The Sanlun school, also known as the Three Treatise school, was a Chinese Madhyamaka school that emerged during the 6th century. It was founded by Jizang, who was a student of the famous Indian philosopher Nagarjuna. The Sanlun school focused on the teachings of emptiness and the Middle Way, and it became one of the most influential schools of Buddhism in China. However, like any other school of thought, the Sanlun school has faced criticisms from both within and outside the Buddhist community.

One of the main criticisms of the Sanlun school's teachings is its emphasis on emptiness. The concept of emptiness, or shunyata, is central to the Madhyamaka philosophy, and the Sanlun school took it to an extreme level. According to the Sanlun school, all phenomena are empty of inherent existence, including the Buddha and his teachings. This led to the criticism that the Sanlun school was promoting nihilism and denying the existence of anything.

Moreover, the Sanlun school's emphasis on emptiness also led to the criticism that it was neglecting the importance of compassion and ethical conduct. The school's focus on emptiness was seen as a detachment from the world and a lack of concern for the suffering of others. This was a major concern for many Buddhists who believed that compassion and ethical conduct were essential aspects of the path to enlightenment.

Another criticism of the Sanlun school was its rejection of the idea of a self. The school taught that the self is an illusion and that there is no permanent, unchanging self. This was seen as a radical departure from the traditional Buddhist belief in rebirth and the concept of karma, which is based on the idea of a self that continues from one life to another. The rejection of the self also raised questions about the continuity of consciousness and the possibility of achieving enlightenment.

The Sanlun school's teachings were also criticized for being too complex and difficult to understand. The school's reliance on logic and reasoning, as well as its use of complex terminology, made it inaccessible to many people. This led to the criticism that the Sanlun school was only suitable for scholars and intellectuals and not for the general population.

In conclusion, while the Sanlun school's teachings have had a significant impact on Chinese Buddhism, they have also faced criticisms for their emphasis on emptiness, neglect of compassion and ethical conduct, rejection of the self, and complexity. However, it is important to note that these criticisms are not universally accepted, and many Buddhist scholars continue to study and practice the teachings of the Sanlun school.