I am reading "Topology 2nd Edition" by James R. Munkres.
I am not good at English at all, but it's a mathematics book.

In this book, there is the following sentence:

Although we shall not deal with the axioms (of set theory) explicitly, the rules we follow in dealing with sets derive from them.

I added "(of set theory)" to the original sentence.

The author wrote "the rules we follow in dealing with sets derive from them." and didn't write "the rules we follow in dealing with sets are derived from them."

I wonder why the author didn't write "the rules we follow in dealing with sets are derived from them."

  • Why he did or didn't write? You repeat the same thing twice...
    – Lambie
    Oct 6, 2021 at 17:56
  • 1
    @Lambie I confess I had to read it multiple times to see the difference: "derive" vs. "are derived". The active voice is so natural here that the difference is practically invisible.
    – David K
    Oct 7, 2021 at 13:00

2 Answers 2


This word
American Heritage Dictionary derive

v.tr. 1.a. To obtain or receive from a source: a dance that is derived from the samba; confidence that is derived from years of experience.
v.intr. To be derived from a source; originate. See Synonyms at stem1.

is used both transitively and intransitively. The passive expression you used is the transitive form. The intransitive sense is that used by the author, which is equally valid.

So, the phrases
rules derive from axioms
rules are derived from axioms
mean the same thing.

  • Is there a name for this type of verb? That means the same thing in both passive and active? The closest I can think of is ergative
    – PC Luddite
    Oct 7, 2021 at 21:58
  • I found an article listing a bunch of ergative verbs: thoughtco.com/ergative-grammar-term-1690608 I'm not sure it's exactly the same thing, because I don't think you can say flatly, The rules derive. , in the way that you can say "The cold froze the milk." and "The milk froze." Oct 8, 2021 at 2:29
  • yeah, I don't think it's ergative since it seems like the voice doesn't have to change (e.g. "he is cooking" and "the turkey is cooking" are both grammatically active voice, but the latter subject isn't the agent).
    – PC Luddite
    Oct 8, 2021 at 23:10

Both sentences sound fine to me, but here in America, people generally prefer the active voice (“the rules ... derive from them.”) over the passive voice (“the rules ... are derived from them.”). They’re both correct, but the first usually is considered better style.

  • Davislor, Thank you very much for your important information.
    – tchappy ha
    Oct 7, 2021 at 2:04
  • 1
    In this case, though, "derive" can also mean something else, and because of that ambiguity I (an American) would typically not use the active form in this context.
    – David Z
    Oct 7, 2021 at 2:51
  • 2
    @DavidZ In context, I felt the meaning was clear. The word derive would mean something else in the sentence, “Mathematicians derive the rules from axioms.” However, rules cannot write proofs. Tthat is a good warning to keep in mind for the future.
    – Davislor
    Oct 7, 2021 at 3:27

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