If we consider humans as finite beings, what evidence do we have that “eternity” actually exists?
Physical bodies are finite, corruptible, but are human beings just their bodies (and their finite minds)? There is a mysterious, undefinable, and unmeasurable entity called consciousness which appears to pervade all sentient beings and nature in general. Nature, all life, is conscious – dare we say? This entity – consciousness – is undeniable, for it is our most direct and unfalsifiable experience. Consciousness – by consensus of a majority of physicists – escapes all parameters of physics, neurophysiology, and brain studies. But not only consciousness, but so-called matter is also in the same category of the intrinsically unknowable, even if there are methods for measuring and experimenting with such entity as matter-energy.
Again, no one knows what eternity might be, such are the limitations of our means of understanding reality, even though physics and mathematics come to our aid in this and also with the phenomenon of space (space-time). What is more, philosophy and metaphysics have a better grasp of the extra-physical dimensions of reality aided and abetted as they are by (universal) intuition. For metaphysics time does not exist outside of our minds, and, rather than eternity-(duration), timelessness – or what is the same, that only the PRESENT exists – is what, as a concept, gives a semblance of reality to reality (all that is and ever has been) – incomprehensible to the unaided mind.
One could say that for an Advaitin evidence that eternity exists is the existence of the Vedas, which are said to be uncreated (apauruseya), eternal (nitya), and intrinsically valid (svatah-pramanya). In his Brahma Sutra Bhashya Shankara uses several different arguments to prove the eternality of the Vedas. He argues that the eternal nature of the Vedas is founded on their uncreated status, which is established by the fact that there is no remembrance of an agent who composed them. Shankara also uses the Mimamsaka argument that the authority and eternality of the Vedas derives from the fact that the Vedic words are eternal and are eternally connected to their denotations, which are also eternal. He argues that the eternality of the Vedas is further established from the fact that the universe, with its fixed, eternal classes, is produced from the words of the Vedas. Finally, Shankara cites proof texts from the Vedas themselves as well as from smrti texts in support of the eternality of the Vedas.