# Why is Perturbation Theory named “a theory”?

From Wikipedia:

In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. Usually a deductive system is understood from context. An element ϕ ∈ T of a theory T is then called an axiom of the theory, and any sentence that follows from the axioms ( T ⊢ ϕ ) is called a theorem of the theory. Every axiom is also a theorem. A first-order theory is a set of first-order sentences.

On the other hand,

A scientific theory is an explanation of an aspect of the natural world that can be repeatedly tested, in accordance with the scientific method [...]. Are testable and make falsifiable predictions. They describe the causes of a particular natural phenomenon and are used to explain and predict aspects of the physical universe or specific areas of inquiry

Perturbation Analysis or Perturbation Methods sound reasonable, but why Theory? How is it a theory?

Just a physicist asking mathematicians. Looking forward to interesting insights.

Thank you

• There are other fields than "mathematical logic" and "science in general". Theory could mean something different there. – Arthur Jan 10 '18 at 23:19
• – littleO Jan 10 '18 at 23:22
• Mathematical fields are often called "theory" : group theory, field theory,... even when they're not, say, first order theories : ergodic theory for instance, information theory. The word "theory" can have many meanings, even formally defined one (a Lawvere theory is very different from a first order theory, and they're both different from a homology theory) – Maxime Ramzi Jan 10 '18 at 23:50
• Assuming the word theory in "perturbation theory " means something precise is misguided. Theory means in that context, and in many others, just "bunch of results, methods, heuristics and what not that's e use to understand something". – Mariano Suárez-Álvarez Jan 11 '18 at 0:02
• (misguided because we rarely use words in technical meanings) – Mariano Suárez-Álvarez Jan 11 '18 at 0:03