/lit/ - Literature

>>15219388
>Is that not the most significant external event that we have no power over?
There are events we have no power over. A lot of those events are formative events and make us into who we are. That is in no way incompatible with us still being able to make decisions and choose for ourselves, i.e. have free will.
>And everything that happens after is just branching out of that regardless of any philosophy?
Branching out in what sense? The past experiences are part of what makes us who we are. It's not in the least the whole part. There is an inborn, genetic component to our identity as well. All these things influence how we think, what decisions and choices we make. What's your point?

>>15209133
>Yes, that why I said ultimately you have to use an integral if you really want to prove it, but I doubt that's what was expected on this Harvard exam.
No you don't, there's an elementary alternative. A bright high school student without any knowledge of integrals would definitely be able to prove it.
>And even when you look at it, the notion of integral is defined so that, in particular, it recovers the usual values for the areas of polygons and circles. Any theory of integration that would not have given pi*r^2 as an area for the circle would have been instantly abandoned (or heavily modified) by even its creator.
True, but the fact that something is intuitively true does not constitute a proof of it.
> Which showcases the circular nature of the problem : at the end of the day you want the area to be of the form C*r^2 because it conforms to intuition.
The problem is not circular. I am able to prove that it's of the form C*r^2 as opposed to some other 2d shapes. Are you?