No, we utilize non-dimensional points (and other mathematical constructions) as strictly hypothetical objects, and recognize that they do not have real existence. — aletheist

Which means, according to you, the Standard Model is wrong. — tom

No, it means that it is irrelevant within mathematics whether its strictly hypothetical models represent anything that really exists. In other words, a non-dimensional point does not necessarily have to represent something that is actually non-dimensional. If it helps, we can amend my initial comment by changing "do not have" to "need not have."

Which means, according to you, the Standard Model is wrong. Please explain. — tom

So if particles are modelled as strings rather than points, the SM is "wrong"?

Sounds legit.

No, it means that it is irrelevant within mathematics whether its strictly hypothetical models represent anything that really exists. In other words, a non-dimensional point does not necessarily have to represent something that is actually non-dimensional. — aletheist

Except that quarks, leptons, and bosons are point particles.

Except that quarks, leptons, and bosons are point particles. — tom

Why do you keep avoiding the "modelled as" point particles? I mean it is normal in physics to understand that it is a specific kind of useful idealisation.

A point particle (ideal particle[1] or point-like particle, often spelled pointlike particle) is an idealization of particles heavily used in physics. Its defining feature is that it lacks spatial extension: being zero-dimensional, it does not take up space.[2] A point particle is an appropriate representation of any object whose size, shape, and structure is irrelevant in a given context. For example, from far enough away, an object of any shape will look and behave as a point-like object.

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

The key idea is that a point particle lacks internal structure. So even with quantum HUP fuzziness, you can still exactly locate it as a quantum superposition of itself. There are no observables resulting from further internal structure to blur the picture.

But equally - if we are talking about ontological reality - you run into problems trying to get close to a massive point particle. There is the Compton wavelength at which your point will start spewing other points. In trying to get close observationally, we produce more particles due to the energy density. And which is now the one we claim to have been there?

So is there some reason you take a monstrously simple approach to your ontological claims about particles. Or do just believe the pictures of things are those things due to some kind of naive realism (kind of like your happy literal acceptance of branching multiverses)?

Your quoted passage clearly states: "Its defining feature is that it lacks spatial extension: being zero-dimensional, it does not take up space." So what's the fuss? Are you and aletheist denying this?

Are we talking about the defining feature of the model or the reality. (You understand the difference by now, right?)

If the defining feature of the model does not describe the reality of the thing being modeled, then it is a falsity. If I state the defining feature as a red 1964 Ford Mustang, then the reality being referred to better be a red 1964 Ford Mustang, or my defining feature is a falsity.

OK. You still don't get how it works. Cool.

Actually it's you who doesn't get it. If there is no correspondence between the model and the reality, it is a falsity.

The point I was making, which started this discussion is that we have no way to establish correspondence between the model and the reality, because the things are modeled as non-dimensional, and we have no way of conceiving of non-dimensional existence. If your argument is that the model doesn't necessarily represent the reality, then you are arguing that we should accept fiction.

The point I was making, which started this discussion is that we have no way to establish correspondence between the model and the reality, because the things are modeled as non-dimensional, and we have no way of conceiving of non-dimensional existence. If your argument is that the model doesn't necessarily represent the reality, then you are arguing that we should accept fiction. — Metaphysician Undercover

Read the wiki page. What physics means is that you can treat an elementary particle as a mathematical point as that is a model of located material being without internal structure.

You can treat the Earth as a mathematical point too - a centre of gravity. And it works so long as you are far enough away not to be bothered by the Earth's material variations - the effect that mountain ranges would have for instance (coincidentally, Peirce's specialist area in science).

Likewise the standard model can call an electron a point. But then string theory or braid theory might discover an internal structure that shows the pointiness to be merely an effective theory of the real deal.

So as usual, you are trying to insist on your lay interpretation of what is being said and not taking in the subtleties of the way science employs its metaphysics.

In general, knowledge is only partially dependent on would-be knowers. While going by the traditional definition, the "justified" "belief" part is our part.

For propositions these differ: absence, indifference, belief, knowledge, certainty, ...

Supposing that to know p, you must also know that you know p, is the first step in a diverging regress. Which, incidentally, might be an argument against certainty (in most cases).

Suppose I was to claim "there was snow on the peak of Mount Everest last Wednesday local time". What, then, would it take for my statement to hold? Well, that would be existence/presence of snow up there back then, regardless of what anyone may or may not believe. And that's the "true" part of knowledge, an ontological condition.

So, we can do our part, justify our claims, and do away with errors.

Right, that's exactly what I'm talking about. We can "treat" something as if it is zero dimensional, meaning that it occupies no space, has no spatial existence. But we have no principles by which we can say that this is the reality of the thing. What I am expressing is that there is a need for principles to allow for real non-dimensional existence. The argument I was making, was that if we want to be able to realistically treat something as non-dimensional, we need some principles whereby a non-dimensional thing can have real existence.

You can treat the Earth as a mathematical point too - a centre of gravity. And it works so long as you are far enough away not to be bothered by the Earth's material variations - the effect that mountain ranges would have for instance (coincidentally, Peirce's specialist area in science). — apokrisis

You're confusing the issue here. Peirce understood the problem, but his solution was to deny the reality of non-dimensional existence, opting for infinitesimals. So deferring to Peirce supports my argument that there is a real problem with representing things as non-dimensional points. The difference between Peirce and I is that I apprehend a need to assume real non-dimensional existence, whereas Peirce saw no need for this and chose infinitesimal existence instead, to account for the existence of the things which physics treats as non-dimensional.

Likewise the standard model can call an electron a point. But then string theory or braid theory might discover an internal structure that shows the pointiness to be merely an effective theory of the real deal. — apokrisis

This illustrates the problem I am referring to. Since there is nothing real which is referred to by "zero dimensional point", then the reality of the entity which is represented as a zero dimensional point may be interpreted in infinitely many different ways. So take your example of the earth. If we represent the earth as a non-dimensional point, then the actual form that the earth has, could be anything. To properly understand the earth would mean to produce a proper representation of its spatial form.

You naturally assume that the thing represented as a zero dimensional point has a spatial form, because you're physicalist, and you cannot comprehend any other type of existence. I accept real non-spatial existence, so my claim is that there are real things, demonstrated by physics to have real existence, which cannot be represented as having a spatial form. These things are non-spatial, non-dimensional. So we need some way to differentiate between things like the earth, which can be represented by a point, but still have a spatial form, and things which are really non-spatial, non-dimensional, having no spatial form. Otherwise we'll be continually trying to give non-spatial things a spatial form, such as in your example with string theory.

I accept real non-spatial existence, so my claim is that there are real things, demonstrated by physics to have real existence, which cannot be represented as having a spatial form. These things are non-spatial, non-dimensional. — Metaphysician Undercover

What things exactly? And what is their relevance to this discussion about modelling particles as located objects with no internal structure?

I recommend not wasting your time. MU clearly has no clue about how mathematical modeling works as diagrammatic abstraction, primarily embodying relations rather than objects. And remember, he believes that every difference makes a difference. :-}

What things exactly? And what is their relevance to this discussion about modelling particles as located objects with no internal structure? — apokrisis

Those are the things I'm talking about., the things with no internal structure.. If a thing occupies space, i.e. is spatial, dimensional, it has a spatial form and that is its internal structure. (For example, a circle has an internal structure expressed by pi.) Therefore it makes no sense to talk about things with no internal structure as anything other than non-dimensional things. Since they have no spatial existence, then the idea of locating them in space is somewhat dubious, and how they relate to things which have spatial existence is questionable. That is why I suggested that this problem may be resolved if a way could be devised to locate them in time.