Devans99

Causality is a physical law (at least at macroscopic level and we are dealing with a macroscopic question here). I referenced mathematical induction m...

But logical impossibility, which actual infinity is (as demonstrated by the paradoxes/contradictions) does imply actual impossibility. The set of natu...

Mathematical induction precludes it: Assume there is no first cause. If there is no nth cause then there is no nth+1 cause. Then there is nothing. The...

Interesting point. But the universe must have some age and it cannot be infinite, so why not 14 billion years? If you believe in 4d spacetime (as I do...

They are not logically possible as you can see from the argument in the OP - assuming that they are logically possible leads to a contradiction. Or if...

An actual infinity of naturals (IE a set with a greater than any number of elements) is impossible. It is not logically possible to complete a task th...

You are missing the point I'm making. I believe that the naturals and reals are purely mental constructs. They exist in our minds only (where the impo...

I'm glad we are in agreement. I think though that not everyone agrees with us. For example, the bedrock of maths: 1. Axiom of infinity. It claims that...

As explained above, you can use mathematical induction to see that all the bananas in each sequence are in one-to-one correspondence. So for all finit...

If space is continuous then my hand moves through an actually infinite number of intermediate positions. But actual infinite leads to contradictions. ...

But what was the cause of time starting? It seems it cannot be gravity as gravity requires time to express itself? Perpetual motion is impossible so t...

Whatever QM says, I feel that in the macroscopic world, 'everything in time has a cause' still holds. The origin of things involves huge amounts of ma...

It takes say 1 second for my hand to pass through 1 meter of space and thereby pass through, if space is a continuum, an actual infinity of intermedia...

I don't think we will reach agreement on this point.

Beyond the boundary is nothingness IMO. Nothing cannot be actually infinite because it is nothing. If it is other universes then they cannot be actual...

If my hand moves from position 0 to 1, it is guaranteed to pass through positions 0.5, 0.25, 0.125, etc... Or are you saying it somehow skips over int...

But the action of movement does mark positions 0 and 1 and all positions in-between. We know that our hand actually passed through all those positions...

I think that there maybe pure nothing beyond spacetime - no time at all so nothing can be in any way whatsoever. Time probably started 14 billion year...

I don't understand you. If my hand passes from position 0 to 1, then it passes through positions 1/2, 1/4, 1/8, 1/16, ... 1/?. So movement in a contin...

I bow to your maths knowledge, but I'd still maintain that there is nothing in our universe to which the axiom 'when it is changed, it does not change...

I think you are splitting hairs between 'believe' and 'aver'. Cantor states he has 'firm conviction' in the belief of the existence of the actually in...

OK. But the problem remains: removing half the elements from the second sequence results in a sequence that is identical to the first sequence. We hav...

I have already given you two clear demonstrations that some people believe in actually infinite collections: - Infinite past time (leading to a belief...

Lets look at what Cantor said again: "Accordingly I distinguish an eternal uncreated infinity or absolutum which is due to God and his attributes, and...

You are just choosing one (fringe) theory of cosmology; many theories do assume past time is actually infinite. See CCC by Roger Penrose as an example...

Assuming for the sake of argument space is a continuum (which I do not believe), when I move my hand from left to right, it would pass through an actu...

You are confusing me. Every element in both sets is indistinguishable and they are lined up with each other (in one-to-one correspondence): {b, b, b, ...

I use the term 'collection' because I'm not a mathematician I'm afraid - I mean a group of (in this case) identical objects. I'm not familiar with mul...

I called the groups of bananas 'collections' rather than 'sets' to get around the issue of sets having to be composed of distinct objects. Hope that i...

Cantor has had a huge impact on the way we regard actual infinity. It is due to his work that actual infinity has gained legitimacy in maths and that ...

For example, many cosmologists hold that time has no start, implying an actual infinity of past time. All those past moments actually happened, so it ...

I'm not claiming {1} = {2}. I am saying that {1} = {1}. And that {1,1}={1,1}. And that, by induction, {1,1, ...}={1,1, ...}.

For example, some folks believe that past time is actually infinite; implying an actually infinite collection of moments in the past. Or some hold tha...

You should have really read the posts above. I did acknowledge my mistake here: https://thephilosophyforum.com/discussion/comment/367343 And I've also...

The point I am trying to make with the bananas is that there can be no actually infinite collections in reality because it leads to contradictions (th...

Numbers exist in our heads only, bananas exist in reality. The point of my argument is to demonstrate that actual infinity can exist in our heads but ...

What about the collection/set of natural numbers? They start at 1 and go on forever.

What I mean is: { b, b, b, b, ... } ^ new banana is inserted here (at the start). So the infinite collection has a start but no end.

I have made a mistake with this argument... sorry. A set is a set is a well-defined collection of distinct objects, so my identical bananas cannot be ...

You can use mathematical induction to see the two sets of bananas are identical: 1. The first pair of bananas is in one-to-one correspondence 2. If th...

You will see in the OP that I did state it was two sets of identical (IE unnumbered) bananas.

If you check the OP, I did consider the possibility that points have no size. That leads to the size of a point being UNDEFINED and all line segments ...

Slight correction, they do reference Euclid's non-sensical definition of a point: "a point is that which has no part" on page 27.

I found the book you are referring to here: https://download.tuxfamily.org/openmathdep/euclid/Euclid_and_Beyond-Hartshorne.pdf It is 500 pages long an...

But people would be happier still if they have had that initial exposure to evil (so that they have a way of measuring/quantifying good). My point is ...

Thanks for the reply! As you no doubt realise I am sort of playing devil's advocate here... But a mind - an information processing machine with a memo...

There is a distinction between: 1. The process of division - we cannot go on dividing an object forever because we would never finish the division pro...

- Yet the Dedekind-Cantor continuum is taught in school along with the fact that a point has zero width. So my objections are bang upto date, as far a...

This is a very interesting video. If anything is infinite, it is our lack of knowledge.

Perhaps you can point to an example of a "proposition regarded as self-evidently true without proof' that is not an axiom? Yes it is, the axiom of inf...