The Ultimate Question of Metaphysics
Thinking about this the other day and finally the question that trumps all questions hit me. Why is there something rather than nothing ? Nothing would be simpler to explain in a sense rather then the existence of something as that would lead to more questions such as where it come from and why.
But as something does actually exist rather than nothing this to me proves that nothing is actually impossible to exist. In fact Im trying to define and imagine nothing I have trouble. I guess most would imagine nothing to be a void. Timeless and dimensionless. Here the concept of nothing really breaks down. (And by nothing I dont mean a state of vacuum which still is something as virtual particles still briefly pop into existence).
Yet here we are so I guess the question then leads to did something come from nothing ? Is that question even meaningful in that context ? Or has something always existed (in one form or another)?
And yet I remain none the wiser as to the nature of existence even having deduced this merely that something has always existed eternally. My mammalian brain still asks where did it come from ? And from this I just realise that this question will never really have a satisfactory answer.
Thoughts ?
But as something does actually exist rather than nothing this to me proves that nothing is actually impossible to exist. In fact Im trying to define and imagine nothing I have trouble. I guess most would imagine nothing to be a void. Timeless and dimensionless. Here the concept of nothing really breaks down. (And by nothing I dont mean a state of vacuum which still is something as virtual particles still briefly pop into existence).
Yet here we are so I guess the question then leads to did something come from nothing ? Is that question even meaningful in that context ? Or has something always existed (in one form or another)?
And yet I remain none the wiser as to the nature of existence even having deduced this merely that something has always existed eternally. My mammalian brain still asks where did it come from ? And from this I just realise that this question will never really have a satisfactory answer.
Thoughts ?
Comments (121)
Why is there something rather than nothing is the common starting point of much Christian apologetics. Because for such folk this leads straight to theism being necessary. The great first cause, unmoved mover arguments which goes back to Aristotle. Personally I don't think 'Why something from nothing?' is a coherent question. Human brains seem to be structured to conceptualize 'things' and 'no things' but how intelligible is this construct when you get to metaphysics? Has 'nothing' ever being identified; can it be identified, or are we talking about a theoretical nothing? What exactly is nothing supposed to be (no irony intended)? Are we conditioned to stick the word 'why' in front of things because our brains also seem to structure our reality in terms of cause and effect?
It cannot be identified if it does not exist. A theoretical nothing can be defined. It would be the opposite of something. Having no qualities or characteristics such as time, mass, dimensions or other such characteristics that would define something. Essentially non-existence. Which would have continued to not exist infinitely yet here we are there is something instead of nothing. And as something cannot arise out of nothing the essence and rules of nothing would prohibit something emerging from it. I then conclude that something has always existed and has done so eternally.
Case closed ?
Are there not philosophers (I think @joshs may be one) who argue that the universe has no intrinsic qualities or characteristics and it is us who find these and actively create what we know as reality? So perhaps something from nothing is the process which happens when humans have conscious experiences.
You just rightly rejected the idea that something could come from nothing. The existence of something already negates the possibility of a true nothing as that true nothing would have to lack the capacity for even the possibility or potentiality of producing a somethingness.
So next up on the batter's order is something from everything. The prior potential could be understood as a plenum, a state of absolute everythingness. And this works quite well as it is pretty quantum. In the quantum path integral or sum over histories, all possibilities exist, but then the majority must also contradict or self cancel. If a fluctuation can go right, it can also go left, and the upshot is the somethingness of a fluctuation that just didn't really get to happen at all.
Quantum field theory tells us reality actually works this way. A neutrino or quark are mixtures of all the particles they could be. The maths has to sum over all the possible states to get the most probable emergent state - the one that cancels away all the everythingness to arrive at some local somethingness, exact to 20 decimal places.
So we already can imagine using a quantum sum over histories to account for the Cosmos as simply what emerges when you average over all possible dimensional and particle arrangements to arrive at whatever final structure doesn't just self-cancel away its own potential to actually exist.
This approach to the Big Bang fits as its trajectory is then towards its own Heat Death. The Universe is also locked into a structure of expanding and cooling which will eventually achieve a state of as close to absolute nothingness as it can get - technically, a de Sitter void with a temperature of absolute zero and empty of particle content apart from the residual sizzle of Hawking radiation produced by the cosmic event horizon itself.
So everythingness must constrain itself via the interaction of all its own conflicting possibilities, which is how a residual somethingness is left. And we can see that the Big Bang cosmos is still manifesting this fate - this dissipative journey towards the nothingness of a void, exhausted of all its possibilities and so able to now exist in peace for all eternity.
But then "everythingness" as an initial conditions becomes something we can refine a little further. It carries connotations of an infinity of actuality - actual interactions, some actual place that was full of rather concrete possibilities. We want to get beyond even that to arrive at some more pure definition of a simple state of unbounded - not yet in anyway constrained - possibility.
That leads us to a logic of vagueness. A state of anything and everything is really just a state of absolute vagueness. The principle of non-contradiction doesn't even apply. It is literally less than nothing as it is beyond any concrete distinction, such as the negation of a nothing, or the affirmation of a something.
To sum up, the big question is the "why anything?" question. If you check ancient metaphysics, the "something out of everything" story is in fact pretty routine. The "something out of nothing" story arose with Greek atomism and its void, then got embedded in Christian theology in particular, with its need for an act of creation.
Modern science has arrived back at "something out of everything" as a mathematical theory. Quantum field theory can simulate the stormy interior of a proton as a suitably constrained potential, getting to the point where the sum over histories calculations shows surprisingly that the internal mass-creating fluctuations produce far more anti-down quarks than anti-up, to give a random example of how well supported this is.
But then, to really shift our thinking, we need to upgrade our metaphysical logic. Vagueness becomes a further category of "existence" that goes beyond the yin and yang of everything vs nothing.
Presence and absence are the crude or emergent categories which folk tend to want to apply to fundamental nature. But we can do better. Vagueness makes an even deeper claim that transcends the distinctions - the dichotomies - which it can thus engender.
To get back to the question, the short answer is that there is something because a state of everything includes its own negation, its own limitation. But not everything could then self-erase or cancel away its possibility of being actualised. Even the Heat Death of the cosmos - as an actualised state of maximal nothingness or void - is still going to be forever a residual something. The Universe will be like an infinitely large box produced so as to definitely and actually lose all the unbound possibilities that an absolute vagueness would have had to have contained.
A potential just wants to burst. And a vague potential has nothing to stop it bursting, but also no direction into which to burst. So the Big Bang is that logical impasse resolving itself in a sum over histories fashion. Spacetime organised as a direction, and matter-energy organised as the contents expressing the constraints of this spatiotemporal structure.
You had the hylomorphism of material impulse and formal order. A path arose to concretely turn a manifested everythingness into a matching "end of time" state of actualised nothingness. And overall this can be seen as a logical trajectory from a pure vagueness to a state of supreme counterfactual definiteness.
Physics and metaphysics come together, as they ought.
I have a follow up as well where I go into what that means for the universe. But its pretty simple. There is no reason why anything exists. It simply does. This is logically concluded, not simply an opinion. So what does that mean for us? Honestly, just enjoy it!
Well this is likely the ultimate metaphysical question, the biggest of them all. Many perspectives can be given.
The best I can do is, we are not equipped with the correct apparatus to clearly understand why something is less problematic than nothing - at least for nature.
