14 ideas
| 10779 | A comprehension axiom is 'predicative' if the formula has no bound second-order variables [Linnebo] |
| 8755 | Maddy replaces pure sets with just objects and perceived sets of objects [Maddy, by Shapiro] |
| 11022 | Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by Read] |
| 10781 | A 'pure logic' must be ontologically innocent, universal, and without presuppositions [Linnebo] |
| 11065 | The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna] |
| 11023 | The logical connectives are 'defined' by their introduction rules [Gentzen] |
| 11213 | Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen] |
| 10778 | Can second-order logic be ontologically first-order, with all the benefits of second-order? [Linnebo] |
| 10783 | Plural quantification depends too heavily on combinatorial and set-theoretic considerations [Linnebo] |
| 10067 | Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave] |
| 10718 | A natural number is a property of sets [Maddy, by Oliver] |
| 8756 | Intuition doesn't support much mathematics, and we should question its reliability [Maddy, by Shapiro] |
| 17733 | We know mind-independent mathematical truths through sets, which rest on experience [Maddy, by Jenkins] |
| 10782 | The modern concept of an object is rooted in quantificational logic [Linnebo] |