Of course not. But that is not what I said. probably, again, a problem with my English.
what I said is that something is true, if that it can be proved to not being false. If it being false is absurd. Or leading to a contradiction. not the same thing at all.
Which is basically one of the principles dictated by logic. As you probably know. It is a principle of logic. Namely, the principle of the excluded middle.
in other words, a (not circularly defined) proposition P is always either true or false. There is no alternative. And it is always either of them. If I cannot prove either of the cases, nor their negation, then I cannot make any conclusion about whether it is true or false. But for sure, if I can prove that it is not false, then it follows that it is true. Like i did.
And, therefore, unless you admit of operating outside the constraints of logic, and its principles, your conclusions will not be logical. By definition of what “being logical” means.
Ciao
- viole
I'm going to focus only on this point until it is resolved. Even if I grant all axiomatic defintions, lies are being conflated as truth.
The law of the excluded middle is philosophy. It comes from Aristotle. That means that in order to justify your position, you are using philosophy. So, there can be no more objections to bringing philosophy into this debate. And honestly, it proves my point. You need to go much further to show that an empty-set obtains all properties and that its "empty-ness" can be used to prove the truth of a positive claim.
The law of the excluded middle correctly and intuitively states that for every proposition A there is a corresponding true statement in the form of "A is true or not". That's it. The law states there is no middle ground. Things are either true or false. That's it.
This means that the proposition "All the german speakers are raising their hands" is NOT true unless it includes "All the german speakers are raising their hands, or not".
That's it. Done.
The law of the excluded middle OPPOSES the empty-set obtaining all properties. It's the proof against it.
en.m.wikipedia.org
Now let's look to see again if you proved that married-bachelors have blue hair.
"It is either true or false that all married bachelors have blue hair. Let's prove it is not false, and it is therefore true. The claim "all married bachelors have blue hair" is false if and only if there is at least one married bachelor that does not have blue hair. But this is clearly impossible, because there are no married bachelors at all, not to speak of the ones having any hair color. Ergo, the claim "all married bachelors have blue hair" cannot be false, and it is therefore true."
You very obviously did not prove that this is NOT FALSE. You proved it was impossible to evaluate. There is not one married-bachelor found, there is no hair. The same exact logic can be used in reverse.
"It is either true or false that all married bachelors have blue hair. Let's prove it is not TRUE, and it is therefore FALSE. The claim "all married bachelors have blue hair" is TRUE if and only if there is at least one married bachelor that DOES HAVE blue hair. But this is clearly impossible, because there are no married bachelors at all, not to speak of the ones having any hair color. Ergo, the claim "all married bachelors have blue hair" cannot be TRUE, and it is therefore FALSE."
See? The entire test is invalid. It proves nothing! Proof by contradiction cannot be used with an empty-set. It fails every time.
The law of the excluded middle states that the original statement is true! "it is either true or false that all married bachelors have blue hair". And that is all that you have proven. The only way to take this further is if it is ASSUMED that married-bachelors have blue hair, and if no others are found, then the assumption holds. This is extreme optimism. I am an optimist. I know it when I see it.
What's really happening is the opposite of the law of the excluded middle. It's not a law, it's rejected by most philosophers. It's called the "principle of explosion". It is extreme optimism.
en.m.wikipedia.org
The principle of explosion claims, "from falsehood, anything". That is just another way of stating, "the empty-set obtains all". The empty-set by definition has no elements. But it is being evaluated as if it does have elements ( that's the only way a proof by contradiction is valid ), then a contradiction is accepted as true: "The empty set obtains all properties AND The empty set contains no properties." This violates the law of the excluded middle.
What this means is, axiomatic set theory accepts contradictions as true! All it needs to do is define the contradiction as true, and then ignore it. This is all based on "Trivialism". Trivialism is opposed by Actualism. Claiming a proposition is true because it is not proven false and not proven it is true is Trivialism. While I have been arguing that propositions need to be "actually" true.
en.m.wikipedia.org
So, simple question: Did you ACTUALLY prove that married-bachlors have blue hair, or did you TRIVIALLY prove that married-bachelors have no hair? Please be honest. Don't worry. I'm an optimist, you will be accepted, and I can certainly argue for the merits of optimism... until... those merits begin to blur the lines between truth and fiction.
