In this case, I mean something like “if you start off with consistent and true beliefs, adding more true beliefs won’t lead to self contradiction.” I can define self-contradiction formally, as asserting both a statement and its formal negation.
This may seem slightly circular, but I think it’s still a useful definition that captures what I want. I also think some circularity is useful to capture what we mean by an axiomatic system.
In this case, I mean something like “if you start off with consistent and true beliefs, adding more true beliefs won’t lead to self contradiction.” I can define self-contradiction formally, as asserting both a statement and its formal negation.
This may seem slightly circular, but I think it’s still a useful definition that captures what I want. I also think some circularity is useful to capture what we mean by an axiomatic system.