Exceptions and logic

One of those fascinating things to me is the power of thinking that comes with coding for computers, which introduces the necessity and power of exceptions.

Doesn't seem like much? Well consider these two examples:

Consider a small village where all men are shaved, the barber is a man, and the barber shaves all and only those men who do not shave themselves, except himself, as the barber shaves himself.

Remove the exception and you run into problems as explained here.

So let's handle the abstraction: consider a set that includes all and only sets that exclude themselves, except itself.

So clearly the first example can exist! You can have a village with the conditions given.

But what about the second example?

If we follow the pattern from the first, it seems there's no reason for it not to exist! As the exception is key to making it logical.

Here remove the exceptions and the results do not work. Prior to computers maybe that was an impassable hurdle and seemed like something magical to the people who spent endless hours puzzling over statements similar to them with the necessary exceptions missing. Their thinking quite simply, was too primitive for the task.

All that effort through years by very intelligent people and I can just type up a quick post which you can read through in a few minutes.

Our civilization is far more advanced today than it was for those who ran in circles without realizing the full power of exceptions. 

We think differently in the modern age--thanks to computers.

Thinking I should tone down this post, but the concept is interesting enough for me to leave it in its strongest form.

That our tools shift our mental approach is not even something I came up with, as really was fascinated by it being mentioned as key in a TED talk by James Flynn.

It got me to thinking again about this area: what if prior people simply thought in a way that made it difficult to handle these things which they called "logical paradoxes" which is an oxymoron because their minds weren't quite ready for the answer?

James Harris