Ok good point I overreached there. A different proof that Actual Infinity cannot exist mathematically:

- Actual Infinity is greater than any number
- But we can only make a number larger through addition or multiplication
- So there is no way to arrive at Actual Infinity.

Actual infinity cannot exist geometrically as there is no way to construct a line segment longer than all other line segments.

If you are a materialistic, you have to acknowledge Actual Infinity is impossible.

You cannot arrive at infinity through a finite number of operations. If you want to arrive at infinity, you need to perform an infinite number of operations.

And an infinite number of operations is impossible in the real world and impossible mathematically

Humans can't perform an infinite number of operations because human consciousness is finite. But that does not mean that it is impossible for an infinite number of events to take place within a bounded period of time.

There is no such "set". The moments after the present moment have not yet come into existence so you cannot collect them into a set, nor can they be members of "a set" in any way or fashion, as they are non-existent. You are claiming to have a set of things which do not exist, but that's impossible so it's pure fiction, nonsense. — Metaphysician Undercover

Putting non-existent things in a set in no way commits one to their existence (goodbye existential import). The set of Harry Potter characters is only populated by non-existent things.

It's a matter of understanding the definition of "set", and understanding the definition of "infinite", and realizing that it is impossible to have an infinite set. These two are incompatible, by definition, so talking about infinite sets is contradictory nonsense. Of course we all know that because of the many paradoxes which are known to arise from the assumption of infinite sets, but some like you, choose to ignore this obvious fact. — Metaphysician Undercover

It's question begging because no one is using your definition of infinity which is defined in a way so as to preclude being actual, nor does the definition of a set preclude it from being infinite. There's no understanding "the" definition because there is no one definition. The maths definition of infinity is actually useful since it's crucial to modern mathematics (see calculus) and introduces no contradictions. There are no paradoxes involving the mere concept of infinity in standard mathematics, otherwise you could provide the proof of such a contradiction from the axioms and inference rules in the standard formalism.

That something has a particular property is a judgement. The thing is a particular the property is a universal. Therefore if "sharing a property" is what is required to be a member of a set, then a judgement is required in order that things be of the same set. So the declaration "you go in this set" is exactly what is required in order that a thing be a member of a particular set. — Metaphysician Undercover

Incorrect. If two things hare a property they share it whether or not I judge them to. Two red objects share the property of being red even if no one exists to recognize such. So to speak of sets having members based on a shared property in no way requires a judgement to make it so.

You seem to either believe that sets just naturally exist without ever being created by human minds, or else that things automatically jump up and join any set which they are supposed to be a member of, without being counted into that set. So either the green grass is naturally a member of the set of green things without that set ever being created by a human mind, or else the green grass jumps into the set, of its own power, as soon as "the set of green things" is named by a human being. Both of these, I tell you are nonsense. — Metaphysician Undercover

You're doing it again. It's not a mechanistic process that occurs over time nor is it necessarily done by an agent. Sets don't exist in the mind. The "set of numbers greater than 500 trillion but smaller than 1 quadrillion" is simply too large to be conceptualized in the mind, but it's obviously a perfectly legitimate set.

But that does not mean that it is impossible for an infinite number of events to take place within a bounded period of time — Magnus Anderson

That would mean a physical system passing through an infinite number of states in a finite period of time. That’s spiritualism. That leads to Zeno’s paradoxes - absurdities. To avoid the absurdities time must be discrete.

Actual Infinity
=
Cardinality of the set of natural numbers
=
Nonsense

I think physics will get along ok with potential infinity. I dont think they need actual.

It's math that needs actual infinity as part of a foundation. Is it ok for math to be foundationless?

Problem is the cosmologists are using the actually infinite. Eternal Inflation and the measure problem is an well known paradox.

I’m not a mathematician but the foundations of calculus are somewhat shaky as far as I can tell. Relies on an axiomatic definition of actual infinity from set theory IE thin air.

By any chance do you have a history of arguing for determinism because of a delay between event and cognition?

Well i am a determinist but I don’t quite see what you mean?

Are you a determinist because there's a delay between events in the world and our recognition of those events?

No I just believe in cause and effect.

Oh. You were reminding me of someone else.

Why couldn't cosmologists get by with potential infinity?

I think they like to complicate things. Actual Infinity (a logical contradiction) is great for complicating things.

Once you rule out Actual Infinity, time has a start and quite a few models go out of the window. Infinity is keeping people in a job.

"Actual" infinity is an Aristotelian concept. He contrasted it with potential infinity.

A beginning point for time is also a challenge to the imagination.

The Big Bang suggests a start of time. For something to exist it must have a start. A more elaborate argument for the start of time:

- Something can’t come from nothing
- So base reality must have always existed
- If base reality is permanent it must be timeless (proof: assume base reality existed forever within time - the total number of particle collisions would be infinite - reductio ad absurdum)
- So base reality must be timeless (to avoid the infinities) and permanent
- Time was created and exists within this permanent, timeless, base reality
- So time must be real, permanent and finite

Your base reality defies your rule that "for something to exist, it must have a start"

No it has a start and and end. Imagine all of finite space time as a static block that exists permanently. It’s the block universe view of Eternalism
https://en.wikipedia.org/wiki/Eternalism_(philosophy_of_time)

There's a long range issue with your approach that has to do with logic-based ontology.

That said, you aren't just producing an old-philisopher-based-word-salad. You're thinking for yourself. And that is awesome.

The base reality has a beginning point?

Actual Infinity
=
Cardinality of the set of natural numbers
=
Nonsense — Devans99

So you are going even further than limiting infinity in physics and just denying the coherence of standard mathematics.

The base reality has a beginning point? — frank

Thanks appreciate it! I’d imagine base reality has finite spacial dimensions so in a sense it would have beginnings and ends.

But where did this base reality come from?

So you are going even further than limiting infinity in physics and just denying the coherence of standard mathematics. — MindForged

I’m not saying maths is incoherent, just pointing out it’s impossible to define the cardinality of an infinite set so maybe infinite set is a flawed concept as was argued earlier...

But where did this base reality come from? — frank

It did not come from anywhere. It has permanent existence outside of time. Never created it just is. Time is a created construct that lives within this permanent base reality. The past present and future are all real. This is the view from Relativity.

That would mean a physical system passing through an infinite number of states in a finite period of time. — Devans99

What's wrong with that?

It did not come from anywhere. It has permanent existence outside of time. Never created it just is. Time is a created construct that lives within this permanent base reality. The past present and future are all real. This is the view from Relativity. — Devans99

Time is a construct created how?

Well continuous time leads to paradoxes like Zeno’s. Archiles never catches the hair with continuous time because that requires Archiles to traverse an infinite number of steps. With discrete time there are no paradoxes, so we can eliminate continuous time I think.

I’m not saying maths is incoherent, just pointing out it’s impossible to define the cardinality of an infinite set so maybe infinite set is a flawed concept as was argued earlier... — Devans99

That is saying standard mathematics is incoherent. Standard mathematics incorporates multiple levels of infinity with different cardinalities. It's not impossible to define said cardinalities, I did so in previous posts. A wholesale denial of the coherence of defining the Cardinality of infinite sets represents and abandoning of standard mathematical formalisms, even the non-classical ones.