Jump to content
BrainDen.com - Brain Teasers
  • 0

Universal Truth Machine


BMAD
 Share

Question

Someone claims to have invented a Universal Truth Machine (UTM), a machine that takes a proposition as input, and returns "true", "false", or "undecidable" as output. Example:

 

Input                                   Output

1+3 = 4                               true

1+2= 4                                false

this proposition is false      undecidable

  

Devise a true proposition that the UTM will claim to be false, thereby disproving the inventor's claim.

Link to comment
Share on other sites

18 answers to this question

Recommended Posts

  • 0

I am baffled.

 

If any statement like that existed, why couldn't the UTM output "true" or "undecidable" instead? The "false" output is already wrong. The other two outputs can't be any more wrong, can they? They're just as good as the "false" answer.

 

On the other hand, I can easily think of an answer that fits bonanova's criteria: "The reader of this proposition is human."

Link to comment
Share on other sites

  • 0

How about slightly modifying bonanova's criteria.

 

"If the statement were posed to the UTM, the UTM would answer False. If any rational third answerer (who you can call observer X if you like, and may be human, machine, or flying spaghetti monster) were told that the statement was being posed to the UTM, then observer X would say that the statement is True."

Link to comment
Share on other sites

  • 0

Suppose the machine outputs "true" to every input except "1+2= 4" and "this proposition is false". Then no true proposition will be reported as false. The only proposition which will be reported as false is "1+2= 4", which is false. So there must be some additional assumption you make about the machine in order for a solution to be reached.

Another way to look at it: consider the proposition you had in mind for the answer. Why would the machine be incapable of answering "true" or "undecidable" to this proposition?

Link to comment
Share on other sites

  • 0

"This statement is true and the Universal Truth Machine will report it as false."

The UTM would have to declare it as false. It certainly couldn't call it true. And because calling it false would not pose a paradox that I can see (because it's an AND statement it would be ok to call it false if the left-hand side is false), I don't think the UTM would be forced to call it unanswerable.

 

However there's no reason a third party couldn't call the statement true.

 

But this is sort of dangerously skirting on the issue of whether a self-referential statement can be considered to be true or false simply on the grounds that such an answer would be logically consistent. By such logic, the statement "This statement is true" might then be called either true or false as you see fit. A third party could call it true, but I guess they wouldn't be forced to do so.

Edited by plasmid
  • Upvote 1
Link to comment
Share on other sites

  • 0

How about slightly modifying bonanova's criteria.

 

"If the statement were posed to the UTM, the UTM would answer False. If any rational third answerer (who you can call observer X if you like, and may be human, machine, or flying spaghetti monster) were told that the statement was being posed to the UTM, then observer X would say that the statement is True."

 

 

Yes.

 

Are you saying plasmid's post is the correct answer?

Link to comment
Share on other sites

  • 0

 

How about slightly modifying bonanova's criteria.

 

"If the statement were posed to the UTM, the UTM would answer False. If any rational third answerer (who you can call observer X if you like, and may be human, machine, or flying spaghetti monster) were told that the statement was being posed to the UTM, then observer X would say that the statement is True."

 

 

Yes.

 

Are you saying plasmid's post is the correct answer?

 

I am saying his rephrasing of what you attempted to clarify is an appropriate rephrasing.

Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Answer this question...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...
 Share

  • Recently Browsing   0 members

    • No registered users viewing this page.
×
×
  • Create New...