March 22, 2017 Wednesday
Bedtime Story
Logical Connectives
In natural languages the logical connectives include the following
words:
Hence,
So,
And,
And then,
And then within,
Or,
Implies,
If…then,
If and only if,
Only if,
Just in case,
However,
But,
Not both,
Neither…nor,
Though,
Although,
Therefore,
It is false that,
It is not the case that.
So you see now, propositional calculus or logic is not that a
scary stuff.
But men like George Boole were not happy; they wanted to formalize
it mathematically.
Boole did show that it is possible.
Yet it was the German genius Gottlob Frege who completely
transformed this field by publishing a remarkable book in 1879 called
Begriffsschrift.
Begriffsschrift roughly translates as “concept writing” or “concept
notation”.
The complete name of the book though translates as: “A Formula
Language, Modeled on that of Arithmetic, and Pure Thought.”
Though we all assume that mathematics is logic, Gottlob Frege
wanted to prove that mathematics grows out of logic.
I wish to delve on Gottlob Frege deeper as he is critical to our
story on Kurt Gödel.
Just to clarify things, all these stories on the history of
mathematical notations is essentially a build up to the climax of Kurt Gödel
and his incompleteness theorem.
These theorems of Gödel are so sophisticated and so intellectually
taxing that without laying the background for it, it will sound complete gibberish
to an average ape.
Even if you are a doctor.
Or maybe, especially if are a doctor since in general people
confuse mastery of a single specific subject to be equivalent of having great
general knowledge.
That often becomes a hindrance in learning anything unaccustomed
or unfamiliar.
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.
Advertisements
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:
No comments:
Post a Comment