Unity of opposites
Philosophers had for some time been contemplating the notion of opposites. Anaximander posited that every element was an opposite, or connected to an opposite (water is cold, fire is hot). Thus, the material world was composed by some indefinite, boundless apeiron from which arose the elements (earth, air, fire, water) and pairs of opposites (hot/cold, wet/dry). There was, according to Anaximander, a continual war of opposites. Anaximenes of Miletus, a student and successor of Anaximander, replaced this indefinite, boundless arche with air, a known element with neutral properties. According to Anaximenes, there was not so much a war of opposites, as a continuum of change. Heraclitus, however, did not accept the milesian monism and replaced their underling material arche with a single, divine law of the universe, which he called Logos. The universe of Heraclitus is in constant change, but also remaining the same. That is to say, an object moves from point A to point B, thus creating a change, but the underlying law remains the same. Thus, a unity of opposites is present in the universe as difference and sameness. This is a rather broad example though. For a more detailed example we may turn to an aphorism of Heraclitus:
The road up and the road down are the same thing. (Hippolytus, Refutations 9.10.3)
This is an example of a compresent unity of opposites. For, at the same time, this slanted road has the opposite qualities of ascent and descent. According to Heraclitus, everything is in constant flux, and every changing object co-instantiates at least one pair of opposites (though not necessarily in simultaneously) and every pair of opposites is co-instantiated in at least one object. Heraclitus also uses the succession of opposites as a base for change:
Cold things grow hot, a hot thing cold, a moist thing withers, a parched thing is wetted.
As a single object persists through opposite properties, this object undergoes change.
Modern philosophy 
Unity of opposites is the central category of dialectics, and it is viewed sometimes as a metaphysical concept, a philosophical concept or a scientific concept. It defines a situation in which the existence or identity of a thing (or situation) depends on the co-existence of at least two conditions which are opposite to each other, yet dependent on each other and presupposing each other, within a field of tension.
In formal logic and mathematics, a unity or identity of opposites cannot exist (it would mean for example that 2 = -2), although it is accepted that 1 follows 0, something from nothing which is something and so dialecticians claim that it can exist in reality or in thought. If the opposites were completely balanced, the result would be stasis, but often it is implied that one of the pairs of opposites is larger, stronger or more powerful than the other, such that over time, one of the opposed conditions prevails over the other. Yet rather than 'stasis' the identity of opposites, there being unity within their duality, is taken to be the instance of their very manifestation, the unity between them being the essential principle of making any particular opposite in question extant as either opposing force. For example 'upward' cannot exist unless there is a 'downward', they are opposites but they co-substantiate one another, their unity is that either one exists because the opposite is necessary for the existence of the other, one manifests immediately with the other. Hot would not be hot without cold, due to there being no contrast by which to define it as 'hot' relative to any other condition, it would not and could not have identity whatsoever if not for its very opposite that makes the necessary prerequisite existence for the opposing condition to be. This is the oneness, unity, principle to the very existence of any opposite. Either one's identity is the contra-posing principle itself, necessitating the other. The criteria for what is opposite is therefore something a priori (and therefore saying that -2 ≠ 2 is a refutation in logic would be considering the identification as a posteriori, and having nothing to do with a "co-instantiate" existence as the postulate of the unity of opposites necessitates.)
The principles of the metaphysical philosophy gave rise to the belief that, when cognition lapsed into contradictions, it was a mere accidental aberration, due to some subjective mistake in argument and inference. According to Kant, however, thought has a natural tendency to issue in contradictions or antinomies, whenever it seeks to apprehend the infinite. We have in the latter part of the above paragraph referred to the philosophical importance of the antinomies of reason, and shown how the recognition of their existence helped largely to get rid of the rigid dogmatism of the metaphysic of understanding, and to direct attention to the Dialectical movement of thought. But here too Kant, as we must add, never got beyond the negative result that the thing-in-itself is unknowable, and never penetrated to the discovery of what the antinomies really and positively mean. That true and positive meaning of the antinomies is this: that every actual thing involves a coexistence of opposed elements. Consequently to know, or, in other words, to comprehend an object is equivalent to being conscious of it as a concrete unity of opposed determinations. The old metaphysic, as we have already seen, when it studied the objects of which it sought a metaphysical knowledge, went to work by applying categories abstractly and to the exclusion of their opposites. 
In his philosophy, Hegel ventured to describe quite a few cases of "unity of opposites", including the concepts of Finite and Infinite, Force and Matter, Identity and Difference, Positive and Negative, Form and Content, Chance and Necessity, Cause and effect, Freedom and Necessity, Subjectivity and Objectivity, Means and Ends, Subject and Object, and Abstract and Concrete.
Coincidentia oppositorum 
Coincidentia oppositorum is a Latin phrase meaning coincidence of opposites. It is a neoplatonic term attributed to 15th century German polymath Nicholas of Cusa in his essay, De Docta Ignorantia (1440). Mircea Eliade, a 20th century historian of religion, used the term extensively in his essays about myth and ritual, describing the coincidentia oppositorum as "the mythical pattern". Psychiatrist Carl Jung, philosopher and Islamic Studies professor Henry Corbin as well as Jewish philosophers Gershom Scholem and Abraham Joshua Heschel also used the term. In alchemy, coincidentia oppositorum is a synonym for coniunctio. For example, Michael Maier stresses that the union of opposites is the aim of the alchemical work. Or, according to Paracelsus' pupil, Gerhard Dorn, the highest grade of the alchemical coniunctio consisted in the union of the total man with the unus mundus.
The term is also used in describing a revelation of the oneness of things previously believed to be different. Such insight into the unity of things is a kind of transcendence, and is found in various mystical traditions. The idea occurs in the traditions of Tantric Hinduism and Buddhism, in German mysticism, Taoism, Zen and Sufism, among others.
See also 
- Craig, Edward (1998). Routledge Encyclopedia of Philosophy: Sociology of knowledge to Zaroastrianism. Taylor & Francis. p. 437. ISBN 0-415-16916-X.
- S.M. Cohen, "Heraclitus on Change and Unity of Opposites"