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        riddles >> general problem-solving / chatting / whatever >> Dealing with Induction (Game)
        
(Message started by: BenVitale on Feb 7^th, 2010, 6:48pm)

Title: Dealing with Induction (Game)
Post by BenVitale on Feb 7^th, 2010, 6:48pm

Dealing with Induction

http://www.philosophersnet.com/games/dealing_with_induction/dws1.php

Quote:

Given that the world is more or less uniform - the laws of physics hold at all times - how easy is it to draw a wrong conclusion about the future from the evidence of the past? Let's play a game to find out.

The game is very simple. We're going to show you a sequence of cards. There is a simple rule that governs whether cards belong to the sequence. For example, imagine the game is played with faces of coins rather than cards. The rule might be "coppers only", "heads only" or "only coins worth over 5p". It could be more complex: "Only heads of coppers or tails of silver".

You need to guess whether the card you see on screen is permitted in the sequence. To do this you will, of course, have to think inductively: you'll need to look at the evidence of the past (the cards already showing) to see what regularity they exhibit. Having worked out what this regularity is, you'll be able to calculate whether the next card fits the sequence. Easy, eh? Let's start!

Find the pattern

Title: Re: Dealing with Induction (Game)
Post by ThudanBlunder on Feb 23^rd, 2010, 1:58pm

You are offered the chance to purchase, for whatever price you wish, a bottle containing a genie who will fulfill your every desire. The only snag is that the bottle must thereafter be resold for a price smaller than what you paid for it, or you will be condemned to live out the rest of your days in excruciating torment. Obviously, no one would buy the bottle for 1¢ since (s)he would have to give the bottle away. And no one would accept the bottle knowing (s)he would be unable to get rid of it. Similarly, no one would buy it for 2¢, and so on. However, for some reasonably large amount it will always be possible to find a next buyer.

Title: Re: Dealing with Induction (Game)
Post by rmsgrey on Feb 24^th, 2010, 5:40am

A man with only one or two hairs on his head is, I think everyone will agree, bald.

Adding one hair to the head of a bald man doesn't stop him being bald (otherwise you could reverse the process and have a non-bald man who becomes bald by plucking a single hair...).

From these two premises, it follows that all men are bald.

Title: Re: Dealing with Induction (Game)
Post by Grimbal on Feb 24^th, 2010, 7:50am

on 02/23/10 at 13:58:12, ThudanBlunder wrote:

You are offered the chance to purchase, for whatever price you wish, a bottle containing a genie who will fulfill your every desire.

Like, for instance, a period of deflation? So bad that a single cent is too large an amount for small purchases and the government has to introduce subdivisions of the cent?