The Aggi-Vacchagotta Sutta is one of the earliest Buddhist references to the classical Indian logical system of catuskoti, the tetralemma (a four-way variation of the philosophical dilemma - the four options in this case being "is", "is not", "both" and "neither"). In it, the Buddha dismisses a number of questions put forth to him by a recurring character, the wanderer Vacchagotta. These questions constitute a small portion of what the Buddha calls avyakrtavastuni - the undetermined, unelucidated, unprofitable questions. They are commonly summarized as the antagahika micchaditthi - the ten wrong views. Different traditions vary in the number of these views they address, with some including "both" and "neither" after every "is" and "is not" to amount to fourteen in total. In the Pali Canon where the Aggi-Vacchagotta Sutta originates, there are generally ten:
1. The cosmos is eternal.
2. The cosmos is not eternal.
3. The cosmos is finite.
4. The cosmos is infinite.
5. The soul and body are the same.
6. The soul and body are different.
7. The Tathagata exists after death.
8. The Tathagata does not exist after death.
9. The Tathagata both exists and does not exist after death.
10. The Tathagata neither exists nor does not exist after death.
The Buddha begins by dismissing all of these views and their corresponding inquiries as unrelated to the path to Awakening. The answers to these questions are utterly disconnected from his liberative teachings. In subscribing to any of these positions, one brings upon oneself unnecessary suffering. The search for absolute truths with regard to these wrong views will be an unending one.
Many have interpreted the Aggi-Vacchagotta Sutta and related discourses as the Buddha's attempt to do away with speculative metaphysics. The Buddha himself says that he has no views, no position on any of these questions, and that their answers are undeclared by him. One need not concern oneself with them. In understanding the impermanence of the skandhas (the aggregates that constitute what we take to be our "self" - form, feelings, perceptions, mental fabrications, and consciousness), one comes to the realization that all activities of the ego, all clinging and possessiveness, are fruitless.
Later in the Aggi-Vacchagotta Sutta, the Buddha describes Nirvana as the exhaustion of sustenance, like a fire no longer fed by grass and timber. Nirvana is the end of suffering, and suffering's fuel is craving. Tanha/trishna (literally thirst, desire) is the sustenance for the fire. Nirvana is the blowing out of this fire. Vacchagotta has reason to be confused. If the Tathagata (Buddha) neither exists, nor does not exist, nor both, nor neither, then what happens to him? The Buddha makes it clear that speaking of the enlightened person as if he/she exists (eternalism), does not exist (annihilationism), both, or neither, do not apply to the situation. To speak of existence or non-existence would invite obvious contradictions. The Buddha merely says the flame is blown out: the fires of greed, hatred, and delusion, all of which play a role in craving (which conditions repeated becoming) are cooled. Through Nirvana (blowing out, cooling), one leaves the fuel of craving behind, and thus extinguishes suffering for good.