PJ MANTRA

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#1

A. Truth was an automatic hereditary property of theoremhood.

B. Mathematical statements in such systems are patterns made up of
arbitrary symbols.

C. The beauty of a mechanistic vision of mathematics was that it
eliminated all need for thought or judgement.

D. As long as the axioms were true statements falsehoods simply could
never creep in.



a. ACDB
b. CDAB
c. BCAD
d. DABC


To appreciate Gödel's theorem, it is crucial to understand how
mathematics was perceived at the time. After many centuries of being a
typically sloppy human mishmash in which vague intuitions and precise
logic coexisted on equal terms, mathematics at the end of the 19th
century was finally being shaped up. So-called formal systems were
devised (the prime example being Russell and Whitehead's Principia
Mathematica) in which theorems, following strict rules of inference,
sprout from axioms like limbs from a tree. This process of theorem
sprouting had to start somewhere, and that is where the axioms came
in: they were the primordial seeds, the Ur-theorems from which all
others sprang.

The beauty of this mechanistic vision of mathematics was that it
eliminated all need for thought or judgment. As long as the axioms
were true statements and as long as the rules of inference were truth
preserving, mathematics could not be derailed; falsehoods simply could
never creep in. Truth was an automatic hereditary property of
theoremhood.

The set of symbols in which statements in formal systems were written
generally included, for the sake of clarity, standard numerals, plus
signs, parentheses and so forth, but they were not a necessary
feature; statements could equally well be built out of icons
representing plums, bananas, apples and oranges, or any utterly
arbitrary set of chicken scratches, as long as a given chicken scratch
always turned up in the proper places and only in such proper places.
Mathematical statements in such systems were, it then became ap


OA B


http://www.jacanaent.com/Biographies/Pages/GodelK.htm


STRATEGY #1 :OPTIONS -- CD occurs a/b AD occurs b/d . Without reading
this PJ ( if i am guessing ) I will mark B . On reading I find B is
the answer In fact reading will confuse me :)

STRATEGY #2 - OPENING SENTENCE - 'truth was .. A unlikely , 'such
systems ' B unlikely , As long as .. D unlikely

STRATEGY # 3 A and D are linked because of truth and false hood . My
2 options are B and D - DA and C - AD . Greater chance of DA - On
examining it looks good . Plus C is a bettter starter than others

Combine S1 and S2 and S3- DEFINITELY Answer is B

YOU CAN NEVER GO WRONG !

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