John Locke's Epistemology
I
really don't know how John Locke saw his position before he started
writing. However, there is a way of looking at Locke that allows us to
understand some important points about the development of philosophy
and the nature of rational thought. Before Locke started writing, two
things were true. The first thing was that, at that point, rationalism
had failed. The doctrine of innate ideas was logically unsupported, and
Cartesian Dualism is logically self-contradictory. The second thing was
that, at that point, not everybody had noticed that rationalism had
failed. Many people still believed in things like innate ideas,
substance, and ontological dualism.
The
working philosopher generally has two kinds of problem. First, she has
the problem of figuring out the right answer and, second, she has the
problem of getting people to accept that right answer. Thus the working
philosopher has to work in both logic and rhetoric. She has to figure
out what the right answer is, and then she has to communicate that
answer in such a way that others will be able to see that it is the
right answer. I think that we can usefully see John Locke as having
recognized the failure of rationalism, and as taking up the problem of
communicating to other people the fact that rationalism had failed. To
do this, he used a different kind of argument, one that rationalist
philosophers had never used.
Occam's Razor.
Ockham's
Razor (spell it any way you like) is the fundamental principle of
knowledge production. We cannot generate knowledge about the universe
without it. There is no piece of actual knowledge of anything that
exists or doesn't exist that isn't based on Ockham's razor. And yet,
rationalists would reject Occam's razor out of hand. The acceptance or
rejection of Occam's razor is, to me, the fundamental dividing line
between empiricists like Locke and rationalists like Plato and
Descartes.
Occam's
Razor is a rule. It is a set of instructions of how to figure out which
explanation you should select. For instance, say we are trying to
explain the fact that, when you place a very hot object near to, but
not touching a very cold object, the hot object will slowly become
colder, and the cold object will slowly become warmer, until the two
objects are the same temperature, even if the two objects are inside a
vacuum.
Let
us say that there are several theories on offer for this phenomenon.
Theory
number one, the "Just Does" theory, holds that heat just does jump from
the hotter object to to the colder object.
Theory
number two, the "Intelligent Warmer" theory, holds that an undetectable
supernatural being invisibly intervenes to move heat from the hot
object to the colder object.
Theory
number three, the "Kinetic" theory, holds that heat is nothing more
than the vibrational movement of of the molecules and atoms that make
up the objects.
Theory
number four, the "Caloric" theory, holds that heat is a fluid that can
be put into an object, and which will leak out of the object in all
directions just so long as there is less caloric in the surroundings
than in the object itself.
Theory
number five, the "Heat Fairies" theory, holds that heat is a fluid that
can be carried from one object to another by tiny beings with insect
wings that dip tiny little buckets into hot objects to get the heat out
so they can carry it over to colder objects, where they pour the heat
in.s
There
are two stages to Ockham's Razor. The first stage is to discard all the
theories that are clearly inadequate. What this means is that, under
Occam's razor, we only consider theories that actually provide some
kind of more or less reasonable explanation for the phenomena.
Theory
number one, the "Just Does" theory, is obviously inadequate. Basically,
it's not even an explanation at all. In fact, it's more like a refusal
to provide an explanation than anything else. Technically speaking, it
shouldn't even be called a theory, because it's logically equivalent to
saying, "the heat moves, and I don't know why."
Theory
number two, the "Intelligent Warmer" theory, is equally inadequate.
Again, it's not even an explanation at all. Imagine that you were to
ask a holder of this theory how the Intelligent Warmer moves heat from
one object to another. The answer would probably be something like "he
just does." Now that's hardly adequate, is it? Basically, theory number
two is just theory number one with the profoundly unhelpful addition of
the completely useless "Intelligent Warmer."
Theory
number three, the "Kinetic" theory, clearly fails to explain how heat
gets from a hotter object to a colder object inside a vacuum. In order
for the movement of one particle to affect the movement of another,
those particles have to come in contact. Molecular movement cannot be
transmitted across a vacuum, because there are no molecules in a vacuum
to carry the movement across.
I
want you to notice how the failure of the Kinetic theory is different
from the failures of the Just Does and the Intelligent Warmer theories.
