Can you give an example of something illogical / contradictory from reality?

I am merely pointing out that if ∞ is absurd (which it is - see the OP) then so is 1/∞.

There is so much math I could learn and life is too short to learn it all. So I choose to learn the areas of maths that are based on sound axioms and disregard areas that are based on unsound axioms.

What about non-standard analysis? Mathematics applies to the world, which is why engineering and physics work — Gregory

It does not really tell us anything about actual infinity - they merely assume such a quantity (and its inverse) exist. It may have applications but telling us about the nature of actual infinity is not one of them.

Logic/language are tools, shaped to conform to our needs in our version of the world as we experience it. That in no way means that the world is itself obligated to conform to either. — tim wood

I have the opinion that reality is 100% logical and anywhere where it seems illogical is just due to our lack of understanding. So we can use logic to probe reality - contradictions just don't happen in reality - so we can trust our logical arguments.

And, you take the meaning of "cause" for granted and leave it undefined — tim wood

A first cause must be able to cause effects without in itself being effected. So it must be self-driven. IE Intelligent.

That means, infinity is a concept, whether actual, potential or other. — BrianW

I agree they are concepts, not numbers. Focusing on actual infinity only, it is an illogical concept that can only have existence in our minds. If we assume actual infinity is possible then it leads to contradictions (see the OP) and absurdities (Hilbert's hotel etc...).

I think we need to look at where infinity comes from. It is simply a product of a kind of human thinking. — Punshhh

Indeed, I think that actual infinity is the product of top-down thinking. Bottom-up thinking shows it leads to absurdities. So with top-down thinking, illogical things are possible in our mind. It only becomes apparent that they are illogical through bottom-up thinking - and illogical things cannot have existence in reality. An example is that top-down thinking suggests we can construct a square with the same area as a circle (using ruler and compass). But 1000s of years of bottom-up thinking has finally proved that is impossible.

Infinite also means non-stop (endless). Even before the addition and division which you mention, the collections must have been constantly progressing in size and, possibly, in as many progressions as is possible e.g. arithmetic, geometric, logarithmic, exponential, etc. — BrianW

I think you are referring to potential infinity? I don't deny the existence of potential infinities; the argument in the OP is squarely aimed at actual infinity.

What about space? Is space finite? What is there outside of space? Nothing/something. The former is space and the latter requires space. — TheMadFool

I believe that spacetime started expanding 14 billion years ago at a finite rate, so hence spacetime must be finite currently. I believe there would be pure nothing beyond the boundaries of spacetime - there being no time or space for anything to exist. Pure nothing has no dimensions so it cannot be infinite.

If we ever come to an understanding of these issues, it will most likely come through years (decades? centuries? millennia?) of continued scientific research - or whatever scientific research evolves into. — EricH

Yes but I cannot wait millennia, I need answers in my lifetime. So I have to use probability. I estimate it is 95% likely that time has a start. So I maybe wrong, but probably not.

This notion of causality has no place in physics. — EricH

Newton's 3rd law - every action has an equal and opposite reaction - does reflect the nature of cause and effect somewhat. Causality does (by appeal to everyday experience) govern everything in the macro world and the origin of the universe is a macro question (huge amounts of matter involved).

As far as time goes, it appears - based on our current understanding - that time started with the big bang some 13 odd billion years ago. However, that knowledge is *very* preliminary - and we cannot draw any other conclusions from it. — EricH

All expanding universes lead to a start of time logically, as mentioned here:

https://thephilosophyforum.com/discussion/comment/368829

I have no idea what you're getting at with the hamsters. — EricH

1. You put the hamster in the cage and observe
2. You take the hamster out of the cage and observe
3. You conclude that there must be a God — Devans99

The universe is not in equilibrium and has never been in equilibrium. All dumb mechanical systems tend to equilibrium. So the universe must have always been more than a dumb mechanical system; there must of always been a hamster (=God) keeping the universe out of equilibrium.

How do you know that life is not merely an evolved state of matter, inevitable where matter is, and enough time? — tim wood

Because even advanced matter (IE atoms/molecules) would not form in the vast majority of hypothetical universes. If you had a computer program generate universes at random with random configurations of forces and particles, the huge majority of generated universes would fall into one of the following categories:

1. Too much adhesion. Everything ends up in one big black hole
2. Too little adhesion. IE quarks bouncing off each other forever (no advanced matter)

Our universe, with atoms/molecules, is a very fine balancing point between these two extremes. The chances that this balance happened by accident are probably billions to one.

"Everything in the spacetime follows the law of cause and effect." Really? Does it? — tim wood

What can I say. You experience causality every second of your life and yet you are in denial of it? It governs every macro level interaction in the universe and the origins of the universe is a macro level question (involving huge amounts of matter).

