And Devans99, why don't you read Aquinas's first book of the Contra Gentiles. He tries to "prove" God is all-knowing. — Gregory

God cannot be all knowing: the clue is 'know thyself'.

If you guys want to believe in medieval physics, go for it. I'm not wasting my time anymore — Gregory

The most obvious metaphysical arguments and therefore the most worthy (according to Occam's Razor) are made first in history. So it would be foolish to disregard them purely because of their antiquity.

But see GBV Theorem for an example of an up to date argument that time has a start:

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

Unchanging causing change is as incoherent as something coming from nothing. — Harry Hindu

I did not say timeless beings cannot cause change. I said that a timeless being can express itself in spacetime and thereby be the agent of change.

See? You can't escape talking about God relative to the universe. You are implying space-time encompassing God and your universe, as God is located relative to the universe and expresses itself in time. — Harry Hindu

I am not implying space-time encompassing God, I said God is external to spacetime but can express himself in spacetime.

Spacetime is fine-tuned for life. That requires a fine-tuner from beyond spacetime. Nothing can exist forever in time, that requires a first cause from beyond time.

They exist only as imaginings in the human mind in this particular universe. — Harry Hindu

You cannot possibly have understanding of every possible reality beyond our own, so you cannot make such a claim.

I dont know what you're talking about. Maybe you're talking about realtive change. There is more or less change in one area relative to another. — Harry Hindu

What I mean is that special relativity says that time is observed to slow down as things move faster (hence the photon moving at the speed of light is a timeless particle). So more change = less time. So time is not change (because that would lead to more change = more time - in opposition to special relativity).

The previous moment defines the next, so all moments in your argument before 1970 Jan 1st 00:00:00 UTC are therefore undefined.

Or, assuming time has a start, then the time at the start of time is 00:00. Subsequent times are given by elapsed % 24. If time has no start, what then?

I am open to counter arguments. Thats why I post here. To get other people's ideas and counter arguments. I have not made up my mind that space is finite and discrete; I merely think there is an approximately 80% chance that is the case, I await further arguments / counter arguments to hone that estimate.

1. suppose there's no 1st cause
2. if there's no nth cause, then there's no n+1th cause
3. so, by induction such causes don't have such (definite) numbering — jorndoe

And 4. if they cannot be assigned a definite numbering, they cannot exist. Leading to 5 - nothing exists presently. Thats a contradiction.

Thats not a counter argument.

TIme starts from the first motion of gravity — Gregory

What causes that first motion?

You're position really is the Third Way. — Gregory

The third way is a beautiful argument that is supportive of my argument in the OP. I paraphrase it as:

1. Can’t get something from nothing
2. So something must have existed ‘always’.
3. (IE if there was ever a state of nothingness, it would persist to today, so something must have permanent existence).
4. It’s not possible to exist permanently in time (you would have no start - no coming into being - could you exist if you were not born?), so the ‘something’ must be the timeless first cause (of time/causality).

Spacetime is fine-tuned for life. So there must be something external to spacetime that did that fine-tuning. Hence a requirement for something beyond spacetime. To imagine the universe in all its magnificence, existing eternally with no cause, is quite a stretch.

Nothing can exist in time without a temporal start, so the universe must have a temporal start. There must be a cause of that temporal start (of the universe).

The world is self-caused, like you say of the dude out there. — Gregory

Self-caused is a logical impossibility. Uncaused as in beyond causality or time is not logically impossible.

Who said anything about discarding arithmetic? It is very useful for very many purposes, especially those encountered in everyday life, which generally involve dealing with finite quantities of discrete things. A different approach is required to handle potentially infinite sets, and yet another is required for true continuity. Whether this accords with "common sense" or not, it is the reality. — aletheist

Your chosen version of reality included continua (incompatible with arithmetic IMO) and infinitesimals (incompatible with arithmetic IMO). My chosen version of reality does not include these two concepts (I think reality is finite and discrete). Time will tell which version of reality is correct.

