When something is a first cause, it is an uncaused thing which then enters into causality. There is no limitation as to what a first cause could be, as it has no prior explanation for its being. It is unlinked from determinism as to why it exists. However, once it exists, its interactions with other existences then involve causality, or determinism — Philosophim

I've always required examples to flesh out philosophical or mathematical ideas, so I will return to the causal chain ${{F}_{n}}(z)={{f}_{1}}\circ {{f}_{2}}\circ \cdots \circ {{f}_{n}}(z)$ which is defined in a region of the complex plane. My colleague at Trondheim proved the theorem I have mentioned, but later I proved a much simpler version,changing the hypotheses slightly.

Think of a large disc in the plane, full of points,z, and each individual function in the chain taking any such point and producing another point in that disc. Assume that each of these functions draw any two points in the disc slightly closer to one another. Then, when you start the chain you can use any point in the disc as a "first cause". The chain will converge to a single value of z within the disc, but the degree of accuracy of that limit will vary depending upon original choice. That is to say some values of z as first cause will take longer to get close to the ultimate limit. Bigger values of n.

(In fact, in a paper of mine in the Proceedings of the AMS many years ago I showed that if the individual functions approach a specific function, f(z), one may be able to choose a "first cause" that will get the ultimate result the fastest.)

Think of a large disc in the plane, full of points,z, and each individual function in the chain taking any such point and producing another point in that disc. Assume that each of these functions draw any two points in the disc slightly closer to one another. Then, when you start the chain you can use any point in the disc as a "first cause". — jgill

If I understand you correctly, you're just talking about a mathematical origin. That's not the same as a first cause as defined in the OP. Lets envision an a thought experiment of an actual chain as a visual.

First, lets stretch a chain from left to right, each link is a prior cause to the next link. The first link in the left is the first cause. It has no prior link of causation.

Now lets take a chain that's looped together to represent infinite causation. What caused there to be a looped chain? There is no prior outside link that formed that chain.

In each case, the reason why there is a finite chain is that there simply is. The reason there is an infinite chain is that there simply is. There is no prior reason why there should be a finite regression of causality, or an infinite regression of causality. Does your formula apply to this? Currently I'm not seeing it.

First, lets stretch a chain from left to right, each link is a prior cause to the next link. The first link in the left is the first cause. It has no prior link of causation — Philosophim

In my example the first cause is on the other end of the chain, the nth function. As one lets n go to infinity, at each step back any z within that disc is an nth cause, I suppose. Infinite means going back in time with no end, for each n computing the accumulated value at the left end of the chain. The further back in time, the more accurate the value at the left end.

Now lets take a chain that's looped together to represent infinite causation. What caused there to be a looped chain? — Philosophim

The correlation between a bank account and the interest it accrues is a simple real world looped chain. A looped chain need not go around like a circle, it is more likely to look like this:

${{C}_{m}}(z)=\left( {{g}_{n}}\circ \cdots \circ {{g}_{1}} \right)\circ \left( {{g}_{n}}\circ \cdots \circ {{g}_{1}} \right)\circ \cdots \circ \left( {{g}_{n}}\circ \cdots \circ {{g}_{1}}(z) \right)$

This time going from right to left. m goes to infinity, as could n. We are still beginning with a "first cause".

7. Because there are no other plausibilties to how causality functions, the only conclusion is that a causal chain will always lead to an Alpha, or first cause. — Philosophim

How about, Originate with an alpha?

You're judging my post based on the title? Isn't that the same as reading the title of a news article, then commenting on it at the bottom of the forum? Come on, you're better than that. — Philosophim

Actually, should be "better than that", since he has a deep understanding of post-enlightenment philosophy. But he seems to dismiss any philosophy before the 17th century as religious (woo-woo) metaphysics. His self-professed worldview is Physicalism/Immanentism*1 {he'll correct me, if I'm wrong}. Which means that the notion of a First Cause, prior to the Big Bang scenario, is literally non-sense . . . from his truncated perspective.

Consequently, his self-assigned role on this forum is the resident nay-sayer to any supernatural notions. He seldom contributes anything positive to the conversation. Apparently, he views himself as a Socratic gad-fly*2. Ironically. Socrates' disciple, Plato, is the one most often identified with the philosophical concept of a necessary First Cause*3*4. So, more-inclusive philosophers on this forum will be more-open to your exoteric/elliptical . . . . arguments. :smile:


*1.Immanentism :
(ˈimənənˌtɪzəm) noun. the belief that the Deity indwells and operates directly within the universe or nature.
https://www.collinsdictionary.com/us/dictionary/english/immanentism
Note --- I don't know if 180 is a Deist. But I can provisionally agree with this concept. However, a temporary universe, like ours seems to be, must have a beginning and an Eternal Cause.

