What do you mean by "nature?" Most people mean something that is intrinsic to a given thing. For example, common people assume the nature of fire is heat, the nature of water is wetness, and so on.

Bhavaviveka, etc., do not accept that things have natures. If they did, they could not be included even in Mahāyāna, let alone Madhyamaka. 
 
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The idea that things have natures is refuted by Nāgārjuna in the MMK, etc., Bhavaviveka, Candrakīrti, etc., in short by all Madhyamakas.

A "non-inherent nature" is a contradiction in terms.

The error of mundane, conventionally-valid perception is to believe that entities have natures, when in fact they do not, being phenomena that arise from conditions. It is quite easy to show a worldly person the contradiction in their thinking. Wetness and water are not two different things; therefore wetness is not the nature of water. Heat and fire are not two different things, therefore, heat is not the nature of fire, etc. For example, one can ask them, "Does wetness depend on water, or water on wetness?" If they claim wetness depends on water, ask them, where is there water that exists without wetness? If they claim the opposite, that water depends on wetness, ask them, where is there wetness that exists without water? If there is no wetness without water nor water without wetness, they can easily be shown that wetness is not a nature of water, but merely a name for the same entity under discussion. Thus, the assertion that wetness is the nature of water cannot survive analysis. The assertion of all other natures can be eliminated in the same way.

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Then not only are you ignorant of the English language, but you are ignorant of Candrakīrti where, in the Prasannapāda, he states that the only nature is the natureless nature, emptiness.

Then, if it is asked what is this dharmatā of phenomena, it is the essence of phenomena. If it is ask what is an essence, it is a nature [or an inherent existence, rang bzhin]. If it is asked what is an inherent existence [or nature], it is emptiness. If it is asked what is emptiness, it is naturelessness [or absence of inherent existence]. If it is asked what is the absence of inherent existence [or naturelessness], it is suchness [tathāta]. If it is asked what is suchness, it is the essence of suchness that is unchanging and permanent, that is, because it is not fabricated it does not arise in all aspects and because it is not dependent, it is called the nature [or inherent existence] of fire, etc."
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