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In my papers, I often need to formulate disjunctions textually (for example, when providing conditions for the fulfillment of a statement).

Let's see two examples:

  1. When you eat (a) apple, (b) pear, (c) orange, (d) banana, or (e) pinapple, you provide important vitamins for your body.

    (inclusive disjunction)

  2. I don't know whether Joe has (a) one, (b) two, (c) three, (d) four, or (e) five children.

    (exclusive disjunction)

Of course, the meaning of or is clear in these sentences, but one could give examples, where it is not evident whether inclusive or exclusive or is used.

Is there any way to emphasize the real meaning of or in (1) and (2)?

I usually fix in my papers that A, B, C, ..., or Z always indicates an inclusive disjunction, but what can I do when A, B, C, ..., or Z should mean an exclusive disjunction? How should I express such an exclusive choice?

user3840170
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TobiR
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    Different sentences may need different specifying strategies, but an obvious one for (2) which includes numbers is 'I don't know whether Joe has exactly (a) one (b) two (c) three (d) four or (e) five children.' (I'd omit commas as unnecessary clutter here, as the bracketed formatting letters offset quite adequately, but check with your in-house style guide.) (For (1), 'all or any of' is cumbersome but works. Slash for 'and/or' is itself ambiguous.) The inclusive/exclusive or ambiguity is well known. – Edwin Ashworth Jan 26 '21 at 11:10
  • @EdwinAshworth Thanks for this important ingredient to my question. The problem with (1) is not only "all or any of them", but "all, any of them, any two of them, any three of them, or any four of them" (shortly, at least any of them?). This makes multiple (triple, quadruple, etc.) disjunctions even more difficultly explicable. – TobiR Jan 26 '21 at 11:15
  • Yes, even 'all or any of ...' is 'inherently' ambiguous but has a default interpretation of 'any subset of' rather than 'the whole set or any single member of' in standard usage. Of course, 'any subset of' is the unarguable way to stipulate inclusive disjunction (subsets, unlike proper subsets, including the original set) but is mathematical jargon. 'Any one of' usually works for exclusive disjunction, and 'any one taken singly' underlines. What does a or b ... mean(not a dupe) is worth a look – Edwin Ashworth Jan 26 '21 at 11:23
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    Does this answer your question? Is there a contraction for non-exclusive or? (@Jason Bassford's doubtless unwelcome answer ... and he only gets as far as a two-element set). – Edwin Ashworth Jan 26 '21 at 11:30
  • @EdwinAshworth I think that your comments are more useful than the answer to the question you linked, because that answer is restricted only to binary formulas. – TobiR Jan 26 '21 at 11:33
  • Just precede your list by *any one of...* or *any combination of...*, according to the required sense. – FumbleFingers Jan 26 '21 at 12:10
  • Please show us an example of an unclear or that you are worried about. Also, are you actually writing "(a) one, (b) two, (c) three, (d) four, or (e) five" instead of one, two, etc? – Yosef Baskin Jan 26 '21 at 14:32
  • @YosefBaskin My instances where or is ambiguous are mainly of mathematical origin. I have recently had a mild dispute with my group leader over the following sentence: A spectroscopic database contains measured or computed transitions. He noticed that it can actually contain both, while I insisted on that this is included in the sentence (since or is inclusive here). The inclusivity of or was confimed by a follow-up sentence which stated that measured and computed transitions are usually mixed, therefore we cannot make a distinction between measured and computed databases. – TobiR Jan 26 '21 at 15:03
  • @YosefBaskin I generally use (a), (b), (c), ..., or (z) if the predicates following these symbols are long. – TobiR Jan 26 '21 at 15:08
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    A spectroscopic database can contain both measured and computed transitions. – Tinfoil Hat Jan 26 '21 at 16:38
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    Is this simply a variation of the familiar problem of how to disambiguate or in everyday English? The question does not make it clear how there being five disjuncts in each of the examples (rather than just two) is supposed to affect the problem. – jsw29 Jan 26 '21 at 16:47
  • @TinfoilHat has it correct. In this case you would not worry about or, but rather just say it a different way. – FeliniusRex - gone Jan 26 '21 at 17:03

1 Answers1

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Your question looks like how you can make "or" explicit between inclusive or exclusive.

  1. The context could provide information to distinguish them.

  2. You can add inclusive or exclusive, using parentheses like 'or(inclusive)', 'or(exclusive)'

ex) the probability of head or tail of one coin(one flip):

head or tail(inclusive (or)) = 1/2 + 1/2 = 1

head or tail(exclusive (or)) = 1-1/2 = 1/2

gomadeng
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