Bhagavad Gita Verse 11, Chapter 18

na hi dehabhritaa shakyam tyaktum karmaanyasheshataha |
yastu karmaphalatyaagee sa tyaageetyabhidheeyate || 11 ||
 
For, it is not possible for an embodied person to completely give up actions. That is why one who has given up the reward of action is called a tyaagee.
 
na : not
hi : for
dehabhritaa : embodied person
shakyam : possible
tyaktum : give up
karmaani : actions
asheshataha : completely
yaha : who
tu : that is why
karmaphalatyaagee : given up reward of action
saha : he
tyaagee : tyaagee
iti : in this manner
abhidheeyate : is called
 
This chapter began with Arjuna asking the question : what is the difference between a sanyaasi and a tyaagi. Shri Krishna used this question as an opportunity to recap the topic of karma yoga. After pointing out some popular notions on the topic, he then asserted that karma yoga refers to performance of duties while giving up attachment to their reward. This is the saattvic type of renunciation or tyaaga. He also explained the raajasic and the taamasic types of tyaaga.
 
Now, Shri Krishna adds another bit of context to the topic of karma yoga. He asserts that one who has a strong sense of identification to his body cannot completely give up action. He uses the term deha-bhrit, which is similar to the term dehi from the second chapter. As long as we identify with a sports team, for instance, we will be happy or say whenever they win or lose. As long as we think we are Mr. or Ms. so-and-so who has a job and a family and a house and so on, we have a strong sense of identification with our body. We cannot fully give up actions since the body has to act in order to live in this world.
 
With this additional context, we can now understand the definition of tyaagi. The ordinary meaning of this word refers to one who has renounced, who has given up all actions. Shri Krishna redefines it to mean someone who has given up all attachment to the reward of action, not given up action itself. If we are true karma yogis, we are tyaagis per this definition. We still need to deal with the issue of our strong identification to the body. This topic is taken up next.

Bhagavad Gita Verse 10, Chapter 18

na dveshtyakushalam karma kushale naanushajjate |
tyaagee sattvasamaavishto medhaavee chinnasamshayaha || 10 ||
 
He does not dislike inauspicious action, nor does he get attached to auspicious action, he who gives up is pervaded by sattva, is wise, and free of doubts.
 
na : not
dveshti : dislike
akushalam : inauspicious
karma : action
kushale : auspicious
na : not
anushajjate : attached
tyaagee : that one who gives up
sattvasamaavishtaha : pervaded by sattva
medhaavee : wise
chinnasamshayaha : free of doubts
 
So far, three types of renunciation or giving up were described. Shri Krishna now describes the nature of the person who conducts renunciation in the proper manner, the saattvic tyaagi. Such a person is pervaded by sattva. This means that his intellect is able to discriminate between what is real and what is not, in other words, what is the eternal essence and what is the illusory world. This person is described as medhaavee, one who is wise due to the knowledge of the eternal essence, the self.
 
What makes this person different than the other so-called renouncers? It is his indifferent attitude towards action. Though he knows that every action has the potential to generate further sorrow and further desires, he does not hate that action but in fact, continues to do his duty. Conversely, though he knows that doing his duty will eventually make him fit for liberation, or if there is some action that he loves to perform, he does not develop a sense of attachment for it.
 
Eventually, a slow transformation takes place in such a person. Performing karma yoga, which is the same as performing saattvika tyaaga, leads a person to slowly recognize his true nature as the unchanging, unmoving eternal essence. He begins to realize that he is not performing any action at all, it is Prakriti that is doing all the work. When he comes to realize this, he becomes chinnasamshayaha, free of all doubts about who he really is, about his true nature.