With the Kinetic theory, there is a mechanism that can be compared to
the phenomena, and we can think about whether or not that mechanism
could possibly make the phenomenon happen. With the other two theories,
there is no mechanism, and there is nothing to think about. This is why
they are not even explanations at all, and should not even really be
called "theories." The only difference between them is that the Just
Does theory basically refuses to give an explanation, and the
Intelligent Warmer theory pretends to give an explanation, but really
doesn't.
Theory
number four, the "Caloric" theory, actually has a reasonably adequate
explanation for how heat gets from one object to another. If heat is a
fluid, an actual stuff that can flow into and out of objects, it could
flow across the vacuum. Hotter objects would spit out more caloric than
colder objects, and so hotter objects would tend to get colder, and
colder objects would tend to get warmer, as caloric moved back and
forth between them.
Theory
number five, the "Heat Fairies" theory is just as adequate, in that it
gives us a mechanism by which heat can move from one object to another
through a vacuum.
So,
after applying the first stage of Occam's razor, we are left with two
reasonably adequate theories. There is the caloric theory, in which
heat is a fluid that moves between objects of its own accord, and the
heat fairies theory, in which heat is a fluid that is carried from
object to object by fairies. None of the other theories is adequate,
because none of them explain how heat gets across a vacuum.
The
second stage of Occam's razor says that we should choose the theory
that requires us to accept the existence to accept the existence of the
fewest new entities. If a theory requires us to believe in something
that we don't see anywhere else in the universe, then we should not
believe in that thing unless we have absolutely no other choice. Both
the caloric theory and the heat fairies theory require us to believe
that heat is a fluid. We don't see this kind of fluid anywhere else, so
Occam's razor says we should not accept its existence if we have any
choice. But, at this point in our deliberations, we don't have any
other choice. Our only two adequate theories both require that heat be
a fluid. On the other hand, the heat fairies theory requires us to
believe in fairies, which we also do not see anywhere else in the
universe. These fairies come with a lot of unanswered questions. Where
do they come from? How do they live? Why can't we see them? Where do
they get the little buckets? The heat fairy theory is therefore much
more complicated in terms of existence of new objects than the caloric
theory. (I like to refer to this as being more "ontologically
complicated.") Occam's razor can be formulated as telling us to accept
only the least ontologically complicated adequate theory. Since the
caloric theory is less ontologically complicated than the only other
adequate theory, Occam's razor says we should accept the caloric
theory, at least as far as this example is concerned.
I
like this example because it allows me to make a very important
additional point about how science makes progress. We can imagine that
a scientist follows the above reasoning and accepts the caloric theory,
at least tentatively. In real life however, there were other situations
involving heat where the caloric theory turned out not to be an
adequate explanation. In real life, the caloric theory was accepted for
a number of years until certain other considerations made it clear
that, overall, the kinetic theory actually turned out to be a much
better explanation of heat. Crucial to this was the discovery of
radiation, and the idea that rapidly moving molecules can generate
infrared radiation as they bang into each other in a hot object. This
allowed the kinetic theory of heat to explain how heat got across a
vacuum. Prior to the discovery of radiation, some physicists accepted
the caloric theory, and others accepted the kinetic theory. This was
entirely appropriate, because neither theory fully passed the test of
Occam's razor. The caloric theory explained more things, but was more
ontologically complicated. The kinetic theory was ontologically
simpler, but it did not explain as much. Once radiation was discovered,
the ontologically simpler theory was also shown to be equally adequate,
and so it became the accepted theory.
I
would also like to note that, if no one had invented the caloric
theory, it would still have been utterly bizarre for someone to offer
the intelligent warmer theory as a serious competitor to the kinetic
theory of heat. Suppose physicists only know about the kinetic theory,
do not know about radiation, and therefore do not yet generally accept
the kinetic theory of heat. If someone came along and said "I can
bridge the gap between molecular movement and transmission of heat
across a vacuum by theorizing that an Intelligent Warmer moves the heat
across the vacuum" he would quite rightly be laughed out of physics.
Even if the kinetic theory of heat is not then adequate to explain the
movement of heat across a vacuum, the intelligent warming theory is not
only equally inadequate, because it does not explain how the Warmer
moves the heat, it is also so ontologically complicated as to be
ludicrous. How did the Intelligent Warmer come into existence? How does
it live? What does it eat? Where does it get the energy to move the
heat?