So here we make the usual mistake of attributing issues that arise in the mind to nature, that are not a problem for nature.
:fire:
e.g. Eternal vacua of fluctuating, virtual universes/clocks.
(Otherwise, there's "nothing" to prevent not-nothing from coming-to-be, continuing-to-be or ceasing-to-be.)
Quoting Manuel
Quoting Tom Storm
:clap: :up:
Re: 'The map is the territory fallacy' (of idealism).
Except the concept of a quantum vacuum is already predicated on a bounded, energy conserved and time symmetric, state. A gone to equilibrium backdrop which thus merely fluctuates. And probably with just three spatial dimensions - as that is the special condition where rotational degrees of freedom are symmetric with translational degrees of freedom. Etc.
So the prior potential has to be far more unstructured than any vacua. We are talking a quantum foam or some other pregeometric understandings of the initial conditions.
Ex nihilo nihil fit (nothing comes from nothing) and ergo, Creatio ex nihilo (something from nothing) is a bona fide miracle and a sine qua non for any miracle whatsoever is God!
To have a vacua is already to have the global symmetries that ensure the local invariances, or degrees of freedom. The breaking of symmetries can follow from the construction of the symmetry.
My point is that you then have to wind back your cosmic clock to whatever supposedly grounds this production of an actual vacua, this actual generalised state of symmetry.
[quote=Ms. Marple]Most interesting![/quote]
Which branch of math do you suppose is most apt for decoding the Big Bang (13.8 × 10[sup]9[/sup] suns ago)? We already tried calculus, arithmetic part & parcel of that, and as per reliable sources we're kinda stuck or have hit a wall. Should we turn to geometry/topology/knot theory/etc.? :grin: These are the only other subfields of math I've heard of.
It all breaks down to computing the path integral of the symmetry of quantum foam, so that a vacuum results. :chin:
Quoting Manuel
:up:
Well youre not alone! :smile:
I recommend Heideggers Introduction to Metaphysics for an analysis of this question. Fascinating, in my view.
Just as this statement ignores the fact that the notion subject is equally silly.
Yes, for there is no "come from" for the Eternal.
One can go on to conclude that the temporaries produced by the Permanent Eternal have to be its rearrangements, such as the elementary 'particles' that are directly the quanta of fields.
All physics likes to cash out in differential equations. And integration - as in path integrals - is just the reciprocal of differentiation. So in terms of the writing out of "laws", the language will look like the same old equations of motion approach.
Then physics strongly expects a final theory of the Big Bang to require an exact model of quantum gravity - the sought-for union of general relativity (GR) and quantum field theory (QFT). So those two bodies of maths would be melded into one capable of at least quantifying gravity, and possibly uniting gravity with the other three already quantified fundamental forces.
So the practical language of the maths is good old functions. And the justification of the unifying frame would be what employs the fancy-schmancy higher maths - stuff like permutation symmetries, topological order, and fibre bundles, and absolutely anything else that helped. Even category theory has been chucked into the fray.
Thus the target of producing a working theory of quantum gravity is a well-defined goal here. It would unite the three fundamental constants of c, G and h which found the differentiation of the "cosmological equations of state". QFT unites h and c. GR unites G and c. What is missing is QG that can unite h, c and G. Then we will be equipped to write out differential equations (and integrals) that contain all three required terms.
But as I say, the more metaphysical - or logic-based - arguments for how the cosmos works would be knitted together out of the usual symmetry/symmetry-breaking mathematical arguments. The conservation principles and least action principles that have been used since Newton, just with ever greater mathematical abstraction.
So for example knot theory tells you that knots only stay tied in three dimensions. And if you can make the argument that particles are really just "knots", then you can say why only a 3D reality could be the case. You don't have to write an ad hoc 3D constraint into your QG theory to make it work. You can say that any other number of dimensions would be a "trivial representation" - one that couldn't even hang together and thus exist.
So the big motivating ideas can come from all over the abstract end of maths. But then it will all be just "metaphysics" unless a framework can be cashed out in the usual concrete differential equations that let's scientists divide their labours into the usual thing of model building and acts of measurement.
That is simply the most practical way to reduce complexity to simplicity. Tell me exactly where something is now and I can calculate its position or action for all times, both prospectively and retrospectively. One number and one constant sums up "everything" about some physical interaction.
Quoting jgill
As I describe, I see these as two extremes of the one intellectual enterprise. We need to go abstract to get the big ideas, and then be able to do something - like compute the integral of a quantum foam - to prove that our theories measure up against the world they describe.
I'm trying to stress that the idea of maths as a branching tree may be a misleading metaphor here. A tree makes it sound like calculus is the sturdy root and knot theory is some tiny obscure twig that might prove to break the dam of misunderstanding.
The difference is instead between the concrete and the abstract. So geometry is done with equations that have to include distances and angles. Topology is the more abstract view that can throw away such concrete measurables and simply envisage a structure of relations. The coffee mug you hold in your hand becomes instead the far more general thing of a torus.
Does that then make the coffee mug the sturdy root of your mathematical description, the torus a random distant branch of your mathematical tree?
You in fact need to go beyond tree metaphors to hierarchy theory - another "branch of maths" :grin: - to see how what is being opposed here is the particular vs the general, the concrete vs the abstract, the local vs the global, etc.
Doesn't the rest of the post suggest that nothing is everything? Especially when vagueness is brought up. There isn't a difference between a state of anything and everything that is really absolute vagueness and nothing.
My argument was meant to lead from the usual monistic framing of the existential question towards a triadic or systems view of the ontology - in the tradition of Anaximander, Aristotle, Hegel, Peirce, etc.
So we start with the undoubted fact that something exists. And we then seem to have to conclude either that this state of embodied somethingness existed forever - there was no creation event or process of evolutionary emergence - or that it arose out of ... nothingness ... for no clear reason ... and by no clear causal mechanism.
People feel these are the only obvious options. Either existence brutely exists in some eternal uncreated fashion, or somethingness can be dialectically opposed to nothingness and so if the cosmos sprang into being - especially in the way that Big Bang science suggests then it had to pop out of a void, a nullity. The opposite kind of thing to a something which is a nothing.
But metaphysics can be more sophisticated than that. It can continue on to create more categories of existence.
So somethingness suggests nothingness as it rightful antithesis. However nothingness can be opposed to everythingness. And then the very idea of dichotomous categories dyads like nothing vs everything - can be seen to themselves resolve into the crispness that is some such extremal division, and the vagueness which is the very "other" of any kind of extremal division at all.
Peirce, for example, developed this in terms of modern logic. He defined vagueness as the category of "existence" to which the principle of non-contradiction fails to apply. Normally, we argue that something has to be one thing or the other in some definite fashion. But this opens up the further option of being simply utterly indeterminate or vague. Nothing is being ruled out and the PNC fails to apply.
Peirce also defined the idea of generality (as opposed to particularity) as that to which the Law of the Excluded Middle fails to apply. Where vagueness is fundamentally indeterminate in regards to some distinction, generality is so inclusive it absorbs all possible distinction.
This shows how metaphysics has more tools in its cupboard than are conventionally employed in these discussions about "why anything?".
Anyway, what I argued towards was the evolutionary or developmental cosmology based on a triadic systems view of the Cosmos. In the "beginning" was a vagueness - an apeiron, an ungrund, a firstness - that was less than nothing in being utter indeterminacy. This vagueness could also be considered an everythingness in being a generality so general it again lacked all distinction.
