Date: Mon, 1 Mar 1999
Axioms
Thomas M. Miovas, Jr.
I disagree with some in this forum who make the claim that the
basic physical aspects of existence -- the building blocks,
whether these be aether, Lewis Little's waves, protons,
electrons, quarks or what have you -- are axiomatic, meaning the
given or the starting point of knowledge. The beginning point of
all knowledge is **perception** (or observation). To quote Dr.
Peikoff in OPAR (Objectivism: The Philosophy of Ayn Rand) (pg 6): "Axioms are the starting points of
cognition, on which all proofs depend....Axioms are *perceptual
self-evidencies*. There is nothing to be said in their behalf
except: look at reality." I don't think anyone in this forum
would make the claim that the fundamental physical building
blocks of existence are perceptual self-evidencies. It takes an
integration of a vast amount of knowledge to come to the
**conclusion** that physical objects are comprised of electrons,
protons, elementary waves, or what have you, each of which has
it's own specific and quantifiable identity.
The philosophic axiomatic concepts are: existence,
consciousness, and identity. All of human knowledge is dependent
upon grasping these fundamental facts of existence, which is why
they are the basic axioms. Axioms are not metaphysical real
things (which is very Platonic), they are a broadly based
*conceptual grasp* of some aspect of existence upon which
further knowledge is built, **starting with perception**. When
we say "existence" is an axiomatic concept, we don't mean all
that stuff out there we can point to, but rather the
conceptualization of all that stuff out there we can point to,
as in "existence exists" (which is the axiom). Hence, saying the
components of physical reality are axiomatic is not only to
confuse a concept with a physical thing, it also completely
inverts the conceptual hierarchy; furthermore, the implication
is that sensory evidence does not give us the direct experience
of existence as it really is.
If we are to move to the axioms of the special sciences, these
axioms would have to be the conceptual grasp of some aspect of
existence that is perceivable, from which all further knowledge
in that field depends, that guides one in any further inquiry
into that field, and yet not be as broad as the philosophic
axioms precisely because it is a subset of existence that is
being investigated.
For Newtonian physics, the axioms are his three laws of motion,
which, to put it in the form of single concepts are: inertia,
momentum, and force. Inertia is more fundamental than momentum,
because a body can have zero momentum (it can be at rest), and
yet take an effort to move it; momentum is more fundamental than
force, because a body can be in motion even though no force is
acting on it. Each of these axioms are verifiable with direct
perception each time one tries to move something in any
direction (which is why weight is out, since one only
experiences the weight of something when one tries to move it up
or hold it up). I say "inertia" and not "quantity of matter,"
because on the perceptual level things can be shown to be made
of parts, but not a certain *number* of similar parts for all
things, which is what the term "quantity" means.
Newton's great achievement was not only that he was able to
formulate these axioms, but also that he was able to quantify
and measure them, thus making physics a subset of mathematics
(yes, I disagree with this aspect of the article in *TIA* on
mathematics).
The mathematical units of these axioms in the
metric system are: mass (kg), P (kgm/s) ["P" is not a unit per
se, but in the math the symbol "P" is used], and the Newton (N)
[as I discussed in an earlier post]. Mechanical engineering is
dependent upon Newtonian physics and is also a subset of
mathematics.
Now, if someone were to come up with valid scientific laws that
were not dependent on Newton's laws of motion, then they would
have to state their axioms and verify these *on the perceptual
level*. One might claim that the physics of fields is one such
type of non-Newtonian physics, since the concepts of inertia,
momentum, and force are not applicable to fields and their
changes, but one could also argue that the physics of fields
started in mid-stream and forgot to apply Newton's axioms to
their study. Perhaps physics reached a point where the basic
concepts of Newtonian physics should have been broadened, but
this wasn't done. I haven't reached a conclusion on this as yet,
but I favor the view that the Newtonian axioms should have been
broadened.
Just to broaden the scope of this essay a bit, I would say
self-sustaining, self generative action (or "life") is at least
one axiom of biology; and the principle of exchange (or "trade")
is at least one axiom of economics.
At any rate, if a scientist doesn't have anything to point to
(actually many similar things or events) that can be
conceptualized on a wide enough scale to be the basis for
further knowledge or investigation, he hasn't identified an axiom.
Date: Wed, 3 Mar 1999 07:04:06 -0500 (EST)
Axioms
Thomas M. Miovas, Jr.
>From: Thomas M. Miovas, Jr.
>If we are to move to the axioms of the special sciences,
>these axioms would have to be the conceptual grasp of
>some aspect of existence that is perceivable, from which
>all further knowledge in that field depends, that guides
>one in any further inquiry into that field, and yet not
>be as broad as the philosophic axioms precisely because
>it is a subset of existence that is being investigated.
>
><HB: That may be too narrow, though it does apply to the
>widest sciences. But what about the science of, say,
>genetics? Its axiomatic concepts, such as "inheritance"
>and "sperm" are not quite perceptually given.>
Inheritance is perceptual. How often do you hear parents say
their newborn child looks like either of the parents, or either
of the grandparents? And anyone who has had pets realize some
characteristics of both the male and the female show up in the
baby pets. The same holds true for plants. In many cases,
however, one needs to have records of several preceding
generations, in drawings or photographs, which are perceptual.
I'm not sure sperm would be an axiom, since there are living
beings that reproduce without it, but the male fluid ejaculate
is perceptual -- so much so in some sea creatures that much of
the waters in coastal regions turn milky white during the
spawning season!
><HB: Engineering is not a subset of either math or physics;
>it is an applied science that applies physics (or some other
>science, such as genetics) to the achievement of some goal.>
This is an interesting issue, and one that deserves it's own
thread. I don't have time to write much on it now, but I once
thought an application was not a species of the science it
applies, and (in part) used that reasoning to conclude that
evaluation is not a species of cognition, since evaluations is
applied morality (or applying the principles of morality to
one's own personal life) and morality is cognitive because it
uses a fact (man's life) as the standard of value. I worked my
way out of this mistake, and will probably write an essay
clarifying how evaluation is a species of cognition; but as a
clue, didn't John Galt basically take the position that
engineering is physics and all work is philosophy?
