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For a simple phrase like "macaroni and cheese" it's clear you want both macaroni and cheese, not one or the other. But as more and more words are added, I've noticed a tendency to begin to read "and" as "or", at least from a Boolean logic perspective; is there any support for that?

I've referenced the specific context before with a different question; the relevant part this time is

... for the purpose of encouraging immigration and increasing the trade in the products of Michigan, or ...

Is there any way to read "the purpose" as two separate items:

  • encouraging immigration
  • increasing the trade ...

Or must they always be together, like "macaroni and cheese"? (I'm not interested in what "encouraging immigration" or "increasing the trade ..." might actually mean.)

That is, have you satisfied the desired purpose by only "increasing the trade ..." or must you also "encourage immigration" at the same time? In Boolean logic, there is absolutely no question you must do both; but does the same always apply to English grammar?

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  • 2
    I agree with you that I've seen situations where "and" is being used more like "or". But I don't think this specific quote is one of those cases. Or, at least, I see no evidence that "and" is used in anything but its standard conjunctive sense. The purpose (note the singular) is both EI and IT.
    – Dan Bron
    May 7, 2015 at 16:46
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    What you have found really is the mathematical definitions of 'and' (and 'or') are somewhat imposed and restrictive. The natural language versions are much more complex and colored by context. But yes, 'and' can sometimes act like 'inclusive or' (or set union) when there are many instances of each.
    – Mitch
    May 7, 2015 at 16:48
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    One of the most common uses of and in English is in narrative, where it has a non-commutative temporal sense of "and then". Many people put and at the beginning of just about every sentence when recounting something; the purpose is to separate successive events in the narrative. He got up early and went to the store. And he got some fancy coffee and croissants, and he came home and fixed me breakfast..
    – John Lawler
    May 7, 2015 at 17:49
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    You cannot treat "and" and "or" as Boolean operators outside of mathematics/engineering. In particular, in law the words are sometimes interpreted in seemingly bizarre ways. And in common speech their meanings are quite context-dependent.
    – Hot Licks
    May 7, 2015 at 22:32

4 Answers 4

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Does the word “and” always mean a logical (boolean) operation?

Certainly not, a quick glance at the dictionary demonstrates that the use of and is not limited to a boolean operation:

conjunction

1.0 Used to connect words of the same part of speech, clauses, or sentences, that are to be taken jointly:
bread and butter
they can read and write
a hundred and fifty

1.1 Used to connect two clauses when the second refers to something that happens after the first:
he turned round and walked out

1.2 Used to connect two clauses, the second of which refers to something that results from the first:
there was a flash flood and by the next morning the town was under water

1.3 Connecting two identical comparatives, to emphasize a progressive change:
getting better and better

1.4 Connecting two identical words, implying great duration or great extent:
I cried and cried

1.5 Used to connect two identical words to indicate that things of the same name or class have different qualities:
all human conduct is determined or caused—but there are causes and causes

1.6 Used to connect two numbers to indicate that they are being added together:
six and four makes ten

1.7 archaic Used to connect two numbers, implying succession:
a line of men marching two and two

2.0 Used to introduce an additional comment or interjection:
if it came to a choice—and this was the worst thing—she would turn her back on her parents

2.1 Used to introduce a question in connection with what someone else has just said:
‘I found the letter in her bag.’ ‘And did you steam it open?’

2.2 Used to introduce a statement about a new topic:
and now to the dessert

3.0 informal Used after some verbs and before another verb to indicate intention, instead of ‘to’:
I would try and do what he said

ODO

And is a conjunction connecting two related units, and the connection is not necessarily boolean:

... for the purpose of encouraging immigration and increasing the trade in the products of Michigan, or ...

The larger context informs of the relationship between encouraging immigration and increasing the trade:

The boards of supervisors of the several counties may levy a special tax on the taxable property within their respective counties for the purpose of creating a fund; or appropriate out of the general fund an amount to be used for advertising agricultural or industrial advantages of the state or county or any part of the state, or for collecting, preparing or maintaining an exhibition of the products and industries of the county at any domestic or foreign exposition, for the purpose of encouraging immigration and increasing the trade in the products of Michigan, or advertising the state and any portion thereof for tourists and resorters.

Recognizing the legislative source, and the productive analysis of parallelism, the exhibition mentioned in the larger context seems to have a three-fold purpose: immigration and trade or tourism. The conjunction and seems to be "boolean" in reference to the purpose--both are included together.

It is not necessarily "boolean" in reference to outcome. At some expositions, the the exhibit may effectively encourage immigration. At some expositions, the the exhibit may effectively increase the trade. At some expositions, the the exhibit may accomplish both.

