Nagarjuna, a renowned Buddhist philosopher of the Madhyamaka school, is known for his profound understanding of emptiness and the concept of dependent origination. In his philosophy, logic plays a crucial role in unraveling the ultimate truth and breaking down the illusion of inherent existence.

One of the key aspects of Nagarjuna's philosophy is the concept of shunyata, or emptiness. According to Nagarjuna, all phenomena, including the self, are empty of inherent existence. This means that they do not possess any inherent or independent existence, but rather arise dependently on other factors. Nagarjuna uses logic to deconstruct the notion of inherent existence and establish the concept of shunyata.

In his writings, Nagarjuna uses a method of logical reasoning called the tetralemma, which involves considering all possible alternatives to a statement and then refuting them. This method is used to show that all phenomena are empty of inherent existence. For example, if we say that something exists inherently, Nagarjuna would ask if it exists inherently, not inherently, both inherently and not inherently, or neither inherently nor not inherently. Through this process of logical reasoning, he shows that all these possibilities are untenable, and therefore, the concept of inherent existence itself is untenable.

Furthermore, Nagarjuna also uses logic to refute the extreme views of eternalism and nihilism. Eternalism is the belief that things have an unchanging and permanent essence, while nihilism is the belief that nothing exists at all. Nagarjuna argues that both these views are incorrect and instead asserts the Middle Way, which states that things exist dependently and are empty of inherent existence.

Moreover, Nagarjuna also uses logic to explain the concept of dependent origination, which is the idea that all phenomena arise dependently on other factors. He uses the concept of cause and effect to show that nothing can exist independently or inherently because everything is dependent on other factors. Through this logical reasoning, Nagarjuna establishes the interconnectedness and interdependence of all phenomena.

In conclusion, logic plays a crucial role in Nagarjuna's philosophy as it is used to deconstruct the concept of inherent existence, refute extreme views, and establish the concept of emptiness and dependent origination. Through his use of logical reasoning, Nagarjuna provides a profound understanding of the ultimate truth and helps us break through the illusions of inherent existence and gain insight into the nature of reality.