Is it true that

Question

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?

Answer 1

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.

Answer 2

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.