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You cannot have solid without space, day without night, life without death.  Such opposites, though, only APPEAR to be opposites when in fact they are two aspects of one reality. They are two side of the same coin.  The Greek philosopher Heraclitus (c.a. 535-475 B.C.) used the analogy "the road down and the road up are the same road."

These opposites arise mutually, called the coincidence of opposites, so that you cannot have one without the other. Taoism states that within every opposite lies its counterpart.  In the yin-yang symbol there is a dot of yin in yang, and a dot of yang in yin.  Within sickness lies health and within health lies sickness.  This, according to Taoism, is because all opposites are manifestations of the single Tao and are therefore not independent of one another.

Advaita Vedanta speaks of the seeming duality of things in terms of the soul, or Atman, and the godhead, or Brahman.  When a person tries to know Brahman through his objective mind, Brahman appears to be separate from him.  In reality, there is no difference between Brahman and Atman.  They are the same thing.  Liberation lies in realizing his. 

Buddhism addresses this issue as well, but regarding Subject and Object generally. This is stated by the Buddha in verses such as “In seeing, there is just seeing.  There is no seer and nothing seen.  In hearing, there is just hearing, no hearer, nothing heard.”  Non-Duality in Buddhism does not mean a merging with a supreme Brahman as in Vedanta, but, instead, an understanding that the duality of a self/subject/agent/watcher/doer in relation to the object/world is an illusion.