Resolution of the question as to whether math is discovered or invented

[godelian]

We only see the map. There is an awareness of the fact that it cannot be the territory, but that's about it. You are seeing too much in it

Yeah, bullshit. I am not seeing anything. Is that "too much"?

All I have on my "map" is a question? Does 0 exist; or not?

That's why I am asking the Platonists. So they can have a look and let me know.

You want to mix inductive metaphysics (Platonism, philosophy) with deductive metaphysics (mathematics). That is where your problem is. It is a category error.

[Skepdick]

You want to mix inductive metaphysics (Platonism, philosophy) with deductive metaphysics (mathematics). That is where your problem is. It is a category error.

Another non-sequitur.

Inference (deductive or inductive) is about validity; not soundness.

The only categories I am interested in are True and not-True. Is it true that 0 exists in Platonic reality; or not?

[godelian]

Is it true that 0 exists in Platonic reality; or not?

That is a belief in Platonism. You believe it or you don't. No word salad can prove or disprove it.

ChatGPT: Is it true that 0 exists in Platonic reality; or not?

The question of whether 0 exists in Platonic reality touches on deep issues in philosophy of mathematics, particularly the debate between Platonism and other views like nominalism, constructivism, or formalism.

From a Platonist Perspective:
Yes, 0 does exist in Platonic reality.
It is considered a perfectly real mathematical object, just like 1, π, or √2.
It has well-defined properties: it's the additive identity, it's less than all positive numbers, etc.
Its existence is independent of whether humans conceptualize it or not.
To a Platonist, 0 exists in the same way that the number 1 or the Pythagorean theorem exists: as a truth about the mathematical universe.

The reason why there are competing ontologies, such as Platonism, nominalism, constructivism, and formalism, is because an ontology is a belief, and there are alternative beliefs possible. In the end, you believe about ontology what you want.

[Skepdick]

Is it true that 0 exists in Platonic reality; or not?

That is a belief in Platonism. You believe it or you don't. No word salad can prove or disprove it.

That's NOT platonism.

On Platonism there is a fact on the matter.

What you believe is immaterial.

The reason why there are competing ontologies, such as Platonism, nominalism, constructivism, and formalism, is because an ontology is a belief, and there are alternative beliefs possible. In the end, you believe about ontology what you want.

Nonsense. ALL ontological traditions are in an equivalence class with Platonism.

Either you believe there is an ontological fact on the matter; or it's time you stopped calling it "discovered".

In the epistemological tradition mathematics is simply invented. The end.
The limits explicated by Godel and Turing are simply the limits of invention; and what you can know about our Mathematical inventions.

[godelian]

Is it true that 0 exists in Platonic reality; or not?

That is a belief in Platonism. You believe it or you don't. No word salad can prove or disprove it.

That's NOT platonism.

On Platonism there is a fact on the matter.

What you believe is immaterial.

The reason why there are competing ontologies, such as Platonism, nominalism, constructivism, and formalism, is because an ontology is a belief, and there are alternative beliefs possible. In the end, you believe about ontology what you want.

Nonsense. ALL ontological traditions are in an equivalence class with Platonism.

Either you believe there is an ontological fact on the matter; or it's time you stopped calling it "discovered".

In the epistemological tradition mathematics is simply invented. The end.
The limits explicated by Godel and Turing are simply the limits of invention; and what you can know about our Mathematical inventions.

We will have to agree to disagree on this.

[Skepdick]

We will have to agree to disagree on this.

Not possible.

https://en.wikipedia.org/wiki/Aumann%27 ... nt_theorem

If you reject convergence to consensus you are the faulty node in the algorithm.

Basic distributed systems thinking.Do you need me to explain what a Byzantine fault is?

[Eodnhoj7]

...

That's a really long-winded way to go about it.

All axioms are invented.
All consequences thereof (theorems) are discovered.

Consequences are merely further axioms composed of axioms and there is no limit to the consequences. I would hardly state it is limited to a linear only approach.

