What does it mean when something has "no self-nature"? I was reading on some later Buddhist and Mahayana sutras and kept seeing the principles along the lines of "all phenomenon have no nature of their own and are thus empty." I've studied on scriptures like this before, like the Heart Sutra, but I don't think the Pali Canon or Tripitaka mentions anything about this doctrine. I'm curious what exactly later Buddhists meant by this, and if the Buddha actually taught this doctrine or if Sunyata has basis in the original sutras. Thank you to all.
The Pali phrase in the Suñña Sutta is,

suññam idaṃ attena vā attaniyena vā

... which Wikipedia translates as,

this world is empty of self or anything pertaining to self

The word attena is a declension of Attan, which is Ātman in Sanskrit/Hinduism:

Ātman is a Sanskrit word that means inner self or soul. In Hindu philosophy, especially in the Vedanta school of Hinduism, Ātman is the first principle, the true self of an individual beyond identification with phenomena, the essence of an individual. In order to attain liberation, a human being must acquire self-knowledge (atma jnana), which is to realize that one's true self (Ātman) is identical with the transcendent self Brahman.

... which is cognate to (or opposed to, to be contrasted with) the Buddhist Pali term Anatta:

In Buddhism, the term anattā (Pali) or anātman (Sanskrit) refers to the doctrine of &quot;non-self&quot;, that there is no unchanging, permanent soul in living beings. It is one of the seven beneficial perceptions in Buddhism, and along with Dukkha (suffering) and Anicca (impermanence), it is one of three Right Understandings about the three marks of existence.
The concept of Anatta or Anatman in Buddhism, is a major difference from the Hindu concept of Atman (self, soul).

Maybe that helps to explain what &quot;self-nature&quot; might mean, or whence it's derived, in &quot;the original sutras&quot;.
See also topics which are tagged anatman.

Furthermore, the term bhava appears a lot in &quot;the original sutras&quot; in that it's one of the 12 Nidanas and thus part of the theory of dependent origination.
In Svabhava (or the Pali sabhāva) there's the word Bhava plus the root Sa which means &quot;own&quot;, a reflexive pronoun cognate to the Latin sui, suus.
In the Pali, &quot;becoming&quot; is dependently originated. The whole wheel of becoming is about how various things which shouldn't be considered 'self' sustain or feed each other, so I take it that (independent) self-becoming is a paradox, a contradiction, which explains the quote in the OP &quot;all phenomenon have no nature of their own&quot;.
If this isn't clear, and/or this appears to contradict other answers, perhaps that's because there are (or there are posited) several categories of self-nature (see e.g. Tri-svabhava-nirdesa).
Wikipedia says,

In the Pāli canon, &quot;sabhāva&quot; is absent from what are generally considered to be the earliest texts.[a] When found in later texts (e.g., the paracanonical Milindapañha), it generically refers to state (of mind), character or truth.
In the post-canonical Abhidhamma literature, sabhāva is used to distinguish an irreducible, dependent, momentary phenomenon (dhamma) from a conventionally constructed object. Thus, a collection of visual and tactile phenomena might be mentally constructed into what is conventionally referred to as a &quot;table&quot;; but, beyond its constituent elements, a construct such as &quot;table&quot; lacks intrinsic existence (sabhāva).

I think that this example (of the non-self of a table) is analogous to the parable of the chariot from the Milinda Panha. Wikipedia dates the Milinda Panha to about 100 CE, which I contrast with the lifetime of the Buddha in about 400 BCE.
As you progress (forward in history) into the foundations of Mahayana you get to Nagarjuna (150 to 250 CE). The SEP says this about Emptiness and svabhāva,

The central concept around which all of Nāgārjuna's philosophy is built is the notion of emptiness (śūnyatā). Emptiness is of course always the emptiness of something, and the something Nāgārjuna has in mind here is svabhāva. Different terms have been used to translate this word into English: “inherent existence” and “intrinsic nature” appear etc.

Fwiw Wikipedia says of Svabhava,

In the Mahāyāna Buddhadharma tradition(s) it is one of a suite of terms employed to denote the Buddha-nature