Paradox?

[Arising_uk]

Except that philosophy of math is set up different from these two categories.

PhilX

Not when it strays into ontology and metaphysics it isn't.

[Philosophy Explorer]

Here's a link that says a dimensionless point can be defined:

https://en.m.wikiversity.org/wiki/Point ... and_planes

As long as it can be defined and it's consistent, it exists.

This is an argument you can't win. Now you're going to say you can't see it. That's your problem. Now put up a link 5hat says dimensionless points can't exist.

PhilX

Of course I agree that if you say a dimensionless point is a conceptual construct of Mathematics then it exists but you appeared to assert that they actually exist inside solid objects are you now saying they don't actually exist?

It is consistent to define oompa loompas as white skinned and golden haired pygmies who come from Loompaland, which is a region of Loompa, a small isolated island in the hangdoodles. It is consistent to define a unicorn as an equine-like a beast with a single large, pointed, spiralling horn projecting from its forehead. It is consistent to define gravity as an effect upon an object due to a pushing battle between invisible white fairies and invisible pink fairies. Do oompa loompas, unicorns and these white or pink fairies exist?

They do exist inside of solid objects.

Consider this:

https://www.mathplanet.com/education/ge ... o-geometry

It reads in part:

"A space extends infinitely in all directions and is a set of all points in three dimensions. You can think of a space as the inside of a box."

Match point.

PhilX

[Arising_uk]

If you mean as a mathematical construct then sure but if you mean as a physical entity then I think you talking bollocks but if you are not then I look forward to watching you collect the Nobel prize for Physics.

So which is it, mathematical construct or actual entity?
p.s.
As an aside try thinking about why Physics and Mathematics are different subjects.

[Philosophy Explorer]

If you mean as a mathematical construct then sure but if you mean as a physical entity then I think you talking bollocks but if you are not then I look forward to watching you collect the Nobel prize for Physics.

So which is it, mathematical construct or actual entity?

Both. The article can mean either one. This now means you're going to have to find an article that denies the actual entity. Debate is over.

PhilX

[Arising_uk]

Do you seriously think any Physicists would actually look for a 'dimensionless point'?

Congratulations you have exceeded my estimation of your philosophical illiteracy by at least an order of magnitude.

[Philosophy Explorer]

Do you seriously think any Physicists would actually look for a 'dimensionless point'?

Congratulations you have exceeded my estimation of your philosophical illiteracy by at least a magnitude.

You're an idiot. The only thing I expect from you now is the white flag. Also you're not a physicist.

PhilX

[Arising_uk]

Come on then brainbox, tell me how you think a physicist would go about detecting a dimensionless point? In fact since you assert that such things are physical entities tell me how you went about detecting them as there's a Noble prize in Physics awaiting you.

[Philosophy Explorer]

Come on then brainbox, tell me how you think a physicist would go about detecting a dimensionless point? In fact since you assert that such things are physical entities tell me how you went about detecting them as there's a Noble prize in Physics awaiting you.

Since you're supposed to be the physicist, I'll let you answer that question. I still expect a white flag (btw it's
Nobel Prize Mr. Physicist).

PhilX

[Arising_uk]

Typos now. Is that it?

You are the one who asserts that what appears to a physical impossibility is possible so tell us how you know this?

You really are a good interweeble as there are good answers to my questions out there but you are too hung-up protecting your fragile ego to find and think about them.

[Philosophy Explorer]

Typos now. Is that it?

You are the one who asserts that what appears to a physical impossibility is possible so tell us how you know this?

You really are a good interweeble as there are good answers to my questions out there but you are too hung-up protecting your fragile ego to find and think about them.

What a perfect description of you.

PhilX

[Arising_uk]

Probably, but still awaiting your answer to how you know your assertion that dimensionless points have a physical reality is true?

Do you have it in you to be able to philosophically explain your words? I doubt it.

[Philosophy Explorer]

Probably, but still awaiting your answer to how you know your assertion that dimensionless points have a physical reality is true?

Do you have it in you to be able to philosophically explain your words? I doubt it.

You've already received my answer. I'm still awaiting yours.

PhilX

[Arising_uk]

But you links don't show that 'dimensionless points' are actually a real thing?

What I'm trying to understand is what you meant by "both" in your previous reply, as I've agreed that there is a mathematical construct called a 'dimensional point' that is essentially a set of co-ordinates that describe a location but what is it that you'd expect to find at that location, say in a solid or in a space? As your reply appeared to say that you'd expect to find some actual entity you call a 'dimensional point'?

[Philosophy Explorer]

But you links don't show that 'dimensionless points' are actually a real thing?

What I'm trying to understand is what you meant by "both" in your previous reply, as I've agreed that there is a mathematical construct called a 'dimensional point' that is essentially a set of co-ordinates that describe a location but what is it that you'd expect to find at that location, say in a solid or in a space? As your reply appeared to say that you'd expect to find some actual entity you call a 'dimensional point'?

I expect to find a dimensionless point. And some links do show they're real. The article that says that lines always have a midpoint implies that the line (it doesn't matter if they're straight or curved) is made up of an infinity of dimensionless points (by logic) and has no gaps.

So where's your proof?

PhilX

[wtf]

Wrong on both counts.Actual solid objects are made up of points, but the size of the object has no relationship to the size of the set of the points within the object. Who are these people who think this? Mathematicians such as Cantor for one. Have you checked Wikipedia?

Why yes Phil, I did check Wikipedia's article on Cantor. There I found:

Cantor's philosophy on the nature of numbers led him to affirm a belief in the freedom of mathematics to posit and prove concepts apart from the realm of physical phenomena, as expressions within an internal reality.

Again: ... concepts apart from the realm of physical phenomena ...

If you know of any specific work of Cantor's in which he claims that mathematical points have anything to do with the physical universe, please feel free to supply that citation.

To the contrary, as Arising_uk repeatedly notes, dimensionless points are purely mathematical abstractions. In physics, nothing smaller than the Plank length can be sensibly spoken about or measured. Physicists build particle colliders to look for quarks, bosons, neutrinos, and the like. But there has never in the history of physics ever been a grant proposal or research program to find dimensionless points. That's because there are no dimensionless points in the physical world. Dimensionless points are mathematical abstractions. Dimensionless points are useful for doing physics but they are not themselves physical.

I'll add that I'm disappointed but not surprised that you never replied to my post in which I debunked your erroneous notions regarding the cardinality of the real numbers.

You seem to read snippets of text on Wikipedia, extrapolate false conclusions, and then close your mind to reason.