[Skepdick]

Consequences are merely further axioms composed of axioms and there is no limit to the consequences. I would hardly state it is limited to a linear only approach.

Did you have salad for lunch? It's coming out your mouth.

Theorems are consequnces.
Axioms aren't.

0 isn't a consequence.
1 is.

[Eodnhoj7]

Consequences are merely further axioms composed of axioms and there is no limit to the consequences. I would hardly state it is limited to a linear only approach.

Did you have salad for lunch? It's coming out your mouth.

Theorems are consequnces.
Axioms aren't.

0 isn't a consequence.
1 is.

Considering your mental constipation over the years I can see why fiber is on your mind....

You are missing the obvious: a simple equation has to be self evident otherwise it is not an equation. Axioms, self-evidence, occur in interwoven conceptual layers.

Zero is only understood relative to a number line, which is self-evident, and an equation containing 0, which is self evident. The inverse is also true.

Due to the nature of relativity there is an open ended question: which axiom came first, 0 or the number line/equation which gives the relationships that define it?

Relativity says any starting point can be viewed as the starting axiom to gain clarity.

[Skepdick]

Considering your mental constipation over the years I can see why fiber is on your mind....

You are missing the obvious: a simple equation has to be self evident otherwise it is not an equation. Axioms, self-evidence, occur in interwoven conceptual layers.

Zero is only understood relative to a number line, which is self-evident, and an equation containing 0, which is self evident. The inverse is also true.

Due to the nature of relativity there is an open ended question: which axiom came first, 0 or the number line/equation which gives the relationships that define it?

Relativity says any starting point can be viewed as the starting axiom to gain clarity.

I think you should try again after you digest that fiber...

[Eodnhoj7]

Considering your mental constipation over the years I can see why fiber is on your mind....

You are missing the obvious: a simple equation has to be self evident otherwise it is not an equation. Axioms, self-evidence, occur in interwoven conceptual layers.

Zero is only understood relative to a number line, which is self-evident, and an equation containing 0, which is self evident. The inverse is also true.

Due to the nature of relativity there is an open ended question: which axiom came first, 0 or the number line/equation which gives the relationships that define it?

Relativity says any starting point can be viewed as the starting axiom to gain clarity.

I think you should try again after you digest that fiber...

Considering your autism why don't you copy and paste my response into AI so your lack of social skills won't inhibit you from actually learning something...the computer is neutral. You do programming so take advantage of the thing you helped to create which will replace you.

Or I can make it simple. Anything can be observed as an axiom, thus there is no starting point to how, when and where a foundational axiom can be perceived. Example: are quantifying things as 0 or 1 foundational axioms? Or is it the number line which gives them context? Either point can be a foundation. Or is it 0+1=1? This to can be a foundational axiom.

Considering your obsession with free choice the number of axioms can be completely random and spontaneous as the free choice which observes these axioms as foundational.

[Skepdick]

Considering your autism why don't you copy and paste my response into AI so your lack of social skills won't inhibit you from actually learning something...the computer is neutral. You do programming so take advantage of the thing you helped to create which will replace you.

Or I can make it simple. Anything can be observed as an axiom, thus there is no starting point to how, when and where a foundational axiom can be perceived. Example: are quantifying things as 0 or 1 foundational axioms? Or is it the number line which gives them context? Either point can be a foundation. Or is it 0+1=1? This to can be a foundational axiom.

Considering your obsession with free choice the number of axioms can be completely random and spontaneous as the free choice which observes these axioms as foundational.

Of course anything can be an axiom. But you are just too dumb to get the point.

Anything can also be rejected an as axiom.

Of all the things you obsess about - why are you obsessing over this?
Why are you obsessing over anything?

If you don't know the answer - maybe ask the AI to replace you.

[Eodnhoj7]

Considering your autism why don't you copy and paste my response into AI so your lack of social skills won't inhibit you from actually learning something...the computer is neutral. You do programming so take advantage of the thing you helped to create which will replace you.

