In daily life, we can define arthāpatti as follows: A conjecture about what is not perceived, derived from what is perceived. A classic example: We see Devadatta not eating all day. He claims to be fasting. Yet, Devadatta is getting fatter and fatter. He must eat at night. It is a conjecture based on reasonable evidence.

Because truth is diametrically opposed to ignorant experience, focused on objects, we must oppose logic that focuses on objects. Science is a means of knowledge focused on the objects of sense perception (pratyakṣa) and its derivatives (anumāna). These are two of the six other legitimate means of knowledge in vedānta.

But with discrimination (viveka), we can distinguish the silent witness and the seen within ourselves. We do this not by perceiving the seer, but by assuming the seer. Even though I don't experience it concretely, there must be a seer who distinguishes everything seen. Similarly, there must be a substance that sustains reality. Similarly, there must have been something from which the universe exploded. These are all reasonable assumptions, arthāpattis.

However, for the fact that the seen is nothing other than the one seer, and that I am that, in its entirety, we need more than arthāpatti. We need the authority of īśvara, after being revealed in the minds of seers, later written down in the Vedas. Thus, we appeal to the means of knowledge, writing (śāstra pramāṇam), or the means of knowledge, words (śabda pramāṇam), or the means of knowledge, hearing (śruti pramāṇam) or reliable words (āpta vacana). These are four synonyms for the central means of knowledge of vedānta. Why central? Because we need to be open for knowledge which comes from outside our ignorance. Then we hear of the facts: Brahman is the self. The self is all that exists. Brahman is one without a second. Then, through logic, we arrive at the following arthāpatti: Brahman is existence. I exist. I must be brahman. And so, gradually, the practice of knowledge goes from assumption to fact for the practitioner.

Arthāpatti is not guessing, it is not believing, it is not imagining; we could say, it is being forced to come to a conclusion. It is being guided through your own existential experience. It is progressive reasoning. It is up to the practitioner, through knowledge and reasoning, to request the recognition (pratyabhijñā) of these facts in their own experience.

We see this frequently in Vedānta. For example, to explain that we experience differences in the world. The basic means of knowledge of Vedānta, the scriptures (śabda pramāṇa), state: "Brahman is all that exists. Brahman is one without a second." Furthermore, Vedānta does not say: "the world does not exist." We simply experience the multiplicity of the world. How is this resolved? It is said: Multiplicity is not existence (sat) itself, nor is it non-existence (asat). We do experience multiplicity. Therefore, it must be mithyā: false or seemingly true. Consciousness/existence is free from it, but multiplicity is completely dependent on consciousness-existence. This, too, is typical arthāpatti.

Great teachers like Gaudapada, Śaṅkara, and Vidyaranya Svāmī (and many others in history after the prasthāna traya) have developed these kinds of arthāpatti reasoning so that we can benefit from it (prayojana). With gratitude!