grownup.also.grown-up.*noun*,.*plural*.grownups.also.grown-ups

an adult;

grow,
grew,
grown,
growing,
grows.*verbs*

*intransitive
verb use*.to
increase in size by a natural.process;
to expand; gain;
when people, animals and plants grow, they increase in size and change
physically over a period of time (we stop growing at maturity;
the business grew under new management); to grow is to increase in amount
or degree; intensify (the suspense
grew as we awaited announcement on how the change was to be handled); to
be capable of growth; thrive
(some plants grow in deep shade); to become attached by or as if by the
process of growth (tree trunks that had grown together); to come into existence
from a source; spring up (love that grew from friendship); to come to be
by a gradual process or by degrees; to become (grow closer)

*transitive
verb use*.to
cause to grow; raise (grow flowers); to allow something to develop or increase
by its natural process (grow a beard)

grower.*noun*,.*plural*.growers

growingly.*adverb*

grow into.*phrasal
verb*

to develop so as to become
(a boy grows into a man); to develop or change so as to fit (the toddler
grew into his older brother's clothes)

grow out of.*idiom*

to develop or come into
existence from (an article that grew out of a few scribbled notes; trust
that grew out of long acquaintance)

Gross National Product
(GNP).*noun*

the total market value of
all the goods and services produced by a nation during a specified period

gaslighting.*verb*

a term
used to describe a particularly.insidious.form
of psychological.manipulation
in which victims are systematically
fed false information that makes them question what they know to be true
(false information as is common for these concerns to disseminate.-.medical/pharmaceutical/chemical
companies along with corrupt health
departments have through lies, managed to get many of the public to believe
the perfect immune system.God
made them with requires poisonious
vaccines
to protect them from diseases)

gaslight.*noun*,.*plural*.gaslights

aa gaslight is a lamp that
produces light by burning kerosene
gas (*not* gasoline as in cars); a gas burner or lamp uses special
gas

Late Greek.*noun*

the Greek language as used
from the fourth to the ninth century A.D.

gelding.*noun*,.*plural*.geldings

a castrated
animal, such as a male horse

geld,
gelded
or gelt,
gelding,
gelds.*transitive
verbs*

to castrate a horse, for
example; to deprive of strength or vigor; weaken

geld.*noun*,.*plural*.gelds

a tax paid to the crown,
actually to the royals of Englnd by English landholders under Anglo
Saxon and Norman
kings; from Middle English
'geld' meaning 'payment'

galosh.*noun*,.*plural*.galoshes

a waterproof overshoe; galoshes
are large waterproof shoes, usually made of rubber or simulated
rubber, which you wear over your ordinary shoes to prevent them getting
wet from snow, slush and rain

Kurt Godel.born
April 28, 1906, Brünn, Austria; died January 14, 1978, Princeton,
N.J., U.S.
Austrian-born mathematician,
logician and philosopher who obtained what may be the *most
important mathematical result of the 20th century*,
his famous Incompleteness Theorem,
which states that within any axiomatic.mathematical.system
there are propositions that
cannot be proved or disproved on the basis of the axioms within that system,
thus,
such a system cannot be simultaneously
complete and consistent. This
proof established Gödel as one of the greatest logicians
since Aristotle and its repercussions
continue to be felt today.

Godel earned his doctorate
in mathematics in 1929 at the University of Vienna and soon after he joined
the faculty there.

Godel's own philosophical
views could not have been more different from others at the university.
Thus, his contact with these others left him with the feeling that the
20th century was inimical to his
ideas.

In his doctoral.thesis
'Über die Vollständigkeit des Logikkalküls' ('On the Completeness
of the Calculus of Logic'), published in a slightly shortened form in 1930,
Godel
proved one of the most important logical results of the century, indeed,
of all time, namely, the *Completeness Theorem*,
which established that classical first-order
logic or predicate
calculus, is complete in the sense that all of the first-order logical
truths can be proved in standard first-order proof systems.

This, however, was nothing
compared with what Gödel published in 1931, namely, the Incompleteness
Theorem; roughly speaking, this theorem established the result that it
is impossible to use the axiomatic method to construct a mathematical theory
in any branch of mathematics that entails all of the truths in that branch
of mathematics.

In England, Alfred North
Whitehead and Bertrand Russell had spent years on such a program, which
they published as *Principia Mathematica* in a set
of three volumes in 1910, 1912 and 1913. For instance, it is impossible
to come up with an axiomatic mathematical theory that captures even all
of the truths about the natural numbers (0, 1, 2, 3,…). This was an extremely
important negative result, as before 1931 many mathematicians were trying
to do precisely that. And that was, to construct axiom systems that could
be used to prove all mathematical truths. Indeed, several well-known logicians
and mathematicians (e.g., Whitehead, Russell, Gottlob Frege, David Hilbert)
spent significant portions of their careers on this project. Unfortunately
for them, Gödel's theorem destroyed this entire axiomatic research
program.

Godel became an internationally
known intellectual figure. He traveled to the United States several times
and lectured extensively at Princeton University in New Jersey, where he
met Albert Einstein. This was the beginning of a close friendship that
would last until Einstein's death in 1955.

In 1940, only months after
he arrived in Princeton, Godel published another classic mathematical paper,
'Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis
with the Axioms of Set Theory' which proved that the axiom of choice and
the continuum hypothesis are consistent with the standard axioms, such
as the Zermelo-Fraenkel axioms of set theory. This established half of
a conjecture of Godel's, namely that the continuum hypothesis could not
be proven true or false in standard set theories. Godel's proof showed
that it could not be proven false in those theories. In 1963 American mathematician
Paul Cohen demonstrated that it could not be proven true in those theories
either, vindicating Godel's
conjecture.

In 1949 Gödel also made
an important contribution to physics, showing that Einstein's theory of
general relativity allows for the possibility of time travel.

In his later years, Gödel
began writing about philosophical issues that would show that mathematical
truth is objective, that is, it goes beyond mere human provability or human
axiom systems.

Godel claimed that, in addition
to the normal five senses, humans also possess a faculty of mathematical
intuition, a faculty that enables
people to grasp the nature of numbers or to see them in the mind's eye.
Godel's claim was that the faculty of mathematical
intuition makes it possible to acquire knowledge of nonphysical mathematical
objects that exist outside of space and time.

Comprised from an article
by Mark Balaguer

Additional Reading

Hao Wang, *Reflections
on Kurt Godel* (1987), written by a close friend of Godel, provides
an excellent overview of Godel's life and work, including some extremely
revealing discussions of some of Godel's philosophical ideas.

*Godel's Proof*, revised
edition, edited by Douglas R. Hofstadter (2001), is a clear, well-written,
introductory level discussion of Godel's Incompleteness Theorem and its
proof.

Palle Yourgrau's, *Godel
Meets Einstein: Time Travel in the Gödel Universe* (1999), is a
lucid introduction to Godel's contributions to the comprehension of the
philosophical implications of relativity.

....entire
article comprised with information from *Encyclopedia Britannica*.