Liar Paradox, The Three Laws of Logic are Intact
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.
Comments (19)
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.
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?
1. The below is false - This statement is false is false.
2. The above is false - This statement is false is false.
Well what do you mean by 'truth'? What has it got to do with the 'laws of logic'?
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.
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.
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.
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.
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".
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'?