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AskPhilosophers - Time Paradox

TheSkeptic
Posts: 1,362
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4/11/2010 2:19:36 AM
Posted: 6 years ago
"Kurt Gödel's incompleteness theorems represent one of the foremost achievements in mathematical logic's proud history. AskPhilosopher's very own panelist Peter Smith obviously is greatly intrigued by these theorems. Suppose out of jealously -- though I doubt he would succumb to such a vice! -- he decided to build a time machine. Imagine, moreover, that he went to a time before Gödel had proven the theorems and gave the great logician, say, the idea of Gödel numbering, the key to proving the incompleteness theorems. My question thus is as follows: Who would deserve credit for proving the incompleteness theorems? Gödel seems to have gotten the idea from Peter; Peter seems to have gotten the idea from Gödel. Is it possible that neither would deserve credit?"

http://www.askphilosophers.org...

I love this website, and this question was great. Anyone want a shot at it? I've been reading philosophy of time recently and this is a similar question (think back to the classical paradox of killing your own biological grandfather).
Puck
Posts: 6,457
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4/11/2010 2:27:14 AM
Posted: 6 years ago
Haha, Depends how you want to go about defining credit. Peter was reliant on Goedel for the inspiration to provide Goedel his own future information, including the formulation he himself presents to Goedel. In this sense Peter is simply a shortcut to Goedel arriving at the exact same idea. In short, Peter gets credit for being a messenger boy, Goedel gets credit for the message.
TheSkeptic
Posts: 1,362
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4/11/2010 3:10:58 AM
Posted: 6 years ago
At 4/11/2010 2:27:14 AM, Puck wrote:
Haha, Depends how you want to go about defining credit. Peter was reliant on Goedel for the inspiration to provide Goedel his own future information, including the formulation he himself presents to Goedel. In this sense Peter is simply a shortcut to Goedel arriving at the exact same idea. In short, Peter gets credit for being a messenger boy, Goedel gets credit for the message.

But couldn't the same be said about Goedel? Goedel formulated the theorem but the critical inspiration (i.e. Peter relayed information sufficient to formulate the theorem) is from Peter, so who get's credit for the message?
Puck
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4/11/2010 3:17:08 AM
Posted: 6 years ago
To be a loop still requires the initial set of circumstances before a loop is enacted. Goedel is the originator before Peter creates the loop where he becomes the originator - it's essentially an usurpation of the causality of the theorem. Goedel however was the original chain, Peter then creates a new one. Without Goedel's initial chain, Peter's would never occur.
TheSkeptic
Posts: 1,362
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4/11/2010 6:38:55 AM
Posted: 6 years ago
At 4/11/2010 3:17:08 AM, Puck wrote:
To be a loop still requires the initial set of circumstances before a loop is enacted. Goedel is the originator before Peter creates the loop where he becomes the originator - it's essentially an usurpation of the causality of the theorem. Goedel however was the original chain, Peter then creates a new one. Without Goedel's initial chain, Peter's would never occur.

How would you refer to Goedel being the originator, or there being an "initial" set of circumstances when Peter creates a time machine? If he does utilize a time, then any talk of an "initial" set of circumstances is misplaced.

The problem with thinking of loops, namely causal ones, is that if we implement the notion of time travel it gets weird how we can assign any temporal aspects to the parties involved, namely Goedel and Peter. Undoubtedly, complicating the temporal aspects will also generate problems of credit/responsibility/etc.
mattrodstrom
Posts: 12,028
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4/11/2010 7:41:08 AM
Posted: 6 years ago
The time machine guy didn't come up with the formula.

Who did? Was it Goedel? Or was the only way he ever got it, getting it from the time machine guy?

If Goedel ever actually did come up with it, instead of having it dropped in his lap, then he deserves credit.

Now knowing whether Goedel ever "really" came up with it would be tough, for maybe he always had it dropped in his lap from mr. time traveler. It would kind of seem that's the answer we'd have to assume, if you only have one "time"...

And if that is the case, then neither really deserve credit, and where did the formula come from!?!
"He who does not know how to put his will into things at least puts a meaning into them: that is, he believes there is a will in them already."

Metaphysics:
"The science.. which deals with the fundamental errors of mankind - but as if they were the fundamental truths."
Zetsubou
Posts: 4,933
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4/11/2010 9:13:48 AM
Posted: 6 years ago
I'm sorry, when was Godel the creator of any time related theories?

