The Sanlun school, also known as the Three Treatise school, is a Chinese Madhyamaka school that emerged during the Tang dynasty in China. This school is based on the teachings of Nagarjuna, an Indian philosopher who is considered the founder of the Madhyamaka tradition. The Sanlun school places great emphasis on the concept of emptiness, which is a central tenet of Madhyamaka philosophy.

According to the Sanlun school, emptiness refers to the ultimate nature of reality. This concept is often misunderstood as a form of nihilism, but the Sanlun school argues that emptiness does not mean that things do not exist. Instead, emptiness is the lack of inherent existence or independent existence of things. This means that all phenomena, including ourselves, are empty of any fixed or permanent essence.

The Sanlun school interprets emptiness through the concept of the Middle Way, which is the middle path between eternalism and nihilism. Eternalism is the belief that things have a permanent and unchanging essence, while nihilism is the belief that things do not exist at all. The Middle Way rejects both these extreme views and asserts that things exist conventionally, but they are ultimately empty of any inherent existence.

The Sanlun school also uses the concept of dependent origination to explain emptiness. According to this concept, all phenomena arise dependently on other phenomena and do not have an independent existence. This means that things are empty of inherent existence because they are dependent on other factors for their existence. Therefore, emptiness is not a separate reality, but it is the nature of all phenomena.

The Sanlun school also distinguishes between two types of emptiness: relative and ultimate emptiness. Relative emptiness refers to the emptiness of all phenomena at the conventional level, while ultimate emptiness refers to the emptiness of all phenomena at the ultimate level. The ultimate level is the level of reality where things are completely devoid of any inherent existence.

In addition to this, the Sanlun school also emphasizes the concept of the two truths. The conventional truth refers to the everyday reality that we experience, while the ultimate truth refers to the ultimate nature of reality, which is emptiness. The two truths are not contradictory but are two different ways of understanding reality.

In conclusion, the Sanlun school interprets the concept of emptiness as the lack of inherent existence of all phenomena. This interpretation is based on the Middle Way philosophy and the concept of dependent origination. Emptiness is not a negative or nihilistic concept, but it is the ultimate nature of reality that can lead to liberation from suffering.