Shankaracharya said in the 20th verse of Brahmajnanavalimala
ब्रह्म सत्यं जगन्मिथ्या जीवो ब्रह्मैव नापरः । अनेन वेद्यं सच्छास्त्रमिति वेदान्तडिण्डिमः ॥ २०॥
Brahma Satyam Jagan Mithya Jivo Brahmaiva Na Aparah
Brahman (the Absolute) is alone real; the world is mithya; Jiva is non-different from Brahman.
The problem arises because mithya is translated as illusion. Mithya actually means it is not sat or asat. This is due to the wrong understanding of what is sat and asat.
sat is defined that is available at all times (trikalaabaadhyami) including dreams and deep sleep. Only Brahman is sat. Shankara explains this in explaining the meaning of the sütra - janmädyasya yatah – Brahma Sutra Bhasya I.1.2,
asat is used to mean unfitness to appear as existent (tuccham) on any locus. For example: hare’s horn or son of a barren woman like the vandhyä-putra.
jagat is not real like Brahman, because it is subject to time/space/change but it is also not asat like vandhyä-putra. However, jagat is mithya, which is neither sat nor asat.
Jivas attribute reality to the world due to avidya (ignorance).
Jivas delusorily thinks he is himself the seer and the knower. Atma Bodha 26
However, avidya is negated when they realize the Self to be Brahman. For the Brahman, jagat is non-existent while for jivas, it is existent in two forms: appearing as real for the ajnani and understood as false for the jnani. It is this unique combination of non-existence and existence that is called mithya. Being mithya and also anadi, avidya cannot affect Brahman just like a wrong perception of the snake in the rope does not affect the rope.
Sankara has used three orders of realities
i) prätibhäshika Relative view
ii) vyävahärika Empirical view
iii) päramärthika Absolute view
From päramärthika, the origin of the jagat is not the intrinsic feature - svarüpa-laksana - of Brahman but incidental - tatastha-lakshana. Therefore, from this view, Brahman is not the creator, sustainer, or dissolver of this jagat but Nirguna (devoid of any attribute). Nirguna Brahman is the intelligent and material cause of the jagat’s origin, existence, and dissolution while Saguna Brahman plays the role of creator, sustainer and destroyer.
upAdAne.akhilAdhAre jaganti parameshvare |
sargasthitilayAn yAnti budbudAnIva vAriNi || 8|| Atma Bodha
Like bubbles in the water, worlds rise, exist and dissolve in Brahman, which is the material cause and the prop of everything. Verse 8
Though Nirguna, it is not sunya and is thus different from Buddhism. The essential feature of Brahman - svarüpa-laksana – is Sat Chit Ananda and thus has bhava.
From the vyävahärika point of view, Brahman is regarded as the cause of this jagat’s origin, existence, and dissolution, because this jagat indeed has an empirical reality. Saguna Brahman (Ishvara) is sarvajna, sarva-saktimän, etc but does not have an absolute reality. As the creator, sustainer and destroyer, Ishvara is worthy of worship. But it's reality is restricted to vyavaharika.
From the prätibhäshika point of view, the appearance of the snake on the rope, or the objects seen in the dream-state, which is negated in waking-state, belong to subjective reality. What is unreal is that it may appear to be real at some time but becomes unreal at some other time. For example, dreams appears real to the dreamer but is rejected by the waker. Similarly, the snake appears to be real in illusory experience in semi-darkness but under clear light is seen to be a rope. Thus, the snake is not real as it sublated when a light is shown.
tAvatsatyaM jagad.hbhAti shuktikArajataM yathA |
yAvanna j~nAyate brahma sarvAdhiShThAnamadvayam || 7|| Atma Bodha
The Jagat appears to be Sat so long as Brahman, the substratum, the basis of all this creation, is not realised. It is like the illusion of silver in the mother-of pearl.
ataH pR^itha~N.hnAsti jagatparAtmanaH
pR^ithak.hpratItistu mR^iShA guNAdivat . guNAhivat
dhiShThAnamAbhAti tathA bhrameNa .. 235.. Vivekachudamani
The world has no existence apart from the Supreme Self and the appearance of its separateness is false like the appearance of a snake in a rope. Can a superimposition have any existence apart from its own substratum? Through delusion, it is the substratum itself which appears like that.
From Talks with Ramana Maharshi (Talk 315)
The tantriks and others of the kind condemn Sri Sankara’s philosophy
as maya vada without understanding him aright. What does he say? He
says: (1) Brahman is real; (2) the universe is a myth; (3) Brahman is
the universe. He does not stop at the second statement but continues
to supplement it with the third. What does it signify? The Universe is
conceived to be apart from Brahman and that perception is wrong. The
antagonists point to his illustration of rajju sarpa (rope snake).
This is unconditioned superimposition. After the truth of the rope is
known, the illusion of snake is removed once for all. But they should
take the conditioned superimposition also into consideration, e.g.,
marumarichika or mrigatrishna (water of mirage). The mirage does not
disappear even after knowing it to be a mirage. The vision is there
but the man does not run to it for water. Sri Sankara must be
understood in the light of both the illustrations. The world is a
myth. Even after knowing it, it continues to appear. It must be known
to be Brahman and not apart. If the world appears, yet to whom does it
appear, he asks. What is your reply? You must say the Self. If not,
will the world appear in the absence of the cognising Self? Therefore
the Self is the reality. That is his conclusion. The phenomena are
real as the Self and are myths apart from the Self. Now, what do the
tantriks, etc., say? They say that the phenomena are real because they
are part of the Reality in which they appear. Are not these two
statements the same? That is what I meant by reality and falsehood
being one and the same.
Similarly the universe cannot be real of itself - that is to say,
apart from the underlying Reality