Around the time when mathematics was becoming formal, the notion of detaching from attaching "contextual interpretation" to symbols in algebra, up to the point of avoiding inconsistency (contradiction) was becoming recognized by people like Peacock and Hankel.

I know this principle was adopted by Peano, but I'm aware that the generally accepted construction of the number systems we have today are not due to Peano, but rather Dedekind and Cauchy.

I realize the principle of permanence while may not exactly recognized is used throughout mathematics since the 19th century even if the exact logic of it may have changed slightly.

So I'm looking for an explanation of how this principle progressed from the 19th century and its influence in the foundations of mathematics.

Thank you.