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# Resolution of the Liar's Paradox

 Posts: 13,773 Add as FriendChallenge to a DebateSend a Message 12/9/2015 7:00:45 PMPosted: 2 years agoIn its simplest formulation, the Liar's Paradox runs as follows:Take the statement "This sentence is false".If the statement is true, then it is false, since that's what it's claiming to be the case.But in order for it to be false, the sentence has to be true, because it claims to be false (and if it claims to be false and is false, then it's true). So if it's true it's false, and if it's false it's true.How is this paradox to be resolved? I think there's more than one way to do it, but I haven't come across any resolution as simple and as straightforward as mine.It comes down to the fact that "This sentence is false" is in effect two entirely different statements wrapped into one string of words. You can't expect logic to make sense of a contradictory statement because there's no sense to be found. Basically, a statement is a claim to some truth. Merely by being a statement, "This sentence is false" implies "This sentence is true". Since it's saying two different things, it's impossible to assign a single truth value to it, because it's not really a single statement. When we claim something, we are basically saying "It is true that...". Notice how we can't assign truth values to a sentences like "Good morning" or "Trucks", because they don't claim anything to be the case.
 Posts: 4,199 Add as FriendChallenge to a DebateSend a Message 12/9/2015 7:25:23 PMPosted: 2 years agoAt 12/9/2015 7:00:45 PM, dylancatlow wrote:In its simplest formulation, the Liar's Paradox runs as follows:Take the statement "This sentence is false".If the statement is true, then it is false, since that's what it's claiming to be the case.But in order for it to be false, the sentence has to be true, because it claims to be false (and if it claims to be false and is false, then it's true). So if it's true it's false, and if it's false it's true.How is this paradox to be resolved? I think there's more than one way to do it, but I haven't come across any resolution as simple and as straightforward as mine.It comes down to the fact that "This sentence is false" is in effect two entirely different statements wrapped into one string of words. You can't expect logic to make sense of a contradictory statement because there's no sense to be found. Basically, a statement is a claim to some truth. Merely by being a statement, "This sentence is false" implies "This sentence is true". Since it's saying two different things, it's impossible to assign a single truth value to it, because it's not really a single statement. When we claim something, we are basically saying "It is true that...". Notice how we can't assign truth values to a sentences like "Good morning" or "Trucks", because they don't claim anything to be the case.How does this solve anything? If it's merely saying two different things, you should be able to isolate those things and give the truth values of each individually. The problem is that, if you try to do so, you end here:"This statement is false"and"This statement is true"Which resolves nothing; you've just produced another contradiction and a tautology.: At 10/2/2017 3:00:43 AM, YYW wrote: : Bossy: You are Regina. :Inferno wrote: :You sound rather gay. -- And the light shineth in darkness; and the darkness comprehended it not. "I believe that my powers of mind are surely such that I would have become in a certain sense a resolver of all problems. I do not believe that I could have remained in error anywhere for long. I believe that I would have earned the name of Redeemer, because I had the nature of a Redeemer. "
 Posts: 11,196 Add as FriendChallenge to a DebateSend a Message 12/9/2015 7:45:09 PMPosted: 2 years agoAt 12/9/2015 7:00:45 PM, dylancatlow wrote:In its simplest formulation, the Liar's Paradox runs as follows:Take the statement "This sentence is false".If the statement is true, then it is false, since that's what it's claiming to be the case.But in order for it to be false, the sentence has to be true, because it claims to be false (and if it claims to be false and is false, then it's true). So if it's true it's false, and if it's false it's true.How is this paradox to be resolved? I think there's more than one way to do it, but I haven't come across any resolution as simple and as straightforward as mine.It comes down to the fact that "This sentence is false" is in effect two entirely different statements wrapped into one string of words. You can't expect logic to make sense of a contradictory statement because there's no sense to be found. Basically, a statement is a claim to some truth. Merely by being a statement, "This sentence is false" implies "This sentence is true". Since it's saying two different things, it's impossible to assign a single truth value to it, because it's not really a single statement. When we claim something, we are basically saying "It is true that...". Notice how we can't assign truth values to a sentences like "Good morning" or "Trucks", because they don't claim anything to be the case.So your solution to the paradox is that the sentence makes no coherent propositional sense (i.e. it's a paradox)....."A stupid despot may constrain his slaves with iron chains; but a true politician binds them even more strongly with the chain of their own ideas" - Michel Foucault
