Dennis, (01)
That statement has no connection with either mathematics
or the universe: (02)
DT> It seems to me that as valid as mathematics may be for the
> purposes of engineering, architecture, other worldly purposes,
> and as a tool for analytical thinking, that it's requirement
> for self-consistency automatically negates its capacity to
> faithfully model the natural universe and its ever changing
> landscape. (03)
First of all, I don't want to defend all uses of logic and
mathematics because people often apply the wrong kind of
math to the wrong problems for the wrong reasons. (04)
However, there are two very important points to make: (05)
1. The fact that something x at time t1 is changing to
something y at time t2 does not in any way create any
kind of contradiction. Certain kinds of mathematics,
such as differential equations, for example, describe
change and rate of change very nicely. (06)
2. Any collection of observations about the universe or any
part of it either at one instant of time or at different
times can *never* create any contradiction of any kind,
whether stated in a natural language or translated to logic. (07)
The explanation of point #2 is very simple: (08)
a) Any observation statement in logic or English or any other
language requires only two logical operators: conjunction
(i.e., 'and') and the existential quantifier (i.e., 'there
is something'). No negations ('not'), disjunctions ('or'),
implications ('if-then'), or universal quantifiers ('all'
or 'every') are required to state an observation. (09)
b) Therefore, any collection of observations about the universe
will contain only positive statements whose only logical
operators are existence and conjunction. (010)
c) Any collection of statements as in (b) can *never* be
contradictory with one another. Therefore, all observations
of the universe or any part of it must always be consistent. (011)
Contradictions can only arise from combinations of observation
statements with other statements that contain an explicit or
implicit negation. Such implicit negations are typical in the
scientific theories and in so-called "common sense" ideas about
how the world (or the universe) works. But those statements
are *never* reports of observations. They are always somebody's
interpretation or hypothesis about the observations. (012)
If a contradiction arises between an observation statement and
some theory, hypothesis, or commonsense idea, then there are
several possibilities: (013)
1. The observation might have been erroneous or perhaps slightly
inaccurate. (014)
2. If the observation was correct, it is possible that the person
who was applying the theory or idea made some mistake in
applying it. For example, the theory was about subsonic air flow,
and the person applied it to an airplane in supersonic flight. (015)
3. If the observation was correct and the person applied it correctly
and the contradiction still remained, then the original theory or
idea is incorrect and must be revised or rejected. (016)
Both science and common sense have followed these procedures for
all recorded history (several thousand years). And people have
frequently found that many theories and ideas about the universe
were wrong. (017)
But *nobody* has ever detected a single example where the universe
or any part of it was self-contradictory. (018)
If you can ever discover such a case, it would truly be a miracle
that is even more miraculous than anything reported in any religious
text of any kind. The miracles reported in any religious text
might contradict theories or ideas about the universe. But as
observation statements, they cannot be self-contradictory. (019)
If you ever observe something that is self contradictory, you
have witnessed a miracle that is far more miraculous than
anything ever reported in any religion. (020)
If you do, don't bother to tell us about it, because we would
simply dismiss you a nut case. (021)
John Sowa (022)
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