But in lacking distinction, it could be the ground for the birth of distinctions. It could spawn dichotomies or dialectical oppositions such as "everything vs nothing". Suddenly, these two metaphysical categories could start to apply in some mutual or relative fashion. There could be nothing to the degree there wasn't everything, and there could everything to the degree there wasn't nothing. Somethingness then could arise with the two limits being set. There could be something because there was not everything and also not nothing.
So vagueness becomes some ultimate state of symmetry - a logical indefiniteness. The breaking of this symmetry by any kind of somethingness then brings with it the opposing extremal bounds of this nascent thingness. The slightest somethingness is already a pointer towards the two ultimate anchoring bounds of nothingness and everythingness - the two distant limits that show the somethingness to be what it is in terms of what it is not ... which is either a nothing or an everything.
Once you have got used to thinking about ontological questions using this kind of metaphysical logic, then you can bring a new resource to the current science of the Big Bang. You don't get hung up at the first step where you start arguing that something must have popped out of nothing ... which doesn't compute as nothing can come from nothing ... etc.
"Rather than"? Do you think there's something called "nothing" which would exist if there wasn't something?
Do you mean to ask "Why is there something?"
Profound or not? Something or nothing? :roll:
Quoting jgill
I appreciate you playing along with my bullshit. :smile:
:smirk:
Very interesting post. Given your thoughts here , you might be interested in Lawvere's work on Hegel's dialectical using adjoint modalities if you haven't already heard of it.
https://ncatlab.org/nlab/show/Hegel%27s+%22Logic%22+as+Modal+Type+Theory
https://ncatlab.org/nlab/show/Aufhebung#lawveres_path_to_aufhebung
But Lawveres adjoint cylinder example does get the essence of the triadic systems architecture in this kind of statement. And it even namechecks Peircean thirdness in doing so. Thus we are feeling the same elephant,
We need an argument that demonstrates that nothing is impossible or that something is necessary, same thing!
It's quite a challenge to answer this question for the simple reason that one needs to have a deep understanding of nothing, but that's quite a difficult task if not impossible; after all how does one reason/experience (about) nothing?
The man who knows nothing well enough to answer this question hasn't been born.
[quote=Socrates]I know that I know nothing[/quote]
:snicker:
Well everythingness must contain its own limitations just because it includes all possible conflicts. A will be cancelled by not-A. The result ultimately would be that everythingness thus cannot exist. It can only be the prior potential which then self-cancels.
Then nothingness ought to actually exist as a consequence. And yet somethingness does exist at the moment. So we know also that everythingness must pass by a state of somethingness on its way to manifesting nothingness.
So somethingness must be just the stepping stone - the host of self-cancelling actions that the Cosmos must pass through to achieve its desired oblivion.
And science says the Big Bang is on its way to its Heat Death. Sound familiar? :chin:
Everything can't exist (MAD - mutually assured destruction - of things and anti-things) and nothing would result. It is possible then, if everything exists, nothing would be the case. Is the something we experience just a phase in the transition from everything to nothing?
Nothing then is everything (they're synonomous from a yin-yang perspective, MAD).
That still doesn't answer the question though, does it? I dunno.
That is the gist of the argument. And it fits the physics. The puzzle for cosmology is that the Big Bang didnt just remain in its simplest possible state of a cooling-expanding radiation bath. Instead it went through a series of further symmetry breakings that led to complex matter.
But then, it will all return to that ultimate simplicity in the long run. All the particles will be swept up in blackholes and radiated away. The only material content left will be the dark energy stretching space until there is nothing around to actually have interactions.
So I offer a general logical argument. And it fits the physics.
The surprise is that the universe as we know it - full of material complexity - is a passing phase. Things had to get messier before they could eventually become simpler again. Not all self-cancellation could happen at once. The task is going to take time.
[quote=Ms. Marple]Most interesting.[/quote]
Danke kind person, danke!
Below, I offer an excerpt from a book on apples:
Apples are not rocks, they don't grow in tar. They're not found in the Arctic and they're not bitter [...]
If we can't know nothing (what it is rather than what it isn't), it's impossible to answer the question "why is there something rather than nothing?"
Consider this ...
Quoting Agent Smith
I gave it a go in this old post
Quoting 180 Proof
and then later on a different thread
Quoting 180 Proof
Yeah, yeah: semantic, concept jugglery (aka 'Hegelian' metaphysics). :smirk:
[quote=TLP, prop. 1.1]The world is the totality of facts, not of things.[/quote]
Let's frame the question in terms of properties/qualities. A thing possesses at least one property. We can say of a thing that it is
We can't say of nothing that it is so and so. I believe nothing is the negation of everything and yet, as apokrisis said, nothing is everything.
Unfortunately, I can't offer a ton of clarification as I just discovered this myself looking for something totally different on nLab.
Some clarifying questions have been asked on Stack Exchange, and the answers are more accessible than the nLab articles. (E.g., https://math.stackexchange.com/questions/466638/what-was-the-lawveres-explanation-of-adjoint-functors-in-terms-of-hegelian-philo)
I am not particularly familiar with category theory so, while I get the Hegel references having read a good deal of Hegel and secondary sources, I get lost in the terminology pretty quickly here and have to keep looking stuff up. My math background is very much focused on applied mathematics. I've had a lot of experience with all sorts of regression techniques used in economics and polsci, game theory, a good deal of simulation work from my time working in intelligence, and a bunch of hybrid programming/stats skills I've developed since joining a startup that is trying to automate some of the work finance/management analysts do in local government/school districts. None of this is very abstract, so for a lot of topics in mathematics (e.g., set theory) I only have a hobbiest level understanding.
It's a shame these areas are not taught in the context of many fields though because I can see how they apply to a lot of work I do programming. For example, setting up a DAX measure to use as categories for a budget to actuals graphs is essentially using a lot of logical arguments to define a set. But I do it without formalism and sloppily in iterations until it works, and it doesn't even produce true definitions because no client's use their chart of accounts correctly.
More abstract mathematics, logic, and coding have a lot in common. I wish there was more cross pollination there.
Indeed.
Instead of thing, I suggest using being.
Then theres a question about beings (things, individuated entities) and being (thing-ness).
When we think about beings we tend to do so in terms of what is before us in experience what is present in the world or in our minds concepts, classes, words, numbers, shapes, colors, individual things, material objects, etc.
It almost cant be helped; in the same way its much more likely that we reflect upon our environment and not whats happening in China or on Mars.
The same is true of our bodies. The process of my kidneys arent before me in experience. Its a kind of absence. Ditto with habits and automaticity so much of our lives goes simply unnoticed. Taken for granted.
Is absence a kind of nothing, then? In the sense that its not present before us, in the background, invisible, withdrawing then its very much like nothing. Its not a thing in the sense we normally mean thing or being as that which is known, present, and there.
Any reasons why?
1. { }. No elements.
2. {{ }}. The { } is the only element.
3. {0}. 0 is the only element.
4. {{ }, 0}. This set is a valid set.
What do you mean by A and not-A? If A is an object and not-A are all objects other than A, I don't see necessarily any contradiction in the simultaneous existence of all these objects, or their mutual "cancellation".
What does it mean for something to "exist"? How does "being logically possible (consistent)" differ from "existing"? I don't know what the difference could be, so it seems to me that there is no difference and therefore all logically possible objects necessarily exist, by definition. In other words, every object that is identical to itself (every object that is what it is and is not what it is not) necessarily exists.