"Therefore logically there must be a cause beyond spacetime." A completely unsupported claim. Please support. — tim wood

1. If there is no first cause, there is no second cause
2. If there is no nth cause, there is no nth+1 cause
3. So there are no causes. But there are causes all around us so this is a contradiction
4. So there must be a first cause
5. A first cause must be uncaused; IE beyond causality; IE beyond time.

t either has a back and front, or it doesn't. That is, it is either real or zero — Gregory

How do you tell the difference between front and back? You could fire photons at the discrete object. But the minimum wavelength of a photon is much larger than the object. So you cannot detect front or back. Front or back are concepts that exist in your mind due to your experience with everyday macro objects. The microscopic world is different and quarks do not have fronts or backs. You can only imagine front and back of a quark because your mind (incorrectly) associates macro level attributes to micro level objects.

Are the parts non-zero? Do they have a front and back? Uh, the front and back are parts! This is the paradox started by Zeno. YOU don't have the solution — Gregory

Does a quark have a front or back? You can imagine it having so in your mind, but in reality it is an indivisible whole and it is not possible to address its front or back; only the whole unit.

A valid solution to Zeno's paradoxes is the universe is discrete and actual infinity does not exist.

Subtly switching between moments and causes in mid-run. :meh:
So, "the creation of space time" is supposedly the 1st cause and the 1st moment?
Anyway, let's have the proof instead. — jorndoe

OK BGV theorem:

1. An expanding universe (the only sort possible) must have a spacetime boundary at the start.

2. Einstein says (and we have empirical evidence for his claim) that time is observed to slow in intense gravitational fields. So as we go back in time in our expanding universe, we observe time to slow down as gravitational forces increase due to increased density of matter. At the first point of expansion, time is logically not flowing. A start of time.

3. Something must have caused the expansion to start. Call it X. What caused X. Call it Y. What caused Y. Call it Z... we are in an infinite causal regress. The only way out of such is to have something uncaused (from beyond causality=time) to start of the whole process.

So expanding universes (which science tells us our universe is) must have a start of time; trebly so.

https://en.wikipedia.org/wiki/Borde–Guth–Vilenkin_theorem

The world is physical, which is made of infinite parts. If it's more like a simulation, than why are you elsewhere arguing for a God? — Gregory

I think the world is made of finite parts; an actual infinity of anything is impossible; see the argument in the OP. What would an actual infinity of things be? It would be a set with greater than any number of elements - nonsensical - such an aberration can only exist in our minds, where the impossible is possible.

I doubt it is a simulation, but if it is, I believe God is the ultimate cause of that simulation.

Does the discrete part have parts. If it doesn't, why isn't it zero? — Gregory

I think it is likely that reality has a nature akin to a computer screen made out of pixels. So each discrete part has a size of 1 (say). It makes sense then (in the mind) to talk of size 1/2, but such cannot exists in reality; it is merely a mental construct (in the mind, the impossible is possible).

Just check the math. In the 1st step the 1st ball is removed but there are more than 1 ball. In the 2nd step the 2nd ball is removed but there are more than 2 balls. Ergo at the nth step then nth ball is removed but there are more than n balls. — TheMadFool

That applies for all n belonging to the natural numbers. But the proof is about what happens at the point of actual infinity, which is not a natural number. The proof is all about showing that actual infinity is impossible.

Then you keep thinking of the division. The numbers of parts go on forever. So infinity does exist — Gregory

∞ leads to contradictions so cannot exist. So neither can the inverse (1/∞) exist.

Do you potentially have a hand, or do you actually have one? How can something have parts only potentially? How can something exist yet not have parts? These are all non-sensical statements. — Gregory

I think that my hand exists in actuality and is composed of discrete parts that move through spacetime in discrete steps.

I would think by definition there can not possibly exist anything more inexplicable and unexplained than god itself. Every property of god is maximally fantastic and magical, to say the least, and not to go into how they are paradoxical as self-refuting or contradicting each other. — Zelebg

That is using a theist definition of God. I use a deist definition of God. He is more like a timeless architect, a designer, as opposed to the omnipotent/omnipresent/omniscient God of ancient scripture.

Discreteness does even mean anything. Does the discrete have parts? If not it's zero and has nothing to do with an object — Gregory

Fundamentally everything is composed of parts and the parts cannot be zero sized or infinitely small. So they must have non-zero finite size. This has been our experience with matter (molecules, atoms, quarks etc...).