Interestingly, the or presses the and toward a boolean interpretation in reference to the purpose. By contrast with the conjunction and, the conjunction or sets the advertising part of the there-fold purpose apart as an alternative to the pair: encouraging immigration and increasing the trade.

Still and would not necessarily have a strictly boolean function in reference to the outcomes. At any exposition, the the exhibit may fulfill any combination of the listed purposes--which were linguistically presented as a single three-fold purpose.

Conclusion:

The semantic complexity of purpose, rooted in the complexity of human reasoning and interaction, transcends a simple boolean arrangement. Unless they anticipate litigation, both the average writer and the average reader can manage this complexity without the need for precise boolean logic. Though this legislative language likely anticipated litigation, it remains a matter of subjective judgement to determine the "purpose" of an exhibit.

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  • The writers are long gone, and different readers want the text to allow different things. (I want very restricted and limited use of the "amount," others not so much.) I was hoping this could be mostly sorted out through just the grammar, but your explanations show that might not be enough.
    – Ðаn
    May 8, 2015 at 2:48
  • This answer english.stackexchange.com/a/133706/3955 says that the second or does not belong with the first because of parallel construction: "for advertising ..." or "for collecting ...". The third activity would also be "for advertising ... tourists" to be consistent.
    – Ðаn
    May 8, 2015 at 2:58
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    I tend to agree with bib's analysis, but as my answer suggested, what comes before the ellipsis might counter our analysis. I haven't seen the rest of the sentence, so I can only go by what I've seen.
    – ScotM
    May 8, 2015 at 15:43
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    @Dan, I have updated my answer after consulting the original document.
    – ScotM
    May 8, 2015 at 16:50
  • this is getting away from my original question about "and" ... but, now that you've looked at the full text, do you see any way to perform "increase the trade" activities other than by participating in an exhibition?
    – Ðаn
    May 8, 2015 at 20:34
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Language can't be squashed into boolean logic. Nor are the meanings of phrases dependent on their fulfilment in the real world.

There are lots of cases where and can be used with essentially the same meaning as or, such as

Our dinner choices are pizza or curry.
Our dinner choices are pizza and curry.

This is because neither and nor or have the same meanings as their corresponding roles in logic. In language they are both conjunctions. And is the most unmarked conjunction; it means there are two things which are related together somehow. Or is more marked and presents the two ideas specifically as alternatives.

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    Fabulous example. Both are acceptable indeed. I'd love to explain how both are consistent with boolean algebra because the sense of choice changes, but I suspect I'll only get more brickbats, so I'll let you have this one.
    – Tushar Raj
    May 8, 2015 at 3:47
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    @Area51DetectiveFiction I too think that would be interesting. I'm not sure if choice changes, or if the scoping changes. I think it's fine to go from language to logical/formal explanations, but the problem is when you try to go back to language again. The logical AND is derived from the language and, not the other way round.
    – curiousdannii
    May 8, 2015 at 7:55
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You ask whether "AND" is always a "Boolean-Operation" meaning both should occur. You also think that, as more words are added to the phrases on the two sides of AND, the meaning changes to OR.

Well, here are some cases which can be taken as counter-examples :

Short Forms :

(1) Drinking AND Driving will be punished : Both are required ; It is an offence only if both are done ; Only one is not an offence. ((Boolean AND))

(2A) Robbery AND Forgery were the main cases against this criminal gang : Some cases were Robbery while some cases were Forgery ; Some cases might have been both. ((Boolean OR))

(2B) Most cases against this criminal gang were involving Robbery AND Forgery : Some cases were Robbery while some cases were Forgery ; Some cases might have both components. ((Boolean OR))

Long Forms :

(3) When traveling to the exotic beach resort, we ensured that we packed all necessary electronics devices for uninterrupted communication AND all necessary ointments for emergency medication : We packed both. ((Boolean AND))

(4) This government is committed to pass all pending bills concerning grave national security issues AND advancement of space technology : A bill which satisfies either condition will be passed. ((Boolean OR))

Human Languages are generally not precise , that is why (1) We require Computer Languages, legalese, Mathematical Languages, etc (2) Artificial Intelligence related to Natural Language Processing is Difficult.

