[FOM] Introducing Librationism

[Frode Bjørdal]

Introducing Librationism

Harvey Friedman has recently asked proponents of alternative
foundational points of views to present such on the f.o.m. email list.
I here give a brief presentation of librationism which is a
foundational system I have developed over many years. I lately coined
its name from the astronomical phenomenon libration in part because
this reminds of its peculiar shift in perspectives in association
with its treatment of paradoxical phenomena. In this brief
presentation I take the precaution to not copy from the abstract of my
upcoming presentation “Librationist accounts of paradox and other
mathematical phenomena” at the European Summer Meeting of the
Association of Symbolic Logic in Barcelona, July 11-16. I hope the
appetite of those who attend there may be whet by this posting.

Librationism is not a formal or logical system, but is stronger than
such systems in that it incorporates non-constructive proof principles
(one such, the Z-rule, is briefly described below).  I have suggested
in lectures and unpublished manuscripts that we should consider such
systems, as similarly omega-logic, contentual systems; one strong
motivation for this terminology is that e.g. omega-logic has a more
categorical fixation of arithmetical content to avoid non-standard
models. This terminology is also to avoid the somewhat uninformative
term “semi-formal”. Furthermore, although librationism is not a
logical system, it is, I want to stress, eminently a mathematical
system. But librationism has some quite unusual features which are
noteworthy. For an introduction to some aspects of the librationist
points of view I now link the reader to a preprint of my paper
“Considerations Contra Cantorianism”, which will be published in The
LOGICA Yearbook 2010 by College Publications and released at the
beginning of the LOGICA 2011 conference:

http://www.duo.uio.no/publ/IFIKK/2010/107944/Considerations-Contra-Cantorianism.pdf

Caveat lector: (1) The Latin names of many of the isolated inference
rules should be corrected; e.g. moduz Barcanicus for modus Barcan. (2)
Librationism is closed under the following Z-rule only for maxims,
i.e. if A(v) is a maxim for all variables v then (x)A(x)  is a maxim.
For the notion of maxim, see my preprint linked to in this message.


-- 
Frode Bjørdal
Professor i filosofi
IFIKK, Universitetet i Oslo
www.hf.uio.no/ifikk/personer/vit/fbjordal/index.html