When do we know something for certain? Often most people don't care particularly, and to be honest that doesn't often matter because in real life common sense is usually good enough to get you through the day.
Sadly in the technical you can't just wave your hands, and the importance of being able to proof something beyond any doubt whatsoever is vital. This is why philosophers who look to be wasting their time arguing over where they even exist actually aren't. Behind the inane rubbish a lot of them spout is a huge amount of work on defining what can and cannot be known, and how to go about proving things. This is what logic is all about.
Sadly for the man in the street, a lot of this is written in arcane language and symbols that just look like nonsense. Take this for example:
Which is of course completely clear so I won't need to explain it.
Anyway, the point of all this is that once again, you need the language of mathematics to express a complicated argument.
So who is the famous person discussed this week? Well, it is all about proof actually and not surprisingly the same person who wrote that lot of meaningless drivel I just showed you. His name is Kurt Gödel and he was one of the pioneers of mathematical logic and set theory as a basis for philosophy. The picture above is in fact a "proof" that if it is possible that some god-like thing exists, then that thing must exist (in fact Ax. 3 is a bit suspect so this is still argued over).
His mathematical forays into theology aside, Gödel also said, more profoundly, that there are limits to what we can prove! His "Incompleteness Theorem" tells is that it doesn't matter what we start with, we cannot prove everything about numbers, and if we can prove everything then at least one of the things we've proved is wrong. That's seriously weird.
In case you don't quite follow what I've just said, here's a nice example: The English Language. Here we assume that everything we say has a meaning that we can understand. Take, however, the following sentence:
This sentence is false.
That sentence in fact has no meaning whatever, yet it's English. It's also terribly confusing. But the point is that in English we can say things that can't be made sense of. Rather like the whole of this post in fact.
The incompleteness theorems are very important for mathematicians, even if not to the rest of us. But Gödel is a name worth remembering.
