Philosophy of Mathematics is Principles of Mathematics.
Laws of Mathematics is Axioms of Mathematics.
“Philosophy of” is Principles
“The Rules” are Laws.
The Rules are ideally derived from the Philosophy OR:
IN PRINCIPLE, Principles come first and Laws are derived from Principles.
So, an UNPRINCIPLED LAW – or an arbitrary rule – is not derived from principles OR it is derived from principles from another domain.===
Science – Principles lead to Laws lead to Theories.
Mathematics: Philosophy leads to Axioms leads to Theorems.
Legal: Policies (or Values) leads to Principles leads to Laws leads to Law Enforcement leads to Justification.
now more teasing out distinctions… usage by Wikipedia for itself is interesting:
Not policy or guidelines: https://en.wikipedia.org/wiki/Wikipedia:The_rules_are_principles
But these are
still, hovering around principles here.
Aphorisms/maxims as source of principles shows up as does cases leading to principles…and an argument for a maxim and case being related (if “Don’t be like a Jones” is a maxim that’s based upon a real Jones, they could be equivalent).
You can lose the source of a maxim/aphorism but it still functions
Ah yes, looking at at this mornings’ work:
when RULES realized it cannot be RULES if it’s not prescribing. If it is PHILOSOPHIZING, it is PHILOSOPHY OF rules not rules.
So I’ll change RULES to PRINCIPLES.
Then it would be PRINCIPLES and PHILOSOPHY OF PRINCIPLES.
This would then lead to a PHILOSOPHY BY PRINCIPLES.
a) Talking “about” principles. (Philosophy of)
b) Listing Principles.
c) Following Principles. (Philosophy by)
The prescription is derived from the description.