March 25, 2017 Saturday
Bedtime Story
Material Conditional and Negation
Material conditional is a logical connective or a binary operator
that is symbolized either by arrow →
So if I write:
P →
If P then Q.
The P is called the antecedent of the conditional.
Q is called the consequent of the conditional.
In simple language, it is equal to the word “implies”.
This material conditional is critical in logic as it helps in
establishing the truthfulness of a statement.
In an ordinary language, it would look like this:
If there is an infection, there will be fever.
If there is fire, there will be smoke.
The next thing that Gottlob Frege developed in his Begriffsschrift
was the idea of negation.
Negation is also otherwise known as logical complement.
Negation is an operation that converts a proposition say p into
“not p” that is written as ¬
It is also another way of saying that a proposition is true when p
is false.
Thus it can be applied as an operation of truth value.
It is also a single-argument or a unary logical connective.
Take for example this statement.
If a person is not dead, then we cannot call it a murder.
The negativity of a fact has a logical implication.
I shall not go into the depth of this remarkable book on
mathematical logic but it is clear that Gottlob was fully aware how monumental
his work was.
He was not shy in stating it and quiet proudly he complements
himself in his own preface.
In the preface of Begriffsschrift, he writes:
“If the task of philosophy is to break the domination of words
over the human mind […], then my concept notation, being developed for these
purposes, can be a useful instrument for philosophers […]
I believe the cause of logic has been advanced already by the
invention of this concept notation.”
Yet, this monumental work of piercing intellect went largely
ignored.
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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