Quite often, “or” is used when “and” is called for, as with (correct) “examples are X and Y” and (incorrect) “examples are X or Y”.
Here, I will attempt some incomplete guidance on when to use “and” and when “or”, and when something else. This, especially, with an eye at the many who use “or” in situations that call for “and”.
Note that I have not always followed my own advice, especially in writings that predate a particular opinion or insight. Some more current examples are mentioned in the continuation.
The first sentence shows how tricky matters can be: In my first draft, I had ‘[...] when to use “and” and “or”,’ and thought nothing of it. Proof-reading, I saw a potential source of ambiguity or something that might be less obvious to the reader, and proceeded to explain that “and” was justified by the phrase being an abbreviation of ‘[...] when to use “and” and when to use “or”.’—but that a weaker case could be made for “or” too. Then I thought better of it, added a second “when”, and saw the issue resolved. This is a good example of how more explicit formulations can be helpful.
(The weaker case for “or” over “and” related to the fact that most of the discussions on this page deal with an either-“and”-or-“or” choice. Actually explaining that case in a reasonable manner was harder than I had anticipated—and a partial motivation for adding that extra “when” was to avoid the explanation.)
Which conjunction is correct can depend on the exact intent: “or” and “and” might both be quite possible but result in different meanings. Contrast e.g. “I will send Jack and Jill” with “I will send Jack or Jill”. In the former case, both are sent; in the latter, just one of them, while leaving open whether it will be the one or the other. (With a secondary ambiguity in that the “or” can have the implication “and/or”—the one, the other, or both.)
For the sake of brevity, I usually have not discussed such alternatives when the one seems much more likely than the other. Instead, there is an implicit disclaimer of “unless the writer [speaker] actually means something other than he appears to mean”. (Of course, that such differences exist makes it the more important to pick the right word, lest the reader be misled about the intentions of the writer and/or has to waste time with re-interpretation based on the overall context.)
In addition to “and” and “or”, I use “[?]” as an indicator of where in an example one of “and” and “or” belongs, with the implication that the correct choice is still not determined. (Be it because of an underlying uncertainty or because uncertainty is temporarily pretended.)
I sometimes emphasize these conjunctions in examples for better contrast (as well as the odd other word). I considered doing so throughout, but (a) too much emphasis can be distracting, (b) the reader presumably will pay attention to the conjunction anyway. (Examples with such emphasis are usually among the first written—not necessarily those where emphasis would be particularly beneficial.)
Letters like “X” and “Y” are occasional placeholders for something more specific, but irrelevant or unknown, e.g. a name of some human that is perfectly replaceable.
The use of some number of items in an example should not normally be taken to exclude other numbers (in particular, in exactly-two vs. more-than-two contrasts, like “Tom and Dick” vs. “Tom, Dick, and Harry”). Exceptions should be clear from the text or context.
My use of “speaker”, “writer”, and similar words is inconsistent, and the choice of word has no particular significance. (This largely as a result of my writing this text in several sessions with weeks in between them. I leave this and some other issues unimproved for now, in order to finally get the text published.)
On occasion, I will use this text, it self, as a source of illustration. I have not attempted to do so throughout, because it would clutter the text immensely, but have saved the approach for cases that, in the moment of writing, seemed to make especially good illustrations.
A good rule of thumb: If a statement using “or” can be countered with “Well, which is it?” (or a similar question adapted to the details of the statement) and that question makes sense, chances are that “and” was the right choice.
Consider “examples of pets are cats or dogs”: Well, which is it? Are cats examples or are dogs examples? (Also see the next section.)
I use this particular type of formulation to match frequent encounters in the writings of others. However, such formulations can also be criticized from other angles, notably through risking an impression of an exhaustive list (implying that e.g. rabbits cannot be pets). Writing for myself, I might have used “examples of pets include cats and dogs”, while “cats and dogs are examples of pets” is a good work-around for those who prefer “are”. Leading with “cats and dogs” also has the advantage of showing how odd “or” would be, as “cats or dogs are examples of pets” is more likely to be recognized as wrong by those using “examples of pets are cats or dogs”.
