When we're faced with the situation 4÷0 we don't say 0 is nonsense or illogical. Rather we tell ourselves that 0 is a ''special'' number that needs, well, ''special'' treatment. We then say 4÷0 is undefined.

Similarly, when we see ∞ + 1 = ∞, it doesn't mean 0=1. Infinity is a special number and normal arithmetic doesn't apply to it. — TheMadFool

4÷0 does not make sense. How can you split 4 loafs into 0 parts? So we have to exclude it from arithmetic for logical reasons. Apart from that, zero behaves fine under the arithmetic operators. Zero has a small quirk but infinity not working with any arithmetic operators is in a completely different league - there is no valid logical reason to exclude infinity from arithmetic and it gives nonsense results with all of them. All other 'numbers' in maths work with the arithmetic operators or analogies of them. Infinity is unlike any other number so we can deduce it is not a number.

If you look at how infinity defined: the cardinality of the set of natural numbers, it must be a positive integer. But there is no integer X wit the property is is greater than all other integers because X+1>X.

Could time be like that? Measurable but not real. — TheMadFool

Space seems real though; its has vacuum/dark energy associated with it and fields so I'd argue they were measuring something real.

If we take a spacial dimension way, maybe we can see what it would be like without time: A 3D cube would become a 2D square. A square is a 2D object with no depth so it does not exist in 3D space (depth=0 so no volume so does not exist).

Imagine then a 3D+time object being changed to 3D-only object by taking time away. A hypercube becomes a cube. By analogy it would cease to exist in 3D+time as it has length zero in time. The object would exist for zero seconds thus not exist in our reality.

So I think time is required for things to exist. We are not living in a pure 3D world, it is a 3D world plus something that enables motion (time).

To be fair I sited 4 separate ideas/theories that all point in the same direction.

If you reject a non-material substrate, how would you explain quantum entanglement?

But we know mathematically that the cardinality of the continuum is such that it can be put into a one-on-one correspondence with a proper subset of itself. — MindForged

But the one-on-one correspondence procedure yields nonsense like Galileo's paradox. And the continuum does not have a cardinality... Cantor should never have made such numbers up. It's down to a deficiency in the core of set theory; the polymorphic definition of set supports two different object types: finite sets and descriptions of set. The first have a cardinality, the 2nd do not. They are different kinds of objects with different properties and need to be treated differently. Cantor tried to shoe-horn both objects into a common facade and ended up making up magic numbers for cardinality - definitely not the right approach.

Nature isn't 'logical' — MindForged

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

A line is an abstract object, you have to investigate it's properties mathematically. And in basically any geometry you like a line is not finitely divisible. — MindForged

Yes but you cannot actually infinitely divide a line - it would take forever. So thats a potential infinity rather than an actual infinity you can describe at best geometrically. It's impossible to describe actual infinity geometrically, mathematically or otherwise so/as it does not exist.

I was a materialist but now I'm having second thoughts. Some sort of material/non-material hybrid is maybe what reality is. So not materialism and not idealism.

Infinity is counterintuitive, is the comment I usually encounter. That it's illogical may not be true. How many natural numbers are there? — TheMadFool

Whats logical about ∞ + 1 = ∞ (implies 1 = 0)? In fact infinity is invariant under all arithmetic operations; what's logical about something that when you change it, it does not change?

In the the mind there are an infinite number of natural numbers, but infinity itself is an illogical concept, so that conception is flawed and cannot exist in reality. The natural numbers do not exist in reality so talking about how many there are in reality makes no sense. How many exist in our mind? A potential rather than actual infinity exist as thats all we can ever visualise.

Looks to me like we're just counting the rhythmic beats of the pendulum or the Caesium atom. There's nothing like an object to which we put a measuring scale and say it's x cm/inches long. — TheMadFool

We use rhythmic beats to measure time but time could exist independently of the beating mechanism and indeed enable the beating mechanism. So time enables motion rather than motion defines time.

So think of a clock and next door empty space, I'm saying I think time flows equally for both even though there is movement only in one.

If the world only had 3 dimensions, everything would be static. Time is a degree of freedom even if you don't class its as a first class dimension. So in that sense, time is as real as space.

Mathematical infinity is an abstract concept. It doesn't claim any physical representation, does it? — TheMadFool

But nature is logical so maths can explain it because it is logical also. Actual infinity is not a logical concept so does not fits in maths or nature.

Is it real (then your argument works) or is it too an abstract concept (your argument is faulty)? — TheMadFool

Thats the question. We can measure time, does that make it real? I can't think of anything we can measure that is not real.

