Given the popularity of Caitanya Vaiṣṇavism these days, there is much use of the term ‘acintya bheda-abheda’. I am not sure if the popular descriptions of this term are accurate. I therefore decided to collect the precise language that Śrī Jīva uses to justify the use of acintya bheda-abheda below along with my translations.
The term ‘acintya bheda abheda’ is explicitly mentioned by Śrī Jīva Goswami in his Sarva-samvādinī commentary on the Paramātmā Sandarbha.
apare tu, tarkāpratiṣṭhānāt [ve.sū. 2.1.11] iti nyāyena bhede’py abhede’pi nirmaryāda-doṣa-santati-darśanena bhinnatayā cintayitum aśakyatvād abhedaṁ sādhayantas tadvad abhinnatayāpi cintayitum aśakyatvād bhedam api sādhayanto’cintya-bhedābheda-vādaṁ svīkurvanti |
Others accept acintya bhedābheda vāda on the basis of tarkāpratiṣṭhānāt. They recognize that accepting bheda or abheda, each, gives rise to the fault of being devoid of conformity with śruti. [They accept acintya bhedābheda vāda realizing the futility of] seeking abheda because of the impossibility of conceiving bheda, [and] similarly seeking bheda because of the impossibility of conceiving abheda.
This mirrors Śrīdhar swami’s commentary that Śrī Jīva Goswami has cited in the Bhagavat Sandarbha Anuccheda 16.2:
yad vā, acintyā bhinnābhinnatvādi-vikalpaiś cintayitum aśakyāḥ, kevalam arthāpatti-jñāna-gocarāḥ santi
Alternatively, the meaning of acintyā is that the śakti of objects cannot be thought of in terms of oneness with (abhinnatva i.e. abheda), or difference from (bhinnatva i.e. bheda), them, but understood only by presumption ( arthāpatti ).
We see the same language in the following passage in in his Sarva-samvādinī commentary on the Bhagavad Sandarbha, where we see an additional important concept:
tasmāt svarūpād abhinnatvena cintayitum aśakyatvād bhedaḥ | bhinnatvena cintayitum aśakyatvād abhedaś ca pratīyate iti śakti-śaktimator bhedābhedāv evāṅgīkṛtau | tau cācintyau iti ||
Therefore, because it is impossible to think of the śakti as being non-different from the svarūpa, bheda is apparent. And. because it is impossible to think of the śakti as different from the svarūpa, abheda is apparent. As such, bheda and abheda alone must be accepted between the śakti and the śaktimān. And this bheda and abheda is acintya (known through śāstra alone).
The main thing to take away is as follows.
In the term ‘acintya bheda abheda’ –
bheda is the denial of abheda,
abheda is the denial of bheda,
– between śaktimān and śakti.
The word ‘acintya’ indicates that all this is known only from śāstra.
In the term, ‘acintya bheda-abheda-vāda’:
1. the word ‘bheda’ is a denial of ‘abheda’ between śaktimān and śakti.
2. the word ‘abheda’ is a denial of ‘bheda’ between śaktimān and śakti.
3. These denials ensure that statements of śruti that propound bheda are not rejected, and statements of śruti that propound abheda are also not rejected.
4. Point 3 implies the word ‘acintya’, meaning denial of bheda and the denial of abheda is known only from śāstra.