What remains to be found is what objects are identical to themselves.
Im talking in the context of quantum field theory and its path integral formalism, particle fields and creation-annihilation operators. Or in very simple terms, if there is a fluctuation - anything at all - then it is just as likely to go left as go right. And doing both, it cancels out doing anything at all.
So when describing a quantum vacuum ground state, any fluctuation has some probability. But these virtual particles are created in mutually cancelling pairs. An electron must generally be accompanied by a positron. And so while they both may briefly exist, they both also just as fast wipe each other out.
It is just built into the quantum view that everything is possible, and yet generally it all self cancels to nothing because the only way to exist as some particular object is to break a symmetry. And yet that very symmetry - if I can go left, then I can also go right - then comes back at you to swallow you up.
This gives you your quantum ground state - an everythingness that is a nothingness. From there, you can start to figure out how anything concrete could persist for any kind of time at all.
And that becomes what cosmology is all about - the messy complexity that saw one in a billion protons failing to be annihilated by a matching antiproton in the first split second of the Big Bang, and so create a universe as something more interesting than a spread-cooling bath of radiation.
Zeroish stuff you mean. Smaller than the smallest imaginable positive real but not zero is how I define infinitesimals. Would a mathematician forgive me for thinking of infinitesimals this way?
I think that to ever get a satisfying answer to the question "Why is there something rather than nothing?", we're going to have to address the possibility that there could have been "nothing", but now there is "something". If any extant solution were satisfying, we wouldn't still be asking the question. Another way to say that you start with "nothing" is with the analogy where you start with a 0 (e.g., "nothing") and end up with a 1 (e.g., "something"). We know you can't change a 0 into a 1 (ex nihilo nihil fit), so you can't start with a 0 unless somehow the 0 isn't really a 0 but is actually a 1 in disguise, even though it looks like 0 on the surface. That is, in one way of thinking "nothing" just looks like "nothing". But, if we think about "nothing" in a different way, we can see through its disguise and see that it's a "something". That is the situation we previously, and incorrectly, thought of as "nothing" is actually an existent entity, or a "something". A proposed mechanism for how that can be is as follows.
I think that to ever get a satisfying answer to the question "Why is there something rather than nothing?", we're going to have to address the possibility that there could have been "nothing", but now there is "something". If any existing solution were satisfying, we wouldn't still be asking the question. Another way to say that you start with "nothing" is by using the analogy that you start with a 0 (e.g., "nothing") and end up with a 1 (e.g., "something"). We know you can't change a 0 into a 1 (ex nihilo nihil fit), so the only way to do this is if that 0 isn't really a 0 but is actually a 1 in disguise, even though it looks like 0 on the surface. That is, in one way of thinking, "nothing" just looks like "nothing". But, if we think about "nothing" in a different way, we can see through its disguise and see that it's a "something". That is the situation we previously, and incorrectly, thought of as "nothing" is actually an existent entity, or a "something". So, something" doesn't come out of "nothing". Instead, the situation we used to think of as "nothing" is actually a "something" if we could see through its disguise. A proposed mechanism for how that can be is as follows.
How can "nothing" be a "something"? I think it's first important to try and figure out why any normal thing (like a book, or a set) can exist and be a something. I propose that a thing exists if it is a grouping. A grouping ties stuff together into a unit whole and, in so doing, defines what is contained within that new unit whole. This grouping together of what is contained within provides a surface, or boundary, that defines what is contained within, that we can see and touch as the surface of the thing and that gives "substance" and existence to the thing as a new unit whole that's a different existent entity than any components contained within considered individually. This surface or boundary doesn't have some magical power to give existence to stuff. But, it is is the visual and physical manifestation of the grouping together of stuff into a new unit whole or existent entity. Some examples of groupings are 1.) the grouping together of paper and ink atoms to create a new unit whole called a book that's a different existent entity than the atoms considered individually; 2.) the grouping together of previously unrelated elements to create a set; and 3.) even the mental construct labeled the concept of a car is a grouping together of the concepts tires, chassis, steering wheel, use for transportation, etc. Here, the grouping is better thought of as the top-level label "car" that the mind uses to group subheadings together into one.
Next, when you get rid of all matter, energy, space/volume, time, abstract concepts, laws or constructs of physics/math/logic, possible worlds/possibilities, properties, consciousness, and finally minds, including the mind of the person trying to imagine this supposed lack of all, we think that this is the lack of all existent entities, or "absolute nothing" But, once everything is gone and the mind is gone, this situation, this "absolute nothing", would, by its very nature, define the situation completely. This "nothing" would be it; it would be the all. It would be the entirety, or whole amount, of all that is present. Is there anything else besides that "absolute nothing"? No. It is "nothing", and it is the all. An entirety/defined completely/whole amount/"the all" is a grouping, which means that the situation we previously considered to be "absolute nothing" is itself an existent entity. It's only once all things, including all minds, are gone does nothing become "the all" and a new unit whole that we can then, after the fact, see from the outside as a whole unit. One might object and say that being a grouping is a property so how can it be there in "nothing"? The answer is that the property of being a grouping (e.g., the all grouping) only appears after all else, including all properties and the mind of the person trying to imagine this, is gone. In other words, the very lack of all existent entities is itself what allows this new property of being the all grouping to appear.
Some other points are:
1. It's very important to distinguish between the mind's conception of "nothing" and "nothing" itself, in which no minds would be there. These are two different things. Humans are stuck having to define "nothing" in our existent minds (i.e., "somethings"), but "nothing" itself doesn't have this constraint. Whether or not "nothing" itself exists is independent of how we define it or talk about it.
This is also why just talking about "nothing" does not reify it. Our talking about "nothing" has no impact on whether or not "nothing" itself exists.
2. The words "was" (i.e., "was nothing") and "then"/"now" (i.e., "then something") in the first paragraph imply a temporal change, but time would not exist until there was "something", so I don't use these words in a time sense. Instead, I suggest that the two different words, nothing and something, describe the same situation (e.g., "the lack of all"), and that the human mind can view the switching between the two different words, or ways of visualizing "the lack of all", as a temporal change from "was" to "now".
3. While no one can directly visualize "nothing" because the mind is not present in "nothing", what we can do is to try to visualize the entire volume of the universe/reality shrinking down to just the size of our mind's eye and then trying to extrapolate what it would be like if the mind weren't there. That's as far as we can get.
If anyone's interested, more details are at:
https://philpapers.org/rec/GRAPST-4
or
https://sites.google.com/site/ralphthewebsite/
Nothingness (Roy Sorensen; Stanford Encyclopedia of Philosophy; updated Feb 28, 2022)
Physicist musings:
The Four Different Meanings Of 'Nothing' To A Scientist (Ethan Siegel; Forbes; May 1, 2020)
From some we might expect "nothingness" to express (exhaustive) absence of everything/anything, i.e. by negation, like the missing complement to existence. Oddly enough, this also implies absence of constraints, conservation (physics), prevention, etc. Not much to speak of it seems. A referent-free word? If there was another reason for it all, for existence, then that reason wouldn't exist, since existence/all is inclusive (by definition). There's something suspect about this inquiry.
Colloquially we might say something like "there's nothing in the fridge", meaning the fridge is empty, ready to be filled (with beer). Rather different from the other uses.
