PHILOSOPHIC AID TO SOLVE THE
                        CROCODILE PARADOX

                          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.
 

           -----oOo-----



 

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