Something discrete is a part and it does not have any sub-parts. It is indivisible. A pixel on your computer screen is an imprecise analogy. In reality it is a particle - a packet of discrete energy, probably taking on a wave form. It is not dividable into subparts.

OK.

1. The universe is indubitably fine tuned for life and the WAP/SAP are both flawed explanations of why. So there can be only one explanation, that a fine tuner exists.

2. Everything in the spacetime follows the law of cause and effect. Therefore logically there must be a cause beyond spacetime.

Your counter arguments please...

#1 Where I live there are lotteries. In one of them the odds are around 250x10^6 against, yet people win them. You are yourself unlikely. Does that mean you do not exist, or that any reasonable account of you is nonsense? — tim wood

This is I think the Weak Anthropic Principle to which you refer. It explains that the universe must be life supporting because we are here to experience it - so no mystery about that. But it does not explain the reason why the universe is live supporting. There are two possible reasons:

1. A complete fluke (billions to one shot)
2. It was fine tuned to be life supporting

Which is the more likely in your opinion?

#2, #3 In a book I have referred to before to you, Just Six Numbers, Martin Rees, it's made clear that in a multiverse environment, there's no law that says the the laws in any given universe match those in another. That is, your comments here are incoherent. — tim wood

Multiverses are fundamentally unobservable so unscientific concepts. So you have to use your common sense and probability when thinking about multiverses. Really what are the chances that each universe is completely different from each other Vs they are all similar. The 2nd is much more probable.

In any case, the predominate multiverse theory, Eternal Inflation, has the universes all manufactured out of the same stuff and go through the same evolution. So the only common sense conclusion is that they all must be live supporting.

#4 Really? You do not seem to grasp that the criticism you receive is substantive and not mere invective. Your "views" are unreasoned, unreasonable, unreasoning expressions of belief. But in the dining room of reason, they're merely an offensive snout that just pokes above the level of the table and tries to steal a morsel. — tim wood

I've told you about this before. Reasoned counter arguments please, not mindless diatribe.

Then what's 1st and nth about here? — jorndoe

To think about time, it is handy to introduce numbering (IE a clock). I am not claiming time is actually numbered, just that in order to think about time, it is useful to have numbering (IE a clock).

So, without such a 1st moment, you can't number such moments like that. (y) (though whatever indexical numbering will do, it's what we already do anyway) — jorndoe

But my point is that there is a first moment. If there is no first moment, then there is no time at all.

A supposed 1st moment, having no defining previous moment, is then undefined? — jorndoe

The first moment of time is caused by the creation of space time. The first moment causes the second moment and so on...

Timeless? In that case, you break the principle of sufficient reason. (and some other things) — jorndoe

That is the whole point of my argument - to propose a revised version of the PSR - IE 'Everything in time has a cause'.

In every your argument I can substitute the word “god” with “universe”, and vice versa. And neither god nor universe as the first axiom explain anything, but god will always be more complicated and thus less reasonable assumption. — Zelebg

The fine tuning argument says there must be something external to spacetime to do the fine-tuning. If you remove God, you are left with something completely inexplicable / unexplained, so that is not a more reasonable explanation, it is a less reasonable explanation.

The universe is fundamentally in-time. Nothing can exist in time forever, so time must have a start. It must of been started by something beyond time.

With god the question about fine tuning is not answered but exaggerated as we can ask not only why is god fine tuned to create life, but also why is “nothing” fine tuned for god to exist in the first place. — Zelebg

Good point. I think that it must be that God does not require a fine-tuned environment to exist. God must be something quite different from our everyday experience I think. The very fact that there is something rather than nothing (we are not living in null universe), points to some sort of miracle. We posit that the universe is fine tuned. That requires a fine tuner. Then something must have fine tuned the fine tuner's environment. So we are in an infinite regress of fine tuners. The only way out is to posit a fine-tuner that does not need a fine-tuned environment. So I think God must be a creature that does not require a fine-tuned environment. Indeed, the start of everything must be timeless and there is clearly nothing 'before' a timeless entity, so it cannot in itself have a fine-tuned environment.

You need to understand that what the mind thinks geometrically of an object actually applies to it. — Gregory

No it does not. My mind thinks of levitating dogs on a regular basis. No dogs levitate in reality. The mind is fundamentally illogical so the impossible is possible in the mind (with the aid of fuzzy, top-down, thinking). What is possible in reality is a completely different question from what is possible in the mind.

How many parts does a banana ACTUALLY have? Don't say one because I can split it in half. And if I was all-powerful I could split it up infinitely. Objects are both infinite and finite at the same time. Logic proves this — Gregory

If you were all powerful you could not split up a banana indefinitely - you would never finish the process so its impossible.

