "mathematics" envy, which is even more absurd.

I get that mainstream economics has become more diverse, but neoclassical economics, which I believe is still the dominant school, is based on postulates that are simply unsupported by empirical -- and even mathematical -- evidence.

>What would you propose instead of Neoclassical economics? Nothing?

A critical synthesis of everything that isn't marginalism? An empirical search for a new framework with postulates backed by evidence?

And perhaps economists should learn more mathematics and have the courage to invent their own tools. After all, if you want to carry on with your physics envy, you should know that Feynman invented his own integral[4], which mathematicians derided for a long time for its lack of rigour... until its power became clear, at which point the functional analysts got down to work to extract the deep mathematics underlying Feynman's formalism.[5]

>It's not ignorance to accept theory that is not always true

This is an acceptance of Friedman's discredited positivism.

>it's stupidity to omit theory without having anything better

We have, and had, better: marginalism (aka neoclassical economics) was heavily criticised even during the 20th century. It's stupidity to cling to a theory when there are better ones.

[0] https://en.wikipedia.org/wiki/Copernican_heliocentrism#Early...

[1] https://en.wikipedia.org/wiki/Preference_(economics)#Applica...

[2] https://en.wikipedia.org/wiki/Physics_envy

[3] https://en.wikipedia.org/wiki/Hilbert%27s_sixth_problem#Stat...

[4] https://en.wikipedia.org/wiki/Path_integral_formulation

[5] https://ncatlab.org/nlab/show/path+integral