Is the sentence The knife is a tool to cut grammatically correct?
My logic is that the sentence phrased thus doesn't convey the intended meaning as it seems to convey the opposite idea, i.e., The knife needs cutting, which, of course, is meaningless. My logic stems from the fact that to cut here is a gerundial infinitive acting as an adjective and modifying the noun phrase a tool. Thus, I suppose, the sentence might better be rephrased, among many possibilities, as The knife is a tool to cut [vegetables with.], or, The knife is a tool that cuts. [no object needed].
Is the original sentence correct or do I need to rephrase it to convey better the meaning?