Something similar applies to “X bought a cat or a dog” below: It matches common patterns of use, but it is far from ideal. Using an “either”–“or” construct would be better (as a more explicit formulation). With both “either”–“or” and just plain “or”, some explanatory words might also be helpful, as with “X bought [either] a cat or a dog. I do not remember which.”.
(Similar remarks can apply elsewhere without comment.)
In contrast, “X bought a cat or a dog” is a less likely target (and “X bought a cat and a dog” is so obviously different in meaning that an accidental error is unlikely), because the speaker would presumably have specified just “cat” or just “dog”, had he known. By implication, it can be assumed that he does not know and the question of “Well, which is it?” does not make sense. With “examples of pets are cats or dogs”, we might have some rare instance when someone really does not know; however, for the vast majority of cases, knowledge will be present and a poor choice of conjunction is a far likelier explanation.
Likewise, if a parent offers that “you may have a cat or a dog for your birthday” to a child, the question does not make sense, because the intent is almost certainly to offer the decision to the child. For the child to counter with “Well, which is it?” would be contrary to the idea. (Notwithstanding the possibility that a sufficiently young child might misunderstand the situation.) If some variation of the question is to make sense, it is not as a counter by the child but as a follow-up by the parent (“Well, which do you prefer? You have to tell me now or I will not have it ready in time.”).
Note that the idea of “makes sense”, in this context, must be seen in light of the speaker’s intentions, knowledge available to the speaker, etc. For “X bought a cat or a dog”, the question is not inherently nonsensical. (While the question directed at e.g. “X bought a cat and a dog” would be inherently nonsensical.) The issue is that the question is contrary to reasonable expectations in the given situation. If it is asked, chances are that the speaker would react negatively and/or give a clarifying answer that explains exactly that if he had known, he would have said just “cat” or just “dog”.
Also note that some similar questions do not pose an obstacle, because they play in better with the speaker’s intentions, whatnot, and do not speak in favor of “and”. For instance, “Well, can you find out which?” makes sense but is perfectly compatible with “or”. Indeed, if this question makes sense, it outright speaks against “and”.
Lists should usually use “and”; lists of examples, in particular. (Assuming that a conjunction is used at all.) The reason is simple—the intent is usually to give a set of elements that all simultaneously have a certain characteristic. For instance, the above “examples of pets are cats [?] dogs” must use “and”—“examples of pets are cats and dogs”. For instance, “students X, Y, [?] Z will receive detention” must use “and”—“students X, Y, and Z will receive detention”. For instance, “none of X, Y, and Z” is correct, while substituting “or” is nonsensical (also see excursion on De Morgan below).
The very abstract formulation of “a set of elements[...]” results from the very many and very differing cases that can apply—and even so should be taken in a wide sense. For instance, an alleged seers claim that “X, Y, and Z will all become kings” uses “and” by this motivation. This despite complications like the claim referring to something that might or might not actually happen, the debatability of whether at some future point (maybe) becoming king is a characteristic, and that the three need not all be kings simultaneously, e.g. should they succeed each other on the same throne. (To the last: The point is rather that the claim of will-become-king applies simultaneously to all three. More generally, interpretation of this-and-that must be done within the claim of the speaker, not the opinions about reality of the hearer. Also note “between” below: Even if only one of two is ultimately chosen, the list of choices includes both.)
Here we also see a case of disambiguation by additional words, as the combination “or” and “all” would be odd indeed. More on this further below.
Here it can also often help to mentally rewrite some cases, e.g. to give a lengthier “X will receive detention, Y will receive detention, and Z will receive detention”. (But I stress that I do not suggest that the actual text be so altered.) The results can be revealing.
The use of formulations with “including”, “such as”, “for example”, and similar are very strong indicators that a list requires “and”. (Below remarks on “e.g.” notwithstanding.) In a twist, the preceding “The use of [...] and similar [...].” is an example of a sentence that could be argued either way: If it is seen more as a list of examples being rounded off, “and” is better; if it is seen more as a broad characterization based on examples, “or” might be superior.
