On consistency in beliefs

Here is an idea you might or might not have thought about: wouldn't it be nice if you would be able to formulate a set of principles that are going to completely encode your ideas of what's right and what's wrong. You or anyone else in possession of those principles would be able to, with some degree of confidence, check if a statement or idea is consistent with those principles.

Imagine far-reaching consequences of such a miraculous invention: you would be able to talk about anything as much as you want without ever making two contradictory statements and being accused of being wrong, because even if your ideas and statements are not universally approved by everyone, at least they are internally consistent.

Here's a problem though: by necessity, such principles would have to be encoded in some language, and languages are quite ambiguous beasts.

For a simple example, you probably know what the words "blue" and "green" mean, and probably would be able to tell these colors apart in most of the cases. (Assuming you don't have color vision deficiency affecting this pair)

Keeping the assumption in brackets, you can probably fairly confidently talk about things being green and blue with other people and generally expect that they will understand you.

However, this understanding of "blue", "green" and the difference between them is fuzzy and can be easily illustrated with a simple linear gradient.


On this linear gradient, where does the blue ends and green starts? Even if you will confidently set a breaking point, this breaking point will vary from person to person. It will probably vary for you over time, or looking at the same gradient on different screens or in different lighting conditions! There's an xkcd post about that which summarizes some experimental data on the topic.

And, unfortunately, colors are not even the most complicated things you might want to talk and reason about.