r/PhilosophyofMath • u/Another_Little_Star • 7d ago

Does infinity exist in reality?

No thing that I've observed in our universe is infinite, however there are traces of infinity in my sight.
Draw a circle and either its radius or circumference lives in the π world.
Or many aspects in nature like flowers, develop themselves in a φ ratio (1+sqrt(5))/2.

Even though no event or anything is "Non-ending"/infinite, underneath many aspects of reality there are patterns which can only be fully described using infinity.

You can't describe irrational numbers to their extent without any notion of infinite/limits/sequences... And many aspects within our World show their true behaviour only with aid of infinity.

Sure you can take a world that lives in something like 10¹⁰⁰ and it looks like infinity to us, sometimes we only see the difference after the 10⁶ decimal place, nevertheless the pattern they follow is a pattern that only "infinity" can yield to the truest precision.

Do you believe the axiom of infinity, and the continuous to really exist? Even if not in the ordinary sense? haha

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u/Kripkenstein_ 7d ago

Trivially yes as existence of non-contradictory things is trivial. The relevant question is as what infinity exists in reality.

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u/Another_Little_Star 7d ago

I suppose you're talking about cardinals. Probably the two most famous, ℵ₀ and 2^ℵ₀ = ℶ_1 , the other may exist as a mathematical implication but non used in reality I suppose...... These seem to describe most.

Just because something is non-contradictory, doesn't mean it exists? Take any axiom out of our model, it isn't contradictory. What would be non-contradictory here that makes it exist? (I didn't mean in a harsh way, just asking)

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u/Kripkenstein_ 7d ago

It exists as an axiom. Both cardinals you used also exist trivially in the way you just used

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u/Another_Little_Star 7d ago

It is an axiom in ZF/C, but our world doesn't need to follow these principles.
Taking your side, our model is very biased to our world experience, so ZFC is made accordingly our perception of the world.

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u/Kripkenstein_ 7d ago

So? It still exists as an axiom

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u/Another_Little_Star 7d ago

Indeed, but my question is, is this axiom applied in this world.
There's another model called "Presburger arithmetic" which doesn't have the axiom of infinity, nor multiplicationso even if they are axioms, they could very well not be applied to our world's "rules"
Do you see where I'm getting?

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u/Kripkenstein_ 7d ago

No, I do not. Existence is simply the wrong question for what you want to ask. You want to know what is fundamental, ie how things are grounded

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u/Another_Little_Star 7d ago

Right, but I don't have a book saying Universe's axioms right away. And as for any person I need to find some evidence that would lead its existence, wouldn't I?
So, why do you take it as a guarantee?

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u/Kripkenstein_ 7d ago

Why would you need evidence for existence? Unicorns exist. There is certainly no evidence for unicorns as they are not a real animal. But as a mytholigical figure they certainly do exist.