December 5, 2011

## How does science work?

As I mention in my post on the not-yet-published book “Mathematics and Scientific Representation”, the author Christopher Pincock says “The success of science is undeniable, but the nature of that success remains opaque.”  That’s an admission that philosophy of science does not fully understand how science works.  In this post, I give my own opinion on the reason for the success of science.

As I see it, science works mainly because it is systematic.  When we are not sufficiently systematic, when we represent the world in a willy nilly manner, it is hard to keep track of a lot of information.  You can see this in the example of the first builder in “The parable of the three builders.”  By being more systematic, science reduces the cognitive cost and that allows us to keep track of far more information about the world.

Because it is systematic, science make available a vastly increased amount of information about the world.  More and better information leads to better predictions.

December 5, 2011

## Why mathematics is useful to science

Philosophers, including philosophers of science, talk about representations.  For example, the statement “the cat is on the mat” might be a representation of one aspect of the world.  When mathematicians talk of representations, they think of a representation as a mapping of one space into another.  For the way that philosophers talk of representations, a mathematician might think of that as a mapping from reality to the space of linguistic expressions.

One way of having representations of the world is to come up with ad hoc methods of representing little bit of the world, and then tossing them together, willy nilly, to provide a more comprehensive representation of the world as a whole.  For want of a better term, I’ll call that way of representing the “willy nilly method” and I will refer to a representation result from such a method as a willy nilly representation.  The naming of houses by the first builder in my post “The parable of the three builders” could be considered a willy nilly representation.