Linear induction and generalization
I previously read about the problems with generalizing observations into a mathematical law.
According to you, there are an infinite number of possible generalizations (polynomials in the example you gave) and not necessarily the simple generalization (linear line) is the correct one.
In the past, I treated this argument as another argument in praise of intuition. But recently I had the opportunity to think about it again and it seems to me that it is simply a special case of using the principle of induction – to date, experience has shown that simple generalizations usually work, and therefore we continue to use them.
In light of this, I have two questions:
1. Do you agree with my description – that using linear generalization is simply a special case of using induction?
2. Besides induction and causality, are there other principles that we use even though they do not stem from observation?
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- I agree that this is a private case, but when you come to establish the use of induction, you cannot use induction to do it. David Hume already insisted on this.
- There are a lot. All the rules of logic, for example. Probability calculations. Occam’s razor.
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Can't we put the rules of probability and Occam's razor on the principle of induction? After all, the reason we use them is because we have good experience with them.
In my opinion, no. They preceded experience. To a certain extent, it is based on them. Of course, in everything it can be based on experience, such as mathematics. We have experience that adding two objects and adding three gives five. But my argument is that the insight 2+3=5 precedes experience. It may help us to discern it (a didactic means) but it is not its source. Of course, this is where our debate began here.
I think it is difficult to say that the use of Occam's razor is justified because of the intuition about it. In contrast to the rules of logic and mathematics, where our thinking is meaningless if we exclude them, it is possible to imagine a world in which the razor does not work. If our experience did not justify the use of the razor, we would probably abandon its use.
Another way to look at the razor is that it assumes that any element of a theory that is not based on observation or logic is "suspicious of error" and that is why we want to exclude such elements as much as possible. In other words, the razor wants us to use intuition as little as possible.
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