Hume's Principle often correlates distinct concepts with the same number (e.g., 'author of Principia Mathematica' and 'positive integer between 1 and 4' are both correlated with the number 2)
A principle codifying the condition under which two concepts are equinumerous, namely when the number of objects falling under each concept is identical
Principia Mathematica(as used in the concrete example)
A famous 1687 book by Isaac Newton that laid out the mathematical laws of motion and gravity.
Notice that Hume’s Principle bears an obvious formal resemblance to Basic Law V. Both are biconditionals asserting the equivalence of an identity among singular terms (the left-side condition) with an equivalence relation on concepts (the right-side condition). Indeed, both correlate concepts with certain objects. In the case of Hume’s Principle, each concept \(F\) is correlated with \(\#F\). However, whereas Basic Law V problematically requires that the correlation between concepts and extensio