In the commentary for BG 2.16 Shankara says:
सर्वत्र बुद्धिद्वयोपलब्धेः, सद्बुद्धिरसद्बुद्धिरिति । यद्विषया बुद्धिर्न व्यभिचरति, तत् सत् ; यद्विषया व्यभिचरति, तदसत् ; इति सदसद्विभागे बुद्धितन्त्रे स्थिते, सर्वत्र द्वे बुद्धी सर्वैरुपलभ्येते समानाधिकरणे न नीलोत्पलवत् , सन् घटः, सन् पटः, सन् हस्ती इति ।
All perceptions have two aspects: one, the unchanging one and the other is the changing one, for example 'pot is', 'cloth is', 'elephant is'. Of these two the unchanging one is Sat, Brahman and the changing one is asat, mithya.
Having said this, he concludes the teaching by saying:
एकाधिकरणत्वं घटादिविशेष्याभावे न युक्तमिति चेत् , न ; ‘इदमुदकम्’ इति मरीच्यादौ अन्यतराभावेऽपि सामानाधिकरण्यदर्शनात् ॥
An objection: It is illogical to say that two aspects are there in a perception ...In reply to this Shankara cites the example of the perception of mirage water where even though there is no water, yet the perception is of the nature 'this is water' where the 'this' aspect is real and the 'water' aspect is unreal.
Shankara says this is the teaching for Arjuna from this verse 2.16:
त्वमपि तत्त्वदर्शिनां दृष्टिमाश्रित्य शोकं मोहं च हित्वा शीतोष्णादीनि नियतानियतरूपाणि द्वन्द्वानि ‘विकारोऽयमसन्नेव मरीचिजलवन्मिथ्यावभासते’ इति मनसि निश्चित्य तितिक्षस्व इत्यभिप्रायः ॥
/Therefore, you too, by adopting the vision of the men of realization and giving up sorrow and delusion, forbear the dualities, heat, cold, etc. -- some of which are definite in their nature, and others inconstant --, mentally being convinced that this (phenomenal world) is changeful, verily unreal and appears falsely like water in a mirage. This is the idea.//
Thus for the same verse, in the commentary Shankaracharya starts off with vyavaharikta Satya example of pot, cloth and elephant and concludes the commentary citing the Pratibhasika Satya analogy of mirage water. Shankara has thereby dovetails the vayavaharika into the pratibhasika.
Thus for Shankara the world is of the nature of pratibhasika satya.
Om Tat Sat
See in kannada foot note by HH Sacchidanandendra Swami:It means, the "it is" or "this exists" can refer to both prathibhasika and vyavaharika objects. The only true sat is "it exists" not the different intended "karya" effects such as vyaharika (like pot, cloth and so on) or prathibhasika ( water in a mirage... and so on). So that "sat" vastu appears as both vyavaharika and prathibhasika objects.
Best Regards,Krishna Kashyap
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corrected as:
'As regards Swami Vidyashankra
Tirtha, he continued to stay in Kanchipuram (the Dakshina-kashi) and
in his old age he left for the
Himalayas and took his samadh in the Dattatreya Guha (cave).'
Thanking you
Sunil K. Bhattacharjya