What I call ‘circle logic’ (not to be confused with circular reasoning) is the situation in which the poles (the two extremes on a linear interval) exhibit the same value of the parameter in question. For example, a patient might not complain because the patient is comfortable and doing well, or because the patient is simply too weak to do so. Of course, this situation can be modeled by any (usually, nonconstant) even function, but it is convenient to choose a well-known function on a finite interval, such as the trigonometric sine function for angle values between -180 degrees and 0 degrees, or a single arch of a cycloid or inverted cycloid.

Another example of circle (or, trig sine) logic: If a fellow invites his girlfriend to dinner at a posh restaurant, it is either to propose marriage, or to break up with her.

Another example:

“Too much or too little wine.

Give him none, he cannot find

truth; give him too much, the

same.”

— Blaise Pascal

Another example: why an item is not found on the store shelves: either because it is so unpopular that it is not worth carrying it, or because it is so popular that it disappears quickly from the shelves by consumers purchasing it.

Another example: You open something slowly fif it is very good, or very bad.

# Tag: notation

# fif

I use the abbreviation ‘fif’ for ‘if, and only if,’.

Because of the implied necessity of things in foreground, the expression ‘if, and only if,’ is seldom casually encountered, even when its sense is present.

Having an abbreviation for the cumbersome expression ‘if, and only if,’ is not a new idea. What has been traditionally used is ‘iff’, but this has the disadvantage of not being aurally distinct from ‘if’. My abbreviation is aurally distinct from ‘if’.