Martian Posted January 3, 2006 Share Posted January 3, 2006 At first reading this, it may not appear that this post really belongs in a mathematics forum, but on closer attention it may be found that its a very appropriate place for this seeming paradoxial word problem. Its nothing new, just (as far as I know) still mathematically/logically unanswered. I would prefer it to be spoken for or against on strictly mathematical terms, but verbal logic may also help. First assumption: Paradoxes cannot exist. Human misunderstanding on logic/truth can. Second assumption: Time travel is possible. Third assumption: There will be at least more than one moderator considering deleting or moving this post. No doubt most are familiar with this paradox that ancient greeks used to stay up all night debaiting and exausting that time period's supply of coffee: Its an established fact that Cretens always lie. A certain man who is of a set of people who are considered Cretens makes the statement "Cretens always lie" thus making a statement that is truthfull. But then, still being a Creten, he is still among the set of those considered Cretens, and having told the truth, the fact exists that there is at least one Creten who tells the truth, and in effect, his statement becomes a lie. Now, if the paradoxial nature of this situation has at some point been solved, and there is no logical contradiction anymore due to modified understanding, then I would invite this post to be deleted as its irrelevent. If not, then here is a suggested answer to this paradox, making it logically sound, and then no longer a paradox. So this man, who is a Creten (a peaple who only speak lies) makes a truthful statement. If it were left to the above we will see him either simultaniously speaking a falsehood and a truth, or we would see him perpetually being changed from the status of a liar to a truthteller to a liar to a truthteller...and so on. Let us make another assumption, as a means to kill the paradox, and with it a few others that revolve around similar logic. Assumption: Regardless of his geneology and cultural status, his statement of truth causes him no longer to be a Creten. Hense, at the moment he said "Cretens always lie" he stopped being a Creten. Now, being that he himself is reading this, he finds it utterly rediculous that his ability to tell the truth altered his inherent status as a Creten by this new assumption, as it would be the logical equivilent of being changed from a boy to a girl based on the influence of nothing more than mere thought and words. So to prove that such reasoning is foolish (he believes his geneology can't be altered based on his actions) and wishes to prove the paradox can exist he decides to travel back in time before he was concieved to kill his great grandfather. He expects that doing so will rule out his existence, as this would be the assumed case: He exists. He goes back to kill his great grandfather, causing his existence to be annulled before it was concieved. If he did not exist, he couldn't kill his grandfather. Likewise, as his argument goes, its meant to be a paradox mentally and likely he will not be able to kill his grandfather as the governing dynamics of reality will probobly show his grandfather will always succesfully evade his murderer. But we are saying that if he kills his grandfather, then the truth is the man was not his grandfather, and when the Creten discoveres who is real grandfather is, he will kill him, only to discover his real grandfather still exists and has yet to be killed, and he murdered two strangers in cold blood. So we have a repetition somewhat similar to the above. (e.i. the man who is responsible for his existence keeps rerouting itself everytime the Creten interpheres with his own existence.) This may seem foolish, but it can be illustrated by a real phenomenon: As long as an electrical positive and negitive potential exists and a number of closed routes exist between the two, the electricity will always take the path of least resistence from its origin to its goal. If that path is blocked, it will find a new path of least resistence untill every concievable path is blocked. Let us assume that there is an infinite number of paths the electricity will always take in an infinitely large system, and its path can never be truly blocked. In a system where time is a mental illusion and cause and effect (governed by the speed of light) are the only true dynamics, the Creten will never truly be able to block the path to his own existence, as an infinite number of possibilites exist and they will always reroute to give the final outcome, regardless of interpherence. (Or more simply said, he merely traveled backward in cause and effect and changed the dynamics that led to his own existence.) So you might then realize that when he killed his great-grandfather, his geneology even preceding his great grandfather was changed, and traveling back in time did not merely change time from that point onward, but time previous to it and after it. I'm certain this translates to a very simple argument in mathematics. I'm also certain many will not agree and this post will be deleted or reassigned to a different catagory. Link to comment Share on other sites More sharing options...

matt grime Posted January 3, 2006 Share Posted January 3, 2006 At first reading this' date=' it may not appear that this post really belongs in a mathematics forum, but on closer attention it may be found that its a very appropriate place for this seeming paradoxial word problem. Its nothing new, just (as far as I know) still mathematically/logically unanswered. I would prefer it to be spoken for or against on strictly mathematical terms, but verbal logic may also help. [b']First assumption:[/b] Paradoxes cannot exist. Human misunderstanding on logic/truth can. Second assumption: Time travel is possible. Third assumption: There will be at least more than one moderator considering deleting or moving this post. No doubt most are familiar with this paradox that ancient greeks used to stay up all night debaiting and exausting that time period's supply of coffee: Its an established fact that Cretens always lie. A certain man who is of a set of people who are considered Cretens makes the statement "Cretens always lie" thus making a statement that is truthfull. But then, still being a Creten, he is still among the set of those considered Cretens, and having told the truth, the fact exists that there is at least one Creten who tells the truth, and in effect, his statement becomes a lie. Now, if the paradoxial nature of this situation has at some point been solved, and there is no logical contradiction anymore due to modified understanding, then I would invite this post to be deleted as its irrelevent. If not, then here is a suggested answer to this paradox, making it logically sound, and then no longer a paradox. what paradox? just because you say something is possible does not make it realizable. note that the completely acceptable statement: this statement is false, is not allowed in logic (it is one of the assumptions, or axioms). Self references are disallowed, and it is any rate a meta statement or a second order statement. cf Russell's paradox. So this man, who is a Creten (a peaple who only speak lies) makes a truthful statement. If it were left to the above we will see him either simultaniously speaking a falsehood and a truth, or we would see him perpetually being changed from the status of a liar to a truthteller to a liar to a truthteller...and so on. no, we don't. you might but that is not our problem. <meaningless stuff snipped> This may seem foolish, but it can be illustrated by a real phenomenon: As long as an electrical positive and negitive potential exists and a number of closed routes exist between the two, the electricity will always take the path of least resistence from its origin to its goal. If that path is blocked, it will find a new path of least resistence untill every concievable path is blocked. Let us assume that there is an infinite number of paths the electricity will always take in an infinitely large system, and its path can never be truly blocked. so it has nothing to do with real life then. I'm certain this translates to a very simple argument in mathematics. I'm also certain many will not agree and this post will be deleted or reassigned to a different catagory. you make certain hypthoseses, that are contradictory, and make some deductions based upon some even more dodgy assumptions, most of which are not expressed. it isn't maths. it might be philosophy. it probably isn't. even assuming your assumptions are more properly expressed, at *best* you're just producing a set of assumptions that do not make 'consistent' sense. that isn't surprising, a lot of people do that. Link to comment Share on other sites More sharing options...

