This is an interesting topic because I've seen the notion of arbitrary in a variety of topics from my study into metaphysics, up into politics. A notion put forward is that arbitrary concepts can't be rational. The unspoken premise being those rational concepts are exact, concise, and not up to interpretation. For example, a square is a polygon of four equal sides and four equal angles. It's not like we'll be discussing whether a circle could apply. I won't discuss it here, but there are arguments around square being arbitrary - at least the way it is applied.
There are two examples I wanted to focus on, one from metaphysics and the other in law:
- The concept of bald
- The age of majority
The Concept of Bald
Bald is hairless where there is normally hair, in this case, we'll speak of the top of the head.
How little hair should one have? None? Half?
Is there an actual quantity one has to fall below to be bald?
What separates a bald person from a balding person?
The Age of Majority
The age of majority is when you're recognized as an adult by law in a specific jurisdiction. In many places, this age is 18.
Why not 17 or 19?
What makes 18 years an adult and 17 years 364 days not?
The Line and Range
The reason I wanted to discuss this topic is that those at war with objective truth push this notion of arbitrariness as a way of declaring that all truth is just fluid and constructed. Unless you're focusing on the ideas at hand here (arbitrary and rational) you may find yourself easily fooled by such an argument.
The problem with this whole discussion boils down to demanding a precise line of definition when you're discussing a concept that has a range.
Someone with a full set of hair is not bald. Someone with no hair is bald. There is a range between a full set of hair to balding and balding to bald. The same is true of the age of majority. Some people are more mature and are very adult by age 16, others don't even make it by 18. A 3-year-old is a child and a 40-year-old is an adult. The area of transition is not a line, but a range. When the age of 18 is picked for the age of majority, it is arbitrary because 17.5 years or 19 years would be just a valid, but that doesn't take away from the rational concept of adult, child and that there is a range in which a child becomes an adult.
The reason I'm harping on this is that there are people out there that view this arbitrariness as a means of completely throwing out the concept. Since there is an arbitrariness to the transition from child to adult, then child and adult aren't real things - they're just constructed by us and we can just easily pick a line, anywhere, and it's just as valid - even if that line was 5.
Arbitrary in Metaphysics
Metaphysics is the study of the is. The things out there in the real world; what they are and what they are like. When the topic of arbitrariness is brought up in regards to metaphysics it is to cripple concept formation in a very Kantian way. It comes down to this requirement of an exact line and without it, they demand we throw out the baby with the bathwater.
Here's an example of something that disables all concept formation. It's the fact that everything is made up of atoms. Think of a human. A human doesn't exist by itself, it exists in a space with a volume of air. How do you cut the line between a human and air? Well, a human is a collection of atoms. Air is a collection of atoms. The arrangement of atoms is different between a human and air. If you could zoom in very close, what is the difference between an atom on the edge of a human and the atom of air next to it? Nothing really, they should be pretty much the same.
This is a rabbit hole many in philosophy have chosen to go down. They view this line between air and a human as arbitrary. In a Kantian way, they view this line drawn purely automatically in pre-consciousness. It's not real, we just constructed it.
Arbitrary in Other Realms
Again, you'll see this pop up in a variety of subjects. This could be as simple as trying one 16-year-old as an adult and another 17-year-old as a juvenile. There is no exact line for them. Copyrights are valid for a period of time. Different countries have different years. Death + 25 years, 5 years, none. It's all just arbitrary lines.
There are probably a million different examples I could give, but I think I've illustrated my point. Even though arbitrary lines have to be drawn with regards to many concepts, it doesn't mean that it being arbitrary is irrational. Where there is an actual range, a line just needs to be drawn for the practical application in the real world. The attribute that makes it rational is that the line is drawn within the range of actual transition. Speaking of the age of majority, a line at 17, 18, or 19 is rational. A line at 5 or 90 would not be rational.