If we grant you were beyond time (timeless), you'd still need a hypothetical continuous substance to subdivide. But no such substance is possible as I pointed out here:

https://thephilosophyforum.com/discussion/comment/368770

Continua are mathematically impossible to define so in all likelihood, they do not exist in reality.

But all balls numbered less than ∞ have been removed from the bag at the end of actually infinite steps. So there are zero balls in the bag.

Mathematical induction leads to 9n balls in the bag at each finite step (where n belongs to the natural numbers). You can't use mathematical induction for the infinite part of this problem as it applies for all n belonging to the natural numbers only and ∞ is not a natural number.

Universe is uncaused cause, it existed before time. — Zelebg

The universe is fine-tuned for life. Saying the universe existed before time means there is no room for a fine tuner so that leaves a billions to one shot that the universe is fine tuned by accident. So the odds are firmly against your explanation.

And although there are reasons to call the universe intelligent and equate it with god, to take that metaphor to biblical proportions and personificate universe as a stupid, angry, jelaous and psychopathic magical being is unnecessary and far more complicated postulate, bringing in more questions than answers, and is thus childishly unreasonable idea. — Zelebg

I am a deist so I do not associate my hypothesised God with the God of ancient scripture.

Things don't potentially have parts. They actually have parts — Gregory

And those parts are discrete and finite:

1. The parts can't be size zero or size undefined as then they could not constitute the whole
2. The parts can't be size 1/∞ because they would not constitute the whole and because ∞ leads to contradictions
3. So the parts must have a finite, non-zero size. IE discrete

You need to understand the difference between what is possible in your mind (where sure you can go on dividing forever and trees can also talk) and what is possible in reality.

Nothing is starting itself. You dont get it. Over your head. Bye — Gregory

It is not over my head; you simply hold an illogical/indefensible viewpoint. I'm sure if you had any valid counter arguments, you would have given them.

The world just is finetuned, just like you say God is just intelligent. Why is God intelligent. You have.to stop somewhere. — Gregory

Exactly, the buck has to stop somewhere. And logic suggests it stops at an intelligent, timeless, fine-tuner.

There is simply the first motion, and time starts. Nothing before. — Gregory

Things don't start by themselves.

You have to really think about it for awhile with an open mind — Gregory

I have an open mind. I calculate the probability of a creator or creator(s) of the universe at approximately 95%, so I am still open minded. I hope to hone that estimate via debate.

Objects are only infinitely divisible in our minds. The process of infinitely dividing an object goes on forever so it is not possible to complete - so it is an example of potential rather than actual infinity.

I say gravity starts time and the first motio — Gregory

What starts gravity?

Obviously the no boundary hypothesis is too hard to understand for you. — Gregory

The no boundary hypothesis is nonsensical in the view of the fine-tuned nature of the universe; there must be a fine-tuner and that fine-tuner must be external to spacetime.

It is only within the last 100 years that we have become aware of the immensity of the universe we live in - and there are still vast gaps in our knowledge. — EricH

I have sympathy with this point of view. Our knowledge of reality is currently very incomplete and no doubt riddled with misunderstandings.

To think that we can unravel the mystery of time based on the functionality of our advanced monkey brains is a case of hubris — EricH

However, I think this is a bit defeatist. With such an attitude, science will not progress. We must try to understand the world around us, as I am trying to do in my own limited way.

We understand time and causality well enough to draw some initial conclusions I feel. It seems likely that time must have a start (as must all things) and there must be a first cause.

Let me try another argument out. You have a hamster and a hamster cage:

1. You put the hamster in the cage and observe
2. You take the hamster out of the cage and observe
3. You conclude that there must be a God

You can't ignore their space-time positions because it's critical to your argument. Why are there infinite bananas? Because they occupy different spaces? If they occupy the same space there would be only one banana. — TheMadFool

I think the two sequences are identical in that if there is a banana at spacial position 1 in the first sequence, then there is also an identical banana at spacial position 1 in the second sequence.

If you don't buy my proof via contradiction that actual infinity is impossible, what about a proof via reductio ad absurdum:

https://en.wikipedia.org/wiki/Ross–Littlewood_paradox

So we have an infinite bag and we add ten balls and remove one. We repeat that an actually infinite number of time. At each finite step, there are 9n balls in the bag. At actual infinity, there are zero balls in the bag. Reductio ad absurdum, actual infinity is impossible.

but then there's a difference between each instance of such identicalness by virtue of their inability to occupy the same space at the same time. — TheMadFool

Each banana has a different spatial position I agree, but the two sequences, ignoring their space time position are identical (same mass, same number of bananas, all bananas in one-to-one correspondence). The definition of a sequence (similar to a set) does not include their relative spacial positions - so the two sequences of bananas remain identical whilst they are changed. Which is a contradiction. Hence actual infinity cannot exist.

imagine the series of motions as a bunch of pictures. Together they flow to create time, but there is no time before the first motion. Gravity causes the whole series to move and time to flow, but there is no before so a God or anything else outside the series is not needed. The world is uncaused, having its own causality within it, as you say of the dude out there — Gregory

What then causes the first motion? What causes there to be a time when gravity starts to take effect? What fine-tuned the universe for life? To be truly uncaused, one must be beyond time - you have something in time that is uncaused - some sort of creation ex nilhilo?

