I'm a professional mathematician.
Whatever.
I have views on the truths of certain unproved or unprovable statements, axioms especially. So does every other professional mathematician.
And I asked you directly what your view is on the conclusion I derived from my axioms. I asked you whether it is an eternal truth. You flat out ignored my question, and redacted it from your quotes of me.
To be brutally honest, you're the only person I've met on this site that I'm actually interested in talking to and understanding. There are a few other educated people, but they are either dishonest or disinterested in engaging. Everyone else is just a cartoonish representation of a Christian, and many are so unbelievably stupid that I cannot tell if they are genuine or if they are atheists pretending to be a stupid Christian.
So I am very disappointed when you dodge serious, tough questions from me. It is a tough question because I already know the answer. You have no escape from it.
You told me one of the things which you believe with unquestionable certainty, and you backed it up with a truth table. Truth tables assume the validity of the law of non-contradiction. So I don't think I'm misrepresenting you if I presume that you hold the law of non-contradiction to be unquestionably true. But quantum mechanics strongly implies that the law of non-contradiction is not even true in this very universe, so it cannot be an eternal truth. I know you know this, so what gives?
I'm sure you do.
But Constructivists consider the diagonalization argument invalid. Indeed, they only accept real numbers for which there is a finite representation, finite description, finite formula, or finite computer program. This gives them a countable set of real numbers. Obviously, you would be struggling to give an example of a specific number they've left out.
You're proving my point. There are no eternal truths. Just things which we accept as tentatively true, such as axioms.
I was. It's commonly used that way.
If you were confused by me mixing symbols from the (&, |) pair and the (/\, \/) pair, I apologise.
Huh?
"And" in common spoken language is different from the "·" operator. Your statement was ambiguous. Sort of like saying sin
x+
y when you really mean sin(
x+
y). No point in you dying on that hill. Just move on.
As I said, I'm a professional mathematician. I'm also, on this forum, anonymous, so I'm not going to list my publications for you.
Based on this statement, and that you told me you're not a PhD, and that you seem to be American, I speculate that you're a PhD student. That does not make you a mathematician. I'm sorry but that's the reality.
No, it doesn't.
And the false statement I allegedly made was...?
It would have been more clear to you had you not redacted my statements. You hold that 2+2=4 with absolute certainty. I showed why certainty in this is not absolute.
I take it that you are conceding that your question was poorly worded, and that you meant "given a line and a point not on it, how many distinct lines parallel to the given line can be drawn through the given point?"
Um, no, I stated the exact opposite. "Line" is well defined, as is "parallel" and so my question was not worded poorly.
The point is that Euclid's fifth postulate is not an eternal truth. It's just an assumption, and we can take it or leave it. Take it, and parallel lines cross by assumption. Leave it, and you have to prove that they cross - but that is known to be impossible - and also you can then have geometry on a sphere where the other axioms still hold.
In that case, which definition of "line" did you mean? I'm aware of several.
The basic definition from geometry.
And in which space do these lines exist?
Does not need to be specified.
The answer depends on what you're talking about. Do the "lines" exist on the surface of a sphere? In Euclidean space? In something like this?
Hopefully my point is clear now.