Math Forum / Mathematics / Mathematical Logic / February 2007

In his initial formulation of the axioms of set theory Ernst Zermelo
used the vague notion of a definite property to define his new axiom
of substitution.  Fraenkel and others improved this by introducing the
formal concept of well formed formulae to the basic terminology of

Godel's first incompleteness theorem states that any consistent theory
capable of expressing basic aritmetical truths about numbers is
incomplete, i.e. there exists a wff S such that neither S nor not(S)
is provable in the theory. But the most interesting thing is that S is

A few years ago Einstein's hypnotists found it suitable to make some
more money by challenging Einstein's principle of constancy of the
speed of light:
http://www.prospect-magazine.co.uk/article_details.php?id=5538

is that true that "if a theory is inconsistent, then any sentence of
the theory turns out to be a theorem (i.e. can be proven via inference
rules)"?
Thanks.

We have two statements to consider.
1. The universe obeys causality (where "causality" is the principle
that every effect has a cause).
2. The universe is deterministic (where "determinism" is the principle

The absurdity that entropy always increases would not hold "the
supreme position among the laws of Nature" (A. Eddington, 1935) if
Clausius had not deduced it gloriously from the fundamental oxymoron
of thermodynamics:

Einsteinians stopped worshipping Divine Albert
http://www.youtube.com/watch?v=vx35zMyFJ94
http://www.physicsforums.com/blog/2006/03/16/albert-hubo-an-einstein-robot/
http://www.haverford.edu/physics-astro/songs/divine.htm

Apparently I've restricted myself to my own theory, being an
objectivist, I don't really care.
Yet, I can prove that.
Ross

we know that the notion of formal system is very generic, i.e. the
alphabet, the set of wff, the set of axioms and the set of inference
rules can be decidabile or not, finite or not, and we still have a
formal system.

A few years ago the journal Nature discussed a "paradox" that
Einstein's theory had produced:
http://www.nature.com/news/2003/030728/full/030728-3.html
The essence of the "paradox" is explained here:

http://www.ias.ac.in/jarch/jaa/20/91-101%20.pdf
John Stachel: "At first Einstein looked for a scalar generalization of
Newton's theory, based on the gravitational potential. By the middle
of 1912, he had worked out what he regarded as a satisfactory theory

The mathematical mind and thus mathematics itself is a creative
product of biological and cultural evolution. This process has created
a kernel of truth that has an absolutist flavor. Godel's
incompleteness proofs suggest that the absolutist portion of

Temporal Geometries
                                         ~v~~
Ordinary Euclidean-Galilean-Cartesian-Newtonian geometry is what I
call isometric meaning the same metric applies in all directions. But

Are there about ten or fifteen, not necessarily old classics, but
modern, wide but still well argued  articles of philosophy of
mathematics about formalism, soundness and platonism, which after
reading them you understand something about philosophy of mathematics?

http://www.nyas.org/publications/UpdateUnbound.asp?UpdateID=41
"A Crisis in Fundamental Physics...Then, about 30 years ago, something
changed. The last time there was a definitive advance in our knowledge
of fundamental physics was the construction ofthe theory we call the