Math Forum / Mathematics / Mathematical Logic / December 2006

In 1964 Einsteinians discovered that Einstein's inconsistency, like any
other inconsistency, is based on two incompatible principles: the
principle of invariability of the speed of light and the principle of
variability of the speed of light. They called the discovery "a

J. Mulligan, INTRODUCTORY COLLEGE PHYSICS, McGraw-Hill, 1985,
pp.631-632:
"Sir Isaac Newton had proposed a particle theory of light which
explained the refraction of light by the difference in the forces

godel's first incompleteness theorem shows us true but unprovable
sentences, so that systems meeting certain conditions are incomplete.
does it follow from these that these systems (say arithmetic with the
usual operators required to achieve godel numbering, etc.) cannot ever

The technical definitions used in mathematics are evolving away from
their originary standard english origins. Technical definitions are now
shorthand for mathematical consistencies. The term 'set' is a case in
point. The term 'concept' is also losing its meaning by conforming to

The naive set theory says that there is no "Universal" set or a
"set of everything" as this set leads to paradoxes.
Considering that in natural language a concept is a set then the
creation of universal sets or sets of everything in the form of

To begin, a proof does not refer to that which is being proved but is
merely mapped to that which is being proved. In other words,
consistency is mapped to that which is being proved. 'Mapping' is a
contingency, an association, and not a relationship whose terms are

Within first order predicate logic with identity, we can show that
these terms (Existence, Self-identity and Uniqueness) are equivalent.
Axiom 1. Ax(x=x)
D1. E!x =df x=x

An interesting campaign has been launched by SCIENTIFIC AMERICAN:
http://blog.sciam.com/index.php?title=laying_down_the_einstein_s_laws
Laying Down the Einstein's Laws
I offered Einstein's 1911 law of VARIABILITY of the speed of light (see

Does the difference between Bishop-Constructive mathematics and
classical mathematics arise only in the case of a proof that shows
that a particular kind of thing exists.  If a theorem doesn't assert
that a particular kind of object exists are classical and

As most of the 'mathematical' advances have arisen through decidedly
non-mathematical means, such as from the use of ingenious, imaginative
geometrical tricks, fantasy sketches, real-world analogies,
inconsistent conceptual manipulations, and metaphysical conjuring

Every consistent first-order theory has a denumerable model. This
result was originally proved by Godel, and subsequently many other
proofs have been given, e.g. Henkin. [Reference Mendelson's
Introduction to mathematical logic]. The proof in Mendelson's book does

Assume we have a blackboard that we can write any number
onto it.
****************
*    4       7

- Can't always be dreaming
It would not make sense to say that my whole life is a dream. If I were
dreaming all the time, then I would have no concept of a dream: I would
have nothing with which to contrast dreaming since I would have no

Imagine a formal system capable of expressing the statement
metaG = "this statement has no proof in any system".
1 Is metaG true?
2 Can you prove metaG?

Can anyone point me to the literature where is clearly stated which axioms
of axiomatic set theory are used in description logic language ALC? And what
is connection to terminological axioms of  TBox?
Thank you.