Existence, In Addition To Being Out There, Is In Here Too

Universal Applicability-- Eliminate Contradictions
Nightmare Continued

"Okay. I'm confused. What exactly is a valid rule?" I said.

"Good question!" responded Dr. Gill. "In mathematics and logic, what
is even more basic than the law of contradiction, is the requirement
that any entity be equal to itself. Symbolically, that idea is
expressed as A=A. To deny it involves absurdity. It is the simplest of
all equations. Without it, science and mathematics would be
impossible, and mind, as we know it, would cease! Heraclitus was
right! You can't step into the same river twice. A=A does not exist in
the empirical world, but in no way does that make it unimportant, or
unreal."

"What's that supposed to mean?" I said.

"If you want me to answer your question, you're going to have to let
me finish my thought," came the reply. "The key discoveries that made
civilization possible were the taming of fire, the discovery of
agriculture, and the idea of abstract identity. In fact, the backbone
of civilization, self disciplined behavior, wouldn't even be possible
without the identification of the norms that permit and encourage
self-disciplined behavior. Norms, at first, are selected on the basis
of utility, but after that the norms themselves get selected in
accordance with further norms until, on a fundamental level, the
definition of a norm is acquired by use. At that level, norms function
the same way primitive terms do in geometry. A line is defined as any
continuous pathway through space. A straight line is defined as lying
evenly with the points on itself. In the same way the activity that
constitutes reciprocity-- the Golden Rule, categorical imperative,
life-affirmation, reverence for life-- gets defined as a norm. The
norm validates itself through its use-value and universal applicability.

"But science," I replied, "ultimately, is based on observation. I get
to see, feel, hear, taste, or smell the results. No matter how
conflated a theory, eventually, it touches base with reality. What
you're suggesting, it seems to me, is that imagination rules. All we
have to do is agree to an `imagined first principle' and that makes us
`right,' or am I missing something?"

"That's not how mathematics works," Dr. Gill replied. "In math `the
elimination of contradiction' is the overriding principle that keeps
the mathematician on track. And besides you have to keep in mind that
in the empirical world change is ubiquitous. Stepping in the same
river twice is impossible—old water always gets replaced by new. Even
Galileo downplayed the significance of the `real world.' `We cannot
understand the universe,' he said, `unless we can understand the
language it is written in.' From primitive terms--from primitive
norms--consistent arguments can be built. Consistency is to an
argument what structure is to a bridge. In analytical thinking,
symbols get repeated without change. In ethics, normative commands
range into disparate areas of application without contradiction.

"In the empirical world points, lines, figures, and rules of inference
do not exist. The North Pole does not exist in the empirical world,
but it exists nevertheless. In nature's world of constant flux, we use
fixed concepts to describe change. Science is permitted because of the
use of concepts like ridged motion, perfect circles, frictionless
falls, and pure oxygen. Contradictions have pretty much been
eliminated from the basic theories of mathematics and physics. That is
most certainly a measure of their success. Whatever stands in a
definite relation to an existing thing exists.

"Existence, in addition to being `out there,' is `in here,' too. We
discover what's `out there;' we also discover what's `in here.'
Related to identity and perhaps derivable from it, is the rule of
contradiction. Whatever does not agree with itself cannot exist.
According to law, contradictory testimony is false. Logic,
mathematics, and science rest on the principle that the absurd is
impossible. Bertrand Russell made it very clear--from a contradiction,
everything follows; in the midst of contradictions, talking sense is
thrown right out the window. In other words, without `consistent fixed
concepts' there wouldn't be an `in here' to discover. Without an `in
here,' identity, self-control, independence, and personal liberty
would be impossible. Judgments, scientific or otherwise, would be
impossible.

See http://bwinwnbwi2.wordpress.com/2011/07/18/objectivity-is-an-internal-subjective-developmental-discovery/ for more Dr. Gill speak