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Opposite:  Negativity vs. Absence

Some people are fond of saying the opposite of love is indifference, not hate.  This is an error.  The opposite of any emotion is its counter emotion.

Love is the opposite of hate.
Joy is the opposite of sorrow.
Courage is the opposite of fear.
Indifference is the absence of any emotion.

Opposition is often confused with absence, and for good reason.  A true opposite of anything is the negative of that thing.  This is obvious with numbers.  Five is the opposite of negative five, not the opposite of zero.  That's why love is the opposite of hate, not indifference.

But some concepts don't have negatives, yet still appear to have opposites.  Everyone knows the opposite of white is black - right?  But white is light, and black is the absence of light - zero light.  There is no negative light that we are aware of (though some physicist will undoubtedly propose it).  Heat has no negative.  Cold is simply the absence of it.  Existence itself has no negative.  There is only existence or non-existence - which is absence.  We will always think of these things as opposites: white and black, hot and cold, existence and absence.  We could call this a pseudo-opposite or acknowledge two kinds of opposites:

Opposite of negativity
Opposite of absence

Does this mean we can call indifference the opposite-of-absence of love?  Nobody can stop us, but if we do that, we will confuse things that have negatives with things that don't have negatives.  If a concept has a negative, then its negative should be recognized as its opposite.

A definition is in order:
Opposition is the relationship of two concepts on a common axis with a midpoint between them.  The axis represents a quality in which both concepts participate.  The midpoint represents a place where neither exists, or a portion of each exist equally.  e.g.  Left is the opposite of right, the center being the midpoint.  Left is also the opposite of right with the subject being the midpoint - the person evaluating leftness and rightness.  Likewise, front and back, above and below, up and down, high and low.  Acid is the opposite of alkaline, neutrality being the midpoint.  Good is the opposite of evil, ethical neutrality being the midpoint.  If the two concepts are on an incremented axis, they must be equidistant from the midpoint, such as five and negative five.  Opposites cannot be identified without identifying that quality which is the criterion for opposition.

An opposite may be absolute or relative.

1.  An absolute opposite has an absolute midpoint.
e.g.  Positive numbers are the absolute opposite of negative numbers, zero being considered an absolute midpoint.
    -4, -3, -2, -1, 0, 1, 2, 3, 4
The set of all positive numbers is the absolute opposite of the set of all negative numbers.
A particular positive number is the absolute opposite of its corresponding negative.

An inward spiral is absolutely opposite in motion to an outward spiral, zero motion being considered an absolute midpoint.
If a spiral is seen apart from motion, then the mirror image of that spiral is its opposite, the surface of the mirror being the midpoint.
If a single spiral is viewed from opposite sides, the spiral is the midpoint, and the views of it are opposite.
If two mirror image spirals are on the same plane, then they are bilaterally symmetrical, with a midline between them.
If they are on unrelated planes, then they are opposite in shape alone, and not in location.  Their opposition consists of a one-to-one correspondence of all points on them, and the midline is reduced to an abstraction - an imaginary line between two lists of corresponding points.
Any two things in absolute opposition imply an absolute midpoint or midline between them.

2.  A relative opposite implies an arbitrary midpoint.
e.g.  3 is the opposite of 7 relative to 5.
1 2 3 4 5 6 7 8
France is opposite Germany relative to the Rhine River.
France is opposite Poland relative to Germany.
A particular black is the opposite of a particular white relative to a particular gray midpoint.
Hot is opposite cold only relative to a degree of heat arbitrarily regarded as neutral.
Fast is the opposite of slow, only because fast exceeds an arbitrarily chosen speed, and slow is less than that speed.

Anything that has a negative value has an opposite.  If something has no negative value (such as light and heat) then its absence can be considered its opposite, assuming an arbitrary neutral midpoint.  Sometimes two things that have no midpoint are still thought of as opposites.
e.g.  Right and wrong are seen as opposites, though they appear to have no midpoint.  But right and wrong are adjectives modifying declarative statements.  A legitimate declarative statement is either right or wrong;  it can't be neutral.  Therefore the absence of a declarative statement must be seen as the midpoint - a place of zero rightness and zero wrongness.

Some things either don't have opposites, or their opposite is identical to them.  A ray or vector in one direction is the opposite of the same ray or vector going the other direction.  But if direction is not considered, the ray or vector is reduced to a line.  What is the opposite of a line?  Its mirror image is identical to it.  If the absence of a line were the opposite of a line, then the absence of anything would be its opposite.  The distinction between absence and opposition would be obliterated.  The opposite of any number would be zero.  Its negative would be just another number, the opposite of which is also zero.

If a thing has a negative value, then its negative value, and not its absence, should be considered its opposite.  Male is the opposite of female, not sexlessness.  Likewise, happiness should be seen as the opposite of unhappiness, not emotional neutrality.  If emotional neutrality is seen as the opposite of happiness, then the midpoint is "half-as-happy", which is still happiness.  The same is true of love, indifference, and hate.