But, amazingly, it's all somehow around. :)
It strikes me that the question, as stated, should never arise. Why assume that "something" requires an explanation because it exists rather than or instead of nothing?
One might reasonably inquire why X exists, i.e. seek an explanation of its existence. This is something we do all the time. We arrive at an answer, or we don't. But it seems that this question, with its assumption of an alternative to something called "nothing", doesn't really seek an explanation, but instead searches for a purpose.
Quoting Ciceronianus
:100:
But doesnt finding that things only persist rather than exist make it harder to take such an a-causal stance on the matter?
Reality seems more a process - a developing structure - than just some eternal set of material objects.
So existence might seem a brute fact, but persistence requires it contextual explanation.
Thanks. I checked over my old notes and was reminded that Fernando Zalamea did these analyses of how CT connects to Peirce (more than Hegel).
https://cesfia.org.pe/villena/zalamea_peirce_translation.pdf
https://uberty.org/wp-content/uploads/2015/07/Zalamea-Peirces-Continuum.pdf
Accepting this, I still don't understand what assuming "nothing", whatever that is meant to mean, as--seemingly--an alternative to existence or persistence, does beyond supporting a belief that something in the nature of a super-explanation, which doesn't merely explain why a phenomenon or event exists or take place, which may be resolved by scientific inquiry or even common sense, is required to account for the universe and every part of it. There must be a super-explanation, or reason or purpose, for everything, because otherwise (instead) there would be nothing.
What is wrong with a super-explanation here? The "why anything" question seems perfectly reasonable to me once you get beyond the beginner level of "something rather than nothing" as the two ontic categories you feel are being opposed.
Quoting Ciceronianus
We have two traditions of super-explanation being opposed here.
Atomism or reductionism is based on the assumption of brute material existence in eternal voids. You seem to be speaking for that. Things just are forever. There is no reason or purpose to be found. In terms of what is real, the mantra is that form and finality are categories which fail to exist in nature.
But then you have holism or the process view. Existence is evolutionary and thus form and purpose are real. Somethingness is the "reasonable" constraint on chaotic everythingness. An overarching principle organises creation - even if it is just the Darwinian imperative to persist as a structure of entropy dissipation.
Atomism requires either transcendence or mutism from its adherents. Either they must find their answer to "why anything" in a creating god, or they must stifle the "why" question itself.
Holism seeks its answer in self-organising immanence. Concrete existence arises because absolute freedom imposes its own organising constraints. Existence is thus a persistent statistical pattern. The emergent sum over all possibilities.
That is where our physical inquiry has led to. It is the metaphysics of quantum field theory. So why not just accept it?
We may be able to theorize that "existence is evolutionary"; we may be able to ascertain a tendency toward organization. I have problems thinking of that as explaining why there is something rather than nothing, however. Does the universe exist in order to evolve, or does the evolution take place because it exists? The super-explanation I was thinking of, which I think is the goal of the question necessitated by the form of the question (why something instead of nothing) would be an explanation along the lines of "there's something because the universe was created for a reason." In other words, the question presumes a transcendent cause with an end in view--not a something which always is instead of nothing.
I personally sypmpathize with the view that any deity or divinity is immanent rather than transcendent, along the lines of what the ancient Stoics thought. They thought the universe organized and guided by a Divine Reason represented by fire, itself a part of the universe. I don't know if we can determine a purpose or reason, because of which there must be something, but we may be able to determine a tendency or process, and speculate from there.
Increasing entropy, I suppose.
Why do you keep framing this as a problem of "something rather than nothing" when that has already been agreed as a self-contradicting metaphysics?
There is something. Therefore nothingness was never going to be the general case. And if it's ontic role is reduced to being some stage in a general evolutionary trajectory, everyone usually agrees nothing can come from nothing. On the other hand, it doesn't seem problematic to posit a general nothingness as the ultimate cosmic future. We already know from the Big Bang that the Cosmos certainly appears to have the creation of an eternalised Heat Death void in mind.
So drop the "something rather than nothing". It's the first thing to get chucked out here.
As the OP stated: Quoting Deus
Quoting Ciceronianus
Does matter exist without a form? Does form exist without being enmattered?
Holism is about the hylomorphic unity of substantial actuality. You are talking like a reductionist in wanting to make matter and form two different species of thingness rather than the complementary aspects of the one holistic thing.
Quoting Ciceronianus
And opposed to the transcendence of the reductionist is the immanence of the holist. The question becomes why something and not everything? Why a state of structured order and not some wild material chaos? The answer is then found within.
The universe was not created for a reason - as if there were some higher power it needed to answer to. Instead the universe emerged as a persisting stable structure because it discovered reason. It was organised by the inevitability of a rational or logical structure. The cosmos is itself the expression of evolutionary reasonableness.
Possibilities: Something/Nothing
Actuality: Something
Why (is there something rather than nothing)?
PSR (the principle sufficient reason): If x then there's got to be a reason[sup]1[/sup]/cause[sup]2[/sup]/explanation[sup]3[/sup] for x.
Why? :roll:
The question answers itself! You won't rest until I prove the PSR and that's exactly what the PSR is - there's always a reason/cause/explanation for things.
Two way to answer that question:
1. Everything we claim hasta have a reason (logic, surely you don't object to that), every event has a perfectly good explanation (science), and last but not the least, every entity that exists has a cause that brought it into existence (no data collected so far is an exception to this rule unless you believe magicians do really pull rabbits outta their hats).
2. An analogy: If someone tells me that I have a red pen in my right trouser pocket, I check my pocket to find out. What am I actually doing? Assuming there is a red pen in my pocket & testing that hypothesis.
Likewise if I ever want to prove the PSR wrong, I have to assume it is true; in other words the PSR is a supposition you'll always havta make, even if it is to disprove it.
Quoting 180 Proof
So 'the cause of causality' doesn't precipitate an infinite regress, Smith, or beg the question?
Is it your position that randomness is explained as the effect of a cause?
Or that reality is explained, even if only in principle, by some 'reason beyond reality?'
In my humble opinion, the idea of causation has evolved since Hume made his claim, that it's simlply the constant conjunction of one event and another. Nowadays there's also the mechanism of causation to consider - correlation which Hume is all about just won't cut it these days. Take for instance the correlation between alcohol, the cause, and its effects on the brain. Scientists go down to the molecular level to explain how C[sub]2[/sub]H[sub]5[/sub]OH produces its neurological effects. In short Hume's take on causation is hopelessly outdated/obsolete.
Quoting 180 Proof
Can I get back to you later. I'm in a bit off a jam right now! Cops! :rofl: Au revoir wise one!
Aye! See ya around homo viator!
Quoting apokrisis
I was under the impression from one or two posts in this thread it was a subject of discussion.
Quoting apokrisis
In what sense is the question "Why is there a state of structured order instead of some wild material chaos?" significantly less problematic than the question "Why is there something instead of nothing?"
Quoting apokrisis
I don't know why the universe emerged. I suspect that's not something we'll come to know through philosophy. Through physics or cosmology, perhaps. It makes sense to me that once it emerged, constituents of the universe interacted and certain things took place as a result of that interaction and continue to take place, and that we're able at least to some extent to determine why and how they took or take place. There is, then, a structure. We can make certain inferences from that, some philosophical. Keeping with the Stoic theme, for example, we may infer that wisdom is that we live "according to nature" (what we perceive to be the reason or intelligence suggested by the structure of the universe).