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    Point taken about the ambiguity having little to nothing to do with "more words." Your examples show that it's just the nature of human languages.
    – Ðаn
    May 7, 2015 at 17:20
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    Example 2 is wrong. Both Robbery AND Forgery were domains. Using boolean OR would imply only one crime was the domain. Example 4 is also wrong. The govt is committed to Boolean AND. Either condition causes boolean OR. Considering my first ever downvote, unless you edit with an explanation.
    – Tushar Raj
    May 7, 2015 at 17:21
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    @Dan , I was able to answer this question because I had the exact same Doubt a while back & I resolved my Doubt with the highlighted last paragraph in my answer.
    – Prem
    May 7, 2015 at 17:38
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    @Area51DetectiveFiction , your Disagreement is exactly the point of this question. When some politician says Example 4, a reporter may well ask for clarification "Do you mean security OR technology ?" and the politician may think the reporter is crazy and will respond "Yes, that is what I said". If I or you were to say it, we would use OR, but this is what is the problem with the imprecise English. So your Disagreement is about when "AND is OR" and (or ?) "AND is AND" which stems from imprecise English.
    – Prem
    May 8, 2015 at 3:29
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    @Prem or even worse, when such imprecision becomes law, as is the case in my original question.
    – Ðаn
    May 8, 2015 at 13:49
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I have to weigh in here. I can't stand by while others butcher logic.

According to me, and based on the examples posted here, in the cases English AND is used logically, Boolean AND and English AND are IDENTICAL. I'll be ready to believe otherwise when I see some solid proof.

Debunking Prem's examples:

(2B) Most cases against this criminal gang were involving Robbery AND Forgery :

Some cases were Robbery while some cases were Forgery ; Some cases might have both components. ((Boolean OR))

NOT.

It means most cases involved BOTH robbery AND forgery. It sounds unlikely, but that's what is being said.

Compare these sentences with the same template:

  • Most movies Hitchcock directed starred Jimmy Stewart OR Cary Grant. (Can't use and here without changing the meaning, can you?)

  • Most successful musicals in the 30's starred Fred Astaire AND Ginger Rogers

Fortunately, English has a simple test for cases like these. For uses in the Boolean sense, you can insert both in case of and; and either in case of or; without changing the meaning.

So, depending on what you want to imply, you should say:

  • Most cases against this criminal gang were involving (both) Robbery AND Forgery

  • Most cases against this criminal gang were involving (either) Robbery OR Forgery

  • Most cases against this criminal gang were involving (either) Robbery OR Forgery OR BOTH.

This third construct is common enough. And people wishing to avoid ambiguity use it.

(4) This government is committed to pass all pending bills concerning grave national security issues AND advancement of space technology : A bill which satisfies either condition will be passed. ((Boolean OR))

Wrong Again, it's a Boolean AND. It seems the govt is saying they'll pass bills that concern both security AND technology.

Compare these sentences with the same template:

  • I've seen all movies starring DiCaprio AND Winslet (2 movies)
  • I've seen all movies starring DiCaprio OR Winslet (more movies than 2)

EDIT: I know I'm fighting a losing battle here. People do use boolean and in the sense of boolean or. I'm saying they shouldn't.

It's like using I don't know nothing to mean I don't know anything. People will understand you. That doesn't make it right.

For all those who say English isn't Boolean algebra, explain to me why the double negative is considered wrong.

In my book, anyone who frowns upon the double negative and think using and to mean boolean or is OK, is a hypocrite.

FURTHER EDIT:

Both of curiousdanni's example sentences satisfy Boolean logic.

Our dinner choices are pizza or curry.

Choice means alternative here.[Oxford, sense 1] As in: "There is no D. You have three choices, A, B AND C" (Saying OR C is a bit more odd here than in the exampe)

Our dinner choices are pizza and curry.

Choice means the thing chosen here.[Oxford, sense 1.3] As in "It's your choice to believe me OR not." (Can't be "and not")

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  • Actually what you have here (given the conditional) is the equivalence between ((if P then R) and (if Q then R)) and (if (P or Q) then R). I was pointing out that the statement given could be interpreted the first way; it seemed to me you were claiming that it must be interpreted as the second.
    – Matt Gutting
    May 7, 2015 at 18:48
  • @MattGutting: Oh, that's what you were saying. Then we're both right.
    – Tushar Raj
    May 7, 2015 at 18:50
  • I love it when that happens :-)
    – Matt Gutting
    May 7, 2015 at 18:51
  • I agree, sort of; but you might consider editing to point out the involvement of a (hidden) conditional in example 4, as I was commenting.
    – Matt Gutting
    May 7, 2015 at 18:54
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    English is neither Boolean algebra nor a propositional calculus. The ordinary understanding of your I've seen all movies starring Tom Cruise and Brad Pitt example (capitalization removed since the word is a word, not an operator) would be that you've seen all movies starring Tom Cruise and all movies starring Brad Pitt (and would likely to be taken as a bit of an exaggeration). If you went all pedantic in a roomful of people who weren't programmers, you'd find yourself standing alone and unloved.
    – bye
    May 8, 2015 at 3:04

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