*2. Gadfly :
A gadfly is a person who interferes with the status quo of a society or community by posing novel, potentially upsetting questions, usually directed at authorities.
https://en.wikipedia.org/wiki/Gadfly_(philosophy_and_social_science)
Note --- Synonym : nuisance. annoyer. pest.

*3. First Cause :
Plato (c. 427–347 BC) and Aristotle (c. 384–322 BC) both posited first cause arguments, though each had certain notable caveats.[7] In The Laws (Book X), Plato posited that all movement in the world and the Cosmos was "imparted motion". This required a "self-originated motion" to set it in motion and to maintain it. In Timaeus, Plato posited a "demiurge" of supreme wisdom and intelligence as the creator of the Cosmos. . . . . In what he called "first philosophy" or metaphysics, Aristotle did intend a theological correspondence between the prime mover and a deity.
https://en.wikipedia.org/wiki/Cosmological_argument

*4. Necessary First Cause for a space-time universe :
For Aristotle, the existence of the universe needs an explanation, as it could not have come from nothing. . . . . Aristotle rules out an infinite progression of causes, so that led to the conclusion that there must be a First Cause.
https://www.qcc.cuny.edu/socialSciences/ppecorino/INTRO_TEXT/Chapter%203%20Religion/Cosmological.htm
Cosmological Argument : This is an argument or proof that is based on Reason. It is an a posteriori argument and by that is meant that it proceeds after considering the existence of the physical universe.

You're judging my post based on the title? Isn't that the same as reading the title of a news article, then commenting on it at the bottom of the forum? Come on, you're better than that.
— Philosophim
Actually, ↪180 Proof should be "better than that", since he has a deep understanding of post-enlightenment philosophy. But he seems to dismiss any philosophy before the 17th century as religious (woo-woo) metaphysics. His self-professed worldview is Physicalism/Immanentism*1 {he'll correct me, if I'm wrong}. Which means that the notion of a First Cause, prior to the Big Bang scenario, is literally non-sense . . . from his truncated perspective. — Gnomon

I appreciate the defense, but he posted that years ago. Its the only time I've ever had an issue with him and its long forgiven. 180 Proof and I are A-ok now. :)

That is clearly a contradiction, as it cannot be both that causation is an infinite regress and that there is a first cause. — Michael

Saint Thomas Aquinas distinguishes between per accidens and per se series; the distinction may be relevant to this discussion.

With 20/20 hindsight "appealing" is not the best choice of words - it goes beyond that.

In superdeterminism even your thinking is predetermined. Every last thought, emotion, sensation you have is predetermined. Your back itches? Predetermined. You replied to this post? Predetermined. You think I'm right (or wrong)? Predetermined.

Since you have no control over your thoughts there is no way to tell if anything is real. You could be a brain in a jar, you could be a robot, you could be a subject in an experiment run by aliens from another galaxy, or perhaps a supernatural being who controls everything in the physical universe could be controlling your thoughts, etc

So if nothing is real maybe you should be a nihilist? But even that very thought was predetermined.

But given that everything we currently know shows that the universe is random (at least at the quantum level)? I go with the evidence.

What is the distinction between determinism and causality?

Lets envision an a thought experiment of an actual chain as a visual. — Philosophim

What I have produced in mathematical terms is an actual chain - I can make it more specific with definitions of functions, etc. if you desire. Your actual chain is a complete abstraction.

What I have shown is that first cause is more complicated than what the ancients understood. In my example, n going to infinity, using the same z at each value of n produces an infinite causal chain having that z as a sort of ultimate first cause. I would think this example would stir original philosophical thought rather than a regurgitation of traditional ideas. :chin:

Another causal chain question: Do infinite chains ever end? Can infinite chains have specific values? Think going the other direction, into the future.

↪Philosophim What is the distinction between determinism and causality? — EricH

Determinism is the idea that everything was completely set by rules from the beginning. Tempral causality simply means that a prior event is the reason why a current event is happening. First causes are not determined because there is no reason for their being besides the fact they exist. This means there is no prior law that necessitated their existence.

What I have produced in mathematical terms is an actual chain - I can make it more specific with definitions of functions, etc. if you desire. Your actual chain is a complete abstraction. — jgill

They are both abstractions. While the math proof is nice, I'm still failing to see how it address the point. I still don't see anything in this other than talking about origins. For example, I could start my origin at 0, or start it at one when counting. But an origin is no the same as a full chain of causality that does not require an observer.

