Agreed-upon, as in subjective.

The objectivity is in the relations.

If you define a system where “2 + 2 = 5”, but also “a square has 5 corners”, “carbon has 5 covalent bonding positions”, etc. your system is coherent, but you actually are stating the abstract property “2 + 2 = 4” in common math, just using the symbol “5” to represent what’s commonly represented as “4”. A bit confusing, a less confusing example is common math, substituting “2” with “B” and “4” with “D”, so “B + B = D, a square has D corners, …”

If you define a system where “2 + 2 = 5, a line segment has 2 ends, a square has 4 corners, 4 < 5”, you’re objectively wrong (unless you’re taking common math and substituting more than digits)…if you extend this system you’ll find contradictions (what happens if you combine 2 parallel line segments of the same length at that length distance?), especially if you try to apply it to the real world.