A gradient paradox is a type of paradox where a gradient can clearly be broken up into sections, but those sections can only be arbitrarily separated. For example, the illustration to the right depicts a gradient from black to white. Clearly there is a black end and a white end, but every single gradation between them is only infinitesimally different from the next, so any attempt to draw a line showing where black stops and white begins is arbitrary.
Reality itself is essentially made up entirely of analog gradients, but the human mind prefers information in easily understood discrete categories. We cope with gradient paradoxes by breaking up gradients into enough sections to fit our needs. The average person may break up the gradient into five sections—black, dark gray, gray, light gray, and white—while a graphic designer might use more like 20 sections for their needs. It's possible to define sections in an objective way, for example, you could say that black is any shade of gray that is 95% black or darker, but the choice of using 95% is still arbitrary (why not 94% or 96%?), so too is the number of sections used (why not 19 or 21?).
Shades of gray may be an abstract example, but gradient paradoxes are common in everyday life as well. Human gestation occurs on a gradient from a fertilized embryo to birth. Obstetricians divide the process into three month blocks called trimesters, and, while their definition may be objective, the choice of three is arbitrary (why not four, or two? Is the fetus really so different one minute after it enters the second trimester?)
Artificial groupings like this become problematic when they're used for legislation. Many legal systems use trimesters as a metric when deciding when to criminalize abortion. However, since a trimester is arbitrarily defined, so too is any abortion law based on them. However, even if the demarcations are arbitrary, they often have to be employed. When it comes to controlling dangerous weapons, there are effectively an uncountable number of levels of danger from literal peashooters to nuclear missiles, but, unless a society wants everyone to have access to nuclear missiles (or only have access to peashooters), they have to draw a line somewhere, even if it is arbitrary.