The question is really about what caused the set of causality to be. If the universe has a finite chain of causality, what caused that to be? If the universe has an infinitely regressive chain of causality, what caused that to be? There is no prior cause in either case. It would be that set without prior explanation; it simply would be.

What I have shown is that first cause is more complicated than what the ancients understood. In my example, n going to infinity, using the same z at each value of n produces an infinite causal chain having that z as a sort of ultimate first cause. I would think this example would stir original philosophical thought rather than a regurgitation of traditional ideas. :chin: — jgill

I'm not sure I see that. Could you clarify more? How is this any different from creating an origin in math? I appreciate the contribution, it just seems I'm not getting how it applies yet.

The question is really about what caused the set of causality to be. If the universe has a finite chain of causality, what caused that to be? If the universe has an infinitely regressive chain of causality, what caused that to be? There is no prior cause in either case. It would be that set without prior explanation; it simply would be — Philosophim

Well, this is certainly a deep issue. Good luck. Nice chatting with you. :smile:

One can maintain some respect for this thread if one sees it as attempting to phrase Fundamentality, in causal terms.

One might better understand what is being said if it is understood in terms of dependence rather than causation. The topic remains an opposition between infinitism and foundationalism, with Philosophim taking a foundationalist position. The alternative is an acceptance of infinite complexity, something that mathematicians may be more comfortable with than physicist. :wink:

Well, this is certainly a deep issue. Good luck. Nice chatting with you. :smile: — jgill

You as well jgill! I greatly enjoyed your contributions to the thread.

↪jgill One can maintain some respect for this thread if one sees it as ↪Philosophim attempting to phrase Fundamentality, in causal terms. — Banno

Fantastic link Banno, I was not aware this was a study of philosophy. After reading it, yes, this is basically what I'm doing.

Logic literally means Order. According to the order of order, it is necessary that there is a First Cause being Order itself. If Logic is the source and principle of all reality, then Logic or Logos is the First Cause. So foolish are those atheists who deny God because they are denying Logos itself.

Tempral causality simply means that a prior event is the reason why a current event is happening. — Philosophim

OK. So let the current event be the radioactive decay of an atom at time T. What is the specific prior event that caused the decay of that atom at that time?

What is the specific prior event that caused the decay of that atom at that time? — EricH

That's a problem with virtually all causality chains. There may not be just one cause at each step, there may be many, and so chains interact with one another. The complications are staggering, as your example implies. To all extents and purposes it appears random.

Here is my attempt to summarize an argument made by Hume in "A Treatise of Human Nature" as elaborated on at places by me (I am a layman). I confess it may not directly engage the content of the OP, but it seems to me to be relevant insofar as it challenges the necessity of a "first cause". In case anyone is interested, I am not suggesting that I personally deny the necessity for a first cause - I just provide this for the sake of the argument. Here it is:

I challenge the idea that whatever begins to exist must have a cause for its existence.

To begin, the claim that everything that comes into existence has a cause is equivalent to the claim that it is impossible for anything to come into existence without a cause. If the second of these claims cannot be sustained, the former cannot either.

The key point is this: we can conceive of an object being non-existent at one moment and existent the next – we do not need to even introduce the notion of “cause” into this thought experiment. I can imagine the absence of an apple on the table at one instant and its presence on the table at the following instant. What underlies this intuition? It is the fact that there is nothing contradictory or absurd about the idea of an apple popping into existence without cause. Sure, our empirical sense tugs at us to insert a cause since most “comings into existence” have clear causes. However, it seems to me that this temptation can be resisted – an apple not existing at t1 and then existing at t2 is a conceivable possibility.

Since we cannot refute this possibility on the basis of the nature of the concepts of existence and cause (as distinguished from the empirical fact that these things always seem to go together), we therefore cannot make the case that it is impossible for anything to come into existence without a cause – after all, anything is possible unless it is logically impossible. And coming into existence without cause appears to be logically possible given the appeal of the thought experiment. It is then simple (see 2nd para) to conclude the hypotheses: that it is not the case that whatever begins to exist must have a cause for its existence.

Objection 1:an object that comes into existence must have a cause since, if there were no cause, the object must have “caused itself”. That, in turn, implies that the object would have to exist before it came into existence, which is impossible. Therefore, everything comes into existence must have a cause. The problem with this objection is that it entails assuming that some cause is necessary (and, in this case, that the cause is the object itself). But the claim is that no cause is needed.

Objection 2: Whatever comes into existence without a cause must be caused by nothing. The problem with this objection is the same as with objection 1 - it also entails assuming that some cause is necessary.

