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In my mathematical writing in grad school there used to be sentences like "Whenever x is a fish, then x is an animal." (Yes, that's what my dissertation was on!) I am a native speaker of English and this seemed fine to me.

My adviser (who is not a native speaker of English, though it's not entirely relevant) insisted that this was incorrect, so I stopped using it because he was pretty much the only one reading what I wrote. He suggested replacing "then" with "we must have that" (which I did).

I still wonder, though...is it really incorrect?

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  • I might suggest deleting “then”: Whenever X is a fish, X is an animal. But why not just: All fish are animals.
    – Jim
    Nov 28 '15 at 4:31
  • From a programmer's perspective, this sounds the same as saying while x is a fish, then x is an animal. I prefer while but won't say whether whenever is incorrect or not.
    – Robert Simpson
    Nov 28 '15 at 4:33
  • @Jim Ignore the specific example. However, I just tried to find a more realistic example in my dissertation and discovered that the word "whenever" appears exactly once, and it isn't used in this way, so maybe I just stopped using it.
    – Matt Samuel
    Nov 28 '15 at 4:34
  • I'm hardly a mathematician, but wouldn't "if ... then..." work just as well and be grammatically correct?
    – Ricky
    Nov 28 '15 at 4:39
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    I believe it is correct, just a bit awkward. "Whenever" mixes better with "it must also be true that" than "then." I must say I've noticed that whenever (no pun intended) you math freaks dig up a problem that isn't related to your own field, everyone's suddenly stumped because a) no one thought of it before b) no one will ever think of it again. (Hey, have any of you figured out yet who killed Kennedy? what's the location of the actual, historical Troy? ...)
    – Ricky
    Nov 28 '15 at 5:00
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... is it really incorrect?

Yes, I think the "whenever X then Y" construct is incorrect. It should be "whenever X, Y", where X is a logical proposition and Y is an assertion (Y could also be a command - e.g. whenever it rains, take an umbrella). The expression "then x is an animal" doesn't stand as an assertion or command on its own.

The adviser's expression "we must have that" is just a filler which can be removed in its entirety without changing the sense of the sentence. What it gives you, though, is more visual separation between X and Y than just a comma - this could be important for clarity when X and Y are equations or other expressions that already contain commas.

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  • That's probably why I felt the need to put something like "then" in. "Whenever x+1=5, x=4" is pretty confusing.
    – Matt Samuel
    Nov 28 '15 at 4:57
  • @MattSamuel Yes - add commas and accidentally skip a conjunction, and it gets worse. E.g. Whenever x=1, y=2, z=3. :)
    – Lawrence
    Nov 28 '15 at 5:01
  • But then why have then in conditionals at all. This is still a conditional. It just has a different type of subordinator.
    – Araucaria - Not here any more.
    Nov 28 '15 at 11:16
  • @Araucaria That might deserve its own question. It can be argued that then carries the sense of in that case. This works when coupled with if, but when / whenever has a slightly different feel (mood?). In that case is already built into the semantics of when / whenever, which makes repeating it sound clumsy.
    – Lawrence
    Nov 28 '15 at 12:32
  • @Araucaria Greg Lee observed that whenever is a quantifier. Although we may quibble about exactly what the domain is, reading whenever as a universal quantifier rather than a conditional expression makes it even clearer that the word then is out of place. We can have "for every [event clause], [assertion]" but not "for every [event], then [description]". E.g. "for every x classified as a fish, x is also classified as an animal" (correct) vs "for every x classified as a fish, then x is also classified as an animal" (wrong).
    – Lawrence
    Nov 28 '15 at 13:01
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He suggested replacing "then" with "we must have that" (which I did).

It might be a bit late, but can I suggest that you find a new supervisor?

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  • He's not my adviser anymore. It never really comes up, but my proper title is Dr. Samuel, and his signature is on the title page of the copy of my dissertation stored in the bowels of Rutgers' archives (but the text is accessible online!).
    – Matt Samuel
    Nov 28 '15 at 4:50
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Anyone who knows some predicate logic will be able to tell that with "Whenever x is a fish, then x is an animal." you are trying to get the logical symbols to correspond directly, one-for-one with English phrases. But it's not really possible to translate in this literal way. Your former adviser's idea of using "we must have it that" for implication is certainly no improvement.

James McCawley was a first class linguist who also knew quite a lot about logic. In The Syntactic Phenomena of English he makes some very specific proposals about how universally quantified implications correspond to English sentences. He begins with the restricted quantification discussed by Hans Reichenbach -- (All x: fish(x))(animal(x)), where the implication operator has been suppressed, and applies more or less motivated syntactic rules to get to "All fish are animals".

Is your version with "whenever" really incorrect? Well, it's pretty bad. It seems to be making a generalization about all times which is just not there in the logic or in the corresponding English.

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  • Unfortunately the book costs far more than $8 so I can't justify buying it. In any case, I've only seen sentences like "All fish are animals" on IQ tests, never in math papers. Perhaps I picked a bad example. What can the logic do with "Whenever {x1, x2, . . . , xn} is a basis of V, then Sym(V) is isomorphic to the polynomial ring F[x1, x2, . . . , xn]"?
    – Matt Samuel
    Nov 28 '15 at 5:44
  • Instead of "whenever", use "if". The "if" ... "then" construction of English is the most common translation of the material implication of classical logic. Material implication "p implies q" or "if p then q" is equivalent to "not p or q". There are other proposals about how to render the "if ... then" construction of English, but mathematicians like material implication because it preserves the validity of modus ponens. ...
    – Greg Lee
    Nov 28 '15 at 6:30
  • ... Concerning your example, I see nothing there relevant to our discussion. Involving some mathematical notions "basis", "isomorphic", "ring" looks to me like a distraction. What do these have to do with logic or its correspondence to English? Is it your idea to scare me away by tossing in some mathematics you think I won't understand? Are you asking a real question?
    – Greg Lee
    Nov 28 '15 at 6:30
  • No scaring intended, and I didn't think it mattered whether you knew the meanings of the words. I just felt that "all fish are animals" was a form that was special to my contrived example and thought maybe you had some logic to English conversion algorithm in front of you and could do something with this. The sentence is an if...then from my dissertation, but instead I put it in this form.
    – Matt Samuel
    Nov 28 '15 at 6:36
  • Well, in case I wasn't clear earlier, "whenever" is no improvement on "if", since it purports to make a generalization about times. "When" means "at the time at which". But a generalization about times does not seem to be involved in any of these examples, so "whenever" is an unwise choice.
    – Greg Lee
    Nov 28 '15 at 6:42

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