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It is a common thing to say that, when an "exception" is found, this proves (as in it provides evidence) there is a rule (or succinctly stated as "the exception proves the rule").

Is there a logical/scientific basis for this claim? In this sense, is it truly valid in argumentation, logical thinking, and scientific enquiry?

The Wikipedia article about the phrase is poor on sources and rich on unsupported claims. A more robust analysis of the issue would be greatly appreciated.

PS: this question, albeit with a related title, doesn't really address the issue, but focuses on a very narrow example.

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    NO; if a rule is a "general" statement, then an exception disproves the rule. This if we wnat to use the word "to prove" in a sense related to logic (as per tag of the question). – Mauro ALLEGRANZA Jan 16 at 15:59
  • @MauroALLEGRANZA the comment sounds like an answer! – luchonacho Jan 16 at 16:34
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    You could claim this is the equivalent of Popper's criterion. Something can only really be a rule if it has a domain of application, and there are things potentially outside that domain. No 'edge cases' means no boundary, which means no domain, which means no rule. Otherwise it is an unfalsifiable assertion, which means it has only misleading uses. (So there is a meta-scientific basis, if you accept the most widely accepted standards for what qualifies as a scientific assertion.) – jobermark Jan 16 at 19:16
  • It is a psychological trick to say that an exception proves the rule. – rus9384 Jan 17 at 8:32
  • I've always understood it to be using the definition of proof that means "able to withstand something damaging; resistant." Exceptional cases are what test the rules. – kbelder Jan 17 at 19:09
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The Wikipedia article referenced by the OP provides a summary of Henry Watson Fowler's analysis of the the phrase "the exception proves the rule" as it is used in English in Modern English Usage.

Fowler traces the original meaning of the phrase to a defense by Cicero. Here is how the Wikipedia article describes that original and most correct use of the phrase according to Fowler:

The phrase is derived from a legal principle of republican Rome: exceptio probat regulam in casibus non exceptis ("the exception confirms the rule in cases not excepted"), a concept first proposed by Cicero in his defence of Lucius Cornelius Balbus. This means a stated exception implies the existence of a rule to which it is the exception. The second part of Cicero's phrase, "in casibus non exceptis" or "in cases not excepted," is almost always missing from modern uses of the statement that "the exception proves the rule," which may contribute to frequent confusion and misuse of the phrase.

The exception shows the existence of a rule for all cases not excepted.

Fowler objected to the use of the phrase when it suggested the following:

  • Exceptions can always be neglected.
  • A truth is all the truer if it is sometimes false.

This appears to be what the OP is objecting to as well when OP asks:

Is there a logical/scientific basis for this claim? In this sense, is it truly valid in argumentation, logical thinking, and scientific enquiry?

Fowler would agree that there is no basis for this claim if it means that exceptions can be neglected or that the truth is always truer if it is sometimes false.

If one considers the use of falsifiability as a criteria for science, identifying possible exceptions to a theory, exceptions that have not yet been observed, would discredit a theory requiring that a revision to the theory be made. As Wikipedia puts it:

A statement, hypothesis, or theory has falsifiability (or is falsifiable) if it is contradicted by a basic statement, which, in an eventual successful or failed falsification, must respectively correspond to a true or hypothetical observation.

These two approaches to exceptions are different. In Cicero's case, the actual existence of the exception proved the existence of a rule in all cases not excepted. A theory is considered falsifiable, on the other hand, if one can identify potential exceptions, that may not ever be found, to show whether a theory needs to be modified or rejected.


"Exception proves the rule" Wikipedia https://en.wikipedia.org/wiki/Exception_that_proves_the_rule

"Falsifiability" Wikipedia https://en.wikipedia.org/wiki/Falsifiability

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    But Cicero was a lawyer and not a scientist... Thus, the historical origin that you reported gives a correct context to understand the dictum and the conclusion is : it has nothing to do with scientific inquiry and "proof" or test in a scientific context. – Mauro ALLEGRANZA Jan 17 at 7:55
  • @MauroALLEGRANZA I think one needs to understand where the phrase comes from to see that it is not correct to apply it in a scientific context where the exception can be used to falsify not prove a theory. – Frank Hubeny Jan 17 at 8:18
  • The exception, however vouches for the possibility of falisifiability. That clarifies that this is in fact a rule, and not a trick of language or a conceptual gap. The need to clarify the domain of application is proof of falsifiability. It is not the only way to vouch for falisifiability, but it is a very common one. Once the rule is edited to exclude the exceptions, then the other half of Cicero's actual standard applies, which we omit. – jobermark Jan 17 at 10:04
  • @jobermark In a scientific context if one found an exception one would modify the rule. After finding a black swan one modifies the rule that all swans are white to allow for both white and black swans. Although I don't know the context, I suspect in Cicero's case, one had an exception but one wasn't sure legally if there was an actual rule or not. In the scientific case, the existence of the rule (or theory) is not the concern. So, I think we agree on this unless I misunderstood. – Frank Hubeny Jan 17 at 10:22
  • @Frank At first one would check if that exception is not simply a result of wrong setting or some kind of error. To find an exception one needs many experiments. – rus9384 Jan 17 at 11:39
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At least in some of the cases, the kind of “proof” that we have in “the exception proves the rule” is a conversational implicature. In other words, it is an implication, in the context of a conversation, or more generally an instance of communication. Where