And comedy. And music. No evolutionary drivers.

Is it common sense that there are numbers incapable of being calculated as fractions of integers? Or that matter consists of atoms that in turn consist of varying quantities of protons, neutrons, and electrons? Or that gravity is the curvature of spacetime, rather than a direct force of attraction between massive bodies? — aletheist

The proof of irrational numbers is common sense. We have empirical evidence for atoms and the curvature of spacetime. So these things are in agreement with common sense.

Nonsense, there is no single set of mathematical assumptions that perfectly matches reality--just different models that are useful for different purposes. — aletheist

But as seekers of a truthful explanation of our reality, we have to make choices between incompatible branches of mathematics. I'm unwilling to discard arithmetic from my set of choices of valid mathematics.

Thanks @3017amen!

Answer: embracing your God given sense of wonderment, and your Kantian intuition. — 3017amen

I think that it is a wonder that there is something rather than nothing. Nothing requires no cause and there is nothing to explain and indeed no-one to ask for an explanation. A clean, simple, null universe is the Occam's razor explanation. The fact that there is anything at all is a miracle IMO.

Do parallel lines ever meet? — tim wood

Who knows. I don't disregard non-euclidean geometry because its axiom that parallel lines meet has a possibility of being true. I do however disregard maths that does not follow the LEM. There is so much maths, all different fields with different axioms that disagree with each other - it is therefore required to be selective in what one chooses when trying to use maths to understand the universe.

I explained why. Pay attention. What vase would be large enough to keep putting in 10 balls while only removing one. The vase works have to be an infinite sized container, which makes no sense. How can something be both infinite and contain? — Harry Hindu

The paradox starts with the assumption that actual infinity is possible, so it is OK to assume an actually infinite bag/vase.

If has an atemporal existence then that is the same as saying that it doesn't exist. How foes something cause everything else without being in time itself? How does it cause anything without changing itself? Even God has to exist in time if God changes. Change is time. — Harry Hindu

I have done a probability analysis of all the arguments and I get 94% certain that time has a start.
That implies something atemporal must very probably exist in order to be the cause of time. I imagine the whole of the universe as a 2d spacetime diagram of finite size. Then I imagine the atemporal thing (God) off to the side (not on the plane) and a mapping between the atemporal thing and each point in the plane. Then the atemporal thing can express itself in spacetime without being part of spacetime.

I am not sure precisely how the atemporal thing (God) could work. But then if you think about all the universes in the multiverse, all the multiverses in reality and all of the different possible realities that might exist, it seems impossible that we would ever understand them all - so things with a drastically different nature very probably exist - including atemporal things.

Time enables change. Time is not change. If time was change then time would flow faster in the presence of change, yet SR indicates time slows down in the presence of change.

But 3 is a non sequitur — jorndoe

Why? If it holds for the base case and holds for the nth+1 case, then it holds for all n. Please explain.

I have proved that there must be a first cause several times to you. Maybe you will take Thomas Aquinas's word for it:

‘The second way is from the nature of the efficient cause. In the world of sense we find there is an order of efficient causes. There is no case known (neither is it, indeed, possible) in which a thing is found to be the efficient cause of itself; for so it would be prior to itself, which is impossible. Now in efficient causes it is not possible to go on to infinity, because in all efficient causes following in order, the first is the cause of the intermediate cause, and the intermediate is the cause of the ultimate cause, whether the intermediate cause be several, or only one. Now to take away the cause is to take away the effect. Therefore, if there be no first cause among efficient causes, there will be no ultimate, nor any intermediate cause. But if in efficient causes it is possible to go on to infinity, there will be no first efficient cause, neither will there be an ultimate effect, nor any intermediate efficient causes; all of which is plainly false. Therefore it is necessary to admit a first efficient cause, to which everyone gives the name of God.’ - Thomas Aquinas, Question 2, Article 3, Summa Theologica

Let me ask you a question - can you prove that there could be something in existence without a first cause?

