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What is a borderline case, and its relationship with vagueness? I have googled a lot but didn't quite find anything that suits my understanding.

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  • In computer science, borderline cases are test cases which may cause undefined behaviour due to illegal operations (eg: division by 0 needs to be handled separately), or due to limitations of the data structure used (null pointer exception). Vague understanding of the problem or algorithm/data structure may hide borderline cases.
    – Ajax
    Jun 1, 2022 at 11:14
  • In abstract, all sets are defined by boundaries (e.g. a set of selected dots is defined by the imaginary border line holding such dots), and borderline cases are those that are produced near a boundary (e.g a dot that touches the border), which in multiple cases are problematic (being it so close to the border, which side does it really belongs to? Is such dot really a member of the set?). For a more concrete definition, please specify the context. For example, water atoms floating at 1nm near the surface of the water, are they part of the sea, or part of the cloud?
    – RodolfoAP
    Jun 1, 2022 at 11:51

2 Answers 2

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Best not to overthink this. A borderline case is merely a case that partially, incompletely, or imperfectly fits a category, theory, or paradigm. For instance, if we think about the category 'motor vehicle' there are the obvious cases like cars, motorcycles, and trucks. But then there are an assortment of things like electric scooters, motor-assisted bicycles, Segues, and hoverboards that are technically 'vehicles with motors' but are not normally thought of as 'motor vehicles'.

Sometimes borderline cases are mere annoyances of the "I don't know what to do with this" variety; sometimes they provide fruitful areas of research or point out places where definitions need to be tightened or refined. In any case, they are pragmatically unavoidable. Every human concept inevitably has a clear center with fuzzy edges.

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  • + 1 And some cases, like a self-identified trans-woman with male genitals, can cause tremendous political strife and test our worldviews.
    – J D
    Jun 1, 2022 at 16:30
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A lot of thinkers fall into a trap of thinking that there is one correct definition, and that somehow language is tidy, like a mathematical theorem. No such luck. Ludwig Wittgenstein famously adduced the family resemblance argument during the linguistic turn to push back on the idea that words have a purely objective status. Today, some linguists defend prototype theory extending from there philosophy of language to show that there are borderline cases, cases that don't neatly fit into a category.

The example I like to use is the spork, and the question, is the spork a spoon or a fork? The claim that it's spoon-like and fork-like appeals to our philosophical intuitions. But if you had to put away in your silverware drawer, do you put it with the spoons or the forks? I think it's fair to say, as trivial as the question is, it raises the same sorts of questions as the sorites paradox. Borderline cases, or any of the synonyms, are thus challenges to our thinking philosophically.

To be technical, some entities have a mix of properties that challenge our categories. These entities then challenge our notions of identity, membership, and analogy, and even our presuppositions about the Laws of Thought. Famously, Victorians tried to argue natural kinds in a last ditch effort to sustain Aristotelian thought. Today, biological notions of clades take a more relativistic approach to categories. A platypus is another example of a borderline case. Borderline cases therefore go to the heart of profound metaphysical debates, such as the validity of the debate between scientific realism and instrumentalism.

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