DannyTR

As far as I’m concerned the axiom of infinity is provably wrong. The definition of a set in set theory is also wrong (polymorphism). - All sets should have a natural number as cardinality (sets after all contain complete objects) - but there is no natural number that is larger than all other natural numbers - so the infinite set does not exist, axiom of infinity is wrong

Actual Infinity is defined here: https://en.wikipedia.org/wiki/Actual_infinity In maths actual infinity is the infinite set concept (whereas potential infinity is closest to the limit concept).

Another example of the non-existence of actual infinity. Consider the numbers on the real number line. EG between 0 and 1. Does the interval contain an actual infinity of numbers? - No. - Numbers have length zero - they are just logical labels on a line - So the length of the interval 1 divided by the length of a number zero equals UNDEFINED. So it’s correct to say that the number of real numbers between 0 and 1 is undefined (rather than Actual Infinity). Actual Infinity does not exist and it should not be used in cosmology. Can anyone give me a counter-example of Actual Infinity from maths or nature?

Evidence for my claim that Actual Infinity does not exist above: Materialistic Argument: - Actual Infinity and the materialistic world view do not mix. - For example, can a physical quantity larger than any other possible physical quantity exist? Numerical Argument: - There is an number X such that X > all N - But X+1 > X - There is no such number - Hence Actual Infinity is not a number. Geometrically: - It is impossible to construct a line segment with the property that it is longer than all other line segments Temporally: - Assume infinite time - so anything than can possibly happen will eventually happen - If it happens once it will eventually happen again - So it will eventually happen an infinite number of times - no matter how unlikely it was in the first place Paradoxes are solved - Zeno’s paradoxes. It’s impossible to travel any distance as movement requires an infinite number of steps. We can move. Reductio ad absurdum. Space must be discrete - Galileo's paradox is solved: - There are less squares than numbers because not all numbers are squares. Yet each number has a square so the number of numbers and squares must be the same. - He is trying to compare two actually infinite sets, IE comparing two undefined things. A set definition is not complete until all its members are iterated. - Hilbert’s infinite hotel paradox is solved; such a hotel cannot exist. - Cantor's Paradox: ‘The set of all sets is its own power set. Therefore, the cardinal number of the set of all sets must be bigger than itself.’ The set of all sets is an ACTUAL INFINITY so not a completly described set. You cannot soundly reason with it. Leads to the paradox. Common sense View: The Actually Infinite exists. Reductio ad absurdum. No it doesn’t.

No it does not work that way: - You are asserting the existence of an irrational and spiritual concept (Absolute Infinity) - There are no provable instances of it in nature - It does not exist mathematically - The burden of proof is on you to show that Absolute Infinity exists

The observed processes happen, but they are processes that don’t involve the infinite. There are no examples of actual infinity in the physical world. The world is discrete but the only sensible way to model it is continuous... catch 22

But we use math to model the universe. Actual Infinity: - does not exist mathematically - does not (provably) exist in nature - yet it is in our cosmological models Actual Infinity is akin to magic... the universe is not magic it’s material...

- Assume a natural number X such that X > all Naturals - But X+1>X - Reductio ad absurdum, no such number exists - Actual Infinity does not exist

What is natural about a quantity larger than any other possible quantity?

- We have not found magic yet so we discount it’s existence in the physical sciences. - We have not found Actual Infinity in maths or nature so we should discount it’s existence likewise

Important to understand the difference between potential and actual infinity: https://en.m.wikipedia.org/wiki/Actual_infinity The program only potentially passes through infinite number of states it never actually achieves Infinity...

First, if space is discrete then there is a finite number of sections between any two points in space. Continuous space leads to Zeno’s paradoxes hence space is discrete (paradoxes are indicative of an underlying logic error IE space is continuous is wrong). Second, even if space was continuous, this is an example of a potential infinity whereas I’m talking about actual Infinity. (https://en.m.wikipedia.org/wiki/Actual_infinity): - Those sections only exits as they are created through some sort of iterative process that tends to but never actually reaches infinity. - Mentally, how could your mind ever conceive simultaneously of an infinite number of sections, that would require infinite brain capacity

But the very concept of Actual Infinity is absurd for any materialistist. Objects have a start for materialists. Objects without start cannot exist. So spacetime has a start. The non-material world is less constraining but let’s not go there.

The measure problem tells us that our models of the universe must be finite; that is the nature of a paradox - it means an error in the underlying assumptions - IE the error of assuming an infinite universe.

You are making things too complicated: - You have a paradox; the measure problem - It’s resolved with a finite universe

But the surface of the earth is bounded by the earth and sky, don’t they count as boundaries?

The complete lack of existence of Absolute Infinity in nature ***IS*** evidence that it does not exist. The impossibility of consistency defining such a term is evident from the many paradoxes that stem from it: https://en.m.wikipedia.org/wiki/Paradoxes_of_infinity These paradoxes go away in a finite discrete universe. No I don’t understand how anything in the material world cannot have boundaries. Could you explain?

Yes the bounded has boundaries of the same nature as the bounded itself. I guess nothing is beyond that boundary there is no time or space there.

I think the universe is finite because: - Actual Infinity does not exist mathematically - There is no proof of Actual Infinity in nature - The concept of the material world and Actual Infinity do not stack up. You buy one or the other. I buy the material world.

One example that you can prove.

Give me one example of Actual Infinity (https://en.m.wikipedia.org/wiki/Actual_infinity) from nature. There are no such examples.

- Ok everything that is not finite is infinite - We note from nature the complete lack of anything non-finite - We conclude empirically that the non-finate does not exist

The integers are purely a concept; in no way are they fully defined. You have to iterate all of the members to fully define a set else you are missing the cardinality (and making up ‘numbers’ for cardinality is not sensible).

- finite is within bound, IE fully defined - Infinite is without bound, IE not fully defined IE undefined.

The natural numbers are potentially infinite, they cannot be Actually Infinite mathematically: there is no number X>all N because X+1>X. Actual infinity cannot exist in the material world either. What is such an illogical concept doing in the core of set theory?