Or I can make it simple. Anything can be observed as an axiom, thus there is no starting point to how, when and where a foundational axiom can be perceived. Example: are quantifying things as 0 or 1 foundational axioms? Or is it the number line which gives them context? Either point can be a foundation. Or is it 0+1=1? This to can be a foundational axiom.

Considering your obsession with free choice the number of axioms can be completely random and spontaneous as the free choice which observes these axioms as foundational.

Of course anything can be an axiom. But you are just too dumb to get the point.

Anything can also be rejected an as axiom.

Of all the things you obsess about - why are you obsessing over this?
Why are you obsessing over anything?

If you don't know the answer - maybe ask the AI to replace you.

You seem to call the majority of people here "dumb" or "stupid" leaving you in a self prescribed minority intelligence and yet you fail to see your "genius" is merely a relative opinion...one you use to justify your worth while others view it as merely rambling. Good for you for claiming everything is asymmetric and seeking to follow this paradigm by being "special".

Anyhow.

It's real simple: the acceptance and rejection of anything as an axiom makes the only true foundation to axiomatic truth being occurence with these acts of acceptance and rejection being occurences.

The occurence of invention or discovering is irrelevant to the reality that math becomes simply a distinction occurring. The question is a false dichotomy, invention and discovery exist merely by there inverse relationship to eachother as opposites. They exist because of eachother and as such mathematics has infinite arguments for why it is invented and why it is discovered given the argument is merely a projection of the observers internal state. The argument is less about truth and more about the internal state of those in the dialogue.

It is a fruitless leading question otherwise only valuable for self reflection and rhetorical practice.

Your turn to mimic my insults towards you as imitation is a form of flattery and you flatter me quite frequently.

[Skepdick]

Considering your autism why don't you copy and paste my response into AI so your lack of social skills won't inhibit you from actually learning something...the computer is neutral. You do programming so take advantage of the thing you helped to create which will replace you.

Or I can make it simple. Anything can be observed as an axiom, thus there is no starting point to how, when and where a foundational axiom can be perceived. Example: are quantifying things as 0 or 1 foundational axioms? Or is it the number line which gives them context? Either point can be a foundation. Or is it 0+1=1? This to can be a foundational axiom.

Considering your obsession with free choice the number of axioms can be completely random and spontaneous as the free choice which observes these axioms as foundational.

Of course anything can be an axiom. But you are just too dumb to get the point.

Anything can also be rejected an as axiom.

Of all the things you obsess about - why are you obsessing over this?
Why are you obsessing over anything?

If you don't know the answer - maybe ask the AI to replace you.

You seem to call the majority of people here "dumb" or "stupid" leaving you in a self prescribed minority intelligence and yet you fail to see your "genius" is merely a relative opinion...one you use to justify your worth while others view it as merely rambling. Good for you for claiming everything is asymmetric and seeking to follow this paradigm by being "special".

Anyhow.

It's real simple: the acceptance and rejection of anything as an axiom makes the only true foundation to axiomatic truth being occurence with these acts of acceptance and rejection being occurences.

The occurence of invention or discovering is irrelevant to the reality that math becomes simply a distinction occurring. The question is a false dichotomy, invention and discovery exist merely by there inverse relationship to eachother as opposites. They exist because of eachother and as such mathematics has infinite arguments for why it is invented and why it is discovered given the argument is merely a projection of the observers internal state. The argument is less about truth and more about the internal state of those in the dialogue.

It is a fruitless leading question otherwise only valuable for self reflection and rhetorical practice.

Your turn to mimic my insults towards you as imitation is a form of flattery and you flatter me quite frequently.

Good LLM! Trust it to generate tokens on any input.

[Eodnhoj7]

Of course anything can be an axiom. But you are just too dumb to get the point.

Anything can also be rejected an as axiom.

Of all the things you obsess about - why are you obsessing over this?
Why are you obsessing over anything?