In the case of two entries, the word “between” is often relevant, as in “the choice between a cat and a dog”. It is always “between”–“and”. This also give a strong analogy argument when, without between, more than two entries are present. An “or” may occur in the same textual context, but then serves some other purpose than coordination with “between”. (Consider “a fight between a cat or a dog and a rat or a mouse tends to be one-sided” and contrast it with “[...] between a cat and a dog or a rat and a mouse [...]”.) The same applies to “both”—it is always “both”–“and”. (Other examples are likely to exist; in reverse, we always have e.g. “either”–“or”, never “either”–“and”.)
My own writings contain at least one very frequent exception in the use of “e.g.” in combination with “or”, as the use of “and” often looks a bit weird or confusing in my eyes. This the more so when the examples given are somewhat longer. Consider “e.g. by playing with a dog or petting a cat”. I am often in two minds about such formulations, but an “or” will usually be a conscious decision. (Here, to avoid the misunderstanding that someone should both play with a dog and pet a cat. More on such misunderstandings below.) A partial issue is that “e.g.” has come to border on punctuation to me, rather than being an abbreviation.
A borderline case is “consider”, which I often couple with “or” and often split into more than one sentence. I might then say “Consider [full sentence example]. Or consider [other full sentence example].” rather than “Consider [full sentence example] and [other full sentence example].”. This can nominally be defended by an “and/or” interpretation (also see below) and a choice left to the reader—the reader may chose to consider the first example, the second example, or both. (Or, obviously, neither.) My intention is typically that he should consider both, but there is hardly a legal obligation for him to do so.
A similar matter of choice can be argued in some “e.g.” cases, including whether to play with a dog or to pet a cat, while an “examples of pets are cats and dogs” is non-negotiable. Things are what they are and the reader is not given a choice in whether it is cats or dogs—it is cats and dogs. (He might disagree with some classification, certainly, but he moves outside the writer’s intentions if he does.)
(Off topic, I also have a long history of redundant formulations like “consider e.g.”. I try to do better.)
There is at least one (likely more) alternate uses of “or” that can cause confusion, namely for purposes like introducing an alternate name or an explanation. Consider “John saw the Evening Star[,] or Venus[,] as he walked home”. (While I would likely write this sentence with the commata, or some other means of parenthesis, many others would leave them out, making a misinterpretation the likelier—and commata are not audible when someone speaks.) Here John did not see one of the two, because the two are the same, but someone lacking the right knowledge might not understand this—including a hypothetical reader from a time when this identity had not yet been established. Likewise, the same type of confusion might arise around some more obscure identity. Now combine this with a tolerance for “or” where “and” should be used and great confusion can arise, in that someone might think that John saw the Evening Star and Venus based on that “or”.
Venus can also be used to illustrate cases where both “and” and “or” can be legitimate, if with slightly different meanings.
Notably, Venus is not just the Evening Star but also the Morning Star. However, not both apply at the same time, because the one is restricted to the evening and the other to the morning. We might then have a claim of “Venus can also be called the Morning Star and the Evening Star” in order to emphasize that both are possible or “[...] or [...]” to indicate some dependency on context (notably, time of day). (In both cases, chances are that such details would be clear from the surrounding text, but there is no guarantee. I would likely have put both variations of “Star” in quotation marks to emphasize the difference between name and underlying entity, but most others do not seem to do so. Likewise, I might have used a more explicit formulation to remove ambiguity.)
Contrast this with e.g. aconite/monkshood/wolfsbane (and further names). These three names seem to be virtually interchangeable and a case for “or” would be weaker than for Venus.
Above, I capitalize “Morning Star” and “Evening Star” in order to emphasize the aspect as name or quasi-name, and to make the combination with “Venus” a better example. Chances are that most other uses see the non-capitalized versions, making the terms more descriptions than names.
This is also potentially reflected in the sometime use of such descriptions for other astronomical objects—a complication that does not affect the above examples, but does open the door for reverse examples.
Many problems are caused by formulations that lack explicitness or are ambiguous. This, especially, through insisting on an ‘X [?] Y” format.
