What is the primary difference between and hypothesis and a theory?
A hypothesis, on the other hand, is similar to a theorem, but it stands pretty much on its own and is not known to be linked to other theorems in any way. A hypothesis usually has no compelling reasons to be true or false. Hypotheses can be classified into the following categories:
- The degrees of freedom of a theory have not yet been determined. These could be properties of a theory that haven't been fully determined yet. A theory can be expressed in a finite number of ways, and accepting one of them is referred to as "forming a hypothesis." It's about the aspects of a hypothesis that aren't fully formed yet.
- Once evidence is discovered, a hypothesis may evolve into a theory.
- A hypothesis that could become a theory if a mathematical formulation can be established.
- A hypothesis based on common sense and known theories that is not intended to become part of a bigger theory, but rather to explain a single fact. This could include things like beliefs regarding the formation of the earth.
A theory derives a large number of predictions from a limited number of theorems or assumptions, which fall into the following categories:
- Things we already knew to be true and can be explained by other theories.
- Things we previously knew to be true, but which no other theory could explain or predict.
- Things that we didn't know were true but were later confirmed to be true.
- Things we didn't realize were true, and don't know if they are still true, but don't contradict current measurements.