  • Party A communicates a content a1
  • Party B understands that A meant a1, and also concludes that A implied another content a2.

A said a1 => A implied a2

where the conclusion a2 is based, not just on the given a1, but also on general, reasonable assumptions about the way people communicate. And since this involves a step like locating the most relevant general rule (as we’ll immediately see) it involves not only logical deduction, but an inference to the best explanation.

The case of “the exception proves the rule” seems to be based on the highly general trait, in communication, which is that we often state only the exceptional, and do not bother to state the rule, the ordinary. So for example when I get to work in the morning, I am not likely to tell my workmates “I brushed my teeth this morning”. I am more likely to tell stuff like “I left my phone at home”. With the implication that, as a rule, I do not leave my phone at home. The exception proves the rule.

Similarly, when a sign adverts that “parking is prohibited between 7am and 5pm”, it is normally implied that parking is not prohibited at other hours. When we read the sign, we are expected to be able to decipher the implied rule, by an inference to the best explanation. In this manner, the exception implies (proves) the rule.

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It's merely a turn of phrase which is asserting that this exception does not disprove the general rule.

This is because in real-life, general rules admits many exceptions and qualifications; but in real-life, no-one has the time or the inclination to state all the many exceptions and qualifications that makes the rule true without exception.

As a general rule, birds are quite small animals; but then you get exceptions like ostriches, emus and condors.

  • No, it most definitely does not mean that. Fowler has had very few people argue against his analysis of the phrase. – jobermark Jan 17 at 16:55
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    @jobermark: Who is Fowler and where did he write about this phrase? – Mozibur Ullah Jan 17 at 17:07
  • 'Fowler's' is the best recognized compendium of prescriptivist corrections to our understanding of English grammatical and usage mistakes, orignally from the Victorian era. The argument quoted in almost all these sources comes from "Fowler's". The original author is a person, but the book has been maintained after his death, even though the arguments included are no longer all his, personally they are usually attributed as if they were. It is like quoting "Merriam-Webster" as if that person existed. – jobermark Jan 17 at 17:14
  • @jobermark: Whats the name of his book? – Mozibur Ullah Jan 17 at 17:14
  • 'A Dictionary of Modern English Usage' More recent editions are "Fowler's Dictionary of Modern English Usage' -- ironically the ones not edited by him. – jobermark Jan 17 at 17:16
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Prove in this context means "test." As in a proving ground for high performance cars, for example. The exception tests the rule. That makes sense, right?

A proving ground (US), training area (Australia, Ireland, UK) or training centre (Canada) is a military installation or reservation where weapon s or other military technology are experimented with or are tested, or where military tactics are tested. [My emphasis]

https://en.wikipedia.org/wiki/Proving_ground

An alternative explanation often encountered is that the word "prove" is used in the archaic sense of "test". Thus, the saying does not mean that an exception demonstrates a rule to be true or to exist, but that it tests the rule. In this sense, it is usually used when an exception to a rule has been identified ...

https://en.wikipedia.org/wiki/Exception_that_proves_the_rule

Prove: to test the truth, validity, or genuineness of

https://www.merriam-webster.com/dictionary/prove

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I would say that people use this expression as shorthand to summarize a situation that has the following conditions:

1) Lots of observations of something that's uninterestingly normal

2) Little talk about the observations or the norm

3) Something unusual happened that we're talking about now.

The long form is like this: "After this unusual event happened, we started talking about it and drew a lot of attention to this one unusual event. You know, it's funny but I've never thought too hard about it, but I always expect things to go the normal way... that's why this unusual event was so surprising!

"It's like there's an unspoken rule about everything always happening normally that's really powerful because we so seldom see it broken. Now that this exception to the rule happened, I can see that I know of so many times when things have gone normally and I can see that that's not about to change just because this one exceptional thing happened.

"It was the exception that proved the rule."

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