Take the complication that “or” is usually an inclusive “or” (an implicit “and/or”), implying that a restriction to one alternative (i.e. an exclusive “or”) might need a more explicit formulation—which is not necessarily provided. The most natural interpretation of “X, Y, or Z will solve the problem” is that at least one of them will, but there is no guarantee that this is what was intended and it is better to be explicit and say, depending on intentions, “at least one of X, Y, and [sic!] Z will solve the problem”, “exactly one of [...]”, or whatever might apply. With only two options involved, a phrasing like “either X or Y will solve the problem” is a cheap way to disambiguate. Ditto, in the other direction, “both X and Y will solve the problem”.
But note that details and context might make such disambiguation unnecessary. For instance, “X, Y, or Z will be the first to solve the problem” points to “exactly one”, because the first solver can usually be taken to be unique. (There can be disagreement about who was first and times of completion can be too close to make a meaningful distinction, but this is more a matter of a problem of identification. Travel at “relativistic” speeds could cause problems, however.) For instance, “X, Y, or Z will win the tennis tournament” will, with typical rules, point to “exactly one of”.
As a counterpoint, it can be dangerous to rely on such details and context, and it is better to err on the side of explicit disambiguation, because the reader might lack the right information, circumstances might change, the writer might overlook some complication, or similar.
In logic, programming, whatnot, the term “xor” is often used to imply an exclusive “or”. I have long been tempted to use it in my own texts, but I fear that too many readers would be confused. However, a language that used separate single words for what amounts to “and”, “and/or”, and “xor” would be a good thing—and if “or” is taken to imply “and/or” without exception, then just adding “xor” would be enough to achieve this.
The counterpart of “X, Y, and Z will solve the problem” does not have this ambiguity, but does have its own problem. (Which might be a partial explanation for the overuse of “or”.) Is the implication that X, Y, and Z will each individually solve the problem or that they will solve it as a group? Here formulations like “each of X, Y, and Z will solve the problem” and “the team of X, Y, and Z will solve the problem” are preferable.
In the other direction, if an inclusive “or” is wanted, then it is often better to explicitly speak of “and/or”. This is often ugly (and frowned upon by many), but it can also be beneficial in light of the many uses of (just) “or” in an exclusive sense—and getting the right message across is more important than aesthetics. (My own use is inconsistent, as can be seen in this text.)
Other examples of words that can make sentences clearer include “neither”–“nor”. Consider a claim like “never work with animals and children”, with an ambiguity of whether the intent is to “never work with animals and never work with children” or to (approximately) “never work with animals and children at the same time and in the same place”. In the first case, the temptation to use “never work with animals or children” is understandable, as it avoids the ambiguity, but it is vulnerable to e.g. a “Well, which is it?” (cf. above). A better choice is “work neither with animals nor with children”. (If brevity is an issue, “work with neither animals nor children” can be used, but at the risk of moving the negative nature of the phrase too far back.)
I will not attempt a complete discussion of all relevant words/phrases, but do note that others exist, e.g. “either of”/“any of”.
Much of this section deals with cases where I do not necessarily practice what I preach, be it out of thoughtlessness, a lack of self discipline, or a wish to avoid the increase in sentence length that tends to follow. (Here “or” is correct, as it generally is with “be it”. In contrast, something like “for reasons that include X, Y, [?] Z” would have required “and”. Here the “Well, which is it?” test can be illuminating.)
I suspect that some misuses go back to a lack of understanding of what is often referred to as De Morgan’s laws and of when they do or do not apply to natural language. (Such an understanding does not require a study of logic. They are fairly intuitive.)
For instance, the claim that “it is not the case that Jack and Jill went up the hill” is equivalent to “Jack did not go up the hill or Jill did not go up the hill” (where “or”, here and elsewhere, is an inclusive “and/or”). It is possible that neither went up the hill—but it is not necessary. Consequently, a translation into “Jack did not go up the hill and Jill did not go up the hill” would be logically faulty, not equivalent to the original statement, and only potentially matching “in-universe reality”.
In terms of phrasings, I stick more closely to the shape of the typical logical formulae than I would in another context, to make matters more obvious to the (I hope) many readers who are familiar with them. (These amount to “not (A and B)” being equivalent to “(not A) or (not B)” resp. “not (A or B)” being equivalent to “(not A) and (not B)”.)
