# Is it true that

Is the following sentence grammatically incorrect?

Is it true that 1+1=2 ?

I know it is easier to say: Is 1+1=2 true?

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No; the sentence "Is it true that 1 + 1 = 2?" is perfectly grammatically correct.

In logic, there are tests that depend on being able to prefix almost arbitrary sentences with "It is the case that ..." or "It is true that ..." and if the result still makes sense, then certain properties hold (it is a declarative sentence which could be a proposition). For example, you can test:

• The sun rises each day

• Go there!

The first is a declarative sentence like 'one plus one equals two' is a declarative sentence; it can be prefixed with "Is it true that" and it makes sense. However, you can't say "Is it true that go there!" -- it is not a declarative sentence.

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Indeed, the sentence is more likely than "Is 1+1=2 true" because the latter is likely to be confusing to hear. – Colin Fine Dec 5 '10 at 20:09

In ordinary usage, “is it true that 1+1=2 ?” and “is 1+1=2 true?” are both grammatically correct, synonyms, and largely interchangeable. The first sentence construction might be preferred because it places the mathematical expression at one end of the sentence. The second construction is particularly awkward when pronounced: when you hear “is complicated mathematical expression true”, it's hard to remember the verb that “true” is a complement of.

In mathematical usage, treating mathematical relations as verbs is frowned upon. A sentence like “is it true that 1+1=2 ?” looks ungrammatical because “1+1=2” looks like a mathematical expression (which happens to be a proposition), distinct from the English phrase “one plus one equals two”. In grammatical terms, “1+1=2” is equivalent to a noun group, it can't function as a verb. This is particularly true amongst logicians, since there is a step of semantic interpretation involved in going from “1+1=2” to “one plus one equals two”, and logicians are used to settings where this step is non-trivial. Even mathematicians and assorted practicioners who aren't logicians often consider “is it true that 1+1=2 ?” bad style.

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I don't get your “1+1=2” is equivalent to a noun group, it can't function as a verb". It's not functioning as a verb, grammatically or logically. It's functioning as a proposition. You can say "Is it true that X?", where X is any proposition. This is grammatically and logically equivalent to "Is X true?". – FumbleFingers Sep 23 '11 at 14:46
@FumbleFingers That's the ordinary usage, but not the dominant usage amongst mathematicians. Ordinary usage tends to treat `=` as the verb equals, and therefore a logical proposition like `1+1=2` can be used as a grammatical proposition. It can also serve as a noun group, like any quote can be treated as a noun group (“‘green ideas furiously’ is meaningless.”). Mathematical usage tends to treat `1+1=2` as a mathematical expression or formula, `=` being just one of the symbols in the logical proposition, and this cannot be used in constructs like “Is it true that X?” where X cannot be a noun. – Gilles Sep 23 '11 at 18:07
I'm not sure that's strictly a mathematical issue. The proposition is 1+1=2, and I don't think deconstructing that proposition into sub-components, or translating arithmetic symbols into lexical ones makes any difference. If there's anything to take issue with, it's that logically we should probably either stick with Is X true? or go the whole hog and say Is it true that X is true?". But however you put it, X is never going to be a "noun". It's a (potentially autonymous) statement. – FumbleFingers Sep 23 '11 at 18:23
@FumbleFingers In mathematical usage, `1+1=2` is not read formally as “one plus one equals two”, but rather as “the equality between the sum of one and one, and two”. “Is is true that the equality between …” is not grammatically correct, because “the equality between …” is not a proposition (in the grammatical sense) but a noun group. – Gilles Sep 23 '11 at 18:56
I topped out at A Level maths, so I can't really argue that one much further. But I've done a lot of programming since then, wherein 1+1=2 is a condition (which evaluates to true or false). It is also a statement, and since we seem to be going nowhere useful, I'll leave that as my final statement on the matter! :) – FumbleFingers Sep 23 '11 at 19:21