I don't think we can say that the universe came into being in order for the structure to be realized, though. You may have no issue with that; I'm not sure.
Because maths tells us that chaos must have structure as free possibility becomes its own system of constraints.
Are you a platonist?
If I have to use labels, then I am a structural realist, with dissipative structure and symmetry breaking being the mathematical meat of that position.
No it doesn't. :roll:
Okaaaaaay. Got my buttery popcorn! :yum: :party:
:gasp:
I don't see how you conclude Quoting apokrisisThe lengthy and frankly overwhelming article is about biology and probability as far as I can tell without reading it carefully - If you can find "chaos" in there please point it out. The author alludes to chaotic behavior when he speaks of sensitive dependence on initial conditions in the terminology of the science, but I don't find anywhere, glancing over the paper, a reference to mathematical chaotic behavior.
One speaks of chaos mathematically in the contexts of certain dynamical systems, those having SDIC properties. Frequently these involve the complex plane, and I am familiar with this environment.
I don't know if this is an assertion based on Peirce's views or on something else. If I recall correctly, though, he thought that chaos would result in structure through the development of what he called "habits" which it seems consist of actions or patterns which have already taken place. But I've always found his thoughts on this issue difficult to comprehend, though very interesting.
Math aside, this part looks interesting. I'd like to see it expanded upon.
I cannot see how from here you derive at the fallacy of idealism. What you argue is that the idea came on the scene, in a human mode...
If matter was all the hot stuff why do insects not consider the question? The map / territory distinction is not a fallacy, it is just that there are maps all the way down. There is no territory. Matter as the territory is just a figment of the imagination, aka, of thought. The question becomes, what is the most meaningful map? I am convinced it is love. In the craw feet, in the grey at her temples, in the curly hair and the girlish smile, there resides the ultimate question of metaphysics. That is not meaningless romantic twaddle, but it means metaphysics resides in 'you' rather than 'I' like Descartes, or even 'we' like Hegel, or 'he' like both religion and science hold.
Mathematical models then track the growth of wildness as constraints are systematically removed. Franks talks about this. A major step is from Gaussian to Powerlaw regimes. The first is merely random. It still has a variance and a mean. The second is chaotic. It now has no constraints on its variance or its mean. Or actually, it does in fact have a geometric mean to precisely define its distributiion.
So in going as far as we can go to remove constraints, we still arrive at some last constraint that can't be removed. Even the most chaotic system has this necessary residual structure.
And then remember I wrote a whole sentence and not merely half a sentence....
Quoting apokrisis
So chaos in nature - in the real world that is the subject of the OP - has this explanation. It is a general characteristic of free growth processes and dissipative structures that they attract to a powerlaw distribution. And this is because they build on themselves, preserving infomation in the way Franks describes.
Earthquakes, weather systems, turbulence and branching processes in general, are self-organising as they become the context of their own further growth. This is known as preferential attachment or the Mathew effect - the rich get richer, the poor get poorer.
So even when the rain falls in the hills and starts to carve out trickles, then channels, then rivers, in the landscape, we can predict the mathematical qualities that the drainage network will have. We have a yardstick of "pure randomness" against which to measure its scalefree-ness or fractal dimensionality. Every individual event might be an accident, and yet as accidents combine, they gather a weight. A flow. And that has its own necessary statistical order.
Thus getting back to the metaphysical argument of the thread, chaos is still a structured state. Even if the local events constituting some world are deemed "total accidents", there will be some form of coherent global structure that emerges from the fact that all these accidents are in interaction.
Everythingness gets reduced to somethingness because a weight of events builds its own global history of constraints. And Franks paper talks about the steps towards the most minimally constrained possible distributions which happen to be the powerlaw regimes that in fact best describe nature in the large. Nature as a cosmic dissipative structure, expanding and cooling - or tumbling into the very heat sink it is constructing.
Quoting Ciceronianus
Peirce did foundational work on probability theory, but in the Gaussian regime and not the Powerlaw regime as far as I know. Cauchy distributions were around in his day, of course.
But to get back to the point I am actually making, I meant to draw attention to the way "vagueness", "chaos", "everythingness", "quantum foam" are all attempts to conceive of a state of Apeiron - of unbounded or unconstrained potential.
And all these states are then being conceived in terms of locality and independence disordered fluctuation. But then dialectically, buried within that definition is the "other" which is what happens when there develops a history of interaction. The pendulum now swings towards global co-dependence. Every new event is adding to, or subtracting from, some collective weight of past action.
This is of course directly Peircean. The firstness of tychic possibility leading to the secondness of individual events and then the thirdness of synechic or continuous habit. Global order emerges out of free possibility as a collection of accidents have to arrive at some self-stable pattern that embodies its "flow".
Thus immanence can explain how somethingness arises from everythingness. And with the revolutions of "nonlinear" maths and physics of the second half of the last century, that became "a scientific fact". :grin:
True. I should have written 'the map = territory fallacy" by which I mean idealists tendency for confusing conflating epistemology (i.e. what I/we know) & ontology (i.e. what there is), that is, there is not anything more than what I/we can 'experience'.
Always the Hegelian. That's the fallacy / incoherence of idealism I mean.
Quoting apokrisis
OK. Your presentation focuses on real world chaotic behaviors that can be approached probabilistically or statistically, not with a more precise iterative tool. I am not familiar with that approach. Thanks for the link.
The theory of chaos in a purely mathematical setting is somewhat more exact:
wiki
wiki
That must be the first part that Wiki calls an interdisciplinary scientific theory then.
Quoting jgill
That must be the branch of maths that specialises in exact algorithms which also famously can't in fact be applied to the real world (without scientific heurism) due to the SDIC/ butterfly effect.
But even your chaotic maps are only interesting if they exhibit local uncertainty paired with global order. The Lorentz strange attractor caused excitement as a model for that reason. Organisation out of chaos. The trajectories or orbits were focused in ways that gave them a fractally constrained dimensionality.
However, you are not here to discuss metaphysics. Sorry to interrupt!
Net Energy of the universe = 0.
Ergo, net Mass m = [math]\frac{E}{c^2}[/math] = 0
There's no something to explain or there's nothing to explain!
I see! Much obliged.
I feel there is a kind of conundrum here. You are right, my expression leads to problems. If there are maps all the way down there is no way to tell whether one map is more accurate than another. ontology collapses into aesthetics. It is impossible to intelligibly uphold that view.
On the other hand assuming there is a territory requires a leap of faith and the assumption of an archimedic point which ultimately leads to some sort of foundationalism. Every foundation leads to problems because there is no way it reveals itself. Claims lead to counter claims. Ontology collapses into metaphysics. Maybe I should read Levinas...
Most of those systems iterate a single complex function. My approach has been infinite compositions of differing functions, producing imagery like the one I use for my icon on TPF.
It seems to me what we have discussed here regarding math and chaos is that along one line of thought math describes chaos and along another line of thought it creates chaos.
You have mentioned symmetry breaking several times in posts. I know practically nothing of it, but it seems to somewhat parallel the fundamental notion of chaos theory, sensitive dependence on initial conditions. How do you perceive it? Does it resonate in metaphysics?
Pragmatism simply says we take that leap of faith - form a hypothesis - and test it. Our opinions of what is foundational then emerge from that process of engagement.
