# Alternative to “to be” in copulae that cannot be understood as defining

In particular in scientific writing, copulae using to be can not only be used to describe the properties of something but also to recapture a definition, to define something or to indicate complete identity. For example, the first of the following sentences gives the definition of a prime number, the second one just describes its properties:

A prime number is a natural number with exactly two divisors.

A prime number is a natural number.

Usually, it is clear from context how a copula is meant to be read, but now I am facing a case where it isn‘t. More specifically, I want a copula or syntactically similar construct to be clearly understood as describing only properties. I am thus looking for verbs or phrases meaning to have the property of being or similar (but less convoluted), i.e.:

A prime number has the property of being a natural number.

I searched thesauri (1, 2) for synonyms of to be and found no satisfying answer as only other meanings of to be, such as to exist, were covered.

I am aware, that as a last resort I can completely rephrase the sentence, e.g.:

Prime numbers are a subset of the natural numbers.

Finally note, that the above are only examples (my actual problem is more complicated and requires background knowledge), so I am not looking for answers specific to this.

• Perhaps what you're looking for is Prime numbers are those natural numbers which have exactly two divisors. Sep 17, 2015 at 12:57
• @FumbleFingers: That’s what I would do if I wanted to ensure that it’s understood as defining. But I want the opposite. Sep 17, 2015 at 13:02
• What's the question? There is nothing wrong with X has the property to be... And yes, that just says that X has that property. It does not say that X has only that property. It does not define X by saying that anything that has that property is an X.
– Drew
Sep 17, 2015 at 15:01
• @Drew: I don't recognise X has the property to be... as syntactically valid. Google Books initially claims "About 13,400 results" for that search string, but scrolling to the second page reveals there are actually only 13. Of which I can only see the full context in 3 cases, all of which I suspect are from non-native speakers. Normal English is X has the property of being... [whatever it is] Sep 17, 2015 at 16:32
• @Wrzlprmft: If I understand your (somewhat obscure) requirement, you seek a statement of the general from X [copula] Y that doesn't imply X is defined as being Y (i.e. - you simply want to make the point that X has the "non-defining" characteristic Y). In which case perhaps All prime numbers are natural numbers would do you. As with All dogs are quadrupeds, this doesn't imply All quadrupeds are dogs. Sep 17, 2015 at 17:18

## 1 Answer

A prime number is a natural number.

That statement is ambiguous because it could potentially apply to just one prime or a set of primes that you happen to be discussing.

The easiest transformation is:

Prime numbers are natural numbers.

You can make this even clearer by saying:

All prime numbers are natural numbers.

but, in grammatical terms, that is unnecessary as the two statements are equivalent.

• Your “easiest transformation” does not work in general: Prime numbers are numbers with less than four divisors. could also be understood as a definition. With an all it might help though. Sep 17, 2015 at 13:07
• @Wrzlprmft -I don't see the force of your argument wrt, "Prime numbers are numbers with less than four divisors." That statement is either true or false - it doesn't make it a definition. You would have to say, "Prime numbers are defined to be numbers with less than four divisors." Sep 17, 2015 at 13:24
• I am the OP (as can be seen by the grey backdrop behind my username). And while you are right that your first version is equivalent to “Prime numbers are a subset of the natural numbers.”, this only works, because natural numbers is a fixed idiom, so it is not the general solution I asked for. Compare to “Gobbleflorps are phantasmagorical and oxyfomastic numbers”, which can be read as a definition. “All gobbleflorps are phantasmagorical and oxyfomastic numbers” works, however. Sep 17, 2015 at 13:25
• I simply disagree. I think that it is you who are confusing a description with a definition. Your, “Gobbleflorps are phantasmagorical and oxyfomastic numbers”, is not a definition at all. It only becomes a definition if you explicity say it is a definition. To me your sentence means that, “Gobbleflorps are a subset of the phantasmagorical and oxyfomastic numbers”. Sep 17, 2015 at 13:28
• You can argue whether it’s defining or only describing a definition or identity, but the sentence can at least also mean “The set of gobbleflorps is identical to the set of phantasmagorical and oxyfomastic numbers.” See, e.g., Merriam Webster, definition 1a. (Also this misunderstanding is an actual problem I was facing with somebody who read my writing, so it’s not limited to me.) Sep 17, 2015 at 13:37