[chickenimprint]

>Science is the business of finding the best explanations that account for all observations.

This is exactly what induction means. Even your wording is almost identical to that of the Wikipedia page on "Inductive reasoning".

> One of the consequences of this methodology is that it turns out that all known observable phenomena can be described by fairly simple mathematical laws. But science does not assume this.

I'm not sure you fully comprehend, it's much simpler. Science does presuppose that observations mean anything related to more general rules, otherwise what would be the point of observations, right? Otherwise all data would be equivalent to TV static and to build a house we would just hope it builds itself. The way you hedge your bets with phrases like "can be described by" and "appear to" makes me think you intuitively understand the limitations of science when it comes to capturing absolute truths, such as analytical a priori truths (e.g. all bachelors are unmarried), which are correct by definition.

[lisper]

> This is exactly what induction means.

No it isn't. You got it right the first time. Induction "presupposes that we have faith in the proposition that something will happen again because it has happened in the past". But that is wrong. Science does not presuppose this.

> Science does presuppose that observations mean anything related to more general rules

No, it does not. It observes that the world behaves according to general rules. It does not presuppose that it does.

[chickenimprint]

> You got it right the first time. No, I gave an example of inductive reasoning common in science. Induction means concluding from the particular to the general. So in this case we might have observed something happening in the past, induced it happens in all of time, deduced that future time is part of all time by definition, and finally concluded that it will happen in the future. Induction is not restricted to time, it can equally be a generalization over time or any circumstance really.

We don't check each and every room in the country to see if general relativity holds there, and then fall in despair once we realize it might have randomly stopped holding in one of them yesterday.

> No, it does not. It observes that the world behaves according to general rules. It does not presuppose that it does.

I'd like to see you explain how you can you observe a rule. Are you God? Can you see all of space and time and all possible dimensions? Science observes particulars and tries to formulate general rules based on these observations. If science would not use induction, any observation would be meaningless, because the exact circumstances the observation was carried out in would cease to exist the moment the observation was concluded.

Therefore, science is susceptible to the induction problem.

[lisper]

> I'd like to see you explain how you can you observe a rule.

You need to read what I say more closely. I did not say that science observes rules. I said that science seeks good explanations for observations, and it just so happens that the best explanations for how nature behaves turn out to look like rules.