Can something be of zero size and still exist?

[Robert Arvay]

Can something be of zero size and still exist?

Physicalist scientists have proposed the existence of a singularity, which is an infinitely small, and infinitely dense, point particle, in which the known laws of physics might not apply.

Such a point particle supposedly occupies the center of a black hole star, or perhaps, the center of the primordial universe before the Big Bang.

Other scientists propose that the smallest possible size of any object is the Planck length, which is larger than zero, but unimaginably small, much smaller than an atomic proton.

A third consideration is that an object could begin shrinking in size toward zero, and never stop shrinking, but never reach zero--at each instant halving in size, for example.

Zero and infinity are problematic for both physics and mathematics.

What does metaphysics have to say about them?

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[SanteriSatama]

Do the spaces between these words exist? Spaces around this sentence?

[Robert Arvay]

Do the spaces have a size of zero?

[SanteriSatama]

Do the spaces have a size of zero?

In relation to what? Why should spaces have a "size", and if they should, what kind of size?

[Robert Arvay]

I asked,
Can something be of zero size and still exist?

You did not answer, but instead asked,
Do the spaces between these words exist? Spaces around this sentence?

I tried to clarify for context:
Do the spaces have a size of zero?

You still did not answer, but asked,
In relation to what? Why should spaces have a "size", and if they should, what kind of size?

Before continuing, I need answers. If you wish not to give them, go in peace.
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[ScottRoberts]

Can something be of zero size and still exist?

Nothing in our sense contents (which is to say: in physical reality) has zero size. We can, however, and every student of geometry does this, think into existence the idea that is a zero-size point.

Zero and infinity are problematic for both physics and mathematics.

Not really. One uses mathematics with zero and infinity to model physical reality, but the fact that physical reality contains neither just means the model is not the territory, but that's the case with all models. One can still use the model to figure out how to send rockets to the moon.

What does metaphysics have to say about them?

If one is an idealist, one says they are ideas that have no existence outside of the minds that think them.

[SanteriSatama]

I asked,
Can something be of zero size and still exist?

You did not answer, but instead asked,
Do the spaces between these words exist? Spaces around this sentence?

I tried to clarify for context:
Do the spaces have a size of zero?

You still did not answer, but asked,
In relation to what? Why should spaces have a "size", and if they should, what kind of size?

Before continuing, I need answers. If you wish not to give them, go in peace.

Let's pretend this is a philosophy forum, where we try to make our questions and their presuppositions more meaningful and coherent. OK?

Does quantification exist, and how? If a phenomenon does not have quantifiable size, does it not exist? Does hunger exist? Most would answer yes, I guess. When feeling hungry, how do you measure the size of your hunger, if you measure? By numbers?

[Robert Arvay]

Santeri said:
Let's pretend this is a philosophy forum, where we try to make our questions and their presuppositions more meaningful and coherent. OK?

Me:
Other than for your snarkiness, and your arrogant condescension, I mostly agree with your statements.

In physics, it is debated whether something can have dimensions of zero--for example a singularity.
There are also proposed massless particles, but the question arises, can the mass of any finite particle be zero?

The problems in math and geometry regarding zero and infinity have not been solved.
A geometric point has dimensions of zero, but zero is not nothing. Zero has properties, and therefore,
is "something."

Infinity is supposedly unreachable, as in an infinite sequence, and yet, a geometrically finite line has
an infinite number of zero-dimension points, so the unreachable is reached.

A corresponding question I have not seen asked before is that of the infinitely collapsing particle.
The cosmos is said to be infinitely expanding toward infinity,
so therefore, can a collapsing particle continually and repeatedly halve its size forever?

George Gamow, in his classic, 1,2,3 . . . infinity put forth a detailed analysis of the topic.

Your question about the quantification of hunger pertains to measures of perception, if that is your point,
but I find it too tangential to fit into this discussion without more context and connection.

Likewise, the comparison of the size of "spaces" is semantical. If it is relevant, it needs more explanation.

" . . . ideas that have no existence outside of the minds that think them.," is not a satisfying answer, because
leprechauns may share that description, whereas conceptual explanations of reality, such as zero-dimensional
particles are quite a different thing.

Best regards,
Robert
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[SanteriSatama]

In physics, it is debated whether something can have dimensions of zero--for example a singularity.
There are also proposed massless particles, but the question arises, can the mass of any finite particle be zero?

The problems in math and geometry regarding zero and infinity have not been solved.
A geometric point has dimensions of zero, but zero is not nothing. Zero has properties, and therefore,
is "something."

Infinity is supposedly unreachable, as in an infinite sequence, and yet, a geometrically finite line has
an infinite number of zero-dimension points, so the unreachable is reached.

Zero is the identity element of addition. It has a clear mathematical meaning. It is also useful for positional writing of numbers.

Hilbert's point reductionist geometry is physically wrong, as is also Cantor's "completed infinity" and theory or real numbers. Zeno proved physically that continua don't reduce to discrete quantification. Hilbert's formalism pollutes mathematics with totally arbitrary counter empirical axiomatics.

By 'physical' I mean empirical, including intuitive experience of continua. The anti-empirical formalist math that post-Cartesian scientism is using is physically wrong and anti-empirical, and hence it's not valid mathematical physics, it's a religious cult of materialism and obsessive quantitative measuring. Mathematics does not reduce to qualia of quantification, continuum is more fundamental than quantification, both intuitively/empirically and constructively.

A corresponding question I have not seen asked before is that of the infinitely collapsing particle.
The cosmos is said to be infinitely expanding toward infinity,
so therefore, can a collapsing particle continually and repeatedly halve its size forever?

Zeno's paradoxes prove that process of halving cannot continue forever. Under LNC, Halting problem is undecidable.

" . . . ideas that have no existence outside of the minds that think them.," is not a satisfying answer, because
leprechauns may share that description, whereas conceptual explanations of reality, such as zero-dimensional
particles are quite a different thing.

Leprechauns are more real than nonsense about "completed infinity".

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[Robert Arvay]

Santeri wrote:
Zero is the identity element of addition. It has a clear mathematical meaning. It is also useful for positional writing of numbers.

Me:
Yes, but its relevance to this discussion is that it is considered to be an infinitely small quantity, which is why it presents difficulties for metaphysics.

Santeri:
Zeno proved physically that continua don't reduce to discrete quantification.

Me:
Really? He is often cited to show that the physical universe must be granular.

Santeri:
a religious cult of materialism and obsessive quantitative measuring.

Me:
I won't argue for materialism. I personally do not engage in the materialist versus idealist argument. I see reality as a hierarchy, with its core an absolute, unknowable essence, which gives rise to all else. Holy Spirit, Creator, Creation.

Santeri:
Leprechauns are more real than nonsense about "completed infinity".

Me:
That is a bold statement that goes far beyond my level of comprehension.
Leprechauns are mythical, completed infinity has at least some geometric support.
However, I am not equipped to debate either.

Best wishes to you!
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