by Franz J. T. Lee
5TH NOVEMBER, 2000
Now, what is a paradox or logical dilemma?
A paradox is an apparently formal-logical self-contradictory statement, the underlying meaning of which is revealed only by careful scientific and philosophic scrutiny, it provokes fresh, original thought. Here is an example that we have used very often in our chats: the "living dead", the Zombies, the morons of Globalization. This is called an oxymoron.
Other paradoxes: "less is more", "loud silence", the "lonely crowd".
Francis Bacon: "The most
corrected copies are commonly the least correct." In George Orwell's
satire Animal Farm (1945), the first commandment of the animals'
commune: "All animals are equal, but some animals are more equal than others."
There exists even an Epimedes' "Liar-Paradox": "I am a liar" -- if "This sentence is not true" is true, then it is not true, and if it is not true, then it is true. Imagine, in what kind of problems it could place our "crocodile"!
This famous formal-logical "Crocodile" dilemma or paradox, that I presented to you all, was formulated by Lucian (Vitarum auction, 22); Quintilian, (Institutio oratoria, 1 10, 5), and then transmitted across the ages.
It indicates the formal logical dilemma or paradox itself; it not only postulates A, A as only being true, and non-A as being "false", but it also cages thinking, intellect, reason and reasoning in an eternal, absolute circulo vicioso of Either-Or. Similarly, it teaches, educates: either "correct" or "false", "truth" or "lie", "have" or "have not", "giving back" or "not giving back", "good" or "bad", "rich" or "poor", etc., and nothing more.
Note, A is true, and non-A is false, A is the "truth", and non-A is a "lie", not B. B, in any case, is forbidden.
Definitely, this formal logic is pure ideology, is logic for barbarians, is malicious brainwashing, surreptitious mind control, cowardly organized manipulation, and bare-faced indoctrination. Not even Labour, not even Alienation, not even the Patria itself, euphemistically called "History", is like that, functions like that. Just study the metamorphosis of an egg under a hen, or in your frying pan, and you'll see what we mean.
These formal-logical paradoxes and dilemmas have a long history; in the Patria, they appear in all forms of labour life, We will give you some examples to demonstrate this.
Guilty Or Not Guilty: Feudal & Bourgeois Law
In criminology, Sherlock Holmes or Hercule Poirot have the following paradoxical problem to find the culprit:
There are four suspects.
Questioned whether they committed the crime, individually, they stated:
Patricia: Frantz
did it.
Frantz: Karl
did it.
Mahatma: I didn't do it.
Karl:
Frantz lied when he said I did it.
Now, Holmes knows that only one of them committed the crime.
For him, who can only be the guilty one?
Worse even, Poirot knows that only one of these statements
are "false".
For him, who is the "culprit"?
To be able to answer these, you will find yourself in the "Crocodile" paradoxical tradition.
Mental Shaving in the Barber Shop
For all those who love to go to the hairdressing salon, to trim their goldie locks, or to the barber-shop, here is a lovely paradox! The original idea came from the famous British mathematician and philosopher, Bertrand Russell, but we will give you our special version.
In a small German town, Deppenhausen, Karl,
the only barber, declared that he shaved
everyone who did not shave himself.
Jutta asked: "There is something that I don't understand. Who shaves the barber, Karl?"
Franz: "Dear Jutta, you know that I shave myself sometimes."
Jutta: "Franz. Seriously, if Karl does not shave himself, then he is one of those who does not shave himself, and so is shaved by himself, namely by Karl."
Franz: "Jutta, this is crazy, is contradictory, is illogical!"
Jutta: "If, like you, Franz, Karl shaves himself,
he is, of course,
one of the people in town who is not shaved
by the barber, by Karl
himself."
Franz: "This smells like Lucian's self-contradictory 'crocodile' paradox!"
Jutta: "Don't you love contradictions? Do they exist? Would they solve your paradox, your dilemma?"
Franz; "Yes, indeed, Jutta. It's a matter of
class. This problem lies close to the philosophical
foundations of mathematics and science. Hegel shook this paradox
in its very marrow!"
Carl's Dilemma: The Prediction of Future Events
Altmann has been sentenced on Saturday. The
hanging will take place at noon
on one of the seven days of next week.
The judge told Altmann: "You will not know
which day it is until you are told
on the morning of the day of hanging."
Altmann told the judge: "Sir, this sentence could not possible be carried out."
The judge: "Why?"
Altmann: "For example,
I can't be hanged next Saturday, the last day of the week, because on Friday
afternoon I'd still be alive and I'd know for sure that I'd be hanged on
Saturday. But I'd known this before I was told about it on Saturday morning,
and this would contradict your statement".
The judge: "Fine, with great pleasure, I could hang you on next
Friday or Thursday!"
Altmann: "Also, you could not hang me on Friday, or Thursday, or Wednesday, Tuesday, or Monday, also not tomorrow, because I know it today!"
Now, logically, not really, would Altmann eventually be sentenced to death next week?
What is crucial here is that formal-logically a statement about a future event can be known to be a "true" prediction by one person but not known to be "true" by another person until after the event has taken place. And there we have the "true" - "false" carousel again.
Finally let's look at another paradox in another field.
