∞ is a free variable

[Skepdick]

I'll let you have the last word. You''ve picked up some terminology that you don't understand

Well, that's your usual exit strategy. You could have just said you are out of your depth.

and you are making the claim that, for example, Tree(3) has no determinate parity.

I have made no such claim.

Informally the claim is that Tree(3) is nether odd nor even.
Formally the claim is that there exists no proof for TREE(3) inhabits the Odd-type AND there exists no proof that TREE(3) inhabits the Even-type.

Maybe you don't understand the terminology?

after finitely many steps. It makes no difference that the number of steps is too large to be practical.

In Classical Mathematics it doesn't. In constructive Mathematics it does.

You don't get to claim an object is either X or not-X without telling me which dusjunct holds - that's just re-stating Excluded Middle.

[wtf]

after finitely many steps. It makes no difference that the number of steps is too large to be practical.

In Classical Mathematics it doesn't. In constructive Mathematics it does.

You're factually incorrect. You have picked up some buzzwords but you don't understand their meaning.

The most charitable thing I can say here is that you're confusing constructivism with ultrafinitism.

and you are making the claim that, for example, Tree(3) has no determinate parity.

I have made no such claim.

Informally the claim is that Tree(3) is nether odd nor even.

You're embarrassing yourself. All the best.

[Skepdick]

You're factually incorrect. You have picked up some buzzwords but you don't understand their meaning.

You are factually incorrect about me being factually incorrect and you are using pejoratives in order to deflect from your conceptual error.

https://en.wikipedia.org/wiki/Brouwer%E ... rpretation

A proof of P v Q is either <0,a> where a is a proof of P, or <1,b> where b is a proof of Q

Translated for your ignorance: In order to claim "Tree(3) is Odd or Even" you actually have to tell us which disjunct holds; and produce a proof to that effect.

Since you can't furnish a proof for either disjunnct it trivially follows that Tree(3)'s epistemic status is neither odd nor even.

This is a factual claim about your ignorance.
In your head Tree(3) is neither odd nor even.

This is true whether you agree or not.

You're embarrassing yourself. All the best.

Well, at least you are feeling some kind of embarrasment. Too bad you are failing to internalize it.

Classical Mathematicians could do with a healthy doze of epistemic humility.

[Skepdick]

There's a Turing machine that executes the division by 2 algorithm and halts on Even or Odd after finitely many steps.

This is the discontinuity in your understanding. Turing Machines aren't Mathematical functions. They have no value.

On an extensional view (such as the one you are consistently defending) all Turing machines are this function: f(x) = ∅.

When it halts all you know is that it halts.

So given a TM which encodes the computation "Even 8" all you get to know is this: The TM has halted!

It's the encoding/configuration of the TM which determines whether the halting event signifies acceptance or rejection of the "Even 8" predicate.

You get to choose what the halting signifies e.g you can signify acceptance OR rejection, but you can't signify acceptance AND rejection.

[wtf]

When it halts all you know is that it halts.

My God you are ignorant even about the very basics.

Halting means that the machine halts on a definite terminal state. Go look it up.

[Skepdick]

When it halts all you know is that it halts.

My God you are ignorant even about the very basics.

Halting means that the machine halts on a definite terminal state. Go look it up.

My God. Halting means halting.

What does halting signify to an outside observer?

The machine has halted? Great!
"Even 8" has been computed? Great!

Was it computed to be true or false? Which definite terminal state did the TM land on?

Oh. I don't know. The TM didn't say.

EXTENSIONALLY the TM looks exactly like f(x)=∅ - its "definite halting" state is NOT referentially transparent

The only way to encode any meaning in such a function is to make sure the halting itself signifies something important.
Which is exactly the conventional encoding used in Computer Science: Halting signifies Yes/Accept. Doesn't halt (runs indefinitely) signifies No/Reject.

[Magnus Anderson]

Are you really that dumb or are you intentionally pretending that you don't understand what you're asked to do?

Are you realy that dumb or are you intentionally pretending that you don't understand I've done exactly what you asked me to do?

You asked for an integer. I gave you one. TREE(3)

https://en.wikipedia.org/wiki/Kruskal%2 ... E_function

You can neither prove it's odd nor prove it's even.

I asked for an integer, imbecile, not for a function evaluation.

[Magnus Anderson]

You can neither prove it's odd nor prove it's even.

And not even this is true.

[Skepdick]

I asked for an integer, imbecile, not for a function evaluation.

TREE(3) specifies an integer, imbecille.

It's referentially transparent

[Skepdick]

You can neither prove it's odd nor prove it's even.

And not even this is true.

https://en.wikipedia.org/wiki/Brouwer%E ... rpretation

A proof of P v Q is either <0,a> where a is a proof of P, or <1,b> where b is a proof of Q

Translated for your ignorance: In order to claim "Tree(3) is either Odd or Even" you actually have to tell us which disjunct holds; and produce a proof to that effect.

Since you can't furnish a proof for either disjunnct it trivially follows that Tree(3)'s epistemic status is neither odd nor even.

This is a factual claim about your ignorance.
In your head Tree(3) is neither odd nor even.

This is true whether you agree or not.

Since you have no clue how to construct either proof all you can do is keep vacuously parroting the Law Of Excluded middle.

[Skepdick]

My God you are ignorant even about the very basics.

Halting means that the machine halts on a definite terminal state. Go look it up.

Clearly you are just another sophist bickering over semantics and "what things mean" so lets cut to the chase.

This is a clear, scientific, falsifiable claim: There exists no Turing Machine which halts if the parity of Tree(3) is Odd AND there exists no Turing Machine which halts if the parity of Tree(3) is even.

No argument is required on your part. All you have to do is produce is counter-evidence: construct the Turing Machines you claim exist.

Platonic existence doesn't equate to concrete, accessible knowledge.

One thing's for sure, the Platonic realm may be too small for an omniscient ego.

[Magnus Anderson]

I asked for an integer, imbecile, not for a function evaluation.

TREE(3) specifies an integer, imbecille.

It's referentially transparent

I don't care that it specifies an integer, it's not what I asked for. I asked for an integer that is represented as a decimal numeral. I did not ask for an integer that is expressed as the result of a function evaluation. And you knew this very well but you chose to not do it because you can't.

It's all you do. You've been more than exposed so you are very very worthy of serious restrictions to your freedom to use this forum.

[Magnus Anderson]

Since you have no clue how to construct either proof all you can do is keep vacuously parroting the Law Of Excluded middle.

Since you do not accept any proof, it's pointless to have any conversation with you.

Give it up, imbecile.

[Skepdick]

I don't care that it specifies an integer, it's not what I asked for. I asked for an integer that is represented as a decimal numeral.

No you didn't. You asked for an integer. You didn't specify a representation. Why are you moving the goalposts?

I did not ask for an integer that is expressed as the result of a function evaluation.

You didn't NOT ask for it either. Aninteger is an integer is an integer. Irrespective of its representation.

And you knew this very well but you chose to not do it because you can't.

Why are you lying?

It's all you do. You've been more than exposed so you are very very worthy of serious restrictions to your freedom to use this forum.

If they don't restrict liars such as you they probably won't mind me.

[Skepdick]

Since you do not accept any proof, it's pointless to have any conversation with you.

You haven't even offered any proofs for me to accept!

Is TREE(3) odd or even?

Whichever one it is - present the proof!

Give it up, imbecile.

How can I "give up" something I haven't even started?