Do numbers exist in nature or are they human contructs?

[Xamonas Chegwé]

I agree that π arises naturally in many phenomena, but I would argue that it does so because it is a vital component of circle geometry. All of its "arisings", if you trace the maths back, would derive from the circle in one way or another, which then forms one basal component of the more complex phenomenon. I can't see π being formed by several, independent mechanisms; or if it were, I would suspect deeper connections between the various occurrences.

Of course there are deeper relationships. And, due to π being integrally tied up with circles, that makes circles "exist" even if there is no such thing as a "perfect circle". The two are inextricably linked.

All a circle (or a spere) actually "is" is the set of points equidistant to another point in two (or three) dimensions. That is where the deeper relationship lies. A circle is also the shortest, stable orbit of one object about another. An expanding sphere is also the limit of the influence of any single spacetime event.

Round things pop up everywhere and, when they do, π is not far behind!

[JimC]

As a broader take on this issue, do logical propositions exist independently of human thought, or in fact the physical universe itself? By this, I don't mean any specific logical proposition about the relationship between particular entities, but the structure behind them, the laws of logical necessity.

[pErvinalia]

NO. Material stuff exists. Non-material stuff dunnant exist. Thread solved!@

[JimC]

Define "exists"...

[pErvinalia]

It's what material stuff does.

[JimC]

It's what material stuff does.

Excellent!

You've just proved the existence of the perfect circle!

[pErvinalia]

The perfect argumentative circle!

[MiM]

Stop this folly already

The Moon and the Earth continues to exists even if we annihilate all life tomorrow. Doesn't matter that nobody is here to name them.
Together they are two celestial bodies. Doesn't matter that there is nobody here to count them.

Any other way to look at this is giving away to some weird mysticism, or even worse to a similar kind of hubris Christians like to fall for: "God made the universe for us" or "Nothing is countable without us" big deal

[Svartalf]

Quite so. Even ultimately unanswerable questions can provoke interesting discussion if one isn't simply dismissive.

does a number exist if it's not counted?

[Svartalf]

NO. Material stuff exists. Non-material stuff dunnant exist. Thread solved!@

Space void doesn't exist?

[JimC]

Quite so. Even ultimately unanswerable questions can provoke interesting discussion if one isn't simply dismissive.

does a number exist if it's not counted?

Yes.

[pErvinalia]

NO. Material stuff exists. Non-material stuff dunnant exist. Thread solved!@

Space void doesn't exist?

Of course not. Nothing can't exist. "space void" is just a human concept. It's an abstract concept, so it exists in the minds of humans.

[Audley Strange]

Ah but wait!

We define what a circle is in the first place, we see irregular looking things in nature, derive some pattern, perfect it, cut out the outliers and come up with a circle, which once we construct, we go on to investigate that construct as if it relates to external processes. However what external processes we know of, we perceive, which means they are restricted by our apparatus and more importantly our ability to turn that raw data into a coherent narrative that we can then analyse anyway. Is it possible that platonic forms and mathematics are somehow like Archetypes we are coded with to make navigation through the insane radioactive hellhole a bit easier, rather than something actually external?

[rainbow]

Quite so. Even ultimately unanswerable questions can provoke interesting discussion if one isn't simply dismissive.

does a number exist if it's not counted?

Yes.

No.

[JimC]

If Godel's theorem has any relevance to Svarty's question, then it would mean that the answer to "does a number exist if it's not counted?" is "unknown", rather than either yes or no...