Some interesting links

*Here are some selected links to other interesting sites on the
web related to G**ödel’s Theorems, the
foundations of mathematics, mathematical logic, philosophy and related
subjects. These pages are designed to encourage researchers yet struggling to
give concrete form to their intuitive vision. Choice of sites is thus
influenced by a subjective assessment of their perceived levels of passion for,
belief in, and commitment towards the subject they espouse, and is not
dependent simply on their existing level of authority, or on any assessment of
the scientific validity of their content. *

**Notes**
► *Random thoughts and extracts from on-going correspondence on issues
of current interest in mathematics, mathematical logic, philosophy and related
issues.*

**On formally undecidable
propositions of Principia Mathematica and related systems I***
►A translation of G**ödel’s
original paper, part of an HTML presentation by
Siegfried. A creditable labour of love. The 1962 translation b*

**A new approach to symbolic logic**
► *A web-page on logic and philosophy by Peter Corsellis. The
focus is on the search for an alternative logical theory that better reflects our
ability to think and talk about our thoughts and our language. Currently under
revision “ ... as the existing version is hopelessly confused and incomplete. I
start by addressing the question of what exists, and argue that all the popular
answers to this question are true to some extent. I suggest that existence is a
matter of degree, and that the more things a theory assumes to exist, the less
it is true.”*

**Foundations of Mathematics**
► *A web-page created by Stephen
G. Simpson that attempts to define the terms ‘foundations’ and
‘foundations of mathematics’ for anybody who wants to understand them.*

**Logic and Mathematics**
► *An excellent overview of logic and the philosophy of mathematics by Stephen G. Simpson, intended
for the general reader.*

__Partial
Realizations of Hilbert's Program __►

**FOM** ► *FOM
is a closed, moderated, e-mail list for discussing foundations of
mathematics. The moderator is Stephen G. Simpson.*

**Links to some key resouces on the
web** ► *A link to Link ^{2}Go’s logic resources.*

**Research groups in Logic and
Theoretical Computer Science** ► *A web-site maintained by
the Group for Mathematical Logic
at Uppsala University, Sweden.*

**Is Arithmetic consistent?**
► *A fascinating discussion in the Set Theory and Foundations*
section of

**Minds, Machines,
and Mathematics** ► *A provocative article where David J. Chalmers,
commenting on Roger
Penrose’s book Shadows of
the Mind, suggests that the deepest flaw in all Gödelian arguments,
essentially articulated by John
Randolph Lucas in his 1961 article Minds, Machines and Gödel,
lies in their assumption, at some point, that we know that we are fundamentally
sound, i.e. consistent, despite occasional aberrant behavior. Chalmers concludes with a
delightfully puckish aside by introducing a light-hearted - yet illuminating -
categorisation of the philosophical inclinations of the scientific community
based on their attitudes towards basic questions regarding the nature and
source of ‘awareness’.*

(*Sorry for the
paucity of published links. This site is under construction. **Please bear with us.*)

**◄ Index
◄ Re-visiting
Gödel’s Theorems (2000) ◄ Beyond Gödel (2001)**
▲ Web_links

(*Updated : 10/11/01
1:49:01 AM by re@alixcomsi.com*)