Respectfully suggest that you re-read and absorb what Seditious has to say. Your reasoning is based — EricH

If you and @Seditious refuse to even trust your own mental faculty then there is little hope that I can win you over with reasoned arguments - you can reply to any and all logical arguments with 'I do not trust my own mind'!

If you think about all of 4D spacetime instead as 3D spacetime (drop a spacial dimension), then the universe must have a definite 3D shape to it. It maybe a cone (with the point representing the BB). Whatever its precise shape is, all 3D shapes have identifiable start points and our universe would be no exception.

5. such time has no such numbering of moments — jorndoe

It's not about the numbering of moments, it's about the fact that the previous moment defines/determines the next moment. So the present moment cannot exist if the previous moment does not exist. So logically, if there is no first moment, there are no moments at all.

Lets quickly do an alternative proof that time has a start:

1. Assume time has no start
2. The universe has a state as defined by the precise position and velocity vectors of all 10^80 particles in it
3. Call the current state of the universe X
4. How many times has the universe been in that exact same state X in the past?
5. Probability of state X is non-zero * ∞ = ∞
6. So the universe has been in state X an actually infinite number of times in the past (IE a greater than any number of times)
7. Reductio ad absurdum, time must have a start

Or if you don't agree with that, how about:

A. Assume time has no start
B. Particle X has a collision 5 minutes ago, call that collision 1, 10 minutes ago call that collision 2, 15 minutes ago call that collision 3, etc...
C. How many collisions has particle X had?
D. Can't be actual infinite because it's impossible to count to infinity
E. So the particle must have had every number of collisions in the past
F. IE The particle has effectively counted 'every number' in the past
G. But it's impossible to count every number, if you count a million, you are 0% done, if you count a trillion, you are 0% done, etc...
H. Hence the particle must have had a finite number of collisions in the past
I. Which contradicts our initial assumption, hence time must have a start

I have a few more proofs that time has a start if you are interested?

Using the human perception of time to argue a Primary Cause outside of time is...it seems, from my perspective, nonsense. — Seditious

For the non realists, there is this argument:

1. Thoughts flow in the mind. There are past thoughts, a present thought and future thoughts.
2. So we can deduce the presence of time with a linear-like structure from our minds alone without using our senses.
3. So time exists.
4. If time has no start, it has no 1st moment. If it has no nth moment, it has no nth+1 moment
5. So time with no start has no moments in it
6. But time has moments (contradiction), so it must have a start
7. If time has a start, something timeless must have created it.

Define "must" please. Others, in other posts (notably 180) have made the observation that the Universe is decidedly not "fine-tuned" for life. Anyone with the slightest understanding of what's out there must concur. — tim wood

You have of course ignored my extensive reply to 180 on the subject of fine tuning:

https://thephilosophyforum.com/discussion/comment/367699

Have a read of it first and then see if you can come up with any decent counter arguments against fine tuning. That would be more useful than your usual habit of clogging up the forum with non-philosophical whining ( 'I don't like devans99 blah...')

So add/remove is the change. How? In what way have you changed the infinite set from which something has been removed and the infinite set to which something has been added? — TheMadFool

We add 1 banana to the sequence (=it should change quantitatively and qualitatively).
But is does not change quantitatively(∞+1=∞) or qualitatively(still identical rows of identical bananas).
So there is something that when we change it, it does not change
That's a contradiction so our premise must be wrong
Hence actual infinity is impossible.

set theory doesn't allow repetitions of elements — TheMadFool

Thats why they are sequences rather than sets (sequences allow duplicate objects).

Well then you're contradicting yourself. Things can change either qualitatively or quantitatively and you say neither has occurred. Then in what way have the sets changed; after all your claim is that when it is changed, it is not changed. — TheMadFool

The argument in the OP is that you can add/remove identical items to an infinite sequence and the sequence remains identical/unchanged (both qualitatively and quantitatively). This results in the contradiction 'when it is changed, it is not changed', which is what I intended - assumption of the existence of actual infinity leads to a contradiction.