## What is Neo-Logicism?

### Authors

Bernard Linsky and Edward N. Zalta
### Reference

*The Bulletin of Symbolic Logic*, 12/1 (2006): 60-99.
### Abstract

**Abstract**: In this paper, we investigate (1) what can
be salvaged from the original project of "logicism" and (2) what is
the best that can be done if we lower our sights a bit. Logicism is
the view that "mathematics is reducible to logic alone", and there are
a variety of reasons why it was a non-starter. We consider the
various ways of weakening this claim so as to produce a "neologicism".
Three ways are discussed: (1) expand the conception of logic used in
the reduction, (2) allow the addition of analytic-sounding principles
to logic so that the reduction is not to "logic alone" but to logic
and truths knowable *a priori*, and (3) revise the conception
of "reducible". We show how the current versions of neologicism fit
into this classification scheme, and then focus on a kind of
neologicism which we take to have the most potential for achieving the
epistemological goals of the original logicist project. We argue that
that the "weaker" the form of neologicism, the more likely it is to be
a new form of logicism, and show how our preferred system, though
mathematically weak, is metaphysically and epistemogically strong, and
can "reduce" arbitrary mathematical theories to logic and analytic
truths, if given a legitimate new sense of "reduction".

[Preprint available online in PDF]