The Limits of Logic
Don't get me wrong, I like logic. I use it everyday in my career in engineering physics. My favourite character in Star Trek is Mr. Spock.
However, being very familiar with logic and its applications I have come to understand its limitations and that it is a tool. A very, very useful tool but a tool nonetheless. And all tools have their limitations.
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In this post I am going to go over a few examples of what I believe to be the limitations of this tool called logic. Maybe you agree, maybe you don't let me know in the comments.
Limitation #1: The Why Game
Have you ever played this word game as a kid where you ask an adult why they think something is true. Then they answer and then you ask why do they think that is true and so on and so forth. Maybe a kid has done it to you, or you even do play this game internally to try to figure out the roots of your beliefs.
The game always comes to a dead-end with some core concept that you believe to be true but cannot prove. The better you are at logic the deeper number of levels that you can go but ultimately it just doesn't matter; it always, always ends up with some unprovable set of assumptions.
This is the first limitation of logic. The logical scaffolding that you build up always has at its foundation an unprovable set of assumptions. It may be subtle and hard to uncover but it will be there nonetheless.
Limitation #2: Concepts Are Fuzzy
There are rules to logic such as if A equals B and B equals C then A equals C. This only works for those few clean mathematical objects that can be defined with perfect precision. Everything else, well, not such much. Almost every (maybe even every) concept you have is fuzzy. The closer you examine it the fuzzier it gets, kind of like looking at a photo in a newspaper. From a distance it is a picture of some recognizable object but get closer and it fuzzes out into a jumble of dots.
This is the next limitation of logic: The logical scaffolding that you build is constructed with concepts that can often be quite fuzzy when examined closely.
Limitation #3: Gödel's Incompleteness Theorem
This theorem of logic demonstrates that there are inherent limitations in every formal axiomatic system. It is quite deep and complicated but in a nutshell, if you have a logical belief system you can always make some self-contradictory set of statements.
I came across this good summation at Math Stack Exchange:
"In layman's terms: Any axiomatic system which is capable of arithmetic is either incomplete or inconsistent. An incomplete system is the one in which there are theorems which may be true but cannot be proven. An inconsistent system, on the other hand, is the one in which there are contradictions. "
For example:
- Jim is a liar, everything Jim says is a lie.
- Jim: "I am a liar."
I also came across this pithy statement at Math Stack Exchange:
"The number of horrible arguments carried out in the name of Godel's incompleteness theorem is so large that we can't even count them all."
I suspect that my example is one of those horrible arguments but the intention is to just give a small hint at the problems presented with logical systems. You can go deep down the rabbit just by searching for the term Gödel's Incompleteness Theorem.
In Conclusion
Why then use logic at all? Well I take the pragmatic approach to this. Knowing that there are inherent limitations to the tool you simply have to build in safety factors into your conclusions in case it all goes wrong. These include playing it safe and having redundancy in your systems and your everyday life.
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