positive good - negative bad?
negative thinking > confusion of arithmetic and ethics
many people equate positive with good, negative with bad Our language is one-sided, and so are the stratagems (social, psychological and other) we adopt. more
but in many situations, the positive is harmful ... Violence is a "positive" idea - it can be depicted directly (in countless films, TV shows, comics and computer games) and triggers strong feelings - including excitement, anger or fear.
... yet attractive ...
Addictions, phobias, obsessions and other unhealthy behaviour patterns are often based on strong positive images - sometimes called attractors.

Proponents of positive thinking point out that positive images are much more strongly motivating than negative ones.

... and the negative is often good Peace is a "negative" idea - it represents the absence of violence. It can only be depicted indirectly - as the calm before, during or after the storm.  You need the storm to make sense of the calm.
... yet vulnerable ...
It can sometimes take a lot of energy and courage to maintain/sustain the absence of something harmful.  The price of freedom is constant vigilance.
so don't confuse arithmetic with ethics more
strong positive images weak negative images
Violence, Warfare, Social Unrest Peace, Stability
Heavy Drinking (or other addictive behaviour) Abstaining
Hell Heaven

Most people assume that the positive is good, and the negative is bad.

Our language is one-sided, and so are the stratagems (social, psychological and other) we adopt.

We have got so used to the notion that growth and acquisition and progress are Good Things, that the word ‘positive’ has come to have a moral meaning.  Positive is good, and so negative is bad.  Even people who reject positivism as a philosophy, or who speak knowingly of the Limits to Growth, often continue to make this moral equation.

Even when this moral equation is not made explicitly, it can be inferred from the common accusation “You’re being negative.” and from the equally common exhortation: “Try to be more positive!”.

Taken literally, this confuses arithmetic with ethics.  There is no moral virtue in adding or subtracting as such; it all depends on what is being added or subtracted, to what degree, in what context.
Energy is a good thing - but not if it’s thermonuclear.
Growth is a good thing - but not if it’s cancerous.
Confidence is a good thing - but not if it’s tricky.

There is a vast literature of popular psychology that distinguishes positive thinking from negative thinking, approving of the former and disapproving of the latter. The authors of this literature - the proponents and defenders of positive thinking - will probably deny that they mean anything as simplistic as elementary arithmetic. So what is it to be positive; what is it to be negative?  The writers of popular psychology books certainly think they know the difference.

But is there really a difference?  A mathematician reading the above might feel uncomfortable that so much moral weight was being placed on the shoulders of such elementary arithmetical constructs.  Surely addition and subtraction are symmetrical, in the sense that the same physical operation can be defined as addition or subtraction, depending on the way it’s described.
To a chemist, there’s no difference between adding alkali and subtracting acid.
Or is there?
To an accountant, there’s no difference between adding debit and subtracting credit.
Or is there?
One country’s emigration is another country’s immigration.

In school, some students discover that subtracting the normal number 4 is equivalent to adding a weird number called minus-4.  They are the ones that pass exams in mathematics.  Some of them are attracted into theoretical physics, where they discover things called anti-particles. These anti-particles are supposed have the same behaviour as negative numbers, producing zero when added to their opposite.  The ability these students have - to think of weird things like negative numbers and anti-particles, and to see symmetries between addition and subtraction - is certainly useful for playing such intellectual games as mathematics and theoretical physics.  But mathematicians need to remember what the rest of us are in no danger of forgetting - that these things are weird, and that addition and subtraction are not really symmetrical.  Ordinary language is not symmetrical, and this reflects the way all of us think - even mathematicians.

“Not bad” is not always the same as “good”, “not unreasonable” is not always the same as “reasonable”.  And although it is frowned on by those superior folk who have been to grammar schools, the double or treble negative - ‘I ain’t never done nothing’ - is a form of expression whose force is lost when it is transformed into a grammatically correct and logically simple form.

The argument goes one step further.  There are pairs of concepts that seem to be opposite, that seem to allow us to switch between a positive and a negative way of talking.  Peace is equivalent to not-war or not-violence; happiness is equivalent to not-sadness; death is equivalent to not-life.

And immortality is equivalent to not-death.  So if death is equivalent to not-life, then immortality is equivalent to non-not-life.  But this is not the same as saying that it is equivalent to life: immortality is both more than life, and yet somehow less than it. 
Page last updated on January 26th, 2001
Copyright © 2000, 2001 Richard Veryard