Intuitively, natural numbers come from and are defined by counting, and that implies that "3" means inherently that something (could be anything) happened or was repeated three times. For example, if you have three apples, that means that you can identify one particular apple that you have, then do that again, then do that again.
Adding a unit to a number is like adding further information on what it is that is being repeated. Three pairs of apples? You just invented the number six!
The meaning of doing something three times (most abstractly: applying the successor function) is already inherent in the meaning of three, so multiplication isn't something that has to be added on top. It's already in there.
Intuitively, natural numbers come from and are defined by counting, and that implies that "3" means inherently that something (could be anything) happened or was repeated three times. For example, if you have three apples, that means that you can identify one particular apple that you have, then do that again, then do that again.
Adding a unit to a number is like adding further information on what it is that is being repeated. Three pairs of apples? You just invented the number six!
The meaning of doing something three times (most abstractly: applying the successor function) is already inherent in the meaning of three, so multiplication isn't something that has to be added on top. It's already in there.