Full Idea
Wright is claiming that HP is a special sort of truth in some way: it is supposed to be the fundamental truth about cardinality; ...in particular, HP is supposed to be more fundamental, in some sense than the Dedekind-Peano axioms.
Gist of Idea
Wright thinks Hume's Principle is more fundamental to cardinals than the Peano Axioms are
Source
report of Crispin Wright (Frege's Concept of Numbers as Objects [1983]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 1
Book Reference
-: 'Notre Dame Journal of Formal Logic' [-], p.189
A Reaction
Heck notes that although PA can be proved from HP, HP can be proven from PA plus definitions, so direction of proof won't show fundamentality. He adds that Wright thinks HP is 'more illuminating'.