It’s not a mess but it’s complicated. In my view, which I consider a universal truth, there is a question: Can you be assured that the Universe can be described in an untyped (or single typed) fashion or must you have a multitude of type? A two type system might be: TRUE vs FALSE. Universal vs Singularity. An untyped system, such as untyped lambda calculus might be: Function. Or Uncertainty. Or another singular that can describe all things.

It’s not a mess but it’s complicated.
 
In my view, which I consider a universal truth, there is a question:
 
Can you be assured that the Universe can be described in an untyped (or single typed) fashion or must you have a multitude of type?
 
A two type system might be: TRUE vs FALSE. Universal vs Singularity.
 
An untyped system, such as untyped lambda calculus might be: Function. Or Uncertainty. Or another singular that can describe all things.
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 Choice allower
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Common ontology
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 Took a long time for that to ‘click in’ for me. It’s only when I rediscovered “Theory theory” and started coming to terms with accepting Platonism as simply a consequence of our natural abstracting of experience, I could marry them together and work with it.
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 “of course”. Assumed common ontology.
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 When a GPS in my phone triangulates my position on the planet, what is the shape it is utilizing?
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 So, lines drawn around a sphere are invalid?
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Rotate globe under pencil.
Not to the pencil.
 —————–
 coordinate systems.
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  A triangle on a spherical coordinate system does not abide by the axioms of a rectangular coordinate system.No or yes?
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 It’s still called a [type of] triangle. Shall I inform mathematicians and geometers that they’ve been saying it wrong?
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 That is not a Euclidean triangle.
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 Your law is only valid within Euclidean geometry.
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Followers of Euclid are passionate. This is a passionate argument with the conclusion:“Euclid was correct: we live in a knowable, measurable universe accurately observable through the human senses. “http://rationalargumentator.com/euclideangeometry.html
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 “The assumption that (in a triangle) the sum of the three angles is less than 180° leads to a curious geometry, quite different from ours, but thoroughly consistent, which I have developed to my entire satisfaction. “– Gauss the troublemaker.https://www.cut-the-knot.org/triangle/pythpar/Drama.shtml
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  If I do, will you then describe it in 2 dimensional terms?
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 You will describe them as arcs, for we are using a 2 dimensional representation system (our screens)
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 I cannot hand you a ball that you can then hold and look at and watch the shapes change from lines to arcs and back again.
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 If I draw a triangle on a flat piece of paper and I then bend the paper such that the triangle no longer has 3 angles adding to 180 degrees, what then?
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 Can you prove the deformation without the paper?
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 I’ve decided that you are a Euclidian and that is ok. I can’t prove it to you in this 2D space we have available, and while I could find a video showing how a triangle stays a triangle even when on a curving and flattening piece of paper, I also know you can validly describe that triangle via different means while it is shifting form.
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 It changes identity as the paper shifts. That’s actually a fascinating outlook and I respect that.
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 a fascinating morphism in category theory is https://en.wikipedia.org/wiki/Zero_morphism as“If a category has zero morphisms, then one can define the notions of kernel and cokernel for any morphism in that category. “
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 ” But you have no reasons to assume that from Euclidean geometry, and yet you do.Bias.

QED.

You and I don’t have a common ontology. However your ontology is a special case of mine. So I can understand you, but you cannot understand me.

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 There’s actually a good reason and it’s one I envy:

Once you have adopted an ontology as truth or fact or self-evident, you can get to work.

Ontology is a framework/foundation you can build upon, and Euclid is powerful, productive and in use for how many centuries now?

Non-Euclidean is more my kind of fun but I _know_ that Chris is far more productive for holding this as truth.

Meanwhile, I’m still building my ontology.

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