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"Without Jiminy Cricket on his shoulder,
Pinocchio would never have become
a real boy – he would have always
remained a puppet." - Patrick Fagan
Liar Paradox shows the common
understanding of the essence of tautologies and fallacies actually leads to
an irreconcilable
contradiction.
Sentences can be
constructed completely in accord with grammar and semantic rules that
cannot consistently be assigned a
truth value.
Consider the
simplest version of the paradox, the sentence;
This statement is false.
If we suppose the statement is true,
everything asserted in it must
be true.
However, because the
statement asserts that it is itself false,
it must be false.
The hypothesis it is true leads
to the contradiction as it is both true and false.
The
hypothesis
the sentence is false also
leads to a
contradiction.
If the statement
is false, then what it says
about itself is not true.
It says that it is false,
so that must not be
true. Hence, it
is true.
Under either
hypothesis, the statement
is both true and false.
We feel the statement
must be either true or false.
This points to a
contradiction in the way we abstractly visualize reality.
As the
Liar Sentence can be shown to be true if it is false and false if it is true
the Liar Sentence can be
neither true or false as it is simply nonsense.
To solve the riddle
of the Liar Paradox one must
reject a common myth about truth and falsity -
the claim every statement has
to be true or false.
This is called the Principle of
Bivalence.
A strengthened version of the Liar Paradox counters the
proposal that the statement is neither true or false.
This statement
is not true.
If this statement is not true, then it is false - which
is not what it says.
Every statement includes an implicit assertion of
its own truth.
For example the statement "It is true that
two plus two equals
four" does not actually need the words "It is true" as this is
implicit in all statements.
Thus the statement;
This
statement is false.
Is logically equivalent to;
This
statement is true and this statement is false.
This is
a simple contradiction of the
form "A and not A".
This statement is false
is a logical contradiction.
This analysis does not
provide a solution to versions of the Liar Paradox that do not use
direct self-reference, such as the two-sentence version:
The next
sentence is false.
The preceding sentence is true.
Neither of
these is by itself contradictory, but there is no way to assign
truth
values to them consistently, so we still have a paradox.
Series of
sentences are paradoxical or
congruent upon contingent facts.
I've been one rotten
kid
Some son, some pride and some joy
But I'll get over these
lousin' up
Messin' up, screwin' up times
You'll see, ma, now
comes the better part
Someone's gonna make good
cross his heart
Make good and finally make you
Proud of your boy
Tell
me that I've been a louse and
loafer
You won't get
a fight here, no, ma'am
Say I'm a goldbrick, a goof-off, no
good
But that couldn't be all that I am
Water flows under the bridge, let it
pass
There's no
good reason you should believe me,
not yet I know, but
someday and soon
I'll make you proud of your boy
Though I can't make myself taller
Or
smarter or
handsome or
wise
I'll do my best,
what else can I do?
Since I wasn't born perfect
like dad or you
Mom, I will try to try hard to make you
Proud of your boy
"When one watches some
tired political hack on the platform mechanically repeating the familiar
phrases -- bestial
atrocities, iron
heel, bloodstained
tyranny, free peoples of the
world, stand shoulder to
shoulder -- one often has a curious feeling that one is not watching
a live human being but
some kind of dummy: a feeling which suddenly becomes stronger at moments
when the light catches
the speaker's spectacles and turns them into blank discs.
This is
not altogether fanciful as a speaker who uses that kind of phraseology has
gone some distance
toward turning himself into a machine.
The
appropriate noises are coming out of his larynx, but his brain is not involved
as it would be if he were choosing his
words for himself.
If the speech he is making is one that he is
accustomed to make over and over again,
he may be almost unconscious of
the script he is repeating.
This reduced state of
consciousness is required for political conformity.
Political speech is largely the
defense of the indefensible.
Things like the continuance of British
rule in India, the Russian
purges and deportations, the
dropping of the atom bombs on Japan, can indeed be defended, but
only by arguments which are too
brutal for most people to face, and which
do not square with the
professed aims of the political parties.
Political language has to
consist largely of euphemism, question begging and
sheer cloudy vagueness to fool
the two wings of political thought.
Defenseless villages are bombarded
from the air, cattle machine
gunned, huts set on fire with incendiary bullets: this is called
pacification.
Millions of peasants are robbed
of farms and sent trudging along roads with what they can carry: this is
transfer of population or
rectification of
frontiers.
People are
imprisoned for years,
shot in the back or sent to die of
scurvy in Arctic lumber
camps: elimination of
unreliable elements." - George Orwell
Critical thinking is
analytical thinking.
Critical thinking questions are
used to explore mental models.
Critical thinking is a process for
actively exploring situational reality.
Critical thinking involves
being skeptical:
identifying ambiguities and
assumptions;
identifying
contradictions;
deciding whether a
definition is adequate;
examining the logic leading to a
given conclusion;
judging whether a
statement is overly general;
critiquing the application of
principles and concepts;
and
determining
whether a statement made by authority is relevant.
"Thinking isn't rewarded because it
isn't wanted.
The idea of creating the need to
gain admission to an elite
university is to make sure bright students channel their energies in
approved ways.
Their study is just a test of
ambition,
endurance and
intelligence.
If a student puts up with such
study she/he will do whatever it takes.
The
expected result of such
Pavlovian training is the ideal
employee.
One
who will automatically think only along approved lines, going along with whatever is demanded of him to
get along. "- Raymond J. Rostan
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