More natural phrasings have similar problems in the underlying logic (or this excursion might be pointless), e.g. with “neither Jack nor Jill went up the hill” instead of “Jack did not go up the hill and Jill did not go up the hill”.
In reverse, “it is not the case that Jack or Jill went up the hill” matches exactly that “Jack did not go up the hill and Jill did not go up the hill” (resp. the “neither”–“nor” of the above side-note).
For instance, while a phrasing like “none of X, Y, [?] Z” might superficially look like something relevant to De Morgan’s laws, it is not, because “none” is a quantifier—not a negation. We then have “and”. (Note: In the following examples I use “was” regardless of number. This, in part, in order to keep the focus on the conjunction and to allow easier comparisons between phrases and with the “number-less” logical formulae; in part, because some cases might see a difference in opinion about whether “was” or “were” is correct.) Compare e.g. the statements “none of the Beatles was born in Paris” with “none of John, Paul, George, [?] Ringo was born in Paris”. For the two claims to match, clearly we must have “and”. In contrast, a formulation actually using a negation would logically require “or”—“it is not the case that John, Paul, George, or Ringo was born in Paris”. This equates to “John was not born in Paris and Paul was not born in Paris [etc.]”, which is the intent. In a double contrast, “it is not the case that John, Paul, George, and Ringo was born in Paris” is equivalent to “John was not born in Paris or Paul was not born in Paris [etc.]”.
A related (but usually off topic) problem is a failure to keep negations where they belong. Above, e.g., “it is not the case that John, Paul, George, or Ringo was born in Paris” is not equivalent to “it is the case that John, Paul, George, or Ringo was not born in Paris”. The former demands that none of them were; the latter, that at least one was not.
Quantifiers might be discussed further at a later time. For now I note that something similar can apply to quantifiers too, e.g. in that “not everyone likes the Beatles” is equivalent to “there are some who do not like the Beatles”—not to “everyone does not like the Beatles”/“no one likes the Beatles”. (With reservations for weird special cases, notably, when the set quantified by “everyone”, etc., is empty.) More generally, there are great similarities between elementary logic and elementary set theory.
Never, ever, under any circumstances use “plus” instead of “and”, “also”, and similar words.
In the weeks after the original publication, I have ever more strongly come to suspect that the reason for the overuse of “or” is often specifically a failure to use a phrasing like “both X and Y”. (Also see parts of the rest of the text for both some reasons and for examples of how to use “both X and Y”—or note this sentence, it self.) This, especially, when an unfortunate word order is chosen, words are stricken, whatnot.
I have also developed the suspicion that I have, myself, underused “both X and Y”...
Consider a phrase like “in the bad weather, it was hard for planes both to land and to take off”. As it stands, the sentence should be clear, but say that someone left the “both” out and/or had a word order/whatnot problem. We might then have “[...] planes to land and take off”, which can create the impression that the combined action of landing and taking off was hard, but, maybe, that each taken individually was not remarkably harder than on a normal day. As with at least one earlier example, it is easy to see the temptation to duck this by going to “or”—“[...] planes to land or take off”. (Which, again, fails on “Well, which is it?”.)
Issues like word order and stricken words are less relevant to this text, but consider e.g. that “both to” and “to both” can have different implications. Using “to both land and take off” above, e.g., would make the impression that the combined action of landing and taking off was hard much more plausible than with the original formulation—even while using a “both X and Y” formulation.
A more subtle case is the comparison of “land” followed by “take off” with “take off” followed by “land”. If the original sentence deals with the situation at a single air port for regular travel, the former combination is more plausible as a “combined action” than the latter. Take offs followed by landings by the same airplane, at the same airport, and without intermediate landings and take offs elsewhere, do happen, even for the likes of Lufthansa, but they are much rarer than landings followed by take offs. A reader might then come to a different conclusion depending on word order. To boot, the conclusion can depend on the reader, the reader’s knowledge, the reader’s assumptions, whatnot. For instance, if one reader assumes an airport with small flights for private entertainment in a Cessna and another long distance travel in jumbo jets, their reactions to word order might be very different. For instance, some readers (I being one of them) might be more likely to pay attention to issues of word order than the majority of readers.