The key point is this: we can conceive of an object being non-existent at one moment and existent the next – we do not need to even introduce the notion of “cause” into this thought experiment. — expos4ever

And that's all it is, a mental feat, like flapping my wings and soaring to the moon. We are blessed with the ability to be creative, and much of which we imagine can be brought forth in the real world through our efforts. But not the miracle apple.

I must, however, admit that my examples of causal chains with/without first causes is nothing more than a mathematical illusion, like your apple. :cool:

Does Superdeterminism save Quantum Mechanics? Or does it kill free will and destroy science?

I do not know if this is true or not but it is relevant to what we discussed. Superdeterminism and free will.

To begin, the claim that everything that comes into existence has a cause is equivalent to the claim that it is impossible for anything to come into existence without a cause. If the second of these claims cannot be sustained, the former cannot either. — expos4ever

Then you agree with the OP. A first cause is an 'uncaused cause'. Or something unexplained that is justified by its own existence, that then can enter into causality chains with others.

Then you agree with the OP. A first cause is an 'uncaused cause'. Or something unexplained that is justified by its own existence, that then can enter into causality chains with others. — Philosophim

Not sure I follow. In the material you quoted, all I am doing is claiming that 2 different statements, each of which I believe is well-formed and meaningful. are equivalent (different ways of expressing the same thing), nothing more.

One can maintain some respect for this thread if one sees it as ↪Philosophim
attempting to phrase Fundamentality, in causal terms.

One might better understand what is being said if it is understood in terms of dependence rather than causation. The topic remains an opposition between infinitism and foundationalism, with Philosophim taking a foundationalist position. The alternative is an acceptance of infinite complexity, something that mathematicians may be more comfortable with than physicist — Banno

I was not aware of the philosophical notion of Fundamentality*1. But that is exactly what my un-orthodox personal worldview is based on. For philosophical, not scientific, purposes, I view Generic Information*2 as the fundamental essence of Reality. As Wheeler implied, the causal power to enform (Aristotelian Potential) is the logical precursor of actual Energy, Matter, and Mind.

I try to avoid "infinite complexity" by postulating a logically necessary First Cause (Zero) to get the cosmic ball rolling (Big Bang . . . .), but make no conjectures into unknowable Infinity. Just as Zero (Potential for all numbers) must precede One in a continuum, the First Cause is "ontologically independent and ungrounded". Just as Zero is immaterial, the hypothetical Cosmic Cause is more like the ethereal potential we commonly call "Energy". All origin theories (Big Bang ; Multiverse : Inflation) take Energy & Laws for granted, as fundamental necessities.

Like Physicalism, my thesis is a metaphysical posit, not a physical fact. It goes one step beyond the matter/energy elements of Physicalism to the predecessor or progenitor of those "its". Other than its logical necessity, we know nothing of the First Cause, but we can understand that everything real is dependent upon actualized Possibility (zero). :smile:


*1. Fundamentality :
The notion of fundamentality, as it is used in metaphysics, aims to capture the idea that there is something basic or primitive in the world. This metaphysical notion is related to the vernacular use of “fundamental”, but philosophers have also put forward various technical definitions of the notion. Among the most influential of these is the definition of absolute fundamentality in terms of ontological independence or ungroundedness.
https://plato.stanford.edu/entries/fundamentality/

*2. Matter from Information :
Physicist John A. Wheeler's philosophical conjecture that information, not matter is fundamental.
"It from Bit symbolizes the idea that every item of the physical world has at bottom — at a very deep bottom, in most instances — an immaterial source and explanation; that what we call reality arises in the last analysis from the posing of yes-no questions and the registering of equipment-evoked responses" ___JAW
https://www.themarginalian.org/2016/09/02/it-from-bit-wheeler/



ALL NUMBERS ARE DEPENDENT UPON ZERO

The topic remains an opposition between infinitism and foundationalism, with Philosophim taking a foundationalist position. The alternative is an acceptance of infinite complexity, — Banno

An infinite chain of reasons or causation chain may be finite in the sense that as one moves further and further back in time the passage or rate at which time moves (I know, sloppy) possibly changes all the way down to zero.

Infinite complexity to me means all the transfinite stuff that set theory produces. It may never arise in the physical world.

There is no limitation as to what a first cause could be — Philosophim

It is limited to things uncaused, surely.

Do multiple causation chains spring into being with first causes or first cause?

An infinite chain of reasons or causation chain may be finite in the sense that as one moves further and further back in time the passage or rate at which time moves (I know, sloppy) possibly changes all the way down to zero. — jgill

Interestingly, your many mathematical expressions contain only a finite number of elements, yet set out infinite sequences. A simple expression such as $0.\dot 9 = 1$ includes infinity - the dot says we "carry on in the same fashion", writing more 9's...

