May
03, 2017 Wednesday
Bedtime
Story
The Third and Fourth Axiom of Principia Mathematica
Tonight
I shall enlist the third and the fourth axiom or the basic assumptions of
Principia Mathematica.
[3]
(p ∨
This
in simple language means, if either p or q, then either q or p.
Its
equivalent in ordinary language would be something like this:
If
(either Navin is an ape or religion is popular), then (either religion is
popular or Navin is an ape).
[4]
(p ⊃
This
in simple language means if (if p then q) then if ((either r or p) then (either
r or q))
Its
equivalent on ordinary language would be:
If
(if America has the most powerful army then there are infinite natural numbers)
then (if (either sugar is sweet or lime is sour) then (either sugar is sweet or
there are infinite natural numbers))
Now
I want you to go back and look at the axioms in their logical form.
The
axioms seem to be very insignificant and inconsequential, not to mention very
apparent and evident.
Yet
from these very simple and trivial 4 axioms, using the stated Transformation
Rules, it is possible to derive a large slate of theorems which are from
obvious.
Now
cast your eyes back at the bizarre and almost ludicrous examples that have been
stated in informal English language, in particular of the fourth axiom.
This
grotesqueness amplifies the importance of using symbols in a formal logic
system.
Remember,
the whole point of this entire exercise was to get rid of any sort of meaning
and pursue pure logic by the rules of the game.
The
meaning or rather the meaninglessness ought not to have any relevance to the
validity of the logical outcomes.
As
stated earlier, the four axioms seem to be rather simple and banal, yet very
advanced theorems can be derived from those simple assumptions following the
transformation rules and rules of inference.
Just
as an example, look at the formula below.
‘((p ⊃ ((u ⊃
This
entire theorem was derived from the four obvious axioms that were stated above
(not by me).
The
complexity that can arise from simple rules should not surprise any modern man;
all it takes is a little learning, initiation and curiosity.
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.in/
Good night mon ami and my fellow cousin ape.
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Another great educator and a teacher that I am aware of is
Professor Subhashish Chattopadhyay in Bangalore, India.
While I narrate stories, Professor Subhashish an electronic
engineer and a former professor at BARC, does and teaches real mathematics and
physics.
He started the participation of Indian students at the
International Physics Olympiad.
Do visit him here:
All his books can be downloaded for free through this link:
For edutainment and English education of your children, I
recommend this large collection of Halloween Songs for Kids:
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