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In general, according to an article in DifferenceBetween.net

The main difference between rules and laws is the consequences associated with breaking them. While each is developed to invoke a sense of order, fair play, and safety, the weight of a law is much heavier than the weight of a rule.

However, in scientific context the situation seems to be somewhat different. For example, in scientific publications we can see Shannon's rule, Shannon's law and Shannon's formula and theorem that all refer to the same concept.

So, the question is what's difference between law and rule in a scientific context, if any?

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    That's a good question. I'm not a scientist so I can't give you a concrete answer, but I think law has more of a connotation of being an observable reaction that can always be replicated? I hope you can get some good answers to this.
    – John Clifford
    Mar 31 '16 at 7:46
  • I understand why you didn't attribute the above quote properly. But it comes across as an incontrovertible statement of fact. While there is much of value in the article, it is, in my opinion, almost claiming that the overlap between 'laws' and 'rules' [as the terms are 'generally used' (your term)] is virtually non-existent.
    – Edwin Ashworth
    Mar 31 '16 at 10:23
  • Also, 'in a scientific context' is ill-defined. By someone who has just read the Ladybat Book of Astronomy, or by Professor Sir Bernard Lovell?
    – Edwin Ashworth
    Mar 31 '16 at 10:40
  • This might be helpful: physicsforums.com/threads/…
    – herisson
    Mar 31 '16 at 11:03
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The only way I've ever heard rule used in a scientific context is with various conventions for solving problems — eg. Right-hand rule (for finding cross-product directions), Kirchhoff's Rules, etc. These are human constructs, but I suppose they're based on phenomena in nature that we've repeatedly observed and that seem to hold true. (so perhaps you could consider them as synonymous to laws).

According to livescience.com, a scientific law is:

"The description of an observed phenomenon. It doesn't explain why the phenomenon exists or what causes it."

As a separate note, it's important to recognize that one can't "prove" a scientific statement, and so no law or rule can be "proven." Science is based purely on making and attempting to explain observations of natural phenomena, and phenomena can of course change at any time and go against long-held observations - we simply don't know enough to make rigorously proven statements about nature.

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    The first paragraph of this response gets at the most important point. A rule is a scientific principle used as a tool, whereas a law is a scientific principle expressed as a fact. The same principle can often be expressed as a law or a rule depending upon the context in which it is used.
    – Solocutor
    Mar 31 '16 at 16:21
  • I think the key is that a rule is always true and a law is true as far as we know.
    – Max Williams
    Nov 22 '17 at 13:03
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There is the strict definitions and there are the coloquial uses (see above). The strict definition comes from statistical Physics (and therefore is valid for all sciencies). In short: laws - define interactions/behaviour while rules - define distributions/physical properties. Therefore, laws are deduced from hypotesis and their verification/falsification and rules come from directly/indirectly but measured physical/any properties. Rules and laws are mutulally exclusive and a given statement cannot be both a rule and a law.

For simplicity outside of certains fields of physics (like statistical Physics, general relativity and all quests for unifying theory) more fluid definitions are used despite not being strictly accurate.

As for theorems, postulates and formula they deal with different types of categorization and are not mutually exclusive in use with rules and laws.

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  • This is a very good explanation. A reference would enhance your answer.
    – Karlomanio
    May 9 '19 at 14:16
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I think they are synonyms when used in a scientific context:

Law:

  • a ​general ​rule that ​states what always ​happens when the same ​conditions ​exist:

    • Newton's laws of ​motion,

    • the laws of ​nature/​physics

(Cambridge Dictionary)

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They are not synonyms in the strictest scientific sense.

A rule is a statement that has been independently proven. The statement is always true. The use of rule in scientific notation is not necessarily as academically rigorous as other terms (e.g. theory, hypothesis or principle). It is used in, for example, Fleming's Left Hand Rule which gives a quick way of predicting motion under set circumstances.

A law is an independently proven statement from which other independently proven statements have been derived. A law is universally applicable.

Although a law is always applicable in all circumstances, in recent years the usage has blurred slightly. For example some of Newton's Laws have been shown not to be true under relativistic circumstances. However, they are still called laws thanks to several hundred years of accepted practice.

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    I don't see how the reference supports your definition of 'law' as used in the scientific domain as that subset of rules from which other rules have been derived. And you don't give a reference to support your claim that your definition of 'rule' is the 'strict scientific' definition.
    – Edwin Ashworth
    Mar 31 '16 at 10:37
  • I've found better links now and improved the answer.
    – Chenmunka
    Mar 31 '16 at 11:14
  • Thanks for the edit. The distinction you describe makes some sense, but it is still a little unclear to me (and I'm still not sure that these are really "strict" scientific definitions). It seems that both laws and rules are universally applicable/always true. So the only difference is that laws are used to derive other true statements (rules). Is that right?
    – herisson
    Mar 31 '16 at 11:16
  • I was always taught that x only became a law if hypotheses of the form "Given x then y must be true" resulted in a proven y.
    – Chenmunka
    Mar 31 '16 at 11:22
  • Are all scientific laws also rules? I guess that would explain variance in things like "Shannon's law/rule" or "Kirchhoff's laws/rules." I feel like a lot of things can be phrased in that format; couldn't we describe Fleming's Left Hand Rule as "Given that your first finger is pointing in the direction of the magnetic field (N-S), and your second finger is pointing in the direction of the current (positive to negative), then it must be true that your thumb is pointing in the direction of the movement of the wire."
    – herisson
    Mar 31 '16 at 11:27

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