Problems with satisfying Law Without Law

[Tuukka Virtaperko]

The CTMU supposedly (p. 49 of the 2002 paper) satisfies the Law
Without Law condition, according to which it contains no arbitrary
declarations (p. 8). But ambiguous concepts can neither be proven to
exist nor proven not to exist, because an unambigous proof cannot
refer to such concepts, and an ambiguous proof would not be much
better than a proof with a mistake. Yet the property of ambiguity can
be formally defined. This entails that either MAP or M=R is an
arbitrary declaration.

[cdipoce]

Do you mean that "Law Without Law" is an ambiguous concept?

My impression is that Langan proves that the CTMU satisfies the
theoretical necessity to account for "Law Without Law".

On Jan 9, 2:22 pm, Tuukka Virtaperko <m...@tuukkavirtaperko.net>
wrote:

[Tuukka Virtaperko]

I tried to send a reply with different content before, but apparently
it has not yet gone through or something. If it doesn't do so soon,
I'll have to investigate.

Here is what I posted to GMBM just recently. It's a better formulation
of the problem than anything I've published before, but not the formal
solution. This is not entirely the work of me, but I apparently have
permission to publish.

Mark,
okay. Why did you moderate away my report of the mistake in the CTMU?
I'll iterate it in better terms.

Langan believes the CTMU to satisfy the Law Without Law condition. But
he also believes it to have the M=R and MAP properties. Here he
implicitly assumes that concepts cannot be used ambiguously.

Ambiguous use of a concept means the concept is used in such a way
that essential information about the theory, in which the concept
belongs, is omitted. To be sure, according to the CTMU every concept
belongs to the CTMU, but this is not enough.

Even within the CTMU, we could, for example, use the concept "A number
whose successor is 0" ambiguously in such a way, that we would not
know whether the 0 is placed in the theory of natural numbers or in
the theory of integers. In this case, we could argue the concept to
have an empty extension, because the theory of natural numbers would
not include --1. But we could also argue the extension of the concept
to be --1, because 0 is the successor of that number in the theory of
integers. The reason why this is possible is that our use of the
concept does not include information that is necessary for defining
the concept unambiguously.

We could deem such use of a concept impossible. But that would be an
arbitrary declaration contrary to Law Without Law. There is no
inherent reason why it would be impossible to communicate in such a
way that information that eliminates ambiguity is omitted.

MAP is an attempt to deem ambiguous use of a concept as impossible.
The CTMU cannot have Law Without Law and MAP.

If we cannot prove that it is impossible to use a concept ambiguously,
we cannot state M=R except as an arbitrary axiomatic declaration. But
if we did that, CTMU again would not have Law Without Law.

-Tuukka

[Tuukka Virtaperko]

cdipoce,
Here's the reply I tried to sen via e-mail:

cdipoce,
Law Without Law is actually not ambiguous. Or if it is, I don't think
the ambiguity arises at this level yet. Langan most definitely does
not seem to
prove it.

Philosophy very unfortunately features many ambiguous concepts, such
as "relevance" and "original objective" in the problem of induction,
which are unsuccessful attempts at eliminating each other's ambiguity
by being more or less circularily defined in such a way that,
unfortunately, does not seem to include actual recursion. Therefore,
even though accusing a philosopher of ambiguity is, in my opinion,
serious criticism of his theory, such criticism is not very cogent
because many would probably find anyone who presents such criticism to
oppose all of metaphysics, even though that's not the case. Carnap,
however, thought such a person would oppose all metaphysics in his
Überwindung-paper. In that paper Carnap himself opposes all
metaphysics on grounds that would be reasonable if metaphysics were
finite-state machines. However, they aren't, and Carnap doesn't
account for this possibility -- probably because necessary theories
were not available at that time except in the field of Buddhism, which
a self-respecting Western academic of his time would not have been
interested of.

The mistake in CTMU is that it is contradictory to state CTMU to
satisfy _both_ Law Without Law _and_ M=R or MAP. The latter two are
arbitrary declarations, of which Langan has to take at least one for
granted in the construction of CTMU, yet adherence to Law Without Law
would require him to take neither one of them for granted.

P.S. Re-sent to get line length right

[cdipoce]

Chris Langan isn't assuming anything other than the fact that reality/
universe (as he defines it) exists and that our minds observe/perceive
it.

If you accept the Reality Principle that reality contains what is real
and nothing else, then MAP naturally follows. And if you accept that
reality exists and that you are perceiving it, then M=R follows.

On Jan 11, 6:09 pm, Tuukka Virtaperko <m...@tuukkavirtaperko.net>
wrote:

[Tuukka Virtaperko]

Does reality contain a number, whose successor is 0, if it has not been
defined, whether this number is a natural number or an integer?

-Tuukka

>> �berwindung-paper. In that paper Carnap himself opposes all