Turns out this is just a re-invention of Dawkins’ Spectrum of theistic probability
Belief is complex and slippery idea, but also an useful everyday word. I enjoy categorising things. Thus.
This scale is about how strongly you hold a belief, not how true, popular, reasonable, explicable or false, unpopular, unreasonable, inexplicable such a belief is.
It is super difficult to think of examples that have even a whiff of universality. Even finding things that don’t interact with identity in rage-inducing ways is tricky.
Thus these (hopefully politically inert) maths examples might help you get the idea.
Unquestioned beliefs. You’re still aware that you can think your way out of this belief, but so many things would change that abandoning this idea is not useful.
e.g. 1 + 1 = 2
Arithmetic requires this or the entire mathematical enterprise falls apart. (assuming a base greater than 2, pedant)
Strong beliefs. You can, at a stretch, put yourself in the mind of someone who doesn’t believe this thing to see where they’re coming from, but they’re definitely wrong, mistaken, deluded, deceived.
e.g. 0.999… = 1
I can see why this is not as immediately obvious as 1 + 1 = 2, but it’s just as true.
Weak beliefs. Your belief of this affects your life and the way you think, yet you can easily put yourself in the mind of someone who disagrees, and either you think it possible you could be wrong or see it as merely preference.
e.g. Imaginary numbers are as arbitrary as negative numbers.
Counting numbers work with the analogy of how many apples you have. Everything else doesn’t. I can see why imaginary numbers seem more made up: you learn them much later and the name certainly doesn’t help, but they’re not in different categories of arbitrariness.
Forced beliefs. If asked, you’d say you believe, but it doesn’t affect your life. It either follows logically from what you do believe or is something you believe due to social pressure, but you possibly wouldn’t believe this in isolation.
e.g. 0! = 1
I watched the video. Sure, whatever.
Disinterested ignorance. You might have an answer if pressed, but it’s a coin toss which way you’d answer. There’s nothing you do believe that requires you to believe about this thing any particular way, so you don’t. You also feel no pressure to learn or have an definite position.
e.g. 1 is/n’t a prime number
1 is an exception either way.
Weak disbelief. Your disbelief of this affects your life and the way you think, yet you easily can put yourself in the mind of someone who believes, and either you think it possible you could be wrong or see it as merely preference.
e.g. 1+2+3… = -1/12
I’m pretty sure this has broken a rule somewhere and done something with infinity or equals that it shouldn’t have.
Strong disbelief. You can, at a stretch, put yourself in the mind of someone who does believe this thing to see where they’re coming from, but they’re definitely wrong, mistaken, deluded, deceived.
e.g. numbers exist
I see mathematics and numbers as internally consistent fictions/human inventions useful for modelling the physical world. I know the majority of people disagree, but any other position seems ridiculous to me.
What you see as absolutely ridiculous to believe. Things that are impossible for you to imagine actually believing. Thought experiments can take there, but surely no-one actually, sincerely believes this.
e.g. 1 + 1 = 3
Arithmetic requires this to be false or the entire mathematical enterprise falls apart.