Liar Paradox, The Three Laws of Logic are Intact
  • BB100
    107
    The Lair Paradox is used by skeptics to prove that The Three Fundamental Laws Of Logic are not certain, you can't be sure they are true. This discussion would start to talk about versions of the liar paradox, and the solutions that do not undermine the three laws. The three laws are Identity , Exluded Middle , And Noncontradiction. Identity is A=A, Exluded middle pV(-p), and Non Contradiction -(p=(-p)). I will start by the basic Liar Paradox , This Statement is False. The implication one might say is since its self refrence that leads to if false to be true then false etc.. The problem of such is what Arthur Prior put for is the very definition of a statement is that is is true. There is no more information by saying "This dog is a mammal" , and "This Statement is True and This dog is a mammal". A statements meaning is implicit by its definition. Just like how one may write 1=1.00000, the adition of the zeros add no new information. Therefore Since This statement is False is , in other words, This Statement is true and thi³s statement is false, this no more than p=(-p), which is a contradiction, which is from ealier just not the case. There are others that I hope you guys could explain and as well make any claim against this one.
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  • A Seagull
    615
    The Lair Paradox is used by skeptics to prove that The Three Fundamental Laws Of Logic are not certain, you can't be sure they are true. — BB100

    The reason one cannot be certain that the 3 'laws of logic' are 'true' is that they are unproven. They are hypotheses, It is not even clear over what domain they are supposed to apply.

    It may be that they apply in a strictly formal symbolic logical system, but that is all.
    A Seagull Options
  • BB100
    107
    ↪A Seagull
    I am just saying the Law of Logics are innherent to the meaning of truth. Truth is based that it is in The laws of logic form.
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  • Michael
    15.6k
    On a related note:

    1. The below is false
    2. The above is false

    They can't both be true and they can't both be false. So which is true and which is false?
    Michael Options
  • BB100
    107
    ↪Michael
    I forget the name of that particular liar paradox name, but we can just break down the meaning of "the below" and "the above" as this statement is false for both, and as I mentioned this is a contradiction with the implicit meaning of statement. Then you have the statement A contradiction is false, and that would be simply be meaning less because a contradiction is nonsense.


    1. The below is false - This statement is false is false.
    2. The above is false - This statement is false is false.
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  • A Seagull
    615
    ↪A Seagull I am just saying the Law of Logics are innherent to the meaning of truth. Truth is based that it is in The laws of logic form. — BB100

    Well what do you mean by 'truth'? What has it got to do with the 'laws of logic'?
    A Seagull Options
  • BB100
    107
    ↪A Seagull
    The laws of Logic, are simply what truth, that which is, to be in. As long as any proposition is in conformity of these laws that you can then first past the bar of then actually saying whether is true or not.
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  • A Seagull
    615
    ↪A Seagull The laws of Logic, are simply what truth, that which is, to be in. As long as any proposition is in conformity of these laws that you can then first past the bar of then actually saying whether is true or not. — BB100

    Well that is an interesting theory. But not one that I would subscribe to. Logically speaking, your ascription of truth to such propositions is entirely illogical.
    A Seagull Options
  • BB100
    107
    ↪A Seagull
    May you elaborate, considering I do not see how such a definition breaks either the three fundamental laws or other logical rules.
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  • A Seagull
    615
    83

    ↪A Seagull May you elaborate, considering I do not see how such a definition breaks either the three fundamental laws or other logical rules.     — BB100

    It comes down to the fact that truth is not contained within most logical systems. If you are going to incorporate truth into a logical system then it must be explicitly shown how this occurs.

    So for example one might claim that all theorems of mathematics are true, albeit within the mathematical system. Then you could set up a meta system that takes the theorems of mathematics and tacks on the end the string of characters 'is true'. However this system is somewhat trivial as all it is doing is taking the theorems and labelling them as true.

    So really the concept of 'truth' has no meaningful place in any logical system, it is superfluous to requirements; it serves no purpose.
    A Seagull Options
  • BB100
    107
    ↪A Seagull
    That would not be a problem for what I said for it to be called true, it must be in Compliance of The three Laws of logic for Truth, defintion is in the form of the three laws. It is self Inherent that these hold. Identity Law is a=a, Law of Exluded Middle aV(-a), Law if Non Contradiction a=-(a). The first law for it is in the definition. Second Law for saying other wise would be saying it is not true and its negation is not true which would be a contradiction -a=-(-a), and contradiction is nonsense. Third law for the reason just stated.
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  • A Seagull
    615
    .
    ↪"BB100


    To claim that the three laws are 'self-evident' does not constitute a proof. At best you can claim that they are axiomatic for the logical system for which they are axioms. Then you can claim, if you wish, that all axioms and theorems of that system are 'true', albeit only within that logical system.

    Then the 3 laws can be used for symbolic manipulation within that system and the domain of the 3 laws is fully defined.
    A Seagull Options
  • BB100
    107
    ↪A Seagull
    I not saying they are self-evident just defining truth, a defining part if it, is the conformity to the laws of logic.
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  • Michael
    15.6k
    ↪BB100


    How did you get from "the below is false" to "this statement is false is false"? Using Prior's approach all we can say is that each statement affirms its own truth, and so all you can say is that "the below is false" means "this statement is true and the below is false" which isn't a contradiction.
    Michael Options
  • BB100
    107
    ↪Michael
    It is indirectly talking about itself. The First one is saying the meaning of the below is false, and, thus in other words, we can replace The below with This statement for it is Logically equvalent.
    BB100 Options
  • Michael
    15.6k
    ↪BB100


    I don't think you can substitute meaning like that. If I say "the next thing you say is true" and if the next thing you say is "Michael is awesome" it doesn't then follow that when I said "the next thing you say is true" I meant the same thing as "Michael is awesome".
    Michael Options
  • BB100
    107
    What someone meant and means are two different things. The wording can be reaarranged if there is an equivalency. Language allows one to say something regardless of intention.
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  • A Seagull
    615
    90

    ↪A Seagull I not saying they are self-evident just defining truth, a defining part if it, is the conformity to the laws of logic.     — BB100

    Well in that case you are referring to an artificial truth, You can 'define' what you like, but then it is only applicable to the system to which you are referring. Why call it 'truth'? Why not 'boojum'?
    A Seagull Options
  • BB100
    107
    Because what is , is called truth, I am making the argument that what is by it's own meaning be in the form of The Three Laws, because the three laws come from the meaning of is.
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  • Gregory
    4.7k
    I don't see a difference between the 3 laws and it does seem violated to me by the paradox, which makes falsehood and truth identical
    Gregory Options
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