Tony Hollick forwarded us an argument by Chris Tame, casting
doubt about the existence of Santa Claus (See below).
This is hard to swallow especially before Christmas.
I hardly resist the pleasure of giving you a straight proof of the
existence of Santa Claus.
Consider the following sentence S
If this sentence is true then Santa Claus exists.
If S is true then Santa Claus exists.
S being that very sentence.
I will first prove that S is true.
To prove it, let us suppose that S is true. But then S is true and
"If S is true then Santa Claus exists" is true. But then
by the usual modus ponens it follows than Santa Claus exists.
So I have proved that from assuming S true it follows that Santa
Claus exists. But this is exactly what S says so I have given
a proof of S.
Now, we know that S is true. But S says exactly that if S is true
then Santa Claus exists. So by applying modus ponens again, we can
conclude that Santa Claus exists. QED.
I hope this settles the matter once and for all ;-)
Comment: this is a version of the well known Curry Paradox which
plays a proeminent role in Lob proof of its generalisation of Godel's
theorem. It is a version of Epimenide paradox which does not use
negation. About both Epimenide or Curry paradox, most people
considers that the paradox comes from the self-referential nature
of the sentence. But since Godel we know that such self-reference
can be construct in the language of a consistent machine or mathematical
(sufficiently rich) theory. What cannot be done, and what really
prevents the paradox in the world of consistent machines, is the
fact that there is no translation of the word "true" (about the
machine) *in* the language of the machine (this is Tarski theorem).
If we use "provable", which *can* be translated in the machine
language, instead of true, well, from Epimenide we get Godel's
incompleteness, and from the proof of the existence of Santa Claus,
we get Lob's theorem. Lob's theorem asserts, among other things,
that sentence asserting their own provability are automatically
true and provable! Isn't it nice? Some positive thought seems
to work in computerland!
>----- Original Message -----
>From: "Dr Chris R. Tame" <[EMAIL PROTECTED]>
>Sent: Wednesday, December 18, 2002 12:58 AM
>Subject: Humour: Santa Claus Hypothesis Debunked
>> >Ok lets get serious for a moment here I've assembled a few relevant
>> >facts here to set the story straight about jolly old St Nick.
>> >There are approximately two billion children (persons under 10) in the
>> >However, since Santa does not visit children of Muslim, Hindu, Jewish or
>> >Buddhist (except maybe in Japan) religions, this reduces the workload
>> >for Christmas night to 15% of the total, or 378 million (according to
>> >the population reference bureau). At an average (census) rate of 3.5
>> >childrenper household, that comes to 108 million homes, presuming there
>> >is at least one good child in each. Santa has about 31 hours of
>> >Christmas to work with,thanks to the different time zones and the
>> >rotation of the earth, assuming east to west (which seems logical). This
>> >works out to 967.7 visits per second. This is to say that for each
>> >Christian household with a good child,Santa has around 1/1000th of a
>> >second to park the sleigh, hop out, jump down the chimney, fill the
>> >stocking, distribute the remaining presents under the tree, eat whatever
>> >snacks have been left for him and get back up the chimney
>> >into the sleigh and get onto the next house.
>> >Assuming that each of these 108 million stops is evenly distributed
>> >around the earth (which, of course, we know to be false, but will accept
>> >for the purposes of our calculations), we are now talking about 0.78
>> >miles per household; a total trip of 75.5 million miles, not counting
>> >bathroom stops or breaks. This means Santa's sleigh is moving at 650
>> >miles per second or 3,000 times the speed of sound. For purposes of
>> >comparison, the fastest man made vehicle, the Ulysses space probe, moves
>> >at a poky 27.4 miles persecond, and a conventional reindeer can run (at
>> >best) 15 miles per hour.
>> >The payload of the sleigh adds another interesting element. Assuming
>> >that each child gets nothing more than a medium sized LEGO set (two
>> >pounds), the sleigh is carrying over 500 thousand tons, not counting
>> >Santa himself. Onland, a conventional reindeer can pull no more than 300
>> >pounds. Even granting that the "flying" reindeer can pull 10 times the
>> >normal amount, thejob can't be done with eight or even nine of them -
>> >Santa would need 360,000of them. This increases the payload, not
>> >counting the weight of the sleigh,another 54,000 tons, or roughly seven
>> >times the weight of the Queen Elizabeth (the ship, not the monarch).
>> >A mass of nearly 600,000 tons traveling at 650 miles per second creates
>> >enormous air resistance this would heat up the reindeer in the same
>> >fashion as a spacecraft re-entering the earth's atmosphere. The lead
>> >pair of reindeer would adsorb 14.3 quintillion joules of energy per
>> >second each. In short, they would burst into flames almost
>> >instantaneously, exposing the reindeer behind them and creating
>> >deafening sonic booms in their wake. The entire reindeer team would be
>> >vaporized within 4.26 thousandths of a second,or right about the time
>> >Santa reached the fifth house on his trip.
>> >Not that it matters, however, since Santa, as a result of accelerating
>> >from a dead stop to 650 m.p.s. in .001 seconds, would be subjected to
>> >acceleration forces of 17,000 g's. A 250 pound Santa (which seems
>> >ludicrous considering all the high calorie snacks he must have consumed
>> >over the years) would be pinned to the back of the sleigh by 4,315,015
>> >pounds of force, instantly crushing his bones and organs and reducing
>> >him to aquivering blob of pink goo. Therefore, if Santa did exist, he's
>> >dead now.
>> >I dare you to argue otherwise.