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Now, we shift our attention to mathematics and logic and in doing so, we get to work on the other end of the big picture; hopefully we’ll be able to link back up with Inception somewhere in the middle.
Many of you will have, at some point, seen a demonstration of a classic mathematical fallacy. For example, a ‘proof’ that one is equal to two.
It goes without saying that this post contains ‘spoilers’ for Inception.
After I’d first seen Inception, I thought that it was good, but not brilliant. Roughly speaking, I’d taken it at face value. I’d taken it as a sci-fi action movie with a nice idea at its core about ‘dreams within dreams’. There were a few plot points it had glossed over, but then every action movie does that. I remember thinking that I’d actually expected it to be cleverer, given all the hype I’d heard. Sure, the idea of a dream within a dream is quite a cool one, but it isn’t a complicated one and the movie itself wasn’t difficult to follow, as a lot of complex thrillers are.
Slowly, however, the ideas began working on me.
As it is almost certain that this blog will include a lot of mathematics and a lot of talk about mathematics, I decided to set myself the somewhat ridiculous task of deciding what mathematics is…
[I had most of these thoughts in the last few days and so they might be a bit rough, but I felt that I did make some sort of progress. I have also (in a radical coup) deliberately avoided the use of examples, to see if I can explain what maths is without actually showing it to you directly, because, although this post will hardly serve as a terribly practical alternative, I am often irritated by having to explain what it is I do by saying “well, imagine a 3-dimensional sphere…”]
After some (light) research, I found out that in philosophy spiel I am much more of a quasi-empiricist, a fallibilist, humanist and relativist than an absolutist or a foundationalist when it comes to my views on mathematics (both the epistemology thereof and its place in society).
What on earth do these silly terms all mean? I am no expert and am throwing them around willy-nilly to poke fun at them myself. I will explain in a rough manner what I am getting at, and with a lot of bias toward my own point.