Inspired from: https://samim.io/p/2019-12-15-abductive-reasoning/
An example of false inductive reasoning:
Here’s another way to phrase it: “I have observed the world, recorded my experiences, and the data shows that all swans are white.” This argument seems reasonable, even though the conclusion is false. Black swans exist; they are rare exceptions and the subject hasn’t seen one yet due to a lack of experience from empirical evidence.
Inductive reasoning is the primary methodology of science. Scientists gather data; they formulate theories based on their data, and they come up with plausible conclusions. Whenever new data arises (whenever a black swan is discovered) their theories have to change accordingly. We are seeing this happening lately with the theory for the expansion of the universe and there are confusions about it because the new evidence doesn’t match our previous theories.
Induction is always at the mercy of experience. This does not mean that inductive reasoning shouldn’t be used. It simply means that it’s a destination towards better thinking and every theory should be treated as temporary, with personal detachment from the concept. Solution: Acquire even more data or experiences, to draw better conclusions
An example of false deductive reasoning:
You don’t need to “go out and test” whether or not mathematics is true in the world. Yet, many people still make mathematical mistakes because they thought that what they were expressing was logical when it wasn’t. Contrary to popular belief, deductive reasoning isn’t impervious to stupidity. As a matter of fact, it requires even less evidence than inductive reasoning to form an argument because it relies on “logic” and that is even more subjective. While inductive reasoning improves with an increase in data, deductive reasoning doesn’t. Proper deductive reasoning requires more minds to input their logic, in order to falsify the previous ones. But even under those circumstance, you may face endless unreasonable debates. This is more of a human problem, than a data problem. Solution: Acquire even more logical opinions, to draw better conclusions
First Principles Thinking an Axioms are most likely derived from Abductive Reasoning
Imagine a situation where the problem you’re trying to solve is so complicated and has so many possibilities that you are unable to find a pattern. This would be analogous to having an unlimited amount of colors.
By going to the root (high-level/fundamental) of colors (such as the primary colors), it allows you to simplify the problem, while being able to predict the scenarios involved. Axiomatic thinking is the process of going back to fundamentals. Finding the three primary colors in a sea of colors would not be easy for a human, since there’s a lot of possible mixtures. The method of axiomatic thinking can be limited at times and the more data is present, the harder it is. Regardless, going back to fundamentals is very necessary as a first step for complicated problems.
Artificial Intelligence works in a similar fashion during training, where it attempts to capture axioms and reframe the decision-making process from those patterns that it found. It finds patterns in a wide amount of data by trying all possible scenarios. For example, it would mix all colors in different sets until it finds all common denominators. These common denominators would them also be pitted against each other, to further reduce them. We tend to think of back-propagation in AI, as only being concerned for finding a matching result. But it’s more than that… When it finds the optimal result, all nodes combined together form a relationship of common denominators through matrix calculations. The meta, is a dynamic Venn diagram of sorts that surfaces the harmonics that are most relevant during decision-making.
Music also works the same way… When the human ear hears a note, there are technically a lot of notes/noises being played. But the brain cancels all noises and resolves what’s called the fundamental note (which is the common denominator), which is what we hear as an esthetically pleasing note. And AI does the same and all results are based-off prominent fundamentals.
Solution: Go back to basic thinking, when trying to understand a problem