Antithesis essentially means opposite.
Thoreau demonstrates his purpose in the final part of the sentence as he states he does not want to realize that he had not lived.
This is the opposite or antithesis of the first part of the sentence which emphasizes to live deliberately, meaning with purpose, to live fully.
In other words, the first part of the sentence emphasizes living wholly. The second emphasizes not achieving any meaning in living.
They are the antithesis of each other.
I went to the woods because I wished to live deliberately, to front only the essential facts of life. . . and not, when I came to die, discover that I had not lived.
