Flawed logic ?15 Jan 2006 I was not going to write about this, because it makes me look like an idiot :)
I try to be as objective and pragmatic as possible in any discussion, but this time I lost my cool.
A silly conversation that started a couple days ago became quite serious for some reason I can not remember. The spark that lighted it all was my "statement" that true logic is the basis of all our science and knowledge. All our knowledge is based on a simple logic: either something is right, or it isn't. (The conversation was about the universe being digital and all perceived reality is just a hallucination that extends the digital universe ;) All our scientific theories are based on this.
The discussion went on to claim that logic is too simplistic to work with. For example according to Schrodinger (Schrodingers atom) an electron can be a particle or a wave at the same time. Based on simple logic you would not be able to tell whether an electron was a particle or a wave. This is of course a theory, like anything else we think we know about the universe, and it could be wrong. My conversation partners seemed to disagree however and used this point to claim that logic could be wrong.
And that's where I lost my cool ;) Telling a scientist that logic, the most fundamental way of thinking we know, the basis of all science, the only way of thinking I know of, could be wrong, is like telling the pope that there is no god.
In science, there are 3 entities we work with. First of all there is the universe we are trying to understand. The universe is all that is physical outside of our mind. Second there is the current theory we have on the workings of our universe. It is our scientific view on the universe, our knowledge. We build it by building on previous knowledge, extrapolating and testing it in the real world. The last entity is logic. We use logic to link the theory with the real universe. If we make an assumption on the workings of the universe, and we do an experiment to confirm it, there are 2 outcomes: either we were right or we were wrong. If we were right, then its partytime because our theory fits the universe. However, if the experiment shows that our theory is wrong, we have to drop this theory and people are usually sad about that. (Although this would be exciting to me because I consider this a bug in the theory, and I love bughunting ;) Whatever the bug is and where-ever it is located, you will always learn something when you track it down and solve it. Even more so with the universe. Every experiment that seems to contradict the current knowledge is important because we WILL learn something new from it.)
Anyway, thats my view on it. My explanation on the whole thing was that asking me whether an electron is a particle or a wave is a trap, because we obviously don't know the difference yet: the terms are not defined! If we would have a clear definition of a particle and of a wave, and both did not overlap, then an electron could only be both at the same time if the universe would allow it. If that was the case, then our current theory is wrong because an apple can't be an apple and a pear at the same time (what a flaky comparison). So, my explanation was that the current knowledge was wrong and needed to be refined.
Although I should have listened more carefully to what was being said, I was too worked up to even consider it. They were saying that I should consider the possibility that our logic is wrong. At the time that was like blasphemy to me. I could not believe that scientists could speak those words.
When evaluating a theory, all 3 entities must be in agreement for the evaluation to be positive. If its negative, then one of the 3 is wrong. (Of course, this conclusion is also based on our logic, but lets not go there :P I'm trying to prove that logic can't be wrong here)
One could speculate that the universe is wrong. That would be very ambitious for mankind :) Claiming that our knowledge is correct and we think correctly, yet the physical reality is inconsistent. God would probably smite the first person who claimed this.
The most obvious conclusion would be that our knowledge is wrong and we need to adjust it. That's the way we've worked for millenia and it worked so far, so why change it ?
Let's however consider the third alternative. What if there is some form of higher logic that we didn't think of ? First of all, would we be able to find it at all ? Our logic is builtin (or so I believe). In our thousands of years of existance, noone has ever proven that our logic is flawed. How would they be able to detect it though ? If our reasoning is wrong, would we be able to prove anything at all ? Wouldn't a flawed reasoning process be able to prove that anything is wrong and right at the same time ? Would flawed logic be able to detect flawed logic ??
Anyway, suppose not us, but some other civilisation (or even God for that matter) would come down to us, point their finger and laugh. Then claim that we use a wrong reasoning process and go on to tell us what the right one is. Would we be able to understand it ?? And if we could and we rebuild our entire knowledge using this new logic, would we run in the same problems ?
It's a lot to think about. We defined our logic to be true. If our logic, our most basic reasoning capability, was wrong, then nothing we have come up with since the stone-ages can be considered to be correct. Sure, all our inventions could work, but we couldn't prove that there are some conditions that it couldn't work, because those conditions would be out of our comprehension. Even worse: we would not be able to add those conditions to our current knowledge, because they are part of our internal logic ! In order for us to use this new logic, our mind would need to be reflashed with some new firmware.
I don't like this idea at all. Before I would accept that our logic was wrong, I would turn every theory upside down, search the entire universe and work myself to death just to prove that our knowledge must be wrong.
The chance that our logic is wrong is terribly small, but it exists. And as a scientist I must accept that.