Furthermore, we know that this process of reasoned enquiry is forming our subjective self as much as it is forming our opinion of what constitutes the outside world.
This is the feature, not the bug, of map-making. Contra idealism, we - as subjects - don't exist beyond the pragmatic modelling relation we form with the world. I am me in terms of the habitual view I come to take of the world with which I interact. My semiotic Unwelt is a running model of "me" in the "world".
So the subjective is entangled in the objective when it comes to reasoned inquiry. And that is a good thing. It is how I as an ego, with will, purpose and creativity, exist along with the worldview I am productively constructing.
Epistemology somehow got hung up on Cartesian doubt. It divided folk into naive realists and mystically-inclined idealists.
Peircean pragmatism is based on a sounder psychology. We engage with reality on the basis of revisable belief. And our own subjectivity is a product of that constructive engagement. Our choices about what are the "right" ways to frame reality emerge from a debate starting at that point.
Natural growth processes are crudely modelled by iterative functions in that the functions build on their own history of accidents. Some arbitrary set of initial values is plugged into the equation and some larger pattern may emerge. It is all completely exact and formal - apart from the fact that some human has plucked the starting conditions out of the air and then run an eye over the results and found the output "exciting" for some reason. That part is completely informal - outside it being woven into a system of scientific modelling.
As with cellular automata, the mathematician sees a pattern emerge from the algorithm and finds it striking because it is a pretty pattern. Maybe even a suggestive pattern. Possibly even what looks like a pair of butterfly wings that might seem to stand as a good model of bistability in a natural system.
It all gets very exciting - a la Wolfram - because it seems to say that (heuristically tuned by some fiddling about to find the lucky equations), maths is showing how simplicity produces "lifelike" natural complexity.
But it is then so easy to skip over the many steps needed to start using these sparkling new toys as actual scientific models. I had close experience with this when I was involved in the debates over how to apply "chaos" models to neuroscience in the 1990s. It was disappointment with the ratio of hype to insight that pushed me onwards to hierarchy theory, biosemiosis and the larger story of dissipative systems.
In short, the problem with deterministic chaos and other "exact" algorithmic approaches is that the formality gets abused by the informality of their interpretation. Pretty patterns get cherry picked. Worse still, the fact that complexity appears to emerge "magically" in supervenient fashion becomes weaponised by reductionist metaphysics. It is used to confirm old atomistic prejudices about how the world "really works".
But algorithmic complexity is merely mechanical complication, not true organic complexity. It is all bottom-up construction and lacks top-down evolving constraints. It exists in a frictionless and sterile world that has no final cause, even in the most basic form of a thermodynamic imperative.
So when I talk about chaos in the natural world sense, I am indeed not thinking it starts and stops in the reductionist trinkets generated by iterative functions. I am clear that these toy systems offer useful tools and arguments. But their shortcomings are just as visible.
Quoting jgill
Symmetry breaking is a huge subject - especially as I've spent the past year really trying to figure out my own view of how it all holds together from a systems science or holist perspective.
But a short answer on this specific question is that spontaneous symmetry breaking has sensitivity because what we are saying is that a system is so poised that absolutely any perturbation would tip its state.
Take the usual examples of a pencil balanced on its point, or Newton's dome with a ball perfectly balanced on the apex of a frictionless hemisphere. The pencil and ball are objects in a state of symmetry, being at rest with no net force acting on them, so they should never move. But then we also know that the slightest fluctuation - a waft of air, the thermal jiggle of their own vibration, even some kind of quantum tunnelling will be enough to start to tip them. The symmetry will be broken and gravity will start to accelerate them in some "randomly chosen" direction.
So metaphysically, this is quite complex. Some history of constraints has to drive the system to the point that it is in a state of poised perfection. The symmetry has to be created. And that then puts it in a position where it is vulnerable to the least push, that might come from anywhere. The sensitivity is created too. The poised system is both perfectly balanced and perfectly tippable as a result. The situation has been engineered so randomness at the smallest scale - an infinitesimal scale - is still enough to do the necessary.
All this is relevant to the OP - as the Big Bang is explained in terms of spontaneous symmetry breaking. And thus the conventional models have exactly this flaw where the existence of the "perfect balance" - a state of poised nothingness - is just conjured up in hand-waving fashion. And then a "first cause" is also conjured up in the form of "a quantum fluctuation". Some material act - an "environmental push" - tips the balance, as it inevitably must, as even the most infinitesimal and unintentional fluctuation is going to be enough to do the job of "spontaneous" symmetry breaking.
The sensitive dependence on initial conditions is unbounded - and hence becomes helpfully something we don't even need to be talking about when pondering the "cause" of the Big Bang. A fluctuation was surely there at the beginning to tip the inflaton field down its potential well, or whatever. But as an efficient cause, it becomes the most minor and random of events. Any other fluctuation would do just as well as the nudge that set things rolling.
Anyway, again we have the "exact mathematical models" that are indeed used very productively to model the creation of the Universe. One can write the various differential equations that generate some particular inflaton potential to explore. The Higgs, the dilaton, the self-interacting, the massive scalar. The pencil is poised. It must surely tip. We can generate a bunch of theoretical patterns and argue about how closely the observables match the latest CMB data.
But from a metaphysics point of view, there is so much to add about what is going on behind the models - the assumptions that have to be built in as their motivation.
Such as how does nature arrive at a generalised state of critical instability - a pencil balanced on its point? And how does that relate to the fact that nature also needs some unintentional fluctuation - even if it is infinitesimal - to start the game going at some actual point in time.
This is where I bring in the contrary view where fluctuation is unbounded and symmetry states emerge as the constraint of fluctuation to some infinitesimal (Planckian) grain. You start with the absoluteness of an everythingness - chaotic or scalefree fluctuation. And then a state of global order crystallises as a generalised constraint of fluctuation to some single universal scale (the scale scaled by the three Planck constants).
So you wind up with a quantum vacuum - a thermal equilibrium state where everything might be fluctuating, but all the fluctuation is compressed to a minimal effective scale. The vacuum as a whole is decohered to a state of simple looking classical Lorentzian symmetry.
A ground has been created. And that becomes in turn its own next level of order-production in the form of the gauge excitations the standard model particle content - that are the further "symmetry breakings" of the Cosmos as an expanding~cooling heat sink structure.
You do write the most interesting posts. This is related to catastrophe theory as well. A frightened guard dog teeters on the edge of attack or retreat, like a pencil balanced on its point, or a married couple at the edges of each other's nerves, the slightest provocation and a serious collapse of wave functions.
Quoting apokrisis
He had such high hopes with what he considered a new science. Like almost everyone who attempted to read his massive book, I gave up after a few hundred pages.
Quoting apokrisis
I have always enjoyed mathematics as a completely abstract playground, never having illusions, nor wishes, that my modest research would have applications. A method of accelerating convergence of certain function expansions as continued fractions years ago, that may have had use in computations in QM. And more recently, a surprising application of convergence of infinite compositions in a paper on decision making within groups. But all the rest unicorns in a velvet sky.
I've wondered whether fixed points (attracting, repelling, indifferent) have any metaphysical properties. Stanislaw lem's ergodic theory of history presents a counterpoint to the butterfly effect in Chaos theory: certain social movements are so strong that minor fluctuations have little to no effect on large scale outcomes.
