1

In a sense, this is a follow up to the question Use of “and” and “or” in lists when intent is to disallow all items. An answer states "Or has the meaning of and when it is inside a negated sentence.", but can a sentence be negated in other ways than using "not"? Are some words, such as free and prohibited, "natural" negators?

For example, which is more clear to convey that a surface has no bacteria and also no viruses on it.

  1. The surface is free of bacteria and viruses
  2. The surface is free of bacteria or viruses

What about to indicate neither kicking nor punching is allowed. I think the first is correct, but is it wrong in that if someone was only kicking, then they would not be doing the prohibited activity of kicking AND punching?

  1. Kicking and punching is prohibited
  2. Kicking or punching is prohibited
Community
  • 1
Celeritas
  • 2,910
  • In the second example, the plurality of the verb seems critical to parsing the sentence. That is: "Kicking and punching is prohibited" = "(Kicking and punching) is prohibited" (so one alone might be permitted); whereas "Kicking and punching are prohibited" = "(Kicking is prohibited) and (punching is prohibited)". – Daniel R. Collins Jan 25 '16 at 03:11

3 Answers3

1

Those are not negations. If you mean that there are no bacteria and no viruses then you use and (your first choice). If you mean that there are no bacteria or there are no viruses (and it is possible that there are neither) then you use or (your second choice.

Likewise for your kicking and/or punching examples. And means both (both are prohibited, in this case). Or means one or the other (or both) (are prohibited, in this case).

Drew
  • 15,241
1

English is English. Not mathmatics or logic. However, some people allow mathmatics and logic to inform the way they use English. Others do not. English is all about usage.

Adding negators (be they not or otherwise) can invert the meaning of and and or. In logic this is called Demorgan's law and can be expressed as:

The negation of a conjunction is the disjunction of the negations.
The negation of a disjunction is the conjunction of the negations.

Which is a confusing way to say:

"not (A and B)" is the same as "(not A) or (not B)" also,
"not (A or B)" is the same as "(not A) and (not B)".

Demorgans law is also true in English but is not well understood by all English speakers. We haven't all taken a class on logic. So English allows the use of a few extra words to make what is being said clear.

  1. The surface is free of both bacteria and viruses.
  2. The surface is free of either bacteria or viruses but not both.

Now these two sentences are clearly saying something different. Before it was posible to see them as meaning the same thing. It was also possible to see them as meaning different things. This is called ambiguity.

You can resolve it using context. If I can't readily think of a reason why someone would only know a surface is free of either one or the other but not both, I assume both is what is meant.

However, if in the preceding sentence a biologist tells me that the surface contains bacteria and viruses that attack and kill each other until one of them wins I'll think about the sentence differently.

Now let's play with negators:

a. The surface is free of bacteria and viruses.
b. The surface is free of bacteria and free of viruses.
c. The surface is contaminated with no bacteria and no viruses.
d. The surface is not contaminated with bacteria or viruses.
e. The surface is free of bacteria or viruses.

There is a way to read these as all being the same. It's the presence of ambiguity that makes a difference.

surface contains:

bacteria   viruses   a b c d e
       F                F         T T T T T
       F                T         F F F ? ?
       T                F         F F F ? ?
       T                T         F F F F F

The ambiguity comes from the possibility to take d and e as:

The surface is, at least, free of bacteria or, at least, free of viruses.

Rather than

The surface is free of either bacteria or viruses.

So yes logic plays a role here but it's completely overshadowed by ambiguity that makes context so important.

Thing is, it's also possible to find ambiguity in a.

Does it mean:

The surface if free of bacteria and it is free of viruses.

or does it mean:

The surface is free of a combination of bacteria and viruses.

Well now the truth table looks like this:

bacteria   viruses   a b c d e
       F                F         T T T T T
       F                T         ? ? ? ? ?
       T                F         ? ? ? ? ?
       T                T         F F F F F

which is more clear to convey that a surface has no bacteria and also no viruses on it?

I can find a way to be confused by either of them.

So either make it clear in context or reword to be more explicit. Most readers aren't going to understand Demorgan's Law (well depending on context) so while it's good to understand logic, it's better to see all the ways you can end up confusing people and try to avoid them.

candied_orange
  • 10,006
0

I had have the same Doubt and my conclusions were : (1) It Depends on the context (2) When somebody says "AND mean this, and OR means that", you should take it as "AND mean this for me in this context, and OR means that for me in this context".

Consider Police warnings in Bangalore : "Do not Drink AND Drive". Here, for them, it means you should not do both at same time, otherwise accidents will happen.
I might have written this as "Do not Drink-AND-Drive".

Consider some restaurants Displaying this: "We Do not serve Beef AND Pork". Many people do not want to enter places where Beef OR Pork are served, and this place is saying, "Come in, we are safe". Here, For them, it DOES NOT mean "we have dishes made of Beef, we have dishes made of Pork, but we do not serve them both at same time".
I might have written this as "We Do not serve Beef OR Pork".

For Natural Speakers of English, there may be "Rules" & "Conventions" which are culturally accepted across the country or society, but other countries or cultures or societies may not be aware of this. In some cultures or countries or societies, there may even be no "Rules" or "Conventions".

Some Random thoughts below, read at your own risk :

When OP says "natural negators", I get what he means and parse his statements like this:
"Is free of" == "Does not contain"
"Is prohibited" == "Is not allowed"

With "Rules" & "Conventions" Differing with cultures, societies, and countries, those who are aware of Mathematical Logic, and De Morgans laws, will have more strict "Rules", even when they are using Natural Languages.
Eg NOT (A AND B) == NOT A OR NOT B
NOT (DRINK AND DRIVE) == NOT DRINK OR NOT DRIVE.

English statement : "Do not Drink-AND-Drive" == "Either Do Not DRINK OR Do Not Drive (or Do neither)". Here, I used hyphens to indicate closeness or "contained in brackets".

In many places, it is not easy to indicate closeness or brackets, in English. Hence, the rule in reference given by OP, "NOT OR == AND" might not be easy to apply.
NOT (A OR B OR C OR D) == NOT A AND NOT B AND NOT C AND NOT D.

Mom to her naughty Kids, who are not finishing the homework assignments : "Do not talk, or hum , or whistle, or fidget, or shake the table, or atleast finish the homework.", where she is Definitely not saying "Do not finish the homework".

Prem
  • 4,736