Who (besides you) has attributed any such property to a continuum? What I said was that if we were to "zoom in" on a continuous line, we would never "see" anything other than a continuous line — aletheist

If we were to try that with a real line, we'd see discrete atoms.

If we start with the common sense notion that there must be more points/intervals in a large line compared to a small line then a continua immediately violates this with ∞ = ∞. Continua are illogical, reality is logical, hence continua don't exist in reality.

Despite it being refuted, and impossible to relativise.

Your attitude is isomorphic to those who adhere to geocentricism and the flat Earth. — Inis

And your attitude is isomorphic to an adherent of magic. How exactly is the universe meant to function without cause and effect, by magic? What mechanism would you replace cause and effect with? Purely random processes we've never been able to achieve so maybe the universe can't do random either? Generating information from nothing is impossible.

If we abandon the axiom of cause and effect we might as well give up on logic and science IMO.

Bohmian mechanics has been refuted so many times, it is getting boring. Physicists don't even mention wavefunction collapse anymore anyway. For the Copenhagenists, it purely imaginary event, for Everettians, it doesn't happen, and the view of the Quantum Bayesians seems to be the same as the Copenhagenists. The wavefunction is just a tool, it's not a thing. — Inis

I just cannot countenance a non-deterministic interpretation and then many worlds Interpretation is IMO crazy so I'm staying with non-local hidden variables.

De Broglie-Bohm is refuted and doesn't work. — Inis

I don't see any valid explanation of quantum entanglement with the Copenhagen interpretation. A non-material substrate would provide a mechanism though.

If there is a non-material reality it should in some way interact with this world effecting its phenomena. If you can give an example of this interaction, and make that example a demonstration/experimentation than you will have proof of a spirit realm. — Josh Alfred

Well dark matter/energy are hidden and do interact with the material world so are a candidate. And I don't believe a purely materialistic explanation of quantum entanglement is possible.

In De Broglie-Bohm, the hidden variables are the particles. Can never figure out if the wavefunction is a real thing in that theory. Probably best avoid it since it has been refuted so many times — Inis

I don't believe the wave function collapse is random, so there must be hidden variables in the non-material substrate. Everything is cause and effect IMO. There is no other way for the universe to get things done; it must apply at some level.

These Dark theories are really just catchy names for particular problems. Not sure how suggesting the observed anomalous effects are caused by something immaterial. Seems to only make matters worse. — Inis

We are missing matter and energy; galaxies are not rotating correctly for the amount of observed mass. That mass has to hidden be somewhere. If a non-material substrate could have the property of mass then it would be a possible answer.

How would hidden variable in a non-material substance do that? How can non-material substances affect material substances, and how do they store variables? — Inis

An atom might have a hidden timer variable(s) that determines when decay is due. I think the non-material and material would interact through forces. Certain forces may effect both the material and non-material worlds. Gravity is maybe one of them (dark matter/energy).

Any explanation that appeals to spooks or the mysterious, or the non-physical, or the superluminal, really doesn't explain anything, and you may therefore reject it. Especially when explanations exist that don't invoke those things. — Inis

How else do you explain spooky action at a distance without something a bit spooky? You are not going to find a local explanation for non-local behaviour so it will always be spooky.

With either the A theory or B theory, you can have infinite time or not — Terrapin Station

I don't think you can have finite time with the A theory. Then there would just be a start of time with nothing (no time) before it so it requires creation ex nihilo with no time which is impossible.

With the B theory, you can have finite time. The end of time precedes and cause the start of time. The Big Crunch causes the Big Bang. An eternal circle of time.

Who said anything about "constructing" a continuum? It is the more fundamental reality. — aletheist

Geometry reflects reality. If we can't construct it geometrically, its probably does not exist.

Who said anything about such an alleged property? — aletheist

If you sub-divide a continuum you get two continua identical to the one you started with - the parts are equal to the whole. Thats a unique and illogical property of continua.

We describe time as continuous--it is not composed of discrete instants or very short durations — aletheist

And what is your definition of a continuum? All the mathematical definitions I've seen use instances or short durations of some form. What do you mean by continuous?

How on earth would you ever construct a continuum? By what magic processes do you construct something with the property 'each part is equal to its whole'? If it is a challenge for us to even conceive of a workable continuum then surely that suggests that nature would incorporate such an illogical concept.

Measurement is a human construct — aletheist

But when we measure time intervals, we are measuring something real. The measurement is not real but the measured is.

