Re: Upstairs--Third Person narration

In article <1hv86o3.49fdqp74bux6N%spam@xxxxxxxxxxxxxxxxxxxx>,
spam@xxxxxxxxxxxxxxxxxxxx says...
Gerry Quinn <gerryq@xxxxxxxxxxxxxxxxxxx> wrote:

We observe part of the universe and observe regularities in its

What do you mean by observe? Or aren't you part of the universe?

Yes - parts of the universe observe other parts, and the regularities
presumaly correspond to correlations at a fundamental level.

If you don't include that *for consideration*, at least before you
choose to reject it, you are assuming your own answer. In which case,
what was the point in asking the question?

I thought it was obvious - the question implies an obviously
contradictory concept: a stone that God both can and cannot lift. What
meaning can be obtained from it?

Just as:
negative numbers don't exist
the square root of -1 is obviously imaginary
etc.?

Negative stones don't exist. What's the square root of a stone?

Numbers are strings, not things. You can make formal systems in which
the substring sqrt(-1) is part of valid propositions, just as you can
put stones in a row. The first says nothing about stones, and the
second says nothing about strings.

By stating that it is "obviously contradictory" you are assuming your
own answer.

No: it clearly contains contradictory propositions asserted at once.
How would you define a contradiction?

Take your original question "What's a logically inconsistent place?"

I take it now that you intended it rhetorically, and that you assume
such a place cannot exist. If you start with that assumption, then
obviously you will (using whatever chain of reasoning you like) end
up with the conclusion that such a place cannot exist.

Reductio ad absurdum good enough for you?

Assume a logically inconsistent place exists.

Therefore the place includes a contradiction.

Therefore our assumption leads to a contradiction.

Therefore it is false.

Q.E.D.

OTOH, if you take the question seriously (just as, by analogy, a
mathematician might, for the moment, pretend that -1 has a square root)
then you might get something else.

Why not go the full way: assume that something is both true and false,
and that true and false have their usual meanings. Where does that get
you, and what can you deduce from it?

It would be unsurprising (by analogy with complex numbers) to discover
that we need to abandon some of our existing certainties. Perhaps, the
Aristotelian two-valued approach to truth? Or maybe something else.
Just as, for arithmetic, we need to suppose a new kind of number, in
order to answer the question
"what are the roots of the equation: x^2 + 2x + 2 = 0 ?"

Whether or not we can come up with a *useful* new system, to answer the
question, we do not know. (Just as, beforehand, it was not obvious that
complex numbers would turn out to be useful.)

Everything that can be modelled with complex numbers can be modelled
with real numbers, or with arithmetic (though that would be more
awkward). Similarly, anything that can be modelled with multi-valued
logic can be modelled with binary logic. Because mathematics is just
strings, and every mathematical system of a certain minimum complexity
(arithmetic should do) contains all possible mathematical systems.

It follows that everything in the universe that can be modelled
mathematically can be modelled using binary logic.

So, to generate laws that will map onto a non-consistent mathematics,
or some attempt at it, it would be necessary to observe non-consistent
behaviour in the universe, or at least behaviour that could only be
described by laws isomorphic to a non-consistent mathematics.

As I hinted at before, some kind of "local" consistency is conceivable.

The simplest sort would be describable (I think) by some sort of meta-
description which would itself be consistent. It's hard enough to
reason about without the added difficulty of an inconsistent
meta-description.

I would suggest that the difficulty of reasoning about it may have
something to do with its inconsistency...

Local consistency is not quite as difficult as it sounds: science uses
it all the time: different branches of science have their own
(consistent) laws. It is an article of faith that all these locally
consistent subjects are part of some globally consistent system (usually
by supposing some kind of reductionism, e.g. biochemistry can be
explained by chemistry, which can be explained by physics etc.)

This assumption has never been found wanting.

Hmmm. I've just thought of another example, which might work better for
visual people: the Penrose triangle. For example
http://www.buckingham.ac.uk/images/photos/2003090501l.jpg

It's locally a consistent image of a 3D object, but globally
inconsistent.

Imagine a scientific geometer-ant mathematician, living on the surface
of such an object. *You* will say it can't happen. I will say, "suppose
it did?" :-)

I can model it easily using binary logic and standard physics: the
system is being continuously modified where the ant isn't. Since the
ant's measurements are local, he can't observe this, but he can deduce
it.

This will obviously cause him philosophical problems, and he will
design experiments to expose the contradiction in the most naked form
possible, setting up mirrors at the corners to reflect light beams etc.

If logic applies, he will detect a systematic misalignment of the beams
as he moves around the surface, because while a locally consistent
arrangement is possible for the ant, none is for the beams.

- Gerry Quinn


.

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