Godel -->
Incompleteness theorems, relation to time?
Continuum hypothesis
Personal Favorite -- Godel's ontological proof.
'sup DDO -- july 2013
mattrodstrom
Posts: 12,028
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4/11/2010 9:15:38 AM
Posted: 6 years ago
At 4/11/2010 9:13:48 AM, Zetsubou wrote:
I'm sorry, when was Godel the creator of any time related theories?

I don't think anybody said he was.
"He who does not know how to put his will into things at least puts a meaning into them: that is, he believes there is a will in them already."

Metaphysics:
"The science.. which deals with the fundamental errors of mankind - but as if they were the fundamental truths."
Zetsubou
Posts: 4,933
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4/11/2010 9:18:00 AM
Posted: 6 years ago
At 4/11/2010 9:15:38 AM, mattrodstrom wrote:
At 4/11/2010 9:13:48 AM, Zetsubou wrote:
I'm sorry, when was Godel the creator of any time related theories?

I don't think anybody said he was.

I noticed, misleading title. "AskPhilosophers - Time Paradox"
'sup DDO -- july 2013
Puck
Posts: 6,457
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4/11/2010 5:39:25 PM
Posted: 6 years ago
At 4/11/2010 6:38:55 AM, TheSkeptic wrote:
At 4/11/2010 3:17:08 AM, Puck wrote:
To be a loop still requires the initial set of circumstances before a loop is enacted. Goedel is the originator before Peter creates the loop where he becomes the originator - it's essentially an usurpation of the causality of the theorem. Goedel however was the original chain, Peter then creates a new one. Without Goedel's initial chain, Peter's would never occur.

How would you refer to Goedel being the originator, or there being an "initial" set of circumstances when Peter creates a time machine? If he does utilize a time, then any talk of an "initial" set of circumstances is misplaced.

The problem with thinking of loops, namely causal ones, is that if we implement the notion of time travel it gets weird how we can assign any temporal aspects to the parties involved, namely Goedel and Peter. Undoubtedly, complicating the temporal aspects will also generate problems of credit/responsibility/etc.

Complicating matters is the point of the exercise! Ok, try this. Without Peter existing, would we have Goedel's theorem? Without Goedel would we have Goedel's theorem? Without Goedel would we have Peter's handing over of Goedel's theorem?

Before Peter can enact his loop, Goedel must be an originating factor, without which no possible Peter scenario exists. If we are using imagery, Goedel is a straight line with Peter's loop at the end of it. The fact that Peter later, hands Goedel his own theorem as inspiration for his own theorem would only matter if somehow Goedel never created this theorem without Peter's aid - however the scenario isn't that. We are fine if Peter never lives, or acts. Not so for Goedel.
TheSkeptic
Posts: 1,362
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4/11/2010 6:51:42 PM
Posted: 6 years ago
Haha, I think a much more simple analogy is autoinfanticide - going back in time and killing yourself as a baby. These examples all basically fall under "grandfather paradoxes". Is this possible?

Many would say the Novikov self-consistency principle answers it, *shrug*
belle
Posts: 4,113
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4/11/2010 6:53:56 PM
Posted: 6 years ago
At 4/11/2010 6:51:42 PM, TheSkeptic wrote:
Haha, I think a much more simple analogy is autoinfanticide - going back in time and killing yourself as a baby. These examples all basically fall under "grandfather paradoxes". Is this possible?

Many would say the Novikov self-consistency principle answers it, *shrug*

lol thats not really an answer, its a dismissal.
evidently i only come to ddo to avoid doing homework...
TheSkeptic
Posts: 1,362
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4/11/2010 8:36:40 PM
Posted: 6 years ago
At 4/11/2010 6:53:56 PM, belle wrote:
At 4/11/2010 6:51:42 PM, TheSkeptic wrote:
Haha, I think a much more simple analogy is autoinfanticide - going back in time and killing yourself as a baby. These examples all basically fall under "grandfather paradoxes". Is this possible?

Many would say the Novikov self-consistency principle answers it, *shrug*

lol thats not really an answer, its a dismissal.

"Resolves" then :P
Ragnar_Rahl
Posts: 19,297
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4/12/2010 9:58:18 AM
Posted: 6 years ago
At 4/11/2010 6:51:42 PM, TheSkeptic wrote:
Haha, I think a much more simple analogy is autoinfanticide - going back in time and killing yourself as a baby. These examples all basically fall under "grandfather paradoxes". Is this possible?
No.
It came to be at its height. It was commanded to command. It was a capital before its first stone was laid. It was a monument to the spirit of man.