Quantum Mechanics: Paradox
of Einstein, Podolsky, and Rosen
Because of the complexity of illustration, let me quote a summary version, a passage from the Encyclopaedia Britannica:
" In
1935 Einstein and two other physicists in the United
States, Boris Podolsky and
Nathan Rosen, analysed a
thought experiment to measure
position and momentum
in a pair of interacting
systems. Employing conventional
quantum mechanics, they obtained
some startling results,
which led them to conclude
that the theory does not give
a complete description of
physical reality. Their results,
which are so peculiar as
to seem paradoxical, are based
on impeccable reasoning,
but their conclusion that the
theory is incomplete does
not necessarily follow. Bohm
simplified their experiment
while retaining the central
point of their reasoning;
this discussion follows his
account.
The proton, like the electron,
has spin 1/2; thus, no
matter what direction is
chosen for measuring the
component of its spin angular
momentum, the values are
always +1/2 or -1/2. (The
present discussion relates only
to spin angular momentum,
and the word spin is omitted
from now on.) It is possible
to obtain a system consisting
of a pair of protons in close
proximity and with total
angular momentum equal to
zero. Thus, if the value of
one of the components of
angular momentum for one of
the protons is +1/2 along
any selected direction, the value
for the component in the
same direction for the other
particle must be -1/2. Suppose
the two protons move in
opposite directions until
they are far apart. The total
angular momentum of the system
remains zero, and if
the component of angular
momentum along the same
direction for each of the
two particles is measured, the
result is a pair of equal
and opposite values. Therefore,
after the quantity is measured
for one of the protons, it
can be predicted for the
other proton; the second
measurement is unnecessary.
As previously noted,
measuring a quantity changes
the state of the system.
Thus, if measuring Sx (the
x-component of angular
momentum) for proton 1 produces
the value +1/2, the
state of proton 1 after measurement
corresponds to Sx =
+1/2, and the state of proton
2 corresponds to Sx = -1/2.
Any direction, however, can
be chosen for measuring
the component of angular
momentum. Whichever
direction is selected, the
state of proton 1 after
measurement corresponds to
a definite component of
angular momentum about that
direction. Furthermore,
since proton 2 must have
the opposite value for the
same component, it follows
that the measurement on
proton 1 results in a definite
state for proton 2 relative to
the chosen direction, notwithstanding
the fact that the
two particles may be millions
of kilometres apart and are
not interacting with each
other at the time. Einstein and
his two collaborators thought
that this conclusion was so
obviously false that the
quantum mechanical theory on
which it was based must be
incomplete. They concluded
that the correct theory would
contain some hidden
variable feature that would
restore the determinism of
classical physics.
A comparison of how quantum
theory and classical
theory describe angular momentum
for particle pairs
illustrates the essential
difference between the two
outlooks. In both theories,
if a system of two particles
has a total angular momentum
of zero, then the angular
momenta of the two particles
are equal and opposite. If
the components of angular
momentum are measured
along the same direction,
the two values are numerically
equal, one positive and the
other negative. Thus, if one
component is measured, the
other can be predicted. The
crucial difference between
the two theories is that, in
classical physics, the system
under investigation is
assumed to have possessed
the quantity being measured
beforehand. The measurement
does not disturb the
system; it merely reveals
the preexisting state. It may be
noted that, if a particle
were actually to possess
components of angular momentum
prior to
measurement, such quantities
would constitute hidden
variables.
Does nature behave as quantum
mechanics predicts? The answer comes
from measuring the components of
angular momenta for the two protons
along different directions with an angle
between them. A measurement on one
proton can give only the result +1/2 or
-1/2. The experiment consists of
measuring correlations between
the plus and minus
values for pairs of protons
with a fixed value of , and
then repeating the measurements
for different values of
, as in Figure 6. The
interpretation of the results rests
on an important theorem by
the British physicist John
Stewart Bell. Bell began
by assuming the existence of
some form of hidden variable
with a value that would
determine whether the measured
angular momentum
gives a plus or minus result.
He further assumed
locality -- namely, that
measurement on one proton (i.e.,
the choice of the measurement
direction) cannot affect
the result of the measurement
on the other proton. Both
these assumptions agree with
classical, commonsense
ideas. He then showed quite
generally that these two
assumptions lead to a certain
relationship, now known as
Bell's inequality, for the
correlation values mentioned
above. Experiments have been
conducted at several
laboratories with photons
instead of protons (the analysis
is similar), and the results
show fairly conclusively that
Bell's inequality is violated.
That is to say, the observed
results agree with those
of quantum mechanics and
cannot be accounted for by
a hidden variable (or
deterministic) theory based
on the concept of locality.
One is forced to conclude
that the two protons are a
correlated pair and that
a measurement on one affects
the state of both, no matter
how far apart they are. This
may strike one as highly
peculiar, but such is the way
nature appears to be.
It may be noted that the effect
on the state of proton 2
following a measurement on
proton 1 is believed to be
instantaneous; the effect
happens before a light signal
initiated by the measuring
event at proton 1 reaches
proton 2. Alain Aspect and
his co-workers in Paris
demonstrated this result
in 1982 with an ingenious
experiment in which the correlation
between the two
angular momenta was measured,
within a very short
time interval, by a high-frequency
switching device. The
interval was less than the
time taken for a light signal to
travel from one particle
to the other at the two
measurement positions. Einstein's
special theory of
relativity states that no
message can travel with a speed
greater than that of light.
Thus, there is no way that the
information concerning the
direction of the measurement
on the first proton could
reach the second proton before
the measurement was made
on it."
Well, folks, now you have enough food for thought to
solve and resolve
the "Crocodile Paradox", and to return the poor child
safely to its Mum.
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