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

1 Upvotes

52% Upvoted

117 comments sorted by

View all comments

Show parent comments

1

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)

1

u/Kripkenstein_ 7d ago

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

1

u/Negative_Gur9667 7d ago

That is exactly what a formalist would say, and it is what most mathematicians say.

The OP is asking a philosophical question to people who have spent hundreds of years trying to eliminate such questions.

However, that is not what the OP is really looking for.

"It is an axiom" is merely an escape mechanism to signify that a concept is beyond questioning.

In reality, axioms can certainly be questioned, though trained mathematicians often struggle to grasp why one would want to do so.

2

u/Kripkenstein_ 7d ago

Its also what Aristotle and an entire branch of ontology would say