A theory is a set of sentences in a formal language.

A theory is a set of principles that explain and predict phenomena. The defining characteristic of a theory is that is makes falsifiable (thus, the questions asked must have boolean answer) or testable predictions.

A theory provides an explanatory framework for some observation, and from the assumption of the explanation follow a number of possible hypotheses that can be tested in order to provide support or challenge the theory.

Some distinguish between theory and hypothesis where a theory is a hypothesis that has been tested against facts. (Is that useful?)


1   Form

An axiom is an element of the theory; a statement that is accepted as true without proof.

A sentence is called a theorem if it an axiom or if it follows from the axioms.

2   Properties

A theory is consistent if no theorem contradicts another otherwise it is inconsistent.

A theory is complete if all true statements are provable.

A theory is sound if all provable statements are true.

A theory is valid if no false statement can be proven.

3   Paradigm shift

A paradigm shift (or revolutionary science) is, according to Thomas Kuhn, in his influential book The Structure of Scientific Revolutions (1962), a change in the basic assumptions, or paradigms, within the ruling theory of science.

Similar to Zeitgeist.

Similar also to duck-rabbit optical illusion.

There are anomalies for all paradigms, Kuhn maintained, that are brushed away as acceptable levels of error, or simply ignored and not dealt with (a principal argument Kuhn uses to reject Karl Popper's model of falsifiability as the key force involved in scientific change).

4   Grading

Sometimes theory can compete.