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Abbreviations The second-order predicate calculus with which we began has been extended with: a primitive \(\#\) operator, so that \(\# F\) can be formulated to signify the number of \(Fs\) a new axiom, namely, Hume’s Principle, to govern the new terms. Frege’s analysis of numbers: \begin{align*} &C_0 = [\lambda x \, x\neq x] \\ &C_1 = [\lambda x \, x= \# C_0] \\ &C_2 = [\lambda x \, x= \# C_0 \lor x= \# C_1] \\ &C_3 = [\lambda x \, x= \# C_0 \lor x= \#...
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