Question
What is the meaning of Gita ch.14 verse 27?
Answer
I will answer this question, from the point of view of advaita. I will quote a portion of the commentary by Madhusudhana Saraswati (MS) in his Gudartha dipika. The gist is based on the translation of Swami Gambhirananda.
MS commentary (partial)
अत्र हेतुमाह -- ब्रह्मणस्तत्पदवाच्यस्य सोपाधिकस्य जगदुत्पत्तिस्थितिलयहेतोः प्रतिष्ठा पारमार्थिकं निर्विकल्पकं सच्चिदानन्दात्मकं निरुपाधिकं तत्पदलक्ष्यमहं निर्विकल्पको वासुदेवः प्रतितिष्ठत्यत्रेति प्रतिष्ठा कल्पितरूपरहितमकल्पितं रूपमतो यो मामनुपाधिकं ब्रह्म सेवते स ब्रह्मभूयाय कल्पत इति युक्तमेव।
Gist of the above: brahman, here refers to sopAdhika brahman or brahman with limiting adjuncts or the conditioned brahman. Roughly speaking, this is same as saguNa brahman or brahman with attributes/qualities or the lower brahman. This sopAdhika brahman is the creator, preserver and destroyer of the world.
Krishna (or vAsudeva) is saying that he is the basis of the sopAdhika brahman. Here, Krishna or vAsudeva is the nirupAdhika brahman, who is unconditioned, and hence is the supreme brahman, which is the essential nature of the conditioned brahman. Krishna/vAsudeva is the supreme reality, which is sat-chit-Ananda or existence, knowledge and bliss. The true nature of the sopAdhika brahman is the nirupAdhika brahman. That is the idea.
Continuation of MS commentary
कीदृशस्य ब्रह्मणः प्रतिष्ठाहमित्याकाङ्क्षायां विशेषणानि। अमृतस्य विनाशरहितस्य अव्ययस्य विपरिणामरहितस्य च शाश्वतस्यापक्षयरहितस्य च धर्मस्य ज्ञाननिष्ठालक्षणधर्मप्राप्यस्य सुखस्य परमानन्दरूपस्य। सुखस्य विषयेन्द्रियसंयोगजत्वं वारयति -- ऐकान्तिकस्याव्यभिचारिणः सर्वस्मिन्देशे काले च विद्यमानस्य। ऐकान्तिकसुखरूपस्येत्यर्थः।
Gist: Now the qualities of the sopAdhika brahman are listed. It is indestructible, immutable, free from transformations, eternal, devoid of decay, it is the Dharma which is attainable through steadfastness in knowledge, it is happiness which is by nature the supreme bliss, the absolute happiness (not the happiness that arises from contact of objects and senses). It is the happiness that exists in all places and times.
Final gist: Krishna is the unconditioned highest brahman, and He is the real nature of the conditioned lower brahman. Krishna is thus the basis of the lower brahman. The lower brahman rests on Krishna. The qualities of lower brahman are, being immutable, indestructible, eternal etc.
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