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Carleas wrote:James, I agree with that; I made that same point earlier. But that applies to scientific inductions, i.e. taking a series of data points and extrapolating a general theory that fits them. It doesn't apply to deductive methods, including mathematical induction (so it doesn't apply to the reasoning used in the Blue Eye problem or the MI portion of the Master Logician problem).
Arminius wrote:The Italian Book.
Last week I bought a book in Italy. The cashier got hundred Euros and gave me twice as much and five cents more back than my entitlement was. Obviously the cashier had confused the amount in euros with the amount in cents.
How expensive was the book?
James S Saint wrote:Another effort to clarify/verify something on that puzzle:
James S Saint wrote:You have to prove that yours is the ONLY one, else yours might not be the one that the master is using. The video was expressing that just because something fits within given certain limited knowledge, doesn't mean that it is the true answer. The puzzle requires that you prove your theory to be the only option.
Carleas wrote:James S Saint wrote:You have to prove that yours is the ONLY one, else yours might not be the one that the master is using. The video was expressing that just because something fits within given certain limited knowledge, doesn't mean that it is the true answer. The puzzle requires that you prove your theory to be the only option.
We've had this portion of the conversation before. The last time you made this point, I brought up the example of the Pythagorean Theorem, which has many proofs, none of which depend on or are threatened by the existence of any other.
James S Saint wrote:We know that the deduction [in the case of the Pythagorean Theorem] works.
Carleas wrote:James S Saint wrote:We know that the deduction [in the case of the Pythagorean Theorem] works.
Here's my point, James. If the deduction works, then we don't need to prove that everyone's using it. That's how deductions work.
Arminius wrote:
You used 100 twice and you should only use it once. Which one you use (/100 or 100*) depends on if the answer is in euros or cents.x = e/100 + 100c
James S Saint wrote:
Arminius wrote:Those equations you mentioned work, but note: they are merely abstract examples and not the solution for my concrete example. I hope you know that.
James S Saint wrote:You have at least two people who have to be "in sync" with the bells. If they are not using the same theory (making a different enabling assumption), they will possibly not be in sync.
The issue, as from the beginning, is that the premise assumption must be the same for everyone[...]
phyllo wrote:You used 100 twice and you should only use it once. Which one you use (/100 or 100*) depends on if the answer is in euros or cents.x = e/100 + 100c
Carleas wrote:James S Saint wrote:You have at least two people who have to be "in sync" with the bells. If they are not using the same theory (making a different enabling assumption), they will possibly not be in sync.
The issue, as from the beginning, is that the premise assumption must be the same for everyone[...]
This objection is overcome by the stipulations about how good a logician the participants are. To turn again the 2 Blue Eye problem as the simplest case of the logic, if there are 2 blues on the island, it seems clear that two perfect logicians, for whom it is common knowledge that they are perfect logicians, will know their eye color on the second day. There is no reliance on a everyone being "in sync" or using the same "theory", there's is pure deductive logic about what the islanders know and how they must behave and how they must deduce from their knowledge and behavior.
Carleas wrote:Returning to the case of the Master Logician, I take the same level of logical perfection to be a given, as the Master will enforce accurate deduction on the other logicians.
Carleas wrote: It's not whim or fancy that he's enforcing, but what the logicians must deduce based on what they know and how they must behave and how they must deduce from their knowledge and behavior (or have such deduction forced on them by the master). The effect is the same.
Is that what you're taking issue with here? I admit the premise is implicit; a more-clear statement of the problem would be explicit in the way the Blue Eyes problem is.
Please don't say no when you don't know.James S Saint wrote:phyllo wrote:You used 100 twice and you should only use it once. Which one you use (/100 or 100*) depends on if the answer is in euros or cents.x = e/100 + 100c
No.. "e" is merely a number of objects received and so is "c", although different objects.
The statement was that those two numbers got reversed: the e number was supposed to be the c number and vsvrsa.
But when translating those numbers into money values, the e number was supposed to be the number of cents, thus
e/100 = amount of cents (proper)
And also the c number was supposed to be the number of euros, thus
c*100 = amount of euros (proper)
So "e/100 + c*100" should be the amount of proper returned change ("entitlement").
But if that was true, it would mean that the received NUMBER of objects, "e + c" had to be 2.55102040816327, which is obviously not possible.
Thus there is a miscommunication going on, as I said in the beginning.
phyllo wrote:Please don't say no when you don't know.
phyllo wrote:If you have amount represented as e.c ...
then the amount in cent is equal to 100e+c
and the amount in euros is equal to e+c/100
James S Saint wrote:But even if it did, the puzzle would be unsolvable (or at least by you).
James S Saint wrote:You didn't solve the Blued problem either, so referring it doesn't get you anywhere.
Carleas wrote:James S Saint wrote:But even if it did, the puzzle would be unsolvable (or at least by you).
That seems like a big proviso. Unsolvable-in-theory is a relatively tiny subset of unsolvable-by-me-in-practiceJames S Saint wrote:You didn't solve the Blued problem either, so referring it doesn't get you anywhere.
Happy to keep that conversation going, if you would deign to respond to my syllogisms. Note, off the bat, that they are pure deductive syllogisms relying on the islander's common knowledge and required behavior, and not on any islander being "in sync" with any other. Like with the Pythagorean theorem, the deduction itself is the proof that no other solution is possible.
James S Saint wrote:It is a very common mental ailment of the day, especially of attorneys who intentionally try to bias themselves toward their client
He gave you a bum steer. All his equations are wrong.James S Saint wrote:phyllo wrote:Please don't say no when you don't know.
I DO know. I am the one who defined it.phyllo wrote:If you have amount represented as e.c ...
then the amount in cent is equal to 100e+c
and the amount in euros is equal to e+c/100
That I know too. But that is not what I had asked Arminius.
To which he answered:
"if the proper entitlement is x, e is the received euros, and c is the received cents, then 2x + 5 = e + c" and
"if the received euros and received cents were confused, then the proper entitlement is, x = e/100 + c*100"
Carleas wrote:James S Saint wrote:It is a very common mental ailment of the day, especially of attorneys who intentionally try to bias themselves toward their client
Yeah, and of mathematicians and Nobel prize-winning economists and authors of encyclopedias on philosophy, who apparently also foolishly believe that deducing a proposition X is the same thing as deducing a proposition ~(~X). How wacky!
Carleas wrote:I do care, James. Deeply. I care because failures of reason irk me.
Carleas wrote:Society works best when people are rational, and rationality works best when people are honest with themselves.
Carleas wrote:And, be honest, you've never pointed to a specific part of the deductive proof of the solution to the Blue Eye problem.
Carleas wrote: You've never grappled with the mathematical induction being used.
phyllo wrote: He gave you a bum steer. All his equations are wrong.
Then why do you keep using those equations???phyllo wrote: He gave you a bum steer. All his equations are wrong.
Yeah, that is all that I was trying to say.
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