Why are the sciences so well trusted, while other subjects are not?

 More specifically, why are sciences (physics, chemistry, engineering, et al) so well-trusted while other subjects (sociology, economics, politics) tend to be less trusted?  

What is asked would require a book chapter or even an entire book. What I’ll give is an answer furnished by the philosophers, but rarely applies to philosophy itself. It is the notion of Justified True Belief,* or JTB. This means you can justify your assertion (i.e. prove it based on accepted knowledge and logic), you establish it is true (thus not refutable), and you believe it. This is not quite how it is discussed in philosophy discussions. In most, one begins with the belief, then proves it’s true by some justification, which has a broad interpretation. What we have presented is how JTB works in the classroom. There we are presented with the truth (e.g. proposition), followed by its justification (e.g. proof, experiment), and finally, the student believes it. In scientific research, the process often begins with a “What if” type of question, and this leads to JTB in some but no specific order. Co-equal with JTB is the consensus of the foundations of the subject (in math called axiom) and methods of justification. For example, if a biologist justifies a truth using postmodern reasoning, it is likely given less credence than another, who uses strictly rigorous biological techniques.

Most of the sciences are built upon Justified True Belief. This gives them credibility, sustainability, and longevity. Yet, all these theories are subject to falsifiability, an event or argument that demonstrates incorrect foundations or spurious logic. All scientific theories have had “revolutions of falsification” over the centuries**. All scientists accept that current science is only temporary. This puts sciences in a permanent state of suspense. Remarkably, science as a whole accepts this, though substantial groups of scientists become wedded to their particular JTBs.

Beware of anyone who claims this science or that is closed, as in permanent and immutable. This is dead wrong.

On the other hand subjects such as politics, sociology, and economics do not have such conclusions, unless you accept what is given knowledge, agree on the structure of argumentation, and believe the conclusions. It is so, for instance, that economics pretends to be a science with rigorous arguments, but the foundation of any particular economic theory is a set of premises that less than a plurality agrees on. (BTW, there are at least 50 viable economic theories.)

Sociology and politics are similar. There is no firmament of foundations for either, each with multiple alternatives. Therefore, while you may have a justified true belief in any particular alternative, only a minority will agree. Consensus has proved impossible to achieve. Specifically, social-political-based consensus and justifications seem to have limited longevity.

This is a brief and incomplete explanation, but it furnishes a starting point to make distinctions.

*Justified true belief was once the lingua franca of new knowledge, but this has been recently demonstrated as incorrect. Check out the Gettier problem, as formulated by philosopher Edmund Gettier in 1963. More is available at https://medium.com/confusions-and-elucidations/justified-true-belief-fda233d35de1 and countless other sources.

** Well, maybe some laws such as Archimedes' Laws of The Lever and Buonancy have survived.