Finally,
if radiation is discovered, and the kinetic theory becomes adequate,
the intelligent warmer theory becomes a sort of mental disease. Imagine
if a defender of the intelligent warming theory were to begin by
saying, "the other theories cannot provide an explanation for how heat
gets across a vacuum, and so the Intelligent Warmer must exist," and
when confronted with the concept of radiation, to reply "I don't accept
that explanation." What would you think about the mental capacity or
intellectual honesty of someone who argued in that fashion? You might
find yourself thinking that nobody would ever offer this kind of
"argument," but unfortunately, at least one defender of Intelligent
Design has offered just exactly that kind of reasoning, and indeed this
style of reasoning seems to be the closest thing that Intelligent
Design has to an argument.
Ptolemy and Copernicus.
Imagine
that you have never seen an astronomy book. Imagine that no one has
ever told you anything about astronomy. Imagine that you don't even
know that there is such a thing as astronomy. Now imagine that you go
out into the open on a very clear night and look up at the sky, and
that what you see with your unaided eyes is everything you know about
the night sky. What would you think, and how would you try to explain
all those little lights?
Ancient
astronomers had no telescopes. All they had were their eyes, and their
starting point was the night sky as you can see it today in any place
without light pollution. Their first method of study was simply to make
note of the positions of the brightest stars relative to the positions
of other bright stars. This careful observation paid immediate
dividends, because they noticed right away that some bright stars did
not stay in the same places relative to other bright stars, but changed
relative position over time. The Greek word for wanderer was "planet,"
and that's what they called these wandering stars.
Now,
I want you to put yourself in the place of an ancient astronomer. You
know nothing about physics. You know nothing about vacuum. You know
nothing whatsoever about these little lights in the sky except what you
can see with your unaided eyes. What would you think is the best
explanation for what you see up there? At the time, the simplest and
most obvious explanation: first offered by Anaximander, was that the
Earth hung at the center of an enormous hollow sphere made of some
"crystal" (transparent material) in which the stars were embedded.
Pythagoras later pointed out that some of the stars moved around
relative to the others. Later thinkers, such as Eudoxus, accounted for
the movements of the wandering stars by assuming that each of them was
carried in the wall of its own smoothly moving crystal sphere that fit
neatly inside the larger sphere. Since several planets, including the
Moon in particular, had complicated motions, it was assumed that they
fit inside smoothly moving spheres that fit inside other smoothly
moving spheres and so on until all movements were accounted for. At the
end of the process, they had an elaborate model of the universe as a
set of many hollow crystal spheres, each one moving in its own stately
circle, and all nested together, one inside the other, around a
central, unmoving Earth.
Based
on the information available at the time, this was an absolutely
brilliant model of the universe. As far as anybody could tell, it
explained everything. And it passed the test of Occam's razor because
there was no ontologically simpler model that also explained the same
facts at that time. I want to emphasize this, because it is sometimes
thought that the ancients held "primitive" or irrational views of the
universe before the enlightened moderns came along and corrected them.
Nothing can be further from the truth. Modern people are no smarter
than ancient people. The difference between modern people and ancient
people is that modern people have the advantage of coming in after the
ancients had already done an enormous amount of hard cognitive work
which enabled the steady incremental process which led to our modern
understanding of the world.
Once
Eudoxus' model was developed it could be checked against more and more
careful observations. Later thinkers such as Callippus, added more
intermediate spheres to make the model better fit the observations.
After a while, people started to think that the model was getting a bit
too complicated. A fellow called Hipparchus decided things would be
simpler if, instead of all the crystal spheres fitting one inside the
other around a common center, some of them were much smaller, and
fitted inside the walls of other spheres. If a star was embedded in the
wall of a small sphere that rotated inside the wall of a much larger
sphere that also rotated, the star would follow a path that would look
like a series of small loops arranged in a circle. Hipparchus called
the larger circle the "deferent," and the smaller loops "epicycles." He
also introduced the idea that the rest of the universe did not revolve
around the center of the Earth, but around an imaginary pointhe called
the "eccentric" lay near the center of the Earth. Hipparchus' system
required far fewer spheres than was thought necessary for Eudoxus'
model and, as far as anyone can tell, it produced more accurate
results. It's true that "spheres embedded in the walls of other
spheres" is a little more complicated than "spheres inside spheres
inside spheres," but it isn't much more complicated, and it was
certainly just as easy to visualize. Hipparchus's model was a major
advance in astronomy and, although his works are now lost to us, his
system was elaborated by Ptolemy, and is now known as the Ptolemaic
system.
