Logicism

[Rossberg, Marcus]

> On Aug 12, 2020, at 10:59 PM, Deutsch, Harry <hdeutsch at ilstu.edu> wrote:
> 
> I wonder what Frege would have thought of the derivation of the Peano postulates in FA (without the help of Basic Law V). Would he think we only have a “free standing” epistemic right to HP, or would he see this idea as a sign of psychologism obtruding in matters of logic?  Harry

In The Foundations of Arithmetic, Frege entertains HP as a foundation (and sketches a derivation of PA from it), but rejects it because of what we now call the Julius Caesar problem.  That’s where we’re all getting it from.

In a letter to Russell, after the discovery of the antinomy, Frege says that the problem with HP is the same as with Basic Law V, so founding arithmetic on HP isn’t an option. It’s a tantalizing remark, since he doesn’t spell out what he takes the problem to be.  Did he think HP was inconsistent or what? 

Marcus