Martian Posted January 4, 2006 Author Share Posted January 4, 2006 Hi. Thanks for the meaningful reply. I saw your webpage and its nice! Just for the record, I'm not questioning mathematics or trying to imply that its ficticious. I'm in the process of learning it myself. Still, I'm tormented with the terrible combination of original thought and the desire to express it. note that the completely acceptable statement: this statement is false, is not allowed in logic (it is one of the assumptions, or axioms). Self references are disallowed, and it is any rate a meta statement or a second order statement. cf Russell's paradox.. Ok. Lets eliminate self-reference. Without any knowledge of past interchanges these statements are made: Martian: "matt grime is telling the truth." matt grime: "Martian is lying." So who is telling the truth? Its a humorous thing, isn't it? Whats a meta statement or a second order statement? you make certain hypthoseses, that are contradictory, and make some deductions based upon some even more dodgy assumptions, most of which are not expressed.. I tried to compensate for my lack of methodical reasoning with humor. A sense of irony is important in science and maths as we will no doubt find the unified theory to be a joke. (42 to be exact.) If you find this funny its ok to laugh. it isn't maths. it might be philosophy. it probably isn't.[/quote=matt grime] To my shame' date=' actually. I dislike philosophy. even assuming your assumptions are more properly expressed, at *best* you're just producing a set of assumptions that do not make 'consistent' sense. that isn't surprising, a lot of people do that. So back to my original request, can at least the original problem (the liar paradox) be tested or disproven by mathematics? In a non-self-reference situation such as the one posted above? In the strictest sense, are the core essense of these questions mathematical or not? Link to comment Share on other sites More sharing options...

matt grime Posted January 6, 2006 Share Posted January 6, 2006 There is an element of logic (as a subject in mathematics) in what you want to know. However mathematics simply ignores such problems by declaring them to be disallowed, thus one cannot have the set of sets, or the set of sets that do not contain themselves, which is equivalent to the liar paradox (if somethingn is true then it's false, if it's false then it's true). Thus these problems are not resolvable in mathematics since they are not a valid part of mathematics. Or if you prefer the resolution is to not study situations where they may arise. That may displease you, but that's they way it is. If you want to debate them and argue that you shouldn't be allowed to ignore these statements then you're into philosophy. If you like mathematics is the art of the possible to paraphrase someone. What you want is a system that is impossible, if your situation were to arise. We ignore lots of things in mathematics to make life easier. Sometimes we consider some problems (eg usually we do not square root -1 in front of the beginner student since they;ve been told that you can't do this by teachers who have no idea about mathematics; we can allow square rooting of -1 and the expense of having to consider large sets than just real numbers; you're kind of problem is far more fundamental than that and cannot be allowed since it creates an inconsistent system). A metestatement is just my loose term for a statement that is about truth/falseness. It refers to 'first order' things like true/false and is thus at a higher level in some sense. Not of course that i really see what your point is: so what, you can write down some statements that are mutually inconsistent. who cares? so can anyone. Link to comment Share on other sites More sharing options...

YT2095 Posted January 6, 2006 Share Posted January 6, 2006 you really should have added Another assumption there too! because when you say electricity takes the shortest path, you actualy mean the Observable phenomenon! in fact when an electron travels from point A to point B it takes MANY MANY different paths at the same time, the one that makes it is the one we See HERE. the fact is we don`t know what happes to the electon that takes all the other paths. now THERE`S food for thought Link to comment Share on other sites More sharing options...

patcalhoun Posted January 17, 2006 Share Posted January 17, 2006 I'm certain this translates to a very simple argument in mathematics. [imath]\omega=\sum_n dq^i \wedge dp_i[/imath] There you go. Run with it. Link to comment Share on other sites More sharing options...

Martian Posted January 17, 2006 Author Share Posted January 17, 2006 [imath']\omega=\sum_n dq^i \wedge dp_i[/imath] Can you translate this to binary for my time machine? Thanks. Link to comment Share on other sites More sharing options...

patcalhoun Posted January 18, 2006 Share Posted January 18, 2006 Can you translate this to binary for my time machine? Thanks. Only in [imath]O(n^2)[/imath] time. Link to comment Share on other sites More sharing options...

Martian Posted January 19, 2006 Author Share Posted January 19, 2006 I have a lot to learn in math. Can you explain what the above equation is or how it works? (Or was it a joke?) ...the first one I mean. Link to comment Share on other sites More sharing options...

matt grime Posted January 19, 2006 Share Posted January 19, 2006 It is a covariant one form wedged with a contravariant one form, and is a indeed a joke. Link to comment Share on other sites More sharing options...

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