There are no "wrong" assumptions in pure mathematics. It is the science of reasoning necessarily about hypothetical states of things. — aletheist

Fair point, but assumptions that stray wildly from common sense / common experience indicate the subject is squarely pure rather than applied maths. IE it tells us nothing about our reality, it is telling us something about an alternative reality where common sense does not apply. I am not interested in maths for maths sake, I am interested in what it tells us about the reality we live in. If parts of maths adopt axioms that depart from common sense, then I have to disregard those parts when searching for a description of our reality.

This is the way you should approach maths (and other fields of human knowledge) - you look at the axioms and decide if you believe them or not. Then you learn about the parts that you believe have sound axioms and disregard the rest. Parts of math claim that for non-zero x, x^2>0. Other parts of maths claim that for non-zero x, x^2=0. The two parts of math are incompatible. It is only possible to hold a belief in one of these two incompatible parts of math. I put my money on basic arithmetic.

There is nothing inherently contradictory about the mathematical concept of an infinitesimal, which is not necessarily defined as 1/∞. Again, if you truly want to understand, please read one or both of the short articles that I linked. If you prefer to remain ignorant, carry on. — aletheist

The problem with the articles you linked is that in both cases, a wrong assumption is made at the start of discourse:

"In order for SDG to be consistent, the law of exclude middle must not hold. SDG does not rely on classical logic but on intuitionistic logic."

I happen to strongly believe that the LEM holds for our universe and indeed all possible universes.

"Now if it were possible to take δx so small (but not demonstrably identical with 0 that (δx)^2 = 0"

I also strongly believe there is no nonzero x such that x^2=0.

Why should I invest time and effort learning subjects that are based on wrong assumptions? All 'knowledge' I'd acquire in doing so would be inherently unsound.

looks (to me) like you want to show that you can't number all such moments non-indexically, but then you call it a day there, still no contradiction derived. :meh: — jorndoe

I've already given you about 5 arguments that infinite causal regresses are impossible, including some that even a child could follow. It's really simple:

1. Assume there is no first cause
2. If there is no nth cause, then there is no nth+1 cause
3. So by mathematic induction, there are no causes/effects at all
4. But there are causes/effects in our universe (contradiction)
5. So there must be a first cause

Could you explain exactly what is wrong with the above argument?

By the way, still treating ∞ as a number (integer in this case)...? — jorndoe

I am treating ∞ as UNDEFINED. Please point out where I treated it as a number.

You think you can peer into the nature of time. You think that proving to yourself that God exists means you have to convince us. Why don't you spend your day trying to communicate with "Him" through prayer and good works instead of starting threads on here? I don't get it — Gregory

Time and God are traditional subjects of philosophy and this is a philosophy forum - I don't see why you are complaining. I happen to be interested in these subjects and would like to discuss them with folks who share my interest. If they are of no interest to you, I suggest you don't read my posts and don't post replies.

BTW I do not pray because I do not believe God is omnipresent. I give to charity.

Again, this reflects a complete misunderstanding of infinitesimals. A moment of time has a duration that is not zero, but is less than any assignable or measurable value relative to any arbitrarily chosen unit. — aletheist

Infinitesimals are deeply illogical/impossible concepts and are shunned by most of maths. As demonstrated in the op, ∞ leads to logical absurdities, so logically 1/∞ must be absurd too.

In other words, continuous lapses of time with finite duration, arranged such that each one starts when the previous one ends. Calling this "discrete time" is a misnomer. — aletheist

They are distinct, like a movie plays at 60 frames a second, each frame a time slice. There is nothing continuous about that.

The last sentence is correct, because the first sentence demonstrates a complete misunderstanding of infinitesimals. — aletheist

OK, what is the infinite sum of every possible infinitesimal:

https://www.wolframalpha.com/input/?i=limit+%28n%2Finfinity%29+as+n-%3Einfinity

It's zero. So infinitesimals cannot be the constituents of time because all time intervals would have zero length and time would not flow from one moment to the next.

