The position of constructive mathematics on the axiom of infinity is outright unsustainable

[godelian]

The core of the disagreement is not philosophical.

You have a physicalist view on computation. I also believe in the existence of a Platonic realm of computation. That is a philosophical disagreement.

[Skepdick]

The core of the disagreement is not philosophical.

You have a physicalist view on computation. I also believe in the existence of a Platonic realm of computation. That is a philosophical disagreement.

This is not about views. Physicalism. Platonism. Constructivism. Philosophy. Bullshit.

Even if I have a cheesecake view of computation.

Agnostic of any view you still can't produce instant factorizations.

[godelian]

This is not about views. Physicalism. Platonism. Constructivism. Philosophy. Bullshit.

That is otherwise a philosophical statement.

[Gary Childress]

The core of the disagreement is not philosophical.

You have a physicalist view on computation. I also believe in the existence of a Platonic realm of computation. That is a philosophical disagreement.

What exactly is a "Platonic realm of computation?" Can you go into a little more detail about that?

I know Plato believed in perfect forms from which all real forms are created in the image of. I've heard it claimed by some that Plato may have also believed there is no progress, only regress from original perfection. That art is second-hand "imitation" and therefore not as "real" as the perfect forms.

[godelian]

The core of the disagreement is not philosophical.

You have a physicalist view on computation. I also believe in the existence of a Platonic realm of computation. That is a philosophical disagreement.

What exactly is a "Platonic realm of computation?" Can you go into a little more detail about that?

I know Plato believed in perfect forms from which all real forms are created in the image of. I've heard it claimed by some that Plato may have also believed there is no progress, only regress from original perfection. That art is second-hand "imitation" and therefore not as "real" as the perfect forms.

https://plato.stanford.edu/entries/plat ... thematics/

[Skepdick]

This is not about views. Physicalism. Platonism. Constructivism. Philosophy. Bullshit.

That is otherwise a philosophical statement.

Your inability to produce instant factorizations isn't.

[Skepdick]

What exactly is a "Platonic realm of computation?" Can you go into a little more detail about that?

It's where God hides all the answers.

[Gary Childress]

You have a physicalist view on computation. I also believe in the existence of a Platonic realm of computation. That is a philosophical disagreement.

What exactly is a "Platonic realm of computation?" Can you go into a little more detail about that?

I know Plato believed in perfect forms from which all real forms are created in the image of. I've heard it claimed by some that Plato may have also believed there is no progress, only regress from original perfection. That art is second-hand "imitation" and therefore not as "real" as the perfect forms.

https://plato.stanford.edu/entries/plat ... thematics/

Frege’s argument notwithstanding, philosophers have developed a variety of objections to mathematical platonism. Thus, abstract mathematical objects are claimed to be epistemologically inaccessible and metaphysically problematic. Mathematical platonism has been among the most hotly debated topics in the philosophy of mathematics over the past few decades

So are you a devout mathematical Platonist? Do you believe in it 100% or are you skeptical to some degree of its truth?

[godelian]

So are you a devout mathematical Platonist? Do you believe in it 100% or are you skeptical to some degree of its truth?

First of all, not everyone can see particularly much in the Platonic realm:

https://en.m.wikipedia.org/wiki/Mathematical_Platonism

Kurt Gödel's Platonism[1] postulates a special kind of mathematical intuition that lets us perceive mathematical objects directly.

The "special kind of mathematical intuition" explains why some people trivially ace on their math exams while other people flunk them, irrespective of how hard they studied for it.

Everybody has some minimum level of talent, though:

This is often claimed to be the view most people have of numbers.

The Platonic belief is a second nature of mine.

In fact, this is actually a bit surprising because I am horrible at classical Euclidean geometry and its visual puzzles. I always put a coordinate system in, and transform the situation into one of algebra and symbol manipulation.

Philip J. Davis and Reuben Hersh have suggested in their 1999 book The Mathematical Experience that most mathematicians act as though they are Platonists, even though, if pressed to defend the position carefully, they may retreat to formalism.

You can't do classical mathematics and you certainly won't understand it, if you do not have enough Platonic talent. So, it's not a question of being devout but one of being talented.

[Gary Childress]

So are you a devout mathematical Platonist? Do you believe in it 100% or are you skeptical to some degree of its truth?

First of all, not everyone can see particularly much in the Platonic realm:

https://en.m.wikipedia.org/wiki/Mathematical_Platonism

Kurt Gödel's Platonism[1] postulates a special kind of mathematical intuition that lets us perceive mathematical objects directly.

The "special kind of mathematical intuition" explains why some people trivially ace on their math exams while other people flunk them, irrespective of how hard they studied for it.

Everybody has some minimum level of talent, though:

This is often claimed to be the view most people have of numbers.

The Platonic belief is a second nature of mine.

In fact, this is actually a bit surprising because I am horrible at classical Euclidean geometry and its visual puzzles. I always put a coordinate system in, and transform the situation into one of algebra and symbol manipulation.

Philip J. Davis and Reuben Hersh have suggested in their 1999 book The Mathematical Experience that most mathematicians act as though they are Platonists, even though, if pressed to defend the position carefully, they may retreat to formalism.

You can't do classical mathematics and you certainly won't understand it, if you do not have enough Platonic talent. So, it's not a question of being devout but one of being talented.

So is being talented at math somehow better than say being talented at something else?

[Skepdick]

First of all, not everyone can see particularly much in the Platonic realm:

While others see a whole lot that isn't even there.

Like |N| mod 2 being a Boolean.

[godelian]

So is being talented at math somehow better than say being talented at something else?

There are so many different talents.

Furthermore, in this context, what exactly does the term "better" mean anyway?

But then again, even animals need some Platonic talent and vision just to survive. They need to distinguish between (the smaller) natural numbers. The reification of counting till 3 into the abstraction of a "number" 3, seems to be a biological ability.

However, you can generally not make money from pure mathematics, just like you can't from just playing tennis. I've always considered it to be just a hobby.

[godelian]

First of all, not everyone can see particularly much in the Platonic realm:

While others see a whole lot that isn't even there.

There are things in the territory ("truth") but not on the map ("provability"). We only see the map. Hence, we cannot see the part of Platonic reality that is true but unprovable.

The reason why we know that the unprovable Platonic truth exists, is Godel's incompleteness theorem. Some part of the map is bullshit ("inconsistent") or not everything in the territory is on the map ("incomplete"), or both.

For the physical universe, it is exactly the other way around. We can certainly see the territory but we do not have a map. So, we can only see what is true but unprovable in physical reality.

[Skepdick]

First of all, not everyone can see particularly much in the Platonic realm:

While others see a whole lot that isn't even there.

There are things in the territory ("truth") but not on the map ("provability"). We only see the map. Hence, we cannot see the part of Platonic reality that is true but unprovable.

The reason why we know that the unprovable Platonic truth exists, is Godel's incompleteness theorem. Some part of the map is bullshit ("inconsistent") or not everything in the territory is on the map ("incomplete"), or both.

For the physical universe, it is exactly the other way around. We can certainly see the territory but we do not have a map. So, we can only see what is true but unprovable in physical reality.

That was another philosophical detour away from facts/truth...

You placed something on the map that is NOT in the territory.

|N| mod 2 ∈ {0,1}

[godelian]

You placed something on the map that is NOT in the territory.
|N| mod 2 ∈ {0,1}

Out of the box, the mod operator is not defined for transfinite numbers. So, evaluating "ℵ₀ mod 2" first requires a legitimate, i.e. consistent, extension of the definition, which may or may not exist.