You're not being a mathematical realist, by the way, are you? — Terrapin Station

I believe nature is fundamentally logical and that it can be accurately described using logic IE maths.

If I were to always exist, there couldn't be a moment of conception for me. — Terrapin Station

Maybe I'm misunderstanding you but that's the B theory of time?

No, there doesn't. If it extends back infinitely then there can't be a first moment.(Also acknowledging that there are no real "moments," there's just real change or motion.) — Terrapin Station

I agree, no first moment in an infinite regress so the whole thing cannot exist.

There wouldn't be a specifiable number, it would be an infinity. — Terrapin Station

Which is not a number. Basic maths says there is no number X greater than all others because X+1>X. No infinite numbers. So my proof holds.

Also, why would there have to be a first member for it to exist? That's contrary to what we'd be positing in the first place. — Terrapin Station

Would you exist if the moment of your conception was removed from time? There has to be a first moment of time (t) for the next moment (t+1) to exist, likewise if t does not exist, t+2, t+3 etc... do not exist. So none of the infinite regress logically exists.

I'll adopt an axiom of cause and effect and then argue that an infinite regression in time is impossible:

1. By the axiom of cause and effect, there would be an infinite regress of events into the past
2. The number of events in an infinite regress is > any number
3. Thats a contradiction (can’t be both a number and > any number)
4. Making up magic numbers is not allowed (can break any theory if magic is admissible)
5. An infinite regress is impossible

Or a more simple argument; time is a series or sequence, it must have a first member for the whole sequence to exist. An infinite regress is missing a first member, so logically the whole thing does not exist.

But A theory is incoherent also because an infinite regress is incoherent. B theory can be combined with finite spacetime to avoid any need for an infinite regress.

With B time, you still have the problem (for intuition) that it either appeared "out of nowhere" or always existed. You don't have an infinite regress, but the intuitive problem isn't the regress so much as either appearing "out of nowhere" or always existing. — Terrapin Station

Something always existing makes sense. You can't get something from nothing so something must have always existed. Could it be what always existed is the B theory version of time and space?

Something changes or moves. That is time — Terrapin Station

I see it more as time is something that enables change and enables cause/effect. Time flows even when nothing changes. If you have a clock and empty space next to it, time is changing equally for both.

As I mention here (https://thephilosophyforum.com/discussion/comment/245002) Einstein's equations suggest that something in the universe is time aware so it can assign mass to objects.

I'm not sure if time exists or not. I suspect it does. Some other arguments that it exists are given here:

https://thephilosophyforum.com/discussion/comment/244990

To be fair, the A theory has logical problems as well, like having no well defined start, being an infinite regress.

Staring with the relativistic energy-momentum equation:

KE = mc² ∕ √ (1 - v² ∕ c²)
So
m = KE × √ (1 - v² ∕ c²) / c²

So time (in the v term) determines mass. So something in the universe must be aware of time else it could not assign a mass. So time seems to be more than just an illusion?

The argument from evil is dependent upon a theist's claim that a god is good - about the nature of god. No claim about the nature of god - no argument from evil is necessary. — Harry Hindu

But a claim is made about the nature of God; that he is all powerful enough to prevent all evil. If God is good but not omnipotent, a universe that contains some evil is maybe the best we can expect (if God is not perfect)?

So taking a realistic view of God as a a non-perfect being then the problem of evil goes away. The amount of evil decreases with time as civilisation improves so things should work out OK in the end.

Exactly--time is not composed of durationless instants, and space is not composed of dimensionless points. Those are human constructs, which are very useful for certain purposes, but not real — aletheist

You can say time is a human construct but it represents something that does/did exist in reality. There was ‘then’ and there is ‘now’ and there is a non-zero distance between them measured in units of what we call time. They both have a length. It can’t be zero because:

- We would not be able to perceive something of zero seconds long
- Time does not flow if ‘now’ is zero length: now + now = now.

If the length of now was 1/∞, time would still not flow.

Here is a different argument that time exists:

If time does not exist it has no properties.
- Time has the property that it flows from one moment to the next enabling cause and effect
- Time has the property that it slows close to the speed of light
- Time has the property that it slows in intense gravity
So time exists

Exactly--time is not composed of durationless instants, and space is not composed of dimensionless points. Those are human constructs, which are very useful for certain purposes, but not real. — aletheist

How do we describe time then? The only models of a continua I've seen have used points or line segments to model it. In both cases its valid to discuss the length of the point or line segment representing 'now'.

Who can deny that the natural numbers are infinite. — TheMadFool

The natural numbers are in our minds only so sure they can be infinite there. Trees can dance in our minds too. But try writing out an infinite list of natural numbers... its impossible.

