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The farther a number is from 0 on its right, the _____ is its value. (Choose between larger and smaller).

If 'its' refers to the subject number, then the correct answer is 'smaller'.

If 'its' refers to 0 then the correct answer is 'larger'.

Does the possesive its refer to the number or 0 (zero)?

Vinit.Ajgaonkar
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    It almost certainly means "to the right of zero", although I will admit that it is a bit ambiguous. What educational level is this question aimed at? – BoldBen Sep 24 '21 at 06:13
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    @BoldBen This was asked in my daughter's 6th grade school Mathematics quiz, yesterday. – Vinit.Ajgaonkar Sep 24 '21 at 08:46
  • It is 100 percent ambiguous in my dialect. Some speakers might make the distinction with different prepositions, on vs to, for instance. But that varies by region. – Phil Sweet Sep 24 '21 at 10:44
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    While it is poorly worded, I think you're supposed to understand 0 as having a fixed value. That is, 0 is always 0 and it can't be larger or smaller, so the its must refer to the subject number. – Canadian Yankee Sep 24 '21 at 13:07
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    Numbers do not exist in spatial dimensions, and don't have a front or back, so they don't have a right or left. If you are talking about writing digits, say so. Before you can discuss complex matters of coreference, you need to be clear what you're talking about. – John Lawler Sep 24 '21 at 16:22
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    @JohnLawler This must be referring to numbers on a number line. Positive numbers are to the right of 0, and negative numbers are to the left of 0. – Mitchell Spector Sep 24 '21 at 18:36

1 Answers1

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In your question, the candidate antecedents to the pronoun "its" are:

  • a number; and
  • 0 (which we'll take as the origin).

To my ear, "its right" refers to the number's right. However, it could be argued that this is influenced by the second instance of "its" - its value refers to the number's value (not the value of "0"), and this affects the parsing of the first "its".

To test whether there is ambiguity in what the first "its" refers to, let's modify the sentence so that "its" can only have one candidate antecedent. We will use a (grammatically) gendered noun that requires its pronoun to not be neuter. Then place the neuter noun in each position in turn, and check whether the result makes sense. Instead of "a number" and "0", let's use "a dog" as the noun matching the neuter pronoun, and "the owner" as the noun without a matching neuter pronoun. We will also hide the second "its" to avoid any contextual colouring it might impose on the first "its".

  1. The farther a dog is from the owner on its right, ...
  2. (*) The farther the owner is from the dog on its right, ...

The first sentence makes sense but the second doesn’t. Even though the only neuter antecedent to "its" is "the dog", the second sentence still sounds as if the author tried to match "the owner" with "its".

That is, both sentences naturally parse to produce a noun phrase "the X on its right", where the antecedent of "its" is something other than X.

So in your example, "on its right" refers to the right of "a number", not to the right of "0".

Now, if you wanted to express the idea of sentence 2 - that is, have the owner to be on the right of the dog - you would need to break the coupling within the noun phrase "the X on its right". One way to do this is to add a comma before "on its right":

1a. The farther a dog is from the owner, on its right, ...

2a. The farther the owner is from the dog, on its right, ...

2b. The farther a number is from 0, on its right, ...

The comma detaches “on its right” from the noun phrase it follows, so the pronoun can refer (ambiguously) to either noun phrase.

Lawrence
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    This isn’t analogous to OP’s sentence; (1) The pronoun “its” in your example has to refer to the dog, not the owner (who would have to be “he” or “she”). (2) The phrase “the owner on its right” can be parsed as “the owner who is on its right” (rather than the dog’s other owner, who is on its left or somewhere else). – Mitchell Spector Sep 24 '21 at 07:39
  • @Mitchell Spector That’s the point of the test - to force the pronoun to try to match with each candidate position in turn. – Lawrence Sep 24 '21 at 09:37
  • @Lawrence, I liked your idea of using nouns having different pronouns. Let's assume that all entities including the observer are facing the same direction so that the everyone's right is in the same direction. Now let's use your strategy: 1) The farther a dog is from the owner on its right, ... 2) The farther a dog is from the owner on his right, ... I agree with you. The first sentence makes more sense. The second sentence needs a comma before 'on his right.' I changed your second sentence to better understand the point you were making. Do you want to edit the second sentence? – Vinit.Ajgaonkar Sep 24 '21 at 11:26
  • On second thoughts, both sentences make sense to me 1) The farther a dog is from the owner on its right, ... 2) The farther a dog is from the owner on his right, ... So shall we conclude that the original sentence in the question is ambiguous? – Vinit.Ajgaonkar Sep 24 '21 at 11:35
  • @MitchellSpector I've clarified the answer. – Lawrence Sep 24 '21 at 14:24
  • @PhilSweet I've edited to clarify. – Lawrence Sep 24 '21 at 14:24
  • @Vinit.Ajgaonkar I hope the redraft of my answer is clearer. The original sentence in your question is not ambiguous. In sentence (2) in your comment,, the natural antecedent to "his" should not be "the owner", as my answer now explains. – Lawrence Sep 24 '21 at 14:28
  • Okay, I can only say we handle this differently. I consider example 2 slightly less terrible than example one because I can contrive a situation where there are two owners and we are restricting consideration to the one on the right. But I can't get number one to parse under any circumstance. The farther a dog is to the right of the owner is the only arrangement that works for me. – Phil Sweet Sep 24 '21 at 17:32