Now that Arcanus is back, I can start a discussion on something I'd been meaning to ask him for quite a while; namely the existence of logical absolutes.
The three laws of logic forming the logical absolutes are:
1) Law of Identity: Something is what it is and isn't what it is not. (A = A)
2) Law of Non-Contradiction: Something cannot be both true and false at the same time in the same sense. ¬(A ^ ¬A)
3) Law of Excluded Middle: A statement is either true or false, without a middle ground. (P v ¬P)
The argument for these logical absolutes is that they all validate each other, and that without one, logic falls apart. Also, that if one of them is not true, you get logical contradictions. The example I'm used to is that if the Law of Non-Contradiction is false, then something can be both true and false at the same time and in the same sense, which means that the Law of Non-Contradiction is true (as well as false). But if the law of Non-Contradiction is true, then something cannot be both true and false at the same time, and so the law of Non-Contradiction cannot be both true and false at the same time, and so it must be true.
There are objections to this argument; namely that it uses the laws of logic in order to show that the laws of logic are valid and absolute.
So this thread is basically a discussion of the laws of logic, whether they are absolute, and whether they can be proved absolute. I haven't done much research on this area, but I've always found it intriguing, and Arcanus probably knows more about it that I do.
The three laws of logic forming the logical absolutes are:
1) Law of Identity: Something is what it is and isn't what it is not. (A = A)
2) Law of Non-Contradiction: Something cannot be both true and false at the same time in the same sense. ¬(A ^ ¬A)
3) Law of Excluded Middle: A statement is either true or false, without a middle ground. (P v ¬P)
The argument for these logical absolutes is that they all validate each other, and that without one, logic falls apart. Also, that if one of them is not true, you get logical contradictions. The example I'm used to is that if the Law of Non-Contradiction is false, then something can be both true and false at the same time and in the same sense, which means that the Law of Non-Contradiction is true (as well as false). But if the law of Non-Contradiction is true, then something cannot be both true and false at the same time, and so the law of Non-Contradiction cannot be both true and false at the same time, and so it must be true.
There are objections to this argument; namely that it uses the laws of logic in order to show that the laws of logic are valid and absolute.
So this thread is basically a discussion of the laws of logic, whether they are absolute, and whether they can be proved absolute. I haven't done much research on this area, but I've always found it intriguing, and Arcanus probably knows more about it that I do.
