‘Bheda’ is vyaapya (pervaded) and ‘abheda’ is vyaapaka (pervader)
In Vedanta we have the Brahman’s svarupa lakshanam being taught as ‘Satyam, Jnanam, Anantham’. In these, the third one is indicative of the Infinite nature of Brahman. Three types of bheda are admitted: desha, kaala and vastu, translating to space-wise, time-wise and object-wise distinction/limitation. While everything in creation is limited in time, space and object, Brahman alone is free of these limitations. Shankara has said while explaining the vastu paricchedatvam, rather the absence of it in Brahman, that Brahman is sarva ananyam, it is non-different from everything in creation. (Taittiriya Bhashya).
If there is any entity admitted as different from Brahman, that object will limit Brahman as an object. This is different from space-wise limitation.
When there are two objects, different from each other, we cognize them as two different things. In other words, the different objects become objects of our cognition and therefore are pervaded by our buddhi. This is called ‘buddhivyaapyam.’ On the other hand, if the objects are realized to be non-different, that is, one only, then we have abheda buddhi. This abheda buddhi pervades the bheda, bhinna vastus, and thereby is vyaapaka. Surely, the pervaded is of a lower status than the pervader.
Supposing someone holds Vishnu to be different from Shiva, then we have two buddhis: Vishnu- buddhi and Shiva-buddhi, both being paricchinna buddhis. As explained by Shankara in the Taittiriya Upanishad, a horse-buddhi and a cow-buddhi limit each other mutually . Vishnu-buddhi and Shiva-buddhi limit each other mutually. This is because the two are admitted to be different. On the other hand, if one has the idea of non-difference between Vishnu and Shiva, then there is abheda buddhi which is vyaapaka, the pervader. Naturally, the pervader is higher than the pervaded. Ultimately, when there are no bhinna vastus, entities, like Vishnu, Shiva, etc. the name ‘vyaapakabuddhi’ is also redundant.
In fact the Upanishad is very smartly avoiding any objection to Brahmabuddhi. In the Kenopanishat we have a mantra: ‘pratibodha viditam matam….’ where it teaches, it is Brahma buddhi that is running through all individual perceptions like pot-perception, cloth-perception, etc. that a person would get in the course of a day. Since it is Brahman that is being wrongly perceived as pot, cloth, etc. the perception itself being in the form ‘pot is, cloth is..’ the ‘is-ness’ in every perception is Brahman. That way, no perception is bereft of Brahman-perception also being the basis/part of it. What constitutes moksha jnanam is, however, the perception of Brahman without the pot-cloth-etc. upadhis.
The Advaitin alone can achieve this since for him even the Vishnu-buddhi is only an aupadhika buddhi, Brahman being the basis for even that. So, naturally, Shiva-buddhi, also aupadhika, which also has Brahman as its basis, evidently limits Vishnu-buddhi. And therefore alone neither Vishnu buddhi nor Shiva buddhi can be moksha phalaka jnanam. Everywhere in the itihasa purana when Vishnu/Shiva buddhi is taught as moksha phalaka jnanam, it is implicit that that Vishnu or Shiva is the Turiya entity that transcends the Trimurtis.
Thus, in the scenario of bheda, the vyaapyatva of bheda (bhinna vastu) is unavoidable; the vyaapaka being abheda.
Here is an article that has more details on the topic:
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