the example abt fermats last theorem is a nice one...

2006-10-11T01:41:00.000+05:30

the example abt fermats last theorem is a nice one , smart but doesnt prove your point , its simply confusing, an analogy that fails. the error is this-
1. a statement is unchanging, static. existence is not. so while it doesnt make a diff discussing a statements truth 200 yrs after it is stated, existence isnt like that. a thing may exist at some point, and it may (not exist)* at a later time. clearly bcoz statements are static, their properties like truth are also static. the appropriate answer to the question of truth of the theorem is "the theorem is either true or not true, and if determined at any instant that it is true/false, then we may infer that it has always been true/false."
no such corresponding statement for existence-existence at one instant cannot be extrapolated to mean existence at every instant.
thus to extend the analogy is wrong.

Secondly,
and this is quite a separate thought,

"Eddy on the other hand would say it had equal probability of being proved true or false before 1994"
wat do you mean by equal probability? a defn-
on performing the experiment infinite times,50% of the times one thing (out of two)happens.

clearly an experiment must be amenable to be performed infinite times. by now u shouldve realized that saying "equal probability of being PROVED true or false" is ridiculous. a proof occurs once and is conclusive- no question of probability.

if you feel i am masking everything in fancy jargon , consider this example-
deck of cards contains 20 cards-15 red 5 black. u are just told there are 20 cards of two types-black,red. u might say there is 50% prob. of picking red/black.but u wud be wrong, there is only 25%prob of picking black(by defn above).

"all other things being equal, there is a 50% of this event occuring " is a sensible statement.
"all other things being equal" is imortant.critical infact.if all other things are not equal,there is no sense in taking abt % probability.
that is, if the rules of the game are not clearly defined, then we cant talk abt probability
the thing to say would be
"we have insufficient info to make any inference as to the outcome of this event"

if you ask me if a chair that i perceived 2 minutes back exists, i would say,
"we have insufficient info to make any statement as to the existence of the chair"
nothing abt 50% probability or any other %prob.

i may be wrong abt some parts of the 2nd argument, but i am pretty convinced abt the general point of the argument.
tell me wat u think.

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the example abt fermats last theorem is a nice one...