I doubt infinity can exist in the real world. It's not a quantity so why should real world quantities ever take the value of infinity or 1/infinity? That leads to the suspicion that time must be discrete.

A couple of other points:

- It sounded perfectly reasonable that matter was infinitely divisible but then we found out different. Maybe the same will happen for space and time?

- A continuum has the property that its parts are each equal to its whole. That is a somewhat mad conception. Should not be part of math IMO - too illogical.

What changes to make ‘now’ ‘then’? There is some measurable quantity we call time that changes. So it is reasonable to discuss the duration of 'now'.

I don't see how you can have a 'durationless instant' surely a contradiction in terms? To say someone eats for zero seconds is to say they don't eat. A durationless instant indicates non-existence.

Length of 'now'

If we consider the length of ‘now’, it cannot be zero seconds because that gives a divide by zero error when we work out the number of ‘nows’ in any finite interval (eg 1 second gives 1/0=undefined). Also if now had zero length, it would not exist.

Could the length of now be 1/∞ ? Problem with that is no matter how many ‘nows’ elapse, the total time period elapsed is still infinitesimal (1/∞ + 1/∞ = 2/∞ etc…). So with now length 1/∞, we’d be stuck forever at a single point in time no matter how many ‘nows’ elapse.

So the length of now must be greater than 1/∞, IE a finite number (else time would not ‘flow’).

That makes time discrete.

∞ * 10 = ∞
∞ / 4 = ∞
etc...

So an axiom of infinity is effectively 'when you change it, it does not change'. What sort of reasonable system of the world would adopt such an axiom? Where is the evidence for these magic objects that can be changed and remain unchanged?

Meaningless ways. Bijection is meaningless. How can there be the same number of naturals as rationals? Each natural is clearly composed of a potentially infinite number of rationals. Bijection is just plain wrong.

You can disagree all you like, but it does not give "the wrong results". — jorndoe

It clearly does give the wrong results. There are more numbers than squares in any finite interval. So we can induce this applies to all intervals. But bijection says the same number. It is basically meaningless to try to compare two 'infinite' sets as neither of them can be fully defined and thus neither of them are fully defined.

As far as I can tell, Devans99 just doesn't have much familiarity with the mathematics. — jorndoe

You do not have much familiarity with basic logic. A number cannot be larger than any number and be a number at the same time.

None of you will address this point directly.

a set is infinite if and only if there is a bijection between the set and a proper subset of itself — jorndoe

I do not agree with the bijection procedure; it gives the wrong results; see Galileo's paradox.

Colloquially, ∞ could be thought of as a quantity that's not a (real) number. — jorndoe

No, it can't be thought of as a quantity; its defined as greater than any quantity therefore its is not a quantity.

Infinity requires 'when you change something it is never changed' as an axiom. If you apply that axiom to real life you find it inductively in error.

That is just waffle. Address the axiom:

'when you change something, it is changed'

Do you buy it or not? If you buy it, you don't buy infinity.

You are arguing contrary to a basic axiom I believe in:

'when you change something, it is changed'.

Infinity in mathematics does not follow this axiom.

I have spent years looking at infinity, I am entitled to my opinions.

You are very closed minded and rude.

It does change. The set has an element it did not have before. But the cardinality does not change. — MindForged

OK so thats equivalent to saying 'I have this set to which I can add to and the size does not change'. Thats nonsense - anything you add (non-zero) to the size changes. That should be an indisputable axiom of mathematics or at least derivable from simpler axioms.

The problem is that relativity does not follow the axiom: "no matter how fast something is traveling, mass, length, and time are constant." That is such a basic axiom, taken as a reality by most people ... — aletheist

But we have good evidence that the speed of light is constant and the rest follows. We have no evidence for 'stuff that we change that does not change' and it makes no logical sense anyway.

Because most people only ever deal with and think about finite quantities, which is the domain in which that axiom applies. — aletheist

A more basic form of the axiom: 'if I change something, it changes' could be adopted. Infinity runs contrary to this axiom (which applies to the domain of 'stuff').

The width of a number is 0, so the number of real numbers between 1 and 2 is 1 / 0 = UNDEFINED.

An actual infinity of numbers may appear to exist in our minds but that's not the case mathematically. Actual infinity is bigger than any number so not a number, so concepts build on it like continua, infinite regress, eternity are not valid mathematically.

How many numbers there are in an interval? or lines can be drawn through a point? are examples of potential infinity which I don't have a problem with.