Modern
thinkers often suffer from the delusion that Copernicus was the first
person to think that the sun might be the center of the universe
instead of the Earth, but this is not so. A fellow called Heracleides
had that idea two thousand years earlier. It was further developed by a
man called Aristarchus, whom Copernicus is known to have read. (The
manuscript of Copernicus's book contains reference to Aristarchus, but
that reference is missing from the published edition.) Why did ancient
thinkers prefer the "geocentric" (earth centered) model of Anaximander
to the "heliocentric" model of Heraclides? Well, one possible answer is
that they thought that the geocentric model was less ontologically
complicated than the heliocentric. The heliocentric model requires
people to believe that the earth moves and the sun doesn't. This idea
radically contradicts every observation that could be made at the time,
and so it is the kind of thing that should not be believed if there is
any less radical alternative. I won't go so far as to say that the
ancients were right to reject Aristarchus' model, (his arguments were
pretty damn good) but that rejection was not unreasonable given both
Occam's razor, and the state of knowledge at the time.
What
Copernicus did was work out a thorough mathematical treatment of the
heliocentric model, and show that it easily explained certain things,
such as the fact that the planets Mars, Jupiter and Saturn periodically
appeared to move some distance backwards in their orbits, much more
easily than the Ptolemaic model could. It's not that the Ptolemaic
model could not explain these things, it's that the Ptolemaic
explanation was very, very complicated, and the Copernican explanation
was very simple. Unfortunately, if you just assumed that the planets
moved at constant speed in circular orbits around the center of the
sun, the Copernican model would not match observations very well at
all. So Copernicus, like Hipparchus, included some eccentrics and
epicycles in his system. For this reason, the Copernican system was not
a clear winner over Ptolemy. You could make the system simple, but only
at the expense of accuracy, or you could make the system accurate, but
only at the expense of simplicity.
The
theories of Ptolemy and Copernicus existed side-by-side inside science
for over a hundred years. It was not until Johannes Kepler had the idea
that the planets might move in elliptical orbits that the Copernican
system finally fit the observations well enough to be considered the
clear winner over Ptolemy. Replacing circles with elipses did not
increase the overall complexity of the Copernican system because,
although the ellipse is a more complicated figure than the circle,
using ellipses allowed astronomers to dispense with the eccentrics and
epicycles that Copernicus had been forced to include in his system.
Indeed, adding the notion of the elliptical orbit to the Copernican
system created a model of the solar system that was both elegantly
simple, and which fit observations to a very high degree of accuracy.
Before Kepler, Occam's razor did not clearly support the heliocentric
model because no version of the heliocentric model could satisfy both
conditions of being both ontologically simpler and clearly accurate. It
was only after the addition of Kepler's ellipses that the heliocentric
model could meet the criteria of being the ontologically simplest
theory that adequately explained the observations.
Occam's Razor in Philosophy.
Occam's
razor was tacitly accepted by natural philosophers long before it was
given the name "Occam's razor." Philosophers who studied epistemology
and metaphysics did not necessarily accept Occam's razor. Rationalists
like Plato and Descartes did not accept that there could be any doubt
about their conclusions. Rather, their method was not to look for the
simplest theory that explained the facts, but for the only logically
possible theory. That is, they believed that they could support their
conclusions by arguments that absolutely ruled out all other
explanations, and which thus proved their conclusions with absolute
certainty. If you can prove something with certainty, then you don't
need Occam's razor.
John
Locke did not just argue for new theories in epistemology and ontology,
he also had to argue for a different method of distinguishing between
theories. He had to argue, at least implicitly, that Occam's razor was
a valid and necessary philosophical tool. In effect, he had to argue
that rationalism could not succeed in producing logically coherent
theories of epistemology and ontology. This is why the mind-body
"problem" is so important in philosophy. The mind-body "problem,"
together with the other failures of rationalism, gives us very good
reason to think that the rationalists methods of Plato and Descartes
cannot possibly produce the kind of knowledge they want, and indeed,
that rationalist philosophy cannot produce reliable knowledge at all.
