So the mathematical inferences would be simplifications of inductive observations. Where would the guarantee be that the world would conform to those simplifications? That's Hume's problem of induction.
By accumulating these simplifications and building entire systems based on them.
It is certainly not the perfect reflection of reality, but that is not the aim of mathematics, but to simplify the complexity according to human perception in such a way that it can be useful in manipulating reality.
Although expanding understanding of reality is one of its goals, the main thing is to expand human domain over reality.
I think that mathematical language, like human knowledge, has its origin in the perception of the predictability of some natural phenomena.
ReplyDeleteFrom understanding some basic rules, you can build models based on those rules and ensure you have some success.
So the mathematical inferences would be simplifications of inductive observations. Where would the guarantee be that the world would conform to those simplifications? That's Hume's problem of induction.
DeleteBy accumulating these simplifications and building entire systems based on them.
DeleteIt is certainly not the perfect reflection of reality, but that is not the aim of mathematics, but to simplify the complexity according to human perception in such a way that it can be useful in manipulating reality.
Although expanding understanding of reality is one of its goals, the main thing is to expand human domain over reality.
At low levels this works very well.