 Posts: 13,773 Add as FriendChallenge to a DebateSend a Message 12/9/2015 7:49:59 PMPosted: 2 years agoAt 12/9/2015 7:45:09 PM, 000ike wrote:At 12/9/2015 7:00:45 PM, dylancatlow wrote:In its simplest formulation, the Liar's Paradox runs as follows:Take the statement "This sentence is false".If the statement is true, then it is false, since that's what it's claiming to be the case.But in order for it to be false, the sentence has to be true, because it claims to be false (and if it claims to be false and is false, then it's true). So if it's true it's false, and if it's false it's true.How is this paradox to be resolved? I think there's more than one way to do it, but I haven't come across any resolution as simple and as straightforward as mine.It comes down to the fact that "This sentence is false" is in effect two entirely different statements wrapped into one string of words. You can't expect logic to make sense of a contradictory statement because there's no sense to be found. Basically, a statement is a claim to some truth. Merely by being a statement, "This sentence is false" implies "This sentence is true". Since it's saying two different things, it's impossible to assign a single truth value to it, because it's not really a single statement. When we claim something, we are basically saying "It is true that...". Notice how we can't assign truth values to a sentences like "Good morning" or "Trucks", because they don't claim anything to be the case.So your solution to the paradox is that the sentence makes no coherent propositional sense (i.e. it's a paradox).....The sentence makes two coherent but opposed claims at once. It begins as a paradox, so attempting to assign a single truth value to it invariably leads to a paradox because a single truth value will make sense for one of the components but not the other.
 Posts: 4,199 Add as FriendChallenge to a DebateSend a Message 12/9/2015 7:58:42 PMPosted: 2 years agoAt 12/9/2015 7:55:22 PM, 000ike wrote:"the sentence makes two coherent but opposed claims at once"....that's literally how a paradox is defined.... you're basically describing the contradiction not resolving it. Perhaps in conceiving it as two separate claims your idea is that we assess their truth value independently rather than simultaneously,.... but that's kind of absurd given that the sentence doesn't allow that independent assessment. If the statement is true, then that means the statement is false, which means it's true, and so on.Have I told you that I love you recently?I love you.: At 10/2/2017 3:00:43 AM, YYW wrote: : Bossy: You are Regina. :Inferno wrote: :You sound rather gay. -- And the light shineth in darkness; and the darkness comprehended it not. "I believe that my powers of mind are surely such that I would have become in a certain sense a resolver of all problems. I do not believe that I could have remained in error anywhere for long. I believe that I would have earned the name of Redeemer, because I had the nature of a Redeemer. "
 Posts: 11,196 Add as FriendChallenge to a DebateSend a Message 12/9/2015 8:06:52 PMPosted: 2 years agoAt 12/9/2015 7:58:42 PM, ShabShoral wrote:At 12/9/2015 7:55:22 PM, 000ike wrote:"the sentence makes two coherent but opposed claims at once"....that's literally how a paradox is defined.... you're basically describing the contradiction not resolving it. Perhaps in conceiving it as two separate claims your idea is that we assess their truth value independently rather than simultaneously,.... but that's kind of absurd given that the sentence doesn't allow that independent assessment. If the statement is true, then that means the statement is false, which means it's true, and so on.Have I told you that I love you recently?I love you.lol just calling it as I see it."A stupid despot may constrain his slaves with iron chains; but a true politician binds them even more strongly with the chain of their own ideas" - Michel Foucault
 Posts: 546 Add as FriendChallenge to a DebateSend a Message 12/9/2015 8:25:14 PMPosted: 2 years agoAt 12/9/2015 7:00:45 PM, dylancatlow wrote:It comes down to the fact that "This sentence is false" is in effect two entirely different statements wrapped into one string of words. You can't expect logic to make sense of a contradictory statement because there's no sense to be found. Basically, a statement is a claim to some truth. Merely by being a statement, "This sentence is false" implies "This sentence is true". Since it's saying two different things, it's impossible to assign a single truth value to it, because it's not really a single statement. When we claim something, we are basically saying "It is true that...". Notice how we can't assign truth values to a sentences like "Good morning" or "Trucks", because they don't claim anything to be the case.This hits the nail on the head, and is an example of how we can twist language to describe stuff that isn't real.