# Difference between a law of logic and a logical principle

The traditional notion of logic, broadly speaking) is that it is a system of laws and principles governing valid inferential reasoning (i.e. laws of logic logical principles). But what precisely distinguishes the one concept/category from the other; and is the distinction roughly the same in Aristotelian logic as opposed to modern propositional logic? In other words, in the domain of logic by what criteria does one characterize a principle as a 'principle' and a law as a 'law'?

Is it that a principle is more general or flexible than a law (or vice versa)? That principles are optional whereas laws are necessary? Is a law is simply stricter in both semantic definition and formalized description? Is a law necessarily reducible to mathematical equations/formulation, whereas a principle not [necessarily]? And do these distinctions hold in domains of [harder?] empirical sciences, such as physics or dynamics (eg. laws of physics vs physical principles)?

(Aside: The impetus of this question was an older post I ran into querying the difference between the law of the excluded middle (LEM) and the principle of bivalence (POB), which turned out to be more contentious and controversial than I expected. What is the difference between Law of Excluded Middle and Principle of Bivalence?)

• People call LEM "principle" and bivalence "law", albeit less commonly, I do not think there is a principled distinction, only colloquial habits. "Principles" are usually vaguer and sometimes have a "meta" quality to them, like Lagrange's principle in mechanics is a blueprint for deriving many specific laws, see use in physics. But this is loose, and they are essentially interchangeable with "laws". – Conifold Jun 28 '20 at 0:12
• Thank you, @Conifold. Particularly for the link, which was simple and very helpful to conceptualizing the purported distinction in the realm of physics. But in the domain of logic, as you imply, the terms are, really, equivalent, pace Quine, synonymous, ["you say "essentially interchangeable", and note that some call LEM a principle and POB a law], are they not. Is there a distinction to be drawn as to the validity of the distinction in the logical domain vs the physical domain? – gonzo Jun 28 '20 at 1:09