October 14, 2017 Saturday
Bedtime Story
Comparing Simple, Reflexive and Reciprocal Pronouns in One Idea
Just to show you how reciprocal pronoun
differs from reflexive pronouns and simple pronouns, let us put them side to
side and that should enlighten us.
First we shall consider a simple pronoun.
Lisa and Mary saw her.
Here “– her” is a simple pronoun and a free
variable since it refers to no antecedent in particular.
The implication that can be derived from
such a statement is that Lisa saw some lady and Mary saw some lady.
The logical form of this statement can be
put as R(x, y).
Now let us consider reflexive pronoun using
that same sentence.
Lisa and Mary saw themselves in the mirror.
In this case the meaning that we can derive
is that Lisa saw herself in the mirror and Mary saw herself in the mirror.
The logical form of this statement can be
put as R(x, x).
Here the letter R signifies the act of
seeing and the variables x and y signify the two ladies.
Now finally we shall consider the same
scenario using a reciprocal pronoun.
Lisa and Mary saw each other in the mirror.
In this case, the reciprocal pronoun is
linked to both the subjects.
That makes a big difference as the meaning
that now is being conveyed to us is that Lisa saw Mary in the mirror and Mary
saw Lisa in the mirror.
The logical form of this statement can be
put as R(x, y) and R(y, x).
Thus to summarize, first we saw the concept
of free and bound variables in mathematics, later in mathematical logic and
lastly in English language.
Now that we have some basic understanding
of the terms free and bound variables, we are now better equipped to understand
the work of Moses Schönfinkel in combinatory logic.
Combinatory logic uses notation that takes
off the need to use quantified variables in mathematical logic.
Quantifiers as you will understand are a
necessity even in a natural language besides a formal language.
Quantifiers found in natural languages
include words such as few, a lot, for all, for some etc.
In formal languages, two universal quantifiers
are “for all” ∀
Combinatory logic uses combinators.
So what is a combinator?
A combinator is a higher-order function
that uses only function application and earlier defined combinators to define a
result from its arguments.
I know that last statement will not go well
with you but I hope to clarify it in the nights to come.
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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