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1.A There is [no way] to prove that he was wrong.

1.B There is [no way] of proving that he was wrong.

2.A There is [no way] to prove that he was right.

2.B There is [no way] of proving that he was right.

Are "of proving" and "to prove" completely interchangeable? If not, is there a correlation betwen these phrases and the words "wrong" and "right"? If yes, why are 1.B and 2.B cases wrong if one drops the phrase "no way"?

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All four sentences are grammatically incorrect if no way is dropped.

One can say:

This {goes / is} to prove that he was {right / wrong}".

In this case, the two phrases to prove and of proving seem to me to be fungible. They're just a style preference.

Have you seen any documents that say There is to prove that he was {right / wrong}? Please provide a link.

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    +1 However, all four are correct when no way is changed to a way. – StoneyB on hiatus Mar 7 '13 at 23:02
  • @StoneyB: Yes, but the OP didn't suggest that possibility. :-) – user264 Mar 7 '13 at 23:03
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    Then that is a deficiency on his part which should be remedied. Perhaps he doesn't know of the possibility and would be happy to be informed of it. :) – StoneyB on hiatus Mar 7 '13 at 23:06
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    @Carlo The NYT examples don't begin sentences; yours do. By the way, it would be easier to talk about these examples with either complete sentences or links to where complete sentences can be found. – snailplane Mar 7 '13 at 23:35
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    @Carlo_R. The example you give is clearly syntactically different, as Bill says: it is a relative clause with a 'null-relativizer': evidence [which] there is to prove that ... Translated into your structure this would be There is evidence to prove that ... (or There is evidence proving that ...). – StoneyB on hiatus Mar 8 '13 at 0:03
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In your base sentence, There is no way, the noun way is what determines what constructions may follow. Way takes (as we used to put it—today the technical term is licenses) the following constructions with the sense [Subject] can prove X

Non-finite clauses
- a way to prove X
- a way of proving X
- a way for Subject to prove X

Finite clauses
- a way (that/in which) Subject can prove X
- a way (that/in which) X can be proven

This is true whether your base sentence is There is no way or There is a way or There may be a way or There are many ways or any other variation on this theme: way determines what constructions are permissible.

But when you drop no way you change the entire structure of the sentence. The construction There is, by itself, can only take a noun phrase as its complement. None of these constructions will work.

The apparent counter-examples you cite belong to different structures:

To someone infected by the conspiracy theory virus it doesn't matter how much evidence there is to prove that 9/11 was indeed an attack ... Once you unpack the relative clause, the relevant piece of the sentence boils down to There is evidence to prove that X.

There is less evidence to support the supposition that Foster's death was a homicide than there is to prove that Nicole Brown Simpson was ... Again, after unpacking, the relevant piece of the sentence boils down to There is more evidence to prove that X.

Evidence performs the same role in both of these as way in your sentence, governing what constructions are permissible.

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