### Oxymorons

"Pascal was a Mathematician long before he became a

programming language" -- Skiena and Revilla in the

book Programming Challenges.

Humour is defined as a correction in a line of reasoning,

a twist of words, a pun, a double entendre. A person without

humour is a dull indeed, and medically speaking without life

(no pun intended). Laughter denotes a flexible mind.

Analyse following sentences:

A professor once wrote a theorem on the board

and said, "The proof is trivial for large N, say 3",

he then stared at the board for half an hour

and finally said "I was right, it is trivial".

So the student asked, "Is the proof trivial or not?"

The professor replied "Yes".

It has to be a Math or CS professor,

probably a knot theorist. Which other

discipline has a concept of a proof?

EE doesn't even have the concept of correctness.

Logic of Knowledge and Time

Monk 1: "How happy are the butterflies in the meadow!"

Monk 2: "You don't know the butterflies are happy,

you think they are happy."

Monk 1: "How can you know what I don't know?"

Monk 2: "I believe in the principle of common knowlege."

A this point Monk 1 hits Monk 2 with his staff.

A host of questions come to mind:

Let us write B(X) if you believe in X,

and K(X) if you know X,

now are the following true:

Note that I haven't defined what is true and what is possible.

Which brings us to the epistemology and logic of beliefs.

Get some of Raymond Smullyan's popular books:

can get them from Amazon or bookfinder.com

After reading Smullyan, you will believe you believe in logic of beliefs.

Smullyan opens can after can of worms, raising more questions:

world model in which the statement will be true or false.

The first person to define the concept of

truth on a firm ground was Alfred Tarski in 1940s.

You can look up Alfred Tarski's monograph "Truth and Proof".

Enderton's "Mathematical Logic" is an

Undergraduate introduction to logic.

Barwise's "Handbook of Mathematical Logic"

is a Graduate level survey.

Modal Logics

You can model beliefs, knowledge, time and proofs in modal logic.

Modal qualifies logical statements with modalities and quantifiers:

"Sometimes it rains". Here Sometimes is a modality on the statement.

"Whenever it rains, the ground is wet" Here whenever is the

universal quantifier over time.

Boolos (The Logic of Provability),

Chellas, and Hughes and Cresswell are

some of the good books on Modal logics.

I still haven't covered Byzantine general's problem

of common knowledge and free will,

and what is "free will"? I am not talking Kant or Russell.

Real life quotes you don't want to hear:

Support engineer: "Our tool works great,

except for the crazy customers who keep crashing it."

Hiring manager asking about an employee referral: "If he

is really good, why does he want to work here?"

Problem: "tool xyz consistently crashes on my computer."

Suggestions "Reboot windows, if that doesn't work

reinstall windows."

programming language" -- Skiena and Revilla in the

book Programming Challenges.

Humour is defined as a correction in a line of reasoning,

a twist of words, a pun, a double entendre. A person without

humour is a dull indeed, and medically speaking without life

(no pun intended). Laughter denotes a flexible mind.

Analyse following sentences:

- Haven't I told you a million times not to exaggerate! -- Hally.
- "No truth is ever a lie" - Barbara Streisand.
- It is true that X is true -- Heard in IITB.
- He caught a cold and a bus -- Wren and Martin.

A professor once wrote a theorem on the board

and said, "The proof is trivial for large N, say 3",

he then stared at the board for half an hour

and finally said "I was right, it is trivial".

So the student asked, "Is the proof trivial or not?"

The professor replied "Yes".

It has to be a Math or CS professor,

probably a knot theorist. Which other

discipline has a concept of a proof?

EE doesn't even have the concept of correctness.

Logic of Knowledge and Time

Monk 1: "How happy are the butterflies in the meadow!"

Monk 2: "You don't know the butterflies are happy,

you think they are happy."

Monk 1: "How can you know what I don't know?"

Monk 2: "I believe in the principle of common knowlege."

A this point Monk 1 hits Monk 2 with his staff.

A host of questions come to mind:

- Is belief different from knowledge?
- Do you believe in what you know?
- Do you know what you believe in?

Let us write B(X) if you believe in X,

and K(X) if you know X,

now are the following true:

- X -> B(X)
- B(X) -> X
- K(X) -> B(X)
- B(X) -> BB(X)

- B(X) & B(~(B(X))

Note that I haven't defined what is true and what is possible.

Which brings us to the epistemology and logic of beliefs.

Get some of Raymond Smullyan's popular books:

- Forever Undecided,
- What is the name of this book?
- To Mock a Mockingbird,
- Lady or the Tiger

can get them from Amazon or bookfinder.com

After reading Smullyan, you will believe you believe in logic of beliefs.

Smullyan opens can after can of worms, raising more questions:

- What is truth?
- What is a proof?

world model in which the statement will be true or false.

The first person to define the concept of

truth on a firm ground was Alfred Tarski in 1940s.

You can look up Alfred Tarski's monograph "Truth and Proof".

Enderton's "Mathematical Logic" is an

Undergraduate introduction to logic.

Barwise's "Handbook of Mathematical Logic"

is a Graduate level survey.

Modal Logics

You can model beliefs, knowledge, time and proofs in modal logic.

Modal qualifies logical statements with modalities and quantifiers:

"Sometimes it rains". Here Sometimes is a modality on the statement.

"Whenever it rains, the ground is wet" Here whenever is the

universal quantifier over time.

Boolos (The Logic of Provability),

Chellas, and Hughes and Cresswell are

some of the good books on Modal logics.

I still haven't covered Byzantine general's problem

of common knowledge and free will,

and what is "free will"? I am not talking Kant or Russell.

Real life quotes you don't want to hear:

Support engineer: "Our tool works great,

except for the crazy customers who keep crashing it."

Hiring manager asking about an employee referral: "If he

is really good, why does he want to work here?"

Problem: "tool xyz consistently crashes on my computer."

Suggestions "Reboot windows, if that doesn't work

reinstall windows."