Thanks. Catastrophe theory was both one of my earliest intellectual thrills and disappointments. It seemed to promise so much and yet deliver so little. It had little practical application and just stood as a signpost to the realisation that nonlinearity is more generic than linearity in nature.
Quoting jgill
My systems science approach is predicated on global constraints that produce local stability. So fixed points emerge due to top-down acting constraints on possibility.
The tricky bit is then that the local degrees of freedom thus created have to be of the right kind to rebuild the whole that is creating them. It is a cybernetic loop where the system maintains its structure in a positive feedback fashion.
So fixed points are important as the emergently stable invariances of a physical system. The symmetries that anchor the structure of the self-reconstituting whole.
This is the guts of physical theory. Lorentz symmetry gives you the fixed point behaviour of spacetime, and the Standard Model gauge group gives you the invariances which in turn define the inner space structure of particle interactions.
:fire: :up:
Such symmetry is pure fiction, a useful principle employed by mathematicians with no corresponding reality in the world. The type of things that you cite, which would break the symmetry, would never allow such a symmetry in the first place.
Quoting apokrisis
So this entire proposal of "spontaneous symmetry breaking" for the creation of the universe is pure "hand-waving" nonsense in the first place. The proposed "state of poised perfection" is an impossible ideal, which could have no corresponding reality, and the entire proposal is a non-starter. This is just an attempt to validate platonic realism, by placing a mathematical ideal, "symmetry", as prior to the physical universe.
In a social setting suppose a very famous and compelling person, say, "William", attracts followers. "Jack" wants to be close to William, but must push aside others surrounding his target. He finally gets very close and stays there, inching forward. William, who remains himself in all of this, is like an attractive fixed point. Now, suppose William, always comfortable with himself, begins to change, but still attracts many if they come at him from a certain direction, but if they come towards him from his bad side he repels them dramatically. Now William has become an indifferent fixed point. Finally, suppose William becomes sullen and angry to all save himself, so that his closest friends flee from him. He has become a repelling fixed point.
However, suppose William is a leader, like a Czar born into his position. He is psychotic and teeters on the edge at all times. If he is provoked in the slightest way, he will explode, taking down friends and enemies alike, his symmetry having been broken.
This is a mathematically formal approach that seeks to find data points of a model of a physical path?
Or does the model apply to a swirling (nominally static) 'hurricane' at the center of a great storm moving over the landscape as dictated by low air pressure sheared by troughs transferring heat from the tropics to moderate zones?
To me, the difference is that the first is a platonic model, the second is a Heraclitean process.
An example would help. Intriguing.
SUBTOPIC: QFT Normalization?
?? apokrisis, et al,
Hummm ... normalization in quantum field theory (QFT)?
I am not sure I understand your application of this idea of normalization relative to metaphysics. When we speak of normalization and renormalization in contemporary times (relative to QFT), it is my understanding that we are referring to Wavefunction Properties, Normalization, and Expectation Values. Vector space of potentially infinite dimensions is implied. But QFT and (say for instance) consciousness are NOT inexplicably linked. QM cannot make thoughts and dreams a reality absent other external influences. And in the simplest way of looking at Metaphysics, you are studying reality. We are looking at a Hilbert Space. But it is very difficult to apply since we do not have a system of wavefunctions that describe a Metaphysical system While QM and the basic systems of Geometries (Euclidean, hyperbolic and elliptical) can help in the detection and experimentation of questions pertaining to reality (Metaphysics), the solution to any question of reality is not ensnared by the various systems of symmetry and constraints implied by the QFT.
Most Respectfully,
R
Tuesday, July 26, 2022
Beyond my pay grade. :smile:
I also don't think there's a satisfactory answer. Assuming the brain has evolved to solve problems (or maybe just the single problem of replication), it's tempting to understand looking for causes in terms of looking for levers and buttons. I want to exploit what I perceive as causal relationships. From this POV, it's tempting to say that 'real' why questions link determinate items to determinate items, all within the causal nexus of reality understood as a web of such items. To ask why there is a causal nexus in the first place is to ask for something within that nexus to explain it, which doesn't make sense to me.
Typically [math] 0 = \{\} [/math], so the set above might not be valid. That depends on whether zero is assigned to the empty set and whether it's OK to repeat elements when specifying sets (it is essentially harmless, if confusing.)
0 = { }
True, { } is the union (additive) identity (just like 0) for sets. However,, I question the validity of the claim 0 = { }. Perhaps you could explain but do keep it simple, I no mathematician.
It's just that the two most popular constructions of the counting numbers from set theory use the empty set as zero. The best is maybe this one (Zermelo ordinals) : https://en.wikipedia.org/wiki/Set-theoretic_definition_of_natural_numbers
There's a somewhat spectacular journey from the natural numbers all the way to functions defined on the real numbers, and everything is built from/on the 'nothingness' of the empty set. There's nothing 'inside' (typical versions of) set theory at all. Real analysis (and everything else) is just ripples in the nothingness.
I recall, vaguely, that it all begins with [math]\phi[/math].
[s]Ex nihilo nihil fit[/s] Creatio ex nihilo
[quote=Greeks]How can nothing be something?![/quote]
:up:
Yes, it's all built of [math] \emptyset [/math]. I also like thinking of it as the bubbleverse. The empty set is an empty bubble. All the other bubbles are just bubbles containing bubbles. From this point of view, the bracket notation is best. I think you can get away (theoretically if not practically) with the finite alphabet of { and } and , (the brackets and a comma, but maybe just a single bracket-- not sure). So 0 = {}, and 1 = {{}} and 2 = {{},{{}}} , and so on... It's even better to draw circles containing circles, but that's not practical here.
0 = n({ })
1 = n({{ }})
.
.
.
That's how I understand it.
Too...
Barring infinity, what's the solution set to the equation x = x + 1?
Not {0} but rather { }.
What's nothing?
Is 0 = { }?
Cipher (0) isn't a set, it is a pattern in sets?
What sayest thou?
Typically, the concept of 0 is just identified with the empty set. So you don't need your "n" as a kind of function.
It should be mentioned that Benacerraf uses the variety of ways of constructing the counting numbers from sets as an argument against platonism and for structuralism.
I sympathize with the intuition that the counting numbers are the deepest and truest thing in math (maybe with Euclidean geometry also.)
You basically need to situate that equation within a number system. Consider that [math] x^2 + 1 = 0 [/math] has a solution in the complex number system but not in the real number system. There are also strange number systems like finite fields. Or "+" could represent the operation of a group. From this POV, infinity is only a solution if this infinity is carefully defined in a systemic context.
The broader point is that serious mathematics tames intuition, beats it into a kind of Chess with strict rules.
Mathematics, though proven as a tool for uncovering truths, is itself not/only partially about truths (truths to be understood in the conventional sense).
I agree with the point I think you are making. We can think of math as an excellent syntax for expressing truths about our world. One of its best features is how quickly we make inferences within this syntax. It's also lean and efficient. Take a messy scatterplot and transform it into two parameters and a measure of fit. That's some juicy, concentrated info. Like bears eating salmon brains.
Think of it as pure potential. Zero, or empty set. is nothing, but it is a type of nothing, or nothing of a specific type of thing. If we proceed to say that the specified type is every type, so that it is nothing of any type of thing, then "every type" is a type. And if types are things, (Platonism), then nothing is something.
I like to make sure statements like this are enshrined on the forum. :cool:
That's what the Quote Cabinet, in the Lounge is for.