(Indeed, I originally had the order “take off” followed by “land”, saw such complications weaken the example, and reversed it to the current “land” followed by “take off” order. Note that this weakening took place through a potential disambiguation that was unwelcome in this specific context. In almost all other contexts, it would not be a negative; in many, an outright positive.)
Another likely cause is the use of a conjunction that might be correct in the one approximately equivalent phrasing but not the other, through a failure to understand what goes on grammatically and/or to think properly about language. Consider the earlier example of “you may have a cat or a dog” which is approximately the same as “you are given the choice between a cat and a dog”. Someone too fixated on the choosing might make the mistake of “[...] between a cat or a dog” because “or” happens to be correct in “you may have a cat or a dog”. (The case can be more obvious with the alternate phrasing “you may choose a cat or a dog”. I go with the “have” version for consistency with earlier portions of the text.)
Some trick formulations can give insight into these matters or point to the right way to think.
Consider two examples (with variations):
A man sees an add in the paper to “Send in $50 and learn how to play the piano!”. He sends in the money to the indicated address and shortly receives a reply: “Thank you for the money. Now remember to learn how to play the piano!”
In this hackneyed joke, the man is tricked by the contextually warranted but logically incorrect conclusion that the “and” brought a causal or reciprocal connection—if he sent in $50, the recipient would, somehow, arrange for the man to learn how to play the piano. In a strict interpretation, however, we simply have two imperatives “Send in $50!” and “Learn how to play the piano!”. A better formulation, had the other party not been a fraudster, might have switched the “and” to a “in order to” or gone down an entirely different road, e.g. “If you send me $50, I will teach you how to play the piano!”. A notable point is that this trick would not have worked with “or”, which (in any formulation that I can immediately think of) does not carry a risk of interpretation as causality. To boot, just sending in the $50 would have fulfilled the imperative to send in the money or to learn how to play the piano, but that would likely be little comfort if the money had still been sent in—the better solution is to learn how to play while keeping the money.
Throwing a wider net, we might even criticize the original formulation for ambiguities in other areas, notably, whether the two activities can be performed separately or are intended to be concurrent. Note “Send in $50 while learning how to play the piano!”. Ditto, for a more realistic example: “Stand on one leg and touch your nose!”, which, as e.g. a test of sobriety, implies that the subject should touch his nose while standing on one leg. (Note that the positions of the respective activities in the “and” case are arbitrary to a higher degree than in the “while” case. In the “while” case, the opposite arrangement is conceivable but highly unlikely because of the nature and presumable length of the respective activities.)
Question: Two (U.S.) coins sum to 30 cents. One of them is not a nickel. What are they?
Answer: A quarter and a nickel.
end{quote}
Here, I suspect two categories who fall for the trap of assuming that neither coin is a nickel, namely, children, who might be weak in comprehension, and those teens or adults who are too forgiving in their interpretation, who might reason that “while he did not say that neither coin was a nickel, this is obviously what he meant”.
Also note how this example plays in with De Morgan’s laws, through the logical equivalence of “neither A, nor B” with “(not A) and (not B)”, etc., while the formulation used in the trick question “One of them is not a nickel.” amounts to “(not A) or (not B)”.
Here an interesting question is when to be forgiving. A too strict interpretation of what someone says relative what he (likely) means can do more harm than good through crippling communication. Still, all too many are all too forgiving even in everyday life; and when it comes to riddles/puzzles, legal contracts, software development, and some other areas, it is often best to err on the side of being unforgiving and asking for a clarification of any ambiguity spotted—even when the right answer seems “obvious”. (If in doubt, the likelihood that some sentence in a long document will be misinterpreted by going with the “obvious” interpretation can be far larger than the likelihood than any given individual sentence is misinterpreted.)
Vice versa, most speakers/writers err on the side of sloppiness and would be well advised to improve—the more so when it comes to riddles/puzzles [and so on]. (But in the above example, we do not have sloppiness but a deliberate attempt to mislead.)
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