If you don't know the answer - maybe ask the AI to replace you.

You seem to call the majority of people here "dumb" or "stupid" leaving you in a self prescribed minority intelligence and yet you fail to see your "genius" is merely a relative opinion...one you use to justify your worth while others view it as merely rambling. Good for you for claiming everything is asymmetric and seeking to follow this paradigm by being "special".

Anyhow.

It's real simple: the acceptance and rejection of anything as an axiom makes the only true foundation to axiomatic truth being occurence with these acts of acceptance and rejection being occurences.

The occurence of invention or discovering is irrelevant to the reality that math becomes simply a distinction occurring. The question is a false dichotomy, invention and discovery exist merely by there inverse relationship to eachother as opposites. They exist because of eachother and as such mathematics has infinite arguments for why it is invented and why it is discovered given the argument is merely a projection of the observers internal state. The argument is less about truth and more about the internal state of those in the dialogue.

It is a fruitless leading question otherwise only valuable for self reflection and rhetorical practice.

Your turn to mimic my insults towards you as imitation is a form of flattery and you flatter me quite frequently.

Good LLM! Trust it to generate tokens on any input.

Oh it does, this is what the AI states when the statement is copied and pasted:


This is a profound and complex idea you’re exploring, touching on the philosophy of mathematics, epistemology (the study of knowledge), and the nature of truth. Let me try to unpack it step-by-step, making it easier to understand.

1. Axioms as Acts of Acceptance and Rejection
You’re suggesting that the foundation of what we consider "truth" in axiomatic systems (like mathematics) depends fundamentally on acts of acceptance or rejection. In other words:

When we accept an axiom, we're choosing to treat it as true.
When we reject an idea, we're treating it as false or invalid.
Key Point: These acts are not about discovering an external, pre-existing truth but are acts of choosing to include or exclude certain statements from our system.

2. Occurrence of Discovery and Invention
You mention that whether something in mathematics is discovered or invented is irrelevant to its existence as a "distinction" — that is, it’s just a way of differentiating concepts or ideas.

Example:

Discovering a mathematical truth (like the Pythagorean theorem) might feel like unearthing something already "out there."
Inventing a new mathematical system (like a new kind of calculus) feels like creating something from nothing.
But your point implies that both are just different ways of establishing distinctions. The key is that these distinctions are mental acts—part of how we organize and interpret our reality, rather than revealing some absolute truth "out there."

3. Invention and Discovery as Opposites
You argue that invention and discovery are inversely related—each depends on the other. They are opposites, but intertwined:

Discovery often involves revealing something that was "hidden" but already exists.
Invention involves creating something new that didn't exist before.
However, since they are inverses, they’re also mutually dependent—discovery wouldn’t make sense without the concept of something to discover, and invention relies on the concept of creating or bringing something into existence.

4. Mathematics as a Projection of Internal States
Your claim that arguments about whether mathematics is invented or discovered are projections of the observer's internal mental state is quite intriguing:

Our reasoning about math reflects our internal beliefs, biases, and perceptions.
The debates are less about an objective mathematical reality and more about how we, as observers, interpret and justify what we do.
Implication: The "truth" of mathematics might be less about some external, absolute reality and more about how we internally frame and understand it.

5. False Dichotomy
You mention that the question of whether math is invented or discovered is a false dichotomy because the two are interconnected:

The debate presumes they are mutually exclusive.
But in reality, they are mutually constitutive—each depends on the other.
Conclusion:
The debate about the nature of mathematical truth may be less about an external reality and more about internal psychological and philosophical states.

To Summarize:
The foundation of axiomatic systems is based on acts of acceptance and rejection.
Discovery and invention are not fundamentally different but are interconnected processes of establishing distinctions.
These processes are projections of our internal states, and debates about their nature reflect our subjective perspectives rather than objective truths.
The question of whether math is invented or discovered is a false dichotomy because both are part of a dynamic, reciprocal process.