I was wondering if this sentence is grammatically correct:

The veracity of mathematical facts transcends the limits of human knowledge, which only precludes our understanding of it.

I wanted to switch "it" with "them" (referring to the mathematical facts), but the subject of the sentence is the veracity (of mathematical facts), so the plural "them" would be incorrect. Am I wrong?

  • No, this is something I am writing for a purpose statement to PhD programs in math. – Kevin Sheng Dec 12 '15 at 20:49
  • If this sentence is intended to mean something more than just "mathematical truth transcends human knowledge" then I'm missing the additional meaning. – Andreas Blass Dec 13 '15 at 1:06
  • That's exactly the idea, where's is the indication otherwise? – Kevin Sheng Dec 13 '15 at 1:09
  • The reason for my comment is that your formulation has more words (including the whole "which" clause, which seems only to repeat the main clause) and a fancier word ("veracity" rather than "truth"), and I hoped you had a reason for that. – Andreas Blass Dec 13 '15 at 1:12
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    I think the new ending, "and ... discovered," is a clearer statement of a Platonic philosophy of mathematics than the previous version. Note that "transcends human knowledge" could be understood in two ways: (1) We do not (and cannot) know all mathematical truths. (2) Mathematical truth does not depend on our knowledge. The second half of your sentence is closely related to (2); in the older version, the second half seemed closer to (1). – Andreas Blass Dec 13 '15 at 9:36

Use "them". (1) There is no rule to say that the antecedent of the pronoun here has to be the subject "veracity" -- the antecedent can be "mathematical facts". (2) "it" makes no sense, supposing it refers to "veracity", since it is unclear what it would mean to have an understanding of the veracity.

  • Thank you. That is exactly why I wanted to change "it" to "them", but I wasn't sure if doing so is grammatically correct. – Kevin Sheng Dec 12 '15 at 20:41

A classic case of potential ambiguity. If you switch to "them", the reader will naturally look for the nearest plural NP antecedent in the vicinity, which is "the limits of human knowledge". If you want the antecedent to be unambiguously the earlier plural NP "mathematical facts", you'll have to recast it. You could consider replacing "it" with "those facts".

  • I agree ... the use if "it" or "them" makes the sentence a difficult read. So - if you do not wish to recast the sentence - the use of "those facts" is the better option. By the way, "mathematical facts" are only a product of accumulated human knowledge (what else could it be?), so there is something odd about the assertion being made. – Cargill Dec 12 '15 at 23:27
  • @Cargill Many mathematicians have a Platonist view of their subject. From that point of view, even if we don't yet know whether some mathematical statement is true, it still has a meaning, and either it or its negation is true. – Andreas Blass Dec 13 '15 at 1:02

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