The
methods of empiricism, as exemplified by John Locke, represent a
trade-off. Adopting Occam's razor as a principle of rationality means
that, like scientists, philosophers must give up the idea that they can
have absolute certainty. This is something that rationalists would
never do. Adopting Occam's razor allows us to take certain propositions
as "knowledge" even though those propositions have not been proved with
absolute certainty. This is the methodology that philosophers have used
since since it became clear that rationalist methods would not work.
The
only fundamental difference between empiricism and rationalism is the
acceptance of Occam's razor. Once Occam's razor is accepted, every
other difference follows. The idea that knowledge is gained from
experience, the "tabula rasa" theory that the mind starts as an empty
slate and the denial of innate ideas all turn out to be logical
consequences of accepting Occam's razor. Thus empiricism, although it
is commonly defined as being based on the idea that all knowledge comes
from experience, is actually logically supported by the fact that
experience is a much simpler explanation for the existence of knowledge
than any explanation offered by the rationalists. The idea of tabula
rasa, otherwise known as the denial of innate ideas, is just a logical
consequence of this. Once Occam's razor is accepted as a principle of
logic, empiricism will turn out to follow as a matter of course. If
Occam's razor is not accepted, and we demand absolute certainty for our
theories, empiricism is not supported at all. Thus, Occam's razor is
the rock upon which empiricism rests, and the basic argument for
empiricism is that, if you do not accept Occam's razor, you will not be
able to generate knowledge at all.
Locke's
basic argument against rationalism has two phases. First, there is the
fundamental argument that Occam's razor is necessary to generate
knowledge at all. Second, there is the argument that the existence of
knowledge in human consciousnesses can be simply and adequately
explained by assuming that all knowledge comes from experience. To make
this second part of the argument work, Locke had to develop a theory of
human knowledge acquisition that was both completely adequate and
ontologically simpler than any rationalist theory. This he did with his
theory of simple and complex ideas.
As
I understand Locke's theory, a "simple idea" is an idea that can be
immediately gained from experience. For instance, the idea of "blue"
can be gained by having one's attention drawn to a blue object.
Similarly, the ideas of "round," "high," "small," and so on can all be
gained simply by directing one's sensory apparatus in the right
direction. For Locke, a "complex idea" is an idea that can be
completely generated by combining simple ideas with other simple ideas.
For Locke, every idea anyone could possibly have is nothing more than a
more or less complicated combination of simple ideas. Every idea in
human consciousness is thus explained by a process of combining simple
ideas with other simple ideas, and combining the combinations, and so
on.
This
works as an explanation of human knowledge if two conditions are met.
First, Occam's razor must be a fundamental principle of logic. Second,
there must be no ideas out there that cannot be broken down into simple
ideas. If it is the case that Occam's razor is not a fundamental
principle of logic, then Locke's argument fails. If it is the case that
there is even one idea out there that cannot be broken down into simple
ideas, then Locke's argument fails. However, if it turns out (as it
did) that knowledge is impossible to generate without Occam's razor,
and it also turns out (as it did) that there are no ideas that cannot
be broken down into simple ideas, then Locke's argument succeeds. To my
mind, Locke's argument succeeds brilliantly. In my view, Locke produced
the first successful epistemology, and provided the starting point for
all subsequent epistemological work.
Locke
was similarly successful in ontology. The simplest explanation for our
experience of what appear to us to be physical objects is that physical
objects actually exist, and that they have properties which the human
senses can detect. Can we prove with certainty that the external world
exists? No, we cannot. Not with absolute certainty. But Occam's razor
says that we do not have to prove anything with absolute certainty. All
we have to do is find the least ontologically complicated adequate
theory. And when you compare "physical objects exist and have
properties that we can detect" to ...... well, to that enormously
complicated theory that Descartes came up with, or to Plato's "simile
of the line," it's very clear which theory is ontologically simpler.
But
is Locke's theory adequate? A critic might legitimately point out that,
while some properties of some objects are beyond dispute, the sensory
apparati of many people give different reports of other properties of
other objects. For instance, celery has a mild taste to some people,
but a strong taste to others. Objects that feel warm to some, feel cool
to others. What feels rough to me might feel smooth to you, and so on.
Furthermore, some sensory properties of some objects appear to change
when viewed at different angles and under different light conditions.
If the property truly is in the object, why would it appear different
to different people at different times?
Locke's
answer was to make a distinction between primary and secondary
qualities. Objects still have properties, and these properties are
entirely in the objects. However, there are two kinds of properties,
and correspondingly two ways that these properties are experienced.
