(May 11, 2016 at 6:57 pm)SteveII Wrote:
I wasn't going to get so formal on a small point like this but...it seems that's what you want so...the term is "possible worlds" and the idea is used to express modal claims. To put it formally, in all possible worlds, I believe the concept of 8 objects and the idea of P then Q; P therefore Q are necessarily true propositions.
Wikipedia has a short article in which they define the types of modal claims you can make when discussing possible worlds. For example from the article:
"Necessarily true propositions (often simply called necessary propositions) are those that are true in all possible worlds (for example: "2 + 2 = 4"; "all bachelors are unmarried").[1] "
So, why do you think these concepts are only true in some possible worlds?
First, I don't necessarily buy into the "possible worlds" hypothesis of philosophy, which your article itself explicitly states "has been disputed." But as for your "Necessarily true propositions," these are purely definitions created by human minds. It's easy to imagine cultures which didn't have the concept of addition (certainly animals don't, and you'd be hard pressed to identify where exactly in our evolution the concept, however first expressed, that 2 + 2 = 4 originated).
But let's imagine I'm from another culture in another world. In my culture, we work solely with binary digits. Your 2 + 2 = 4 makes no sense to us. I insist that 10 + 10 = 100! This is a necessarily true proposition, despite your insistence that 10 + 10 = 20. And what do you mean by marriage, or bachelor? In my world, the males and females mate at will, without monogamous commitment. This is a necessarily true proposition, and all others are false!
To borrow from a quote I agree with...
(May 11, 2016 at 5:13 pm)Jörmungandr Wrote: Numbers and relationships don't exist in the natural world. They are functions of the concept of quantity which itself is a function of the idea of an object.
So, these concepts are only true definitionally, and thus, only true in the models we build inside our own heads.
Now it's your turn... Prove that the concept of "unmarried" or "bachelor" or "plus" exists outside of human minds.