On the contrary--if time were discrete, then it would necessarily consist of durationless instants at some fixed interval. The fact that "now" cannot have zero duration requires time to be continuous, such that "now" has a duration that is infinitesimal--not zero, yet less than any assignable or measurable value. — aletheist

Discrete time would consist of discrete, non-zero, non-infinitesimal time slices - so they would have a duration.

On the other hand, if time was composed of infinitesimal time slices, then each fixed period of time would be composed of 1/∞=0 length time segments giving a zero total length for all elapsed intervals. Which cannot be right.

You physically can't keep putting 10 balls in a vase, while only removing one. It's an unrealistic thought experiment. — Harry Hindu

Why is it unrealistic?

If causation (space-time) isn't infinite, then you have to come up with an explanation as to how something came from nothing. — Harry Hindu

I don't believe everything came from nothing, I believe that something has permanent, atemporal existence and that something caused everything else. See here:

https://thephilosophyforum.com/discussion/7391/everything-in-time-has-a-cause/p1

How about the negative integers:

{ ..., -5, -4, -3, -2, -1 }

- We can see it is possible to define the negative integers if we start at -1 and work downwards through -2, -3, etc...
- Yet it is impossible to start at '...' and define the negative integers - there is no starting point so nothing can be defined/derived from that
- So if we now consider cause-effect, then the cause defines/derives the effect and the cause must exist before the effect
- So equivalently, it is not possible to define effects starting at '...' because all of the subsequent effects would be undefined.

Think about causality as a giant pyramid - the first cause is the pointy end and effects multiply towards the base of the pyramid (example: the break off shot in pool is the pointy end and then the balls colliding with each other lead to the middle/base of the pyramid). If there is no first cause, then the pyramid simply does not exist.

Interesting video. I have sometimes wondered about the length of 'now' - it seems it cannot be zero length else 'now' would be nothing (nothing length zero has existence). This type of thinking leads to consideration that time maybe discrete and eternal, over which the is much controversy.

I wonder if it is simply an " illogical abstract " that actually exists in reality. Much like the metaphysical phenomenology of how the subconscious and conscious mind work together in an illogical manner (violating the laws of bivalence/LEM). — 3017amen

I think reality is strictly logical; I can find no instances of paradoxes/contradictions in reality. I think that the paradoxes/contradictions result from our models of reality rather than reality itself. Fundamentally our minds are capable of illogical reasoning but reality seems constrained to be logical only.

Our minds are part of a logical reality, but yet they are not constrained to purely logical concepts. When we think top-down about concepts, illogical concepts can surface in our mind. When we think bottom-up about concepts, these 'illusions' are often banished.

I think that 'abstract reality' might be a product of top-down thinking. It is easy to imagine that it is possible to square a circle when you think about it top-down. Yet it took 1000s of years of maths to prove it is logically impossible. So when we think about actual infinity, we are thinking about something in a top-down manner (sure something can go on forever). It is only when the concept of actual infinity is probed in detail that we see the problems - the paradoxes/contradictions show us that in fact we are imagining something illogical.

Examples of abstract reality include the paradox of time, mathematics (Pi), cosmology (infinite universe theories), metaphysical phenomena, consciousness, so on and so forth.. — 3017amen

I think I see what you mean, maybe you can expand? I see that Pi cannot, in our reality, ever be actualised as it has infinite digits. A perfect circle cannot exist in our reality. But a perfect circle exists as an idea in the mind (along with talking trees). Is therefore a perfect circle an illogical/impossible idea or would you call it abstract reality?

I think the example of the axiom of choice is an interesting point. It claims it is possible to select one ball from an infinite number of bins:

1. Clearly in concrete reality, it is not possible to complete a never ending task
2. It also seems illogical for the mind to allow that we can complete a never ending task
3. Yet we can imagine it so and imagine the consequences. This is maybe the abstract reality you refer to?