We don't expect to be able to write all the 9's down. But we do, in a finite time, understand what is going on, and can follow subsequent arguments and discussions without getting trapped in our inability to actually write an infinite number of 9's...

Well, some of us can.

What I have produced in mathematical terms is an actual chain - I can make it more specific with definitions of functions, etc. if you desire. Your actual chain is a complete abstraction. — jgill
They are both abstractions. While the math proof is nice, I'm still failing to see how it address the point. I still don't see anything in this other than talking about origins. For example, I could start my origin at 0, or start it at one when counting. But an origin is no the same as a full chain of causality that does not require an observer. — Philosophim

As you noted, 's numerical chain is an abstract concept, not a perceptible "actual" thing. But he also doesn't seem to realize that the "First Cause" of his mathematical chain of abstractions was not "1" or "0" but his own imaginative mind. His chain would not exist in any sense, if he had not mentally pictured it in the first place.

It's easy to see that the First Cause of an abstract concept is an intentional Mind, but not so easy to accept that the First Cause of an actual physical evolutionary chain of creative events could originate in a creative Mind of some kind. In that sense, the Big Bang could be called a Conception, both literally (impregnation) and figuratively (creative idea). But the causal origin of that fetal conceptus had to exist, as a Potential, prior to the prime causal event (e.g. big bang). And its causal power had to be infinitely greater that that of any human intention.

Plato's First Cause was imagined as an abstract symbol of Causation, not a thing or being. His Logos was also an imaginary abstraction to represent the idea of a rational Principle responsible for the unique human ability to think logically, and to know that they are reasoning in accordance with the rules of Nature. So the First Cause/Logos was not a Real Thing --- because Reality had not yet been invented --- but merely the Potential to create real & thinking things.

"First" is a countable position in a sequence. But First Cause is the Origin or Genesis of the series from nothing : typically zero or infinity. Creative Causation is an immeasurable abstract idea, which implies an a priori Impetus or Force. And, an unreal non-physical Potential Origin of any physical series is a logical necessity to explain the emergence & existence of the Actual chain, from Potential no-chain. But, since we have no physical evidence of what existed prior to step "1", we can just call it "zero" or "infinity", or "god" --- all abstract concepts, with no instance in reality. :smile:


Intention : purpose ; to imagine a future state

Potential : capable of becoming real : possible.

Priority : the state or quality of being earlier in time or occurrence.

Generic : the cause of a whole genus (system of things & events)

Genesis : the origin or mode of formation of a thing or system.
Note --- My own Original Cause, of the chain of evolution, is what I call EnFormAction : the act of forming (manifesting) novelty. It's postulated as the precursor of Energy, Mind, and Matter. The origin of my own concept of generic causation was physicist John A. Wheeler's "it from bit" motif : a hypothetical conceit combining Quantum & Information theories into the kernel of a Theory of Everything.

Interestingly, your many mathematical expressions contain only a finite number of elements, yet set out infinite sequences. A simple expression such as 0.9˙=1
0.
9
˙
=
1
includes infinity - the dot says we "carry on in the same fashion", writing more 9's...

We don't expect to be able to write all the 9's down. But we do, in a finite time, understand what is going on, and can follow subsequent arguments and discussions without getting trapped in our inability to actually write an infinite number of 9's...

Well, some of us can. — Banno

:"Some of us" get lost in self-deception. The question is which are the ones who are lost. The two expressions, the 1 and the 0.9˙ are said to be equal. And as you say, we can readily understand what's going on without getting trapped. The two do not actually have the same meaning, it's a form of "rounding off", with the convention allowing the use of "equal". When rounding off we assign a different meaning, which better serves the purpose, and we allow that the rounded is equal to the pre-rounded.

I would assume that those who do not understand that this is a form of rounding off, and claim that the two expressions are actually the same, despite the glaring difference in meaning between them, are lost in self-deception. They have fallen into the trap of saying that two different things are the same, just because the convention allows us to say that they are equal. It seems common at TPF for mathematicians to fall into the trap of saying that "equal" means "the same as".

"0.999..." and "1" represent exactly the same number.

Do multiple causation chains spring into being with first causes or first cause? — jgill

Possibly. Once something begins, it immediately has relations with anything around it. Something small or large could appear and its gravity would suddenly now be an influence on other things, as well as itself may be influenced by other things. It could be as simple as an uncaused helium atom entering the world and then existing within it. Once an uncaused thing is within the rest of the interplay of existence, it is no more special than anything else.

There is no limitation as to what a first cause could be
— Philosophim

It is limited to things uncaused, surely. — AmadeusD

Ha ha! Of course. :)

@Gnomon Well said.