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paradox
sacrilege heresy
blasphemy
"They that approve a
private
opinion, call it an opinion; but they that mislike it,
heresy: and yet
heresy signifies no more than
private
opinion." - Thomas Hobbs
The Liar Paradox
Sentences can be constructed that cannot consistently be
assigned a truth
value
even though they are
completely in accord with grammar and semantic rules.
Consider the simplest version of
the paradox, the sentence;
This statement is false.
If we suppose that 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. So the
hypothesis that it is
true leads to the
contradiction that it is
true and false.
Yet we cannot conclude that the sentence is false for that hypothesis also leads to
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, we end up concluding
that the statement is both true and
false. But it has to be either
true or false (or
so our intuition lead us to
think), hence there seems to be a
contradiction at the
heart of our beliefs about truth
and falsity.
Since the Liar Sentence can be shown to be
true if it is false
and false if it is true
has have incorrectly concluded that it
is neither true or false.
To solve the riddle of the Liar Paradox one must reject a
common myth about truth and falsity - the
claim that every statement has to be either 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 nor
false.
This statement is not
true.
If it is neither
true nor false,
then it is not true, which is what it says;
hence it is true 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" contains no more
information than the statement "two plus two is four", because the
phrase "it is true that..." is always
implicitly there.
Thus the statement;
This statement is
false.
is said to be equivalent to;
This statement is true and this
statement is false.
The latter is a simple
contradiction of the form "A
and not A", and hence is false.
There is
no paradox because the claim that this statement is false does not lead to a
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.
A series of sentences becomes paradoxical or congruent
upon contingent facts.
There are two politicians, Smith and Jones;
The only
thing Smith says about Jones is;
Most of what Jones says about me is false.
Jones says only these three
things about Smith:
Smith is
a big spender.
Smith is soft on crime.
Everything
Smith says about me is true.
If
the empirical facts are that Smith is a big spender but Smith is
not soft on crime, then Smith's remark about Jones and Jones's last remark
about Smith are both paradoxical.
If a statement's
truth value is ultimately tied up in some
evaluable fact about reality, call that
statement "grounded."
If not, call that statement "ungrounded."
Ungrounded statements do not have a truth
value.
Liar statements and
liar-like statements are ungrounded,
and therefore have no truth
value.
Thus does comedy marginalize the tragedy by
producing questions
about the obviously neurotic
answers of the politicians.
The
repression,
oppression and lack of
possession of sufficient contrary
skepticism regarding complex analytical intricacies allows intimidation and
ingratiation of an individual by
the politician through
conscious intervention
designed to con-vince the
individual of the
truth or falsity of the
reality presented as fact.
It is sacrilege, heresy, and blasphemy
to
avoid apparently paradoxical reality
by
shuttering one's mind.
history
"The
capitulation of academic institutions
to the cult of materialism is the
reason for the demise of the Enlightenment and the resurrection of
superstition .
The seeds
of the Enlightenment were laid during the
Middle Ages when European universities created
the liberal arts curriculum - a combination of
arts, humanities, mathematics and
sciences.
The objectives were
breadth of knowledge and
freedom of thought.
Academic
institutions today are dominated by
professional schools, administrators must be
good fund
raisers and students are interested
only in jobs.
During 37 years of teaching history at four universities, I
never ceased to be amazed at the typical student's appalling
ignorance of
political and social history.
College graduates are
trained but not educated." -
Forrest G. Wood, Professor of History Emeritus Cal State Bakersfield
"My God,
America, learn world history so you can make
intelligent decisions about American
policies." - Ivan Goldin
"If we're honest with
ourselves we have to factor into America's
lead in science and technology in the
20th century Europe's and Japan's capacities were largely bombed out of
existence during World War II.
America was not a leading place for science
before the World War II. We also have to thank
Adolf Hitler for unintentionally
sending all those first-rate Jewish scientists over here." - Fred G. Miller
"For future
generations to truly
know about America's history, they must be exposed to the
historical facts as well as the cultural
effects of these historical facts. It is only then that the full
image is seen and
understood. It's embarrassing to think that
students today know more about Paris Hilton
than Ernest Hemingway." - Adriana Dermenjian
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