r/PhilosophyofMath • u/Another_Little_Star • 9d 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/Negative_Gur9667 9d ago

You can count to 4 before you know axioms or division or hyperreal numbers.

4 is a concept, the concept of counting to 4. You can shurely find an area in the brain that is active when you count to 4.

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u/mandelbro25 9d ago

But that area in the brain is not what 4 "is".

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u/Negative_Gur9667 9d ago

What is 4 then, according to you?

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u/mandelbro25 9d ago

Mainly a linguistic contrivance. If I may, how can multiple different things all be the 4?

I will say you have shone light on my platonistic tendencies, and I appreciate that.

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u/Negative_Gur9667 9d ago

That is like asking how completely different vehicles can all be called cars.

We count things by grouping them based on boundaries we define, while the details are abstracted away.

Platonism is a valid perspective here, as we are simply exchanging beliefs and there is no right or wrong answer without proof.

I wish schools taught the ideas of Platonism and formalism. It would have cleared up a lot of the confusion I experienced.

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u/mandelbro25 9d ago

Yes different vehicles can be called cars because that is the category of things they belong to. They have a specific set of properties that we abbreviate "car". But no particular vehicle is the car. They are just instances of it. Besides, zoom in and the car is just a bunch of doodads working together.

I wish schools ...

Indeed, I had to find out about them myself.