July
29, 2017 Saturday
Bedtime
Story
When Philosophy Got Mathematized
So
let’s read what Bertrand Russell had to say of analytical philosophy.
“Modern
analytical empiricism differs from that of Locke, Berkeley and Hume by its
incorporation of mathematics and its development of a powerful logical
technique.
It
is thus able, in regard to certain problems, to achieve definite answers, which
have the quality of science rather than philosophy.
It
has the advantage, in comparison with the philosophies of the system-builders,
of being able to tackle its problems one at a time, instead of having to invent
at one stroke a block theory of the whole universe.
Its
methods, in this respect, resemble those of science.”
Tarski’s
1933 landmark paper was essentially an attempt to resolve the Liar Paradox,
though in this endeavor he made great many metamathematical discoveries.
The
paper is long and I shall not go very deep into it.
I
shall squeeze it into a short bedtime story by extracting the general essence
of it.
As
discussed earlier in the Liar Paradox, Tarski considered it vital that a
language needs to be distinguished and separated into two parts, the object
language and the metalanguage.
Metalanguage
just like metamathematics is when language or its symbols is being used to
discuss language itself.
In
this case the language that is spoken about or examined becomes the object
language.
These
two are separated from each other by the use of either quotation marks or
putting the object language in italics or separating them apart in different
lines.
A
very simple example of metalanguage that is known as embedded metalanguage is
found in our ordinary or natural languages.
The
words such as verb, noun, adjective that describe features of their language
are in fact metalanguage.
Tarski
encouraged that whenever a sentence spoke about the other sentence say P, the
sentence P should be rendered in quotes.
With
this Tarski had introduced a condition that came to be known as Convention T (I
fancy that letter T stands for Tarski).
Any
viable truth for every sentence “P” must have the following form:
“P”
is true if, and only if, P.
In
the field of logic, if and only if (often abbreviated to iff), is a
biconditional logical connective between statements.
An
example of this would be,
“Rose
is red” is true if, and only if, rose is red.
Such
kind of statements are called ‘T-sentences’.
The
part then within the quotation marks is the object language and the rest that
follows it is the meta-language.
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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