July
18, 2017 Tuesday
Bedtime
Story
The Three Fundamental Laws of Thought
Since
we are discussing logic and we have come as far as the principle of bivalence,
it would be a crime not to introduce the laws of thought.
What
are these laws of thought?
I
think these laws form the fundamental basis of everything that I have come to cherish
in my useless existence: science, mathematics, reason, rationality and
understanding how things happen.
The
laws of thought are the fundamental axiomatic rules on which rational discourse
is based.
It
cannot get more basic or fundamental than this.
Whatever
that I have come to despise, namely religion, spirituality and other forms of
mumbo jumbo that have always ruled the planet, defy these axiomatic rules.
The
laws of thought are three.
[1]
The Law of Identity
‘Whatever
is, is.’
[2]
The Law of Non-Contradiction
‘Nothing
can both be and not be.’
[3]
The Law of Excluded Middle
‘Everything
must either be or not be.’
If
you care to notice, the second and third law seems very alike.
The
difference between the law of non-contradiction and law of excluded middle is
very subtle and becomes visible when they are stated in more formal logic.
The
difference will become more visible if you study the Hindu Chatușkoți wherein
following four possibilities for a proposition P has been described:
[1]
P; which means, being
[2]
Not P; which means. not being
[3]
P and not P; which means, being and not being
[4]
Not (p or not P); which means, neither being nor not being
Aristotle
notion of truth does not allow for the last two possibilities.
P
and not P violates the law of non-contradiction which states that there exists
no P such that P is both true and false.
Not
(p or not P) violates the law of excluded middle which says there exists no P
such that P is neither true nor false but some third state.
Almost
all the logicians since the time of Plato, including the Indian logicians
(Śrauta sutras, the grammar of Pānini, Brahma sūtras of Vyasa) followed by John
Locke, Gottfried Leibniz, Schopenhauer, George Boole, William Hamilton (1788 –
1856), Bertrand Russell, Kurt Gödel and Alfred Tarski have either alluded to
these or contributed to them.
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