It only leads to absurdities if one insists on attempting to apply the same rules to infinite sets as to finite sets. Mathematicians have long recognized this, which is why there are different rules for infinite sets. — aletheist

The same rules apply for finite and infinite sets. And if you don't like the absurdity in the OP, see this famous example for proof that actual infinity is logically absurd:

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

Imagine a hotel with infinite rooms and with an infinite number of guests a1, a2, a3,... Now imagine a new guest b1 who wants to stay in that hotel. The manager simply moves a1 to a2, a2 to a3, aN to aN+1,... and b1 gets a1's room. Notice that though the quantity, infinity is still infinity, hasn't changed, the quality has: b1 is the new guest. — TheMadFool

My argument uses sequences of identical bananas, so that the 'quantity' and 'quality' of bananas both are constant whilst bananas are added and removed from the sequences - resulting in absurdity.

Yet again: mathematical existence does not entail metaphysical actuality. Within mathematics, the number 10^100 (1 googol) indubitably exists and is a member of the set of natural numbers; but according to physics, the total quantity of actual particles in the entire universe is only about 10^80. — aletheist

A googol-sized set could have logical existence if our universe was bigger. A greater than any number sized set does not even have logical existence (leads to absurdities so it cannot be logically sound).

You keep saying so without showing it. :confused: — jorndoe

I've demonstrated it several times quite clearly to you. Maybe you will take Leibniz's word for it:

’Suppose the book of the elements of geometry to have been eternal, one copy having been written down from an earlier one. It is evident that even though a reason can be given for the present book out, we should never come to a full reason. What is true of the books is also true of the states of the world. If you suppose the world eternal, you will suppose nothing but a succession of states and will not find in any of them a sufficient reason.’ - Leibniz, Theodicy

IE a first cause is required to give solidness to the succession of states of the world.

He won't even consider Hawking's no boundary hypothesis — Gregory

I've considered it. It uses a complex variable for time. That is unlike any time I'm familiar with. So I do not think it reflects the universe we live in.

Thanks for the conversation. Happy new year to you to!

The axiom of infinity:

$\exists \mathbf {I} \,(\emptyset \in \mathbf {I} \,\land \,\forall x\in \mathbf {I} \,(\,(x\cup \{x\})\in \mathbf {I} )).$

I believe (I'm not a mathematician so forgive me if I'm wrong) this reads ‘there exists a set I for which the null set is a member of I and for all x belonging to I, x union the set formed by x also belongs to I’.

I do not believe this is a declaration of potential infinity - it is a declaration of actual infinity. It says there exists such a set - it does not reference limits or sequences or any of the mechanisms of potential infinity. It does not say such a set exists potentially - it says to me it actually exists.

I take your point that one could perhaps interpret it as potential infinity but I do not believe this is the common / mainstream interpretation.

How can you possibly know this? Have you traversed the spectrum? — jgill

No. Multiple universe theories are not testable so not scientific IMO.

I don't really believe in multiple universes, but if they do exist, then which of the following is more likely:

1. They are all made of completely different stuff and evolve in completely different ways
2. They are all made of similar stuff and evolve in similar ways

I think the 2nd is much more likely, leading to the conclusion that most or all such universes support life; a conclusion that fatally undermines the so called strong anthropic principle.

Well, merely saying so doesn't make it so.
Can you at least deduce a contradiction then? — jorndoe

The contradiction is:

- Effects are currently happening in our universe
- But if there is no first cause, no effects are possible (contradiction)
- So we must conclude that there is in fact a first cause

Causality is not a physical law; it's a speculative category (metaphysics) or methodological principle (epistemology applied to model theory/building e.g. classical physics). And if the topic is 'the origin of the universe' then we are always, necessarily dealing with the "macroscopic level" at its microscopic - plamck scale, or quantum - initial conditions (i.e. quantum cosmology). — 180 Proof

I think you are a believer in phenomena such as quantum fluctuations. They do not exist IMO. They are purely theoretical... there is no clear empirical evidence that they exist. In any case, they respect the law of conservation of energy and are extremely tiny so can account for precisely squat in the macroscopic universe. Even if they did naturally produce matter/energy (somehow), that would lead to infinite matter/energy density (with infinite time). You can call causality what you like but it is an inescapable truth that everything in the macroscopic world is bound by it. And the BB was a hugely macroscopic event, so its clear that it needs a macroscopic cause.

