August
02, 2017 Wednesday
Bedtime
Story
Wittgenstein on Properties of Atomic Sentences
As
I said last night, an atomic sentence only makes a proposition without invoking
logic.
Only
the truth or the falsity matters which is not the scope of logic but is the
realm of science through the judicious use of empirical evidence.
This
has an interesting bearing on the theory of truth and philosophical logic and
it is considered by some of the greatest minds that atomic sentences are
directly linked to atomic facts.
In
my view, atomic sentences are atomic facts that will not contain in them either
variables or conjunctions.
Wittgenstein
in his Tractatus Logico-Philosophicus (1921) refers to these atomic facts as
elementary propositions.
(4.21
The simplest kind of proposition, an elementary proposition, asserts the
existence of a state of affairs.)
Bertrand
Russell referred to them as atomic proposition in his introduction to the
Tractatus.
(A
proposition (true or false) asserting an atomic fact is called an atomic
proposition).
Wittgenstein
thought deeply about this subject of truth and then described the following
properties of atomic statements:
[1]
If there are any atomic statements, then there have to be corresponding atomic
facts.
[2]
No atomic sentence can be deduced from any other atomic sentence.
[3]
No two atomic sentences are incompatible.
[4]
No sets of atomic sentences are self-contradictory.
[5]
Conjunction of all true atomic sentences would say all that was the case, in
other words, “the world”.
It
is from the fifth property of the atomic statement that Wittgenstein derived
these immortal words, “The world is all that is the case.”
If
you happen to search on the internet for Wittgenstein, there is an extremely
high probability that the search engine will generate these words out which are
very enigmatic unless you take pain to study in the context that it was written
originally.
Taking
this to the next level, Wittgenstein had written that the set of all sets of
atomic sentences corresponds to the sets of all possible worlds and in his
words “all that could be the case”.
This
is all that I have to say about Tarski’s 1933 Polish paper - The Concept of
Truth in Formalized Language.
Next
we shall move to Tarski’s undefinability theorem that was published just five
years following the publication of Gödel’s incompleteness theorems in 1931.
I
shall take this new topic 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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