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Be consistent in your search for what’s true

February 23, 2012

I’m participating in the reddit read through of Godël, Escher, Bach: an Eternal Golden Braid by Douglas R. Hofstadter. Which, yes, makes me a bit of a nerd. But more importantly, it’s also been making me very confused. Not a bad confused, but more like the kind of fun confused that you can come out of with an “Ah, ha!” kind of moment at the end – hopefully.

Anyhow, I came across a passage today that relates well to other things I often think about. There is a small subsection of a chapter titled Varieties of Consistency that I found very helpful. Hofstadter is referring generally in this section to consistencies within formal mathematical systems, but the ideas can be used anytime we think about logical or philosophical problems.

When a system is said to be consistent, it simply means that statements within it are compatible with one another. Hofstadter uses the following example (the names make more sense if you’ve read the book):

The Tortoise always beats Zeno at chess.

Zeno always beats Egbert at chess.

Egbert always beats the Tortoise at chess.

These statements are not incompatible, even though they may seem to indicate, as Hofstadter puts it, “a rather bizarre circle of chess players.” Importantly, though, even though these statements are compatible, this indicates nothing regarding their truth. Frankly, they may or may not be true.

Hofstadter shows in a similar example that consistency does matter, but only as one step in the process of finding truth. If you change the statements “always beats at chess” in the above example with “was invented by” you get something entirely different:

The Tortoise was invented by Zeno.

Zeno was invented by Egbert.

Egbert was invented by the Tortoise.

Neither of these three statements make sense in the context of the other two. It’s a system that can’t possibly be true. Which tells us more than the first set of statements, in that when searching for truth we can at least rule systems such as those out.

This is really important. There are plenty of internally consistent ideas out there in the world that people think are true, but may be FAR from it. Because while consistency is important, it’s not everything. Finding an ideology that is basically internally consistent can get you a long way, just ask Ron Paul; but so what?

Biblical creationism, for instance, is “internally consistent,” but’s it’s laughably untrue. It can’t be proven as untrue from within its own system though. And that’s what this rambling, late night post is meant to illustrate. Sometimes we have to look outside of a system we already understand to ideas that we don’t. It’s the only way to find out if the ideas we see are consistent are actually worth holding as true.

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