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Full Idea
The neo-logicists take up Frege's claim that Hume's Principle introduces a new concept (of a number), but unlike Frege they go on to claim that it by itself gives a complete account of that concept.
Gist of Idea
Neo-logicists agree that HP introduces number, but also claim that it suffices for the job
Source
David Bostock (Philosophy of Mathematics [2009], 9.A.2)
Book Ref
Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.268
A Reaction
So the big difference between Frege and neo-logicists is the Julius Caesar problem.
Related Idea
Idea 18142 One-one correlations imply normal arithmetic, but don't explain our concept of a number [Frege, by Bostock]
| 21718 | Ramified types can be defended as a system of intensional logic, with a 'no class' view of sets [Russell, by Linsky,B] |
| 18144 | Neo-logicists agree that HP introduces number, but also claim that it suffices for the job [Bostock] |
| 18147 | Neo-logicists meet the Caesar problem by saying Hume's Principle is unique to number [Bostock] |
| 7804 | Wright has revived Frege's discredited logicism [Wright,C, by Benardete,JA] |
| 13899 | The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals [Wright,C] |
| 13896 | The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes [Wright,C] |
| 10622 | The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright] |
| 8783 | Logicism might also be revived with a quantificational approach, or an abstraction-free approach [Hale/Wright] |
| 12225 | Neo-Fregeanism might be better with truth-makers, rather than quantifier commitment [Hale/Wright] |
| 10580 | Mathematics is both necessary and a priori because it really consists of logical truths [Yablo] |
| 9224 | Proceduralism offers a version of logicism with no axioms, or objects, or ontological commitment [Fine,K] |
| 13664 | Logicism is distinctive in seeking a universal language, and denying that logic is a series of abstractions [Shapiro] |
| 18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
| 19295 | Add Hume's principle to logic, to get numbers; arithmetic truths rest on the nature of the numbers [Hale] |
| 21648 | Neo-Fregeans are dazzled by a technical result, and ignore practicalities [Hofweber] |