∞ is a free variable

[Magnus Anderson]

And if you operate with your imaginary, made up, fantasy version of logic something can be resolved before you do any thinking.

Quality over quantity. You can think all you want but if it's not guided by logic it's worth nothing. And that's what you're doing. It's called over-thinking.

There aren't any proofs to reject.

0 proofs for Oddness + 0 proofs for evenness = 0 proofs in total.

Several proofs in favor of the claim that TREE(3) is either even or odd and not something else = several proofs in total.

Everything is either a teletubby or it isn't!

So you are a teletubby?

[Skepdick]

It very much is. It tells us that every integer is either even or odd which is the opposite of your claim that it's something else ( neither even nor odd. )

You are using a Classical frame to misinterpret a Constructive claim.

You also keep ignoring that "Neither even nor odd" is self-contradictory since it translates to "Odd and not odd" given that "not even" means "odd".

Indeed! That's the very problem with your Classical frame. No such problem exits in a Constructive frame.

In a constructive setting Odd and Even aren't DEFINED via complementarity.
They are defined independently.
The complementarity is proven.

You are, once again, refusing to actually think.

I think it's pretty obvious which one of us can think.

It's either you or me.
The right disjunct holds.

It has been proven more than once here in this thread that it is one of the two -- even or odd -- rather than something else.

Which one of the two was proven?

Quite contrary to your constructive mathematics bullshit, there is no need for anyone to prove whether TREE(3) is even or odd. Proving that it MUST be one of the two is ENOUGH.

Of course it's enough! Which ONE (of the TWO) did you prove?

Making things artificially and unnecessarily difficult is not a sign of intelligence.

The difficulty is not artificial. But it is absolutely necessary if you care about the answer.

You're claiming that you've proven that TREE(3) is neither even nor odd.

You are using a Classical frame to misinterpret a Constructive claim.

Learn the difference between "I don't know if it's even or odd" and "I know it's neither even nor odd".

I know it's neither odd; nor even.

You wish.

I don't need to wish. I know that I am igorant of TREE(3)'s oddness AND I am ignorant of its evenness.

So I neither know it to be odd; nor know it to be even.

[Skepdick]

Quality over quantity. You can think all you want but if it's not guided by logic it's worth nothing. And that's what you're doing. It's called over-thinking.

It's literally formal logic. Overthinking is what people who can't think call it.

Several proofs in favor of the claim that TREE(3) is either even or odd and not something else = several proofs in total.

Yes. You have offered me plenty proofs for a question I am not asking and zero proofs for the question that I am asking.

Maybe try some of that overthinking?

So you are a teletubby?

Either I am or I am not.

[Magnus Anderson]

It very much is. It tells us that every integer is either even or odd which is the opposite of your claim that it's something else ( neither even nor odd. )

You are using a Classical frame to misinterpret a Constructive claim.

I asked you to give us an integer that is neither even nor odd, i.e. that is something other than even and odd.

I did not ask you to give us an integer for which, in your mind, there is no proof that is even and no proof that it is odd.

Indeed! That's the very problem with your Classical frame. No such problem exits in a Constructive frame.

That problem exists everywhere.

In a constructive setting Odd and Even aren't DEFINED via complementarity.

So? Why should anyone care how THEY (re)define terms?

They are defined independently.
The complementarity is proven.

You were responding to wtf who defined the two terms as complementary ( which is the standard practice. )

I think it's pretty obvious which one of us can think.

Absolutely. And it's not you. You're the animalistic logic-hating anti-thinker.

It has been proven more than once here in this thread that it is one of the two -- even or odd -- rather than something else.

Which one of the two was proven?

Quite contrary to your constructive mathematics bullshit, there is no need for anyone to prove whether TREE(3) is even or odd. Proving that it MUST be one of the two is ENOUGH.

Of course it's enough! Which ONE (of the TWO) did you prove?

Are you really THAT stupid?

What has been proven is that it's one of the two and not something else.

And THAT is enough.

The difficulty is not artificial. But it is absolutely necessary if you care about the answer.

It is artificial and unnecessary and merely a way for a dumb person to feel smart.

[Magnus Anderson]

"Oh look how much thinking I've done, it does not matter that I do not abide by the principles of proper reasoning, i.e. logic, all that matters is quantity, i.e. how many deductions I've made, that certainly makes me smarter than those other guys who can arrive at conclusions using far less thought than I do!"

You're pathetically delusional.

[Skepdick]

I asked you to give us an integer that is neither even nor odd, i.e. that is something other than even and odd.

And I did. 1 is odd. 2 is even. TREE(3) is neither odd; nor even.