Physical constants belong to scientific models and not to what they model, namely, the universe — 180 Proof

It is a minor miracle that the atom exists and it requires specific fine tuning of the properties of quarks, electrons, the strong nuclear force, the electromagnetic force. All have to have their current values else no complex matter would exist and therefore no elements, no chemical compounds, and no life.

Also, the Many-Worlds Interpretation of QFT, especially with respect to QG (quantum cosmology) entails that the Planck Era universe c13.8 billion years ago in superposition (so-called) BB consisted in a countless universes each constituted by every possible physical value (i.e. ratios we designate "constants"), with this, our current "anthropic" universe just one of many possible universe; thus, the plausibility of which alone debunks the "need for" "intelligent" "fine tuning" as the late particle physicist & philosopher Victor Stenger points out at length in his The Fallacy of Fine-Tuning. — 180 Proof

I do not buy such explanations:

- Any explanation of origins of the universe that involves a billions to one shot coming off is not worth the paper it's written on.
- Each of those countless universes is made of the same stuff and evolve in the same way, so they all support life
- Certain physical law apply across all possible universe and those laws must be fine tuned else our universe would not support life
- We have a sample size of 1 that all universes support life so the statistics indicate they all support life

Sure, but in the quoted text, he did not claim that there is an actual set containing all the natural numbers. And his (incorrect, in our view) belief that there is an "actually infinite number of created individuals" does not somehow falsify all of his mathematical ideas about infinity. — aletheist

He believed actual infinity is possible logically and in reality. And many people are still under that impression. What we are all taught at school - the Dedekind-Cantor continuum - a line is an actual infinite set of points - is an actual infinity.

Please provide an authoritative reference for the claim that "all sets are actual." Remember, mathematical existence does not entail metaphysical actuality. — aletheist

"In mathematics, a set is a well-defined collection of distinct objects, considered as an object in its own right" - https://en.wikipedia.org/wiki/Set_(mathematics)

Something that has potential but not actual existence is not well defined.

How does that work? Can you set it out concisely? — jorndoe

An example from pool. Cue hits the white ball. White ball hits the black. Black ball goes in the pocket. If the cue does not hit the white, then nothing happens. So removing the first element in a finite causal regress nullifies the rest of the regress. Infinite causal regresses have no first element/cause by definition so they cannot logically exist.

Another example from pool. A frictionless, perfect pool table. The balls are currently wizzing around. They will go on wizzing around for a potential infinity of time. Can we deduce a first cause - the break off shot by the player. Or should we assume that the balls have 'always' been wizzing around. The second would be an infinite causal regress - an impossibility.

How exactly can the set of naturals be potentially infinite? That would suggest it is a partially defined set, IE an undefined set. It is defined as an actual infinity (all sets are actual).

No, it is defined as a potential infinity. One more time: mathematical existence does not entail metaphysical actuality. No one, except perhaps an extreme platonist, claims that there is an actual set containing all the natural numbers. — aletheist

Cantor did claim actual infinity exists:

"Accordingly I distinguish an eternal uncreated infinity or absolutum which is due to God and his attributes, and a created infinity or transfinitum, which has to be used wherever in the created nature an actual infinity has to be noticed, for example, with respect to, according to my firm conviction, the actually infinite number of created individuals, in the universe as well as on our earth and, most probably, even in every arbitrarily small extended piece of space. - Georg Cantor