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Brahma satyam, jagat mithya is one of the hallmarks of Adi shankara's philosophy. The usage of jagat being Mithya is later, an addition by Adi Shankara. There is reference of the world being referred to as a MithyA entity by any of his predecessors.
The meaning of this popular phrase is beautifully enfolded when we look at the acutual meanings of the term involved. The terms involved in the phrase are-
Brahman - ब्रह्मन - literally, it means one which expands.
Brahman is the most fundamental physical entity which makes up universe.Using modern physical terms as an analogy, it can be said that quantum fields which is hypothesized to make up everything in universe is Brahman. Now quantum fields may or may not be brahman.If it is proven that quatum fields do make up everything in this world including space-time and dimensions then it will be proven that quantum field is Brahman.If not, then perhaps there something even more fundamental in this universe than quantum fields.
It was just that they expected, just like modern physicists, universe is madeup of some fundamental entity. Indian philosophers did not inquire into the physical nature of that fundamental entity. Practically, it was impossible as they were bronze age people with bronze age technology. Hence they simply named this expected fundamental physical entity as Brahman, without inquiring much about its nature.
Satyam - one which is eternal, changeless and existent
Jagat (Universe/World)- This is an interesting term to think upon.
Jagat - Ja + Ga
Ja - jaayate (to arise, originate, born)
ga - gamana: - ga - (one which goes/moves or changes)
It means, one which is born (janana) out of gati (speed/change) is Jagata: That is Universe is said to have come into existent due out of constant change.
Mithya - has word root as 'Mith'. This is the most interesting and illuding term on this phrase.
As given by Apte Sanskrit Online dictionary, Mith - to associate with; to unite; to hurt; to understand; to wrangle; to grasp
Thus, when we apply these meanings to the phrase Brahma Satyam Jagat Mithya, following meanings are deduced.
1) Brahman is existent, jagat is associated (with Brahman)
2) Brahman is Existent, jagat is united (with Brahman)
3) Brahman is existent, jagat is hurt (does not make sense)
4) Brahman is existent, jagat is understood by (brahman)
5) Brahman is existent, jagat is wrangled/tended/herded (by brahman) (wrangle = to herd, to tend)
6) Brahman is existent, jagat is grasped by brahman
The popular translation of Brahman is truth and world is false is in fact a disbelief.I guess the word root Mith which makes up the word MithyA, is also the word root for Mithuna and Maithuna (sexual intercourse), which again is related to union or being associated with.
When translated all the words, the phrase becomes-
"That one which originates/exists due to constant change (jagat) is associated with/United with/being tended by (mithyA) Brahman which is changeless existence (satya) - Brahma Satyam, jagat MithyA..."
There is one more meaning of word MithyA - to be made up/ to fall in place.
Perhaps the word Mith is originated from same Proto-Indo-European ancestor which also makes up the greek word (mythos). Mythos also means to be made up. From Mythos comes Mythology.
When applied this meaning, the phrase translates as
"That which arises out of change (jagat) is a phenomenon of things falling in place/made up, where as Brahman is changeless existence."
There is a catch though. This meaning is not corroborated from any online sanskrit dictionary, but I distinctly remember reading it in some authentic source.
Furthermore, the interpretation of word Mithya determines whether a person is advaitin OR dvaitin OR vishishtadvaitin.
If Mithya is taken as United, then a person is advaitin (brahman and jagat are united and satya). This is in sync with Sarvam Khalu Idam Brahma (everything that exists is Brahman)
If mithya is takes as association, then the person is vishishtadvaitin. (brahman is satya and jagat is associated with satya, but not completely satya).
If mithya is taken as wrangled (to tend), then, he becomes a dvaitin (brahman is satya, jagat is being wrangled/tended/herded (by brahman)). Here, World is being herded by the separate herder that is God.
Thus we can see, differential interpretation of this phrase by Shankara eventually ends up in conjuring vastly different world views towards life and universe. I pay my homage to great genious, Adi Shankaracharya...