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When is the definite article the appropriate before an abstract noun? In particular, I have the following examples.

Which are correct?

Case I

  1. In the Theorem 4.4, we prove property A for all graphs.
  2. In Theorem 4.4, we prove property A for all graphs.

Case II

  1. From the Theorem 4.4, we know about property A for all graphs.
  2. From Theorem 4.4, we know about property A for all graphs.

Case III

  1. From the following Theorem, we know about property A for all graphs.
  2. From following Theorem, we know about property A for all graphs.
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    You're mixing up abstract nouns and proper nouns (i.e. names): "Theorem 4.4" is a proper noun, the name of a specific object, and so does not take an article. Later, when you refer to "Theorem", without the 4.4 (rendering it non-specific), it's a standard noun, and so should not be capitalized, and requires an article. In that particular case, you want the definite article: "the thereom [we were just discussing]".
    – Dan Bron
    Commented Nov 25, 2014 at 12:34
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    This may be better on English Language Learners
    – Kris
    Commented Nov 25, 2014 at 12:46
  • Jardine, the question itself is required in the body, even if stated in the title. Edited.
    – Kris
    Commented Nov 25, 2014 at 12:47
  • @DanBron The confusion may be due to the unavoidable professional blindness of a mathematician or a theoretician. To me, Theorem 4.4 is an abstract mathematical object, that I can neither see nor smell nor feel with my hands. I can only hear or read the 'statement' of the theorem, that is, how it is stated, but not the theorem itself. A theorem can be stated in many ways which might not seem to be the same thing, even though they are the same. Thanks, any how. It makes sense I believe.
    – Jardine
    Commented Nov 25, 2014 at 13:03
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    Well, love is an abstract concept, yet it can take an article or not. Consider the following references from music: "Love is a many-splendored thing," "A Love Supreme," or "The love you take is equal to the love you make."
    – Robusto
    Commented Nov 25, 2014 at 13:46

3 Answers 3

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I'd say, I sentence 2, II sentence 2, and III sentence 1 are correct; the latter, since dropping the in this case would yield a gap in the sentence.

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When is the definite article the appropriate before an abstract noun?

When you are referring to a specific instance of that abstract noun, e.g. a specific idea or theorum, and aren't identifying it by e.g. following the noun with a number specific enough for the reader to know exactly which theorum you're discussing.

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In this very case the article the is referred to an abstract noun - in this case theorem - which is already known to both speakers, i.e. they already have background knowledge about that very theorem which is determined by the article the.

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