[HM] Logicism
Jeremy Gray (j.j.gray@open.ac.uk)
Mon, 11 Jan 1999 13:45:12 -0000
Dear All,
Advice please - if you have not already debated this at length.
I take the historians party line on logicism (in the spirit of Russell) to
be this: the reduction of mathematics to logic fails. Hilbert tried to
establish logic as a part of mathematics, but in the end Gvdel destroyed
Hilberts programme, although what remained became the orthodoxy among
philosophers of mathematics. A number of stories are mixed in with this one,
such as axiomatics and intuitionism.
At its simplest, such a story blurs essential distinctions, such as those
between first and second order logic and set theory, and syntax and
semantics. The question of what has been established, and what historical
effect this had, is blurred (at least in my eyes).
My question is: What are the best historical accounts of the logicist
debates in the foundations of mathematics, 1900-1940?
I am looking for something that attains reasonably high standards in these
respects:
the treatment is comprehensive, the analysis of claims is detailed and
precise, the level of historical argument is high.
My impression is that there is an older historical literature, which is a
mixture of many high-level technical papers and some books that give the
party line. Recently there have been a number of fine studies that go more
carefully over the ground (eg, on Peirce, Russell, Gvdel, and Hilbert). But
I know of no account that integrates these separate accounts, and I find
myself unable to tell myself a satisfactory story about these events. It is
very likely that I am missing some good work, quite probably by members of
this list. Whence my question.
With best wishes, and thanking you in advance for your help
Jeremy Gray