I did not ask you to give us an integer for which, in your mind, there is no proof that is even and no proof that it is odd.

You asked for an integer which has no identifiable parity.

That problem exists everywhere.

I do believe the problem disappears. Soon as you give up your imaginary logic for my imaginary logic.

So? Why should anyone care how THEY (re)define terms?

Because that way the contradiction of "neither odd nor even" disappears?

You were responding to wtf who defined the two terms as complementary ( which is the standard practice. )

Sure. And that's why your logic blows up when I say "neither odd nor even"

What has been proven is that it's one of the two and not something else.

Are you this fucking stupid. Why do you need to prove somethign that has been DEFINED have only two possibilities?

And THAT is enough.

No, it's not.

It is artificial and unnecessary and merely a way for a dumb person to feel smart.

I'm sure you feel very smart. Havin paraphrased the Law of Excluded middle a thousand different times.

While failing to tell us which disjunct holds.

[Skepdick]

"Oh look how much thinking I've done, it does not matter that I do not abide by the principles of proper reasoning, i.e. logic, all that matters is quantity, i.e. how many deductions I've made, that certainly makes me smarter than those other guys who can arrive at conclusions using far less thought than I do!"

You're pathetically delusional.

Another medal for irony.

You've done a full mental Boston marathon to avoid identifying which disjunct holds.

None of your mental gymnastics are making inroads towards identifying TREE(3)'s parity.

[Skepdick]

You seem to believe TREE(3) has no determinate parity. That's wrong, if not flat out insane.

Methinks all of your conceptual problems stem from your equivocation of "parity".

You are failing to distinguish between Parity and Parity-value which would be an anallagous error if you were to fail to distinguish between a Booleans and the truth-value of a Boolean.

You are essentially confusing type-checking with value-checking.

You are failing to distinguish between two different kinds of determinations:

* Determining whether some abstract object has a parity (type-checking): HasParity(X) -> {0,1}
* Determining what the specific parity of the object is odd; or even (value-checking) GetParity(X) -> {Odd, Even}

Dependent type theory cures such dysfunction.

[wtf]

Dependent type theory cures such dysfunction.

All the best.

[Skepdick]

Dependent type theory cures such dysfunction.

All the best.

OK, Mr MOD2((P=NP) -> {0,1}) has determinate parity.

[wtf]

OK, Mr MOD2((P=NP) -> {0,1}) has determinate parity.

Nothing personal. Just not finding this productive at my end.

Then again, that doesn't necessarily mean I'm finding it unproductive, right?

You like this in real life? "Is it raining out?" "Well there could be a massive hurricane. Or it coul be sunny and mild. Why don't you use dependent type theory to find out."

[Skepdick]

OK, Mr MOD2((P=NP) -> {0,1}) has determinate parity.

Nothing personal. Just not finding this productive at my end.

Then again, that doesn't necessarily mean I'm finding it unproductive, right?

You like this in real life? "Is it raining out?" "Well there could be a massive hurricane. Or it coul be sunny and mild. Why don't you use dependent type theory to find out."

Why don't you look outside your window and check TREE(3)'s parity?

[wtf]

Why don't you look outside your window and check TREE(3)'s parity?

LOL.

[Magnus Anderson]

Another medal for irony.

You've done a full mental Boston marathon to avoid identifying which disjunct holds.

None of your mental gymnastics are making inroads towards identifying TREE(3)'s parity.

You wish.

[Magnus Anderson]

And I did. 1 is odd. 2 is even. TREE(3) is neither odd; nor even.

Yes and your proof for that is argument from ignorance.

1. Skeppie McFucked Up Dickie has no proof that TREE(3) is even.
2. Skeppie McFucked Up Dickie has no proof that TREE(3) is odd.
3. Therefore, TREE(3) is neither even nor odd.

Keep denying it all you want but that's argument from ignorance.

You asked for an integer which has no identifiable parity.

No, I asked for an integer that is neither even nor odd. An integer that has no identifiable parity is something else.

I do believe the problem disappears. Soon as you give up your imaginary logic for my imaginary logic.

At least you admit your logic is imaginary.

Because that way the contradiction of "neither odd nor even" disappears?

Yes, once you redefine the terms and misinterpret the original author's claim.

Are you this fucking stupid. Why do you need to prove somethign that has been DEFINED have only two possibilities?

Because there are morons who are denying it, morons such as yourself.

I'm sure you feel very smart. Havin paraphrased the Law of Excluded middle a thousand different times.

I haven't done any such thing but I can tell that you have a personal beef against logic. You really, really, hate it.