Nederlog

May 10, 2013
me+ME:  Two fundamental theorems + the world's funniest jokes
Sections
Introduction
1. Two fundamental theorems
2. The world's funniest jokes

Introduction:

Well.. I am still paying back my walk of over two weeks ago, and so I am still not feeling very well, and also I did not sleep enough last night, so I am going to use a logical note.

And in order not to loose most of my readers, I throw in the world's funniest jokes.

1. Two fundamental theorems

The following I never saw in print, though it
is - I think - quite neat.

The following uses HOL - Higher Order Logic - but that is quite natural. In fact I assume very little:

1. The distinction between predicates and subjects: Only subjects are identified as names, and predicates then defined as anything that when added to zero or more names makes a statement. I will distinguish them as lower and upper case, respectively.
2. Ordinary bi-valent logic: This has rules for &, V, ~, and = which are precise forms of and, or, not and equals. Such rules may be as follows, with
x and y and z as variables, as are p and q, and a is a constant. The appended ' means that the predicate it is appended to is a specific predicate:
p&q |- p           p |- pVq                ~~p |- p      x=y, F'x |- F'y
p&q |- q           q |- pVq
p,q  |- p&q      pVq, ~pVq |- q
This suffices for propositional and predicate logic.
3. Quantifiers for predicates and for subjects:
(Ex)F'x -||- F'a  with a new             (x)F'x =def ~(Ex)~F'x
(EF)Fa  -||- G'a  with G'a
(F)Fa =def ~(EF)~Fa
This suffices for higher order and first order logic. And "a new" says that a must be new to the proof, while "(Ex)" is "for some x" and "(x)" is "for all x". And "=def" is "is by definition the same as".
4. The principle of abstraction: |x:F'x = the x such that x is F' and
a e |x:F'x -||- F'a
This also introduces "e" for "is a": a is a x such that x is F' if and only if a is F'.

One may use much more time to state the above, but the above is adequate, and it permits the following two fundamental theorems:

T1. ~(F)(Ez)(z=|x:Fx)
Proof:
1.
(F)(Ez)(z=|x:Fx)                 Assumption of indirect proof
2.
(Ez)(z=|x:~(xex))           Fx IFF ~(xex)
3.          (a=|x:~(xex))           E-elimination
4.          aea IFF ~(aea)          a for x

If one objects against introducing a logical particle, one can start with
1. (F)(Ez)(z=|x:~Fx)
Otherwise, the proof is the same.

T2.  (z)(EF)(z=|x:Fx)
Proof:
1. ~
(z)(EF)(z=|x:Fx)               Assumption of indirect proof
2.   (Ez)(F)(~(z=|x:Fx))           Quantifier-laws
3.         (F)(~(a=|x:Fx))           E-elimination
4.               (~(a=|x:xea))         Fx IFF xea
5.
(~(aea IFF aea))      a for x
6.

This is quite neat. The first in effect says there is no Russell-set (defined as a set z such that ( z = |x: ~(xex) ), and the second in effect says that every subject does have some defining property.

Maybe I should write these out, using "the Russell-set" for "the set of things that are not elements of themselves", and use "set" for "subject":

T1. Some properties do not define a (consistent) set.
For suppose all do. Then the one used for the Russell-set must define a set. But then it is an element of itself if and only if it is not an element of itself, which is a contradiction.

T2. Every
(consistent) set has a defining property.
For suppose not. Then there is a (consistent) set that is not defined by any property, and so the property of not being an element of that set cannot define it either. But then the set is an element of itself iff it is not an element of itself, which is a contradiction.

Note that the two theorems are just the same, except for having subjects and predicates interchanged.

2. The world's funniest jokes

There are people who do not like logic. Actually, there are far more people who do not like logic than who do like it. (See: Stupidity.)

In any case... for those who do not like logic, and also for those who do, here is the world's funniest joke:

Two hunters are out in the woods when one of them collapses. He doesn't seem to be breathing and his eyes are glazed. The other guy whips out his phone and calls the emergency services. He gasps, "My friend is dead! What can I do?" The operator says "Calm down. I can help. First, let's make sure he's dead." There is a silence, then a gun shot is heard. Back on the phone, the guy says "OK, now what?"
If you don't like it that much, you might consider that it is originally by Spike MIlligan, who was voted to be "the funniest persion the last 1000 years", though he also was a - real - manic depressive.

No, none of the previous paragraph was a joke. Here is a runner up in the same contest that landed the above one Number One:
A woman gets on a bus with her baby. The bus driver says: "That's the ugliest baby that I've ever seen. Ugh!" The woman goes to the rear of the bus and sits down, fuming. She says to a man next to her: "The driver just insulted me!" The man says: "You go right up there and tell him off – go ahead, I'll hold your monkey for you."
Still not a laugh on your face? One more time:

"Why is Australian beer like making love in a canoe?"
"Because it is fucking close to water, mate!"

I know that one from Monty Python, and dealt with it in my discussion of humour (in Dutch). I think it is the best on this page.

If you still haven't smiled, I give up. And the same if I did.

--------------------------------

About ME/CFS (that I prefer to call M.E.: The "/CFS" is added to facilitate search machines) which is a disease I have since 1.1.1979:
 1 Anthony Komaroff 2 Malcolm Hooper THE MENTAL HEALTH MOVEMENT:   PERSECUTION OF PATIENTS? 3 Hillary Johnson The Why  (currently not available) 4 Consensus (many M.D.s) Canadian Consensus Government Report on ME (pdf - version 2003) 5 Consensus (many M.D.s) Canadian Consensus Government Report on ME (pdf - version 2011) 6 Eleanor Stein 7 William Clifford The Ethics of Belief 8 Malcolm Hooper Magical Medicine (pdf) 9 Maarten Maartensz Resources about ME/CFS (more resources, by many)

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