September
12, 2017 Tuesday
Bedtime
Story
Gottlob Frege on 'What it is to be True'
As
I as saying, Gottlob Frege was an extreme introvert, keeping himself away from
dialogues, discussions and arguments.
Even
while lecturing, he would most of the times face the blackboard and pass witty
and sometimes sarcastic remarks.
It
was this largely forgotten introvert Gottlob Frege who began this revolution
that can perhaps be called “The Mechanization of Mathematics”.
He
was almost obsessed with the notion of formal proof.
In
his book “The Basic Laws of Arithmetic” 1893, 1903 that was published after his
masterpieces Begriffsschrift and the “Foundations of Mathematics”, he writes:
“Being
true is different front being taken as true, whether by one or many or by
everybody, and in no case is it to be reduced to it.
There
is no contradiction in something’s being true which everybody takes it to be
false.
I
understand by ‘laws of logic’ not psychological laws of takings-to-be-true, but
laws of truth…
If
being true is thus independent of being acknowledged by somebody or other, then
the laws of truth are not psychological laws: they are boundary stones set in
eternal foundation, which our thought can overflow, but never displace.
It
is because of this that they have authority of our thought if it would attain
truth.
They
do not bear the relation to thought that the laws of grammar bear to language;
they do not make explicit the nature of our human thinking and change as it
changes.”
On
studying these sentences deeply, you will come across a mind who was enormously
suspicious of human thinking and I would say, very rightly so.
Not
only that, he even considered that the mathematics so far, which is up to his
time, was not laid upon a strictly scientific method; it was up to him to set
that right.
This
implies that he knew that the men of mathematics who came before him were also
humans and thus prone to errors.
His
idea of introducing new symbols and formal proof was a huge improvement over
the old psychological one.
The
first thing that was needed to formalize mathematics was the introduction of
formal language in mathematics.
We
had discussed this in my bedtime stories while laying the groundwork before the
proofs of Gödel’s theorems.
Similar
treatment had to be given to language.
Clear
rules had to be established in defining what would be sentence from other
expressions.
Similarly
precise rules of inference had to be established in language too which would
precisely define how one sentence could be derived from another.
There
is a formality to the shapes that sentences can take or acquire.
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.com
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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