First, there are primary qualities, such as extension, shape, rigidity
and so on which are in the objects and thus are directly experienced by
anyone who interacts with the object, and therefore are the same for
everyone who experiences the object. Second, there are secondary
qualities which are not properties of objects. Rather, what is in the
object is a power to induce a secondary quality in an observer. Color,
taste, smell and so on are all secondary qualities. A particular object
does not have a car, a taste, or a smell per se. Rather, it has the
power to induce sensations of color, taste and smell in observers. This
power operates in exactly the same way on everyone who observes the
object, but individual differences between human beings mean that there
will be variation in how different people perceive the same object.
The
distinction between primary and secondary qualities makes Locke's
theory somewhat complicated, but it is still both adequate and far less
complicated than any theory offered before it. This fact, plus Occam's
razor, gives us good reason to accept Locke's theory, at least until
some more adequate or less complicated adequate theory comes along.
Reading Questions
- Did John Locke agree that knowledge came from innate ideas?
-
Where did Locke think that ideas came from?
-
What is Ockham's razor?
-
How was Ockham's razor related to the fall of the system of epicycles?
-
How would you explain a simple idea to someone who's never heard of it before?
-
How are complex ideas different from simple ideas?
-
What are the three kinds of complex ideas?
-
What mistake did Locke think that the rationalists had made?
-
What mistake did the rationalists think that Locke had made?
-
What are the primary qualities?
-
What are the secondary qualities?
-
How are primary qualities different from secondary qualities?
-
Did Locke think that our ideas of primary qualities were accurate representations of features of objects?
-
Did Locke think that our ideas of secondary qualities were accurate representations of features of objects?
Potential questions for Quiz
In the system of epicycles, what did the heavenly bodies all move around?
In Johann Kepler's theory, what did all (or most) of the heavenly bodies move around?
What is the difference between simple and complex ideas?
Where did John Locke think that knowledge came from?
Make a list of primary qualities, and say where they exist.
Make a list of secondary qualities, and say where they exist.
Do our ideas of secondary qualities pertain to the mind, or the world?
Potential Exam Questions
The following questions may appear on the next exam. Your answers
should fully explain and properly organize all the information relevant
to each question. This will include a variety of ideas developed in
response to the above questions, in your personal reading and in class
discussions.
Explain Ockham's razor, and give the argument for the claim that Occam's razor is a fundamental principle of logic. Explain Occam’s razor and place it as best you can in the larger development of modern epistemology. Does epistemology requite Occam’s Razor, or can we develop a logically acceptable theory of knowledge without it? Explain possible criticisms of Occam's razor and say why they fail.
Clearly and completely explain and illustrate Locke's doctrine of simple and complex ideas.
Give a list of simple ideas and a list of complex ideas. How
is the existence of simple ideas different from the existence of complex ideas?
Clearly and completely explain and illustrate Locke's doctrine of primary and secondary qualities.
Give a list of primary qualities and a list of secondary qualities. How
is the existence of primary qualities different from the existence of
secondary qualities?
Explain how Locke's doctrine of simple and complex ideas, and how
it may be taken as part of a larger argument against the doctrine of
innate ideas. Does this view require the existence of
innate ideas? How is this view used to refute
rationalist views innate ideas?
Explain Locke's doctrine of primary and secondary qualities,
and how it may be taken as part of a larger argument against the
existance of such things as platonic forms and substance. Does this view require the existence of immaterial forms? How is this view used to refute
rationalist views of Platonic forms or "substance?"
Briefly explain Locke's
doctrines of ideas and of qualities, and how they may together be taken
as part of a larger argument against rationalism as a
method of doing philosophy. Does these doctrines require the existence of
innate ideas or immaterial forms? How are these doctrines used to refute
rationalist views of Platonic forms or "substance?"
Any exam answer can be enhanced by addition of any comments that occur
to you. The more you think about a topic, the more likely you are to
come up with something that can earn you a little more credit for your
answer. I never deduct points, so it can't hurt to add your own thoughts.
Any exam answer can be enhanced by addition of any comments that occur
to you. The more you think about a topic, the more likely you are to
come up with something that can earn you a little more credit for your
answer. I never deduct points, so it can't hurt to add your own thoughts.
Copyright © 2008 by Martin C. Young
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