Is every Jeeva “eternal” like the ultimate God (nirguna Brahman) or “temporary” within cycle?
From our discussions in the chat room, since we stumbled upon this, I will formalise it as an answer:
Gita Chapter 15, Verse 7
mamaivāḿśo jīva-loke jīva-bhūtaḥ sanātanaḥ
manaḥ-ṣaṣṭhānīndriyāṇi prakṛti-sthāni karṣati
Gambhirananda: It is verily a part of Mine which, becoming the eternal individual soul in the region of living beings, draws (to itself) the organs which have the mind as their sixth, and which abide in Nature.
Word to word: Among the living world, the living being (bhuta = body) is my eternal fragment only; It (fragment or body) keeps attracting 5 senses & mind as the 6th towards the material nature.
Thus from the Gita it is said that the jiva is an 'ETERNAL' fragmented part.
This is without getting into any particular Vedantic Philosophy. As discussed by other answers, in Advaita, there is one more addition to this. i.e. You are not a Jiva (individual consciousness). You are Brahman (Existence-Consciousness-Bliss). This makes all of "jivahood" illusory.
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