Yes, I technically disagree, but not in a way that undermines fdrake or StreetlightX's main points. There are systems where even if you could perfectly specify the initial conditions, they still would not give the same end results. Those are truly random, non-deterministic systems. Any system where if you perfectly specified the initial conditions then you would get the exact same end results is deterministic. The impossibility of doing so doesn't actually make the system non-deterministic.

I'm not sure what your point about the Mandlebrot set is regarding chaos theory, though what you say about it sounds true as far as I know.

My point about chaotic systems is that you can have a perfectly deterministic system (where if you perfectly specified the initial conditions then you would get the exact same end results) which behaves in the way you would expect of a deterministic system, where tiny changes in the initial conditions produce only tiny changes in the output and so tiny errors in measurements of the initial conditions produce only tiny errors in the predicted output. That is a non-chaotic system. On the other hand, you could have a different, still completely deterministic system (where if you perfectly specified the initial conditions then you would get the exact same end results), which behaves in a wildly different way, where a tiny change in the initial conditions produces drastically different output, and so a tiny error in measurement of the initial conditions produces wildly incorrect predictions. That is chaos.

Determinism is about whether the output would be exactly the same given the exact same inputs. That might or might not be the case, regardless of how well you can in practice measure the exact same inputs.

Chaos is about whether or not, given a deterministic system (as above), differences in output/predictions are disproportionate to differences in input/measurement.

If we somehow knew the Galton box did behave in a perfectly deterministic manner (exact input leads to exact output; say we're dealing with a simulated Galton box) but we didn't have the exact initial state (say because we were measuring the initial condition of a real Galton box and inputting it into our virtual one), we would have great difficulty predicting even the approximate output because even the tiniest errors in the measurement of the initial state would produce huge differences in the prediction, because the system is chaotic, not because it is non-deterministic.

If the system were truly non-deterministic, then even if we rewound the virtual Galton box to the exact same initial conditions and ran it forward again, we might still get different results.

...where a tiny change in the initial conditions produces drastically different output, and so a tiny error in measurement of the initial conditions produces wildly incorrect predictions. That is chaos. — Pfhorrest

Hmm. I'm going to be pedantic and point out that chaotic systems are algorithmically calculable... so if you put in a "1" you will get the same result every time. What characterises them is that if you put in "1.0000000001" you may get back a wildly different result. But if you put "1.0000000001" in again, you will get the very same answer.

Is that not so?

That is so, yes. In being “algorithmically calculable”, chaotic systems are still deterministic.

Now instead imagine a system that is not chaotic, but is still deterministic. If you change the input by 0.00001, the output changes only by 0.0001, or something proportional to that; not in a crazy complex way.

Now take that deterministic and non-chaotic system, and put a rand() function in there somewhere. Now if you put in 1, you get, say, a number between 2 and 4. If you put in 1.00001, you get a number between 2.00002 and 4.00004. But WHICH numbers in those ranges you get will vary every time you run it. The system is non-chaotic, because changing the inputs only changes the outputs a proportional amount, but it’s truly random, because even the exact same inputs won’t always give the exact same outputs.

...a rand() function... — Pfhorrest

...but see https://mathworld.wolfram.com/RandomNumber.html

Rand() is an algorithm.

It follows that given the same initial conditions, you get the same results. — Harry Hindu

Yes, but even aside from the measurement problem if quantum events are uncaused, then tiny divergences from initial conditions will add up over time to great divergences. What evidence can you adduce that no quantum events are uncaused? The only evidence I think is available to you to call upon is expert opinion and the expert consensus is that (at least some) quantum events are uncaused.

So back to the Anscombe article, and that last bit...

Even a philosopher acute enough to be conscious of this, such as Davidson, will say, without offering any reason at all for saying it, that a singular causal statement implies that there is such a true universal proposition – though perhaps we can never have knowledge of it. Such a thesis needs some reason for believing it! ‘Regularities in nature’: that is not a reason. ...

Presumably this is a reference to Davidson's first paper, Actions, Reasons and Causes. SEP sets the issue out thus:

In that paper Davidson sets out to defend the view that the explanation of action by reference to reasons (something we do, for instance, when we refer to an agent’s intentions or motives in acting) is also a form of causal explanation. Indeed, he argues that reasons explain actions just inasmuch as they are the causes of those actions. This approach was in clear opposition to the Wittgensteinian orthodoxy of the time. On this latter account causal explanation was viewed as essentially a matter of showing the event to be explained as an instance of some law-like regularity (as we might explain the whistling of a kettle by reference to certain laws involving, among other things, the behaviour of gases under pressure). Since rational explanation was held, in general, not to involve any such reference to laws, but rather required showing how the action fitted into some larger pattern of rational behaviour, explanation by reference to reasons was held to be distinct from and independent of explanation by reference to causes.

Anscombe being Wittgenstein's proxy.

An issue for me, since I rather like both accounts. What to do?

A pseudorandom function is algorithmic. The decay of a radioactive isotope is not. @Kenosha Kid back me up here.

Yes; but then you are going back to quantum phenomena to produce randomness.

What we in the article though is indeterminism in a classical system without reliance on quantum phenomena.

The salient point is that determinism is not found in classical physics but assumed. The article goes some way to showing that the assumption might be removed without cost.

If that is the case it is a point worth making, especialy given the number of threads involving causal chains hereabouts:

• @turkeyMan's Evolution & Growing Awareness
• @substantivalism's Infinite casual chains and the beginning of time?
• @PhilosophyNewbie's Kalam cosmological argument
• @Pippen's Refutation of a creatio ex nihilo
• @Samuel Lacrampe's Simple Argument for the Soul from Free Will
• @Benj96's Why does the universe have rules?

Much hinges here. We ought be clear about it.

The salient point is that determinism is not found in classical physics but assumed. — Banno

As indicated in my first post, the conventional interpretation of Newton's first law is what produces the assumption of determinism. To get beyond this, we need an unconventional, or flat out denial of this law. The common theological/metaphysical/mystical perspective is to understand that the temporal continuity
of existence, described by this law, and expressed as inertia, (and in general, the existence of matter), requires a cause itself. So at each moment of passing time, a "cause" is required to ensure that things continue in an orderly manner, consistent with the last moment, instead of random difference at each passing moment. This "cause" is often expressed as the Will of God.

There's a simple argument to consider. The human will can create an action at a randomly determined time, therefore uncaused by any external physical force. Free will is demonstrated by the randomly determined act, and so that the causal force of the act must be the will itself. This action could change the world in a materially significant way (the POTUS could push the nuke button for example, at any random time). Therefore the continuity expressed by the law of inertia is not necessary. The human will can interfere with this continuity. So the law of inertia does not have complete, universal, and absolute application. It is not necessary. If the temporal continuity of existence expressed by the law of inertia is not necessary, it is contingent, and therefore its observed reality requires causation. Without this necessity the assumption of determinism is not supported.

There are clearly two distinct perspectives. One is that Newton's first law is true, absolute, and therefore expresses a universal necessity. This leads to the determinist assumption. The other perspective is that this law is incomplete, and the argument for this is that free will acts are outside the inertial framework. These acts are understood as constituting a force outside the concept of inertia, or perhaps a force internal to matter; as if a piece of matter can decide to start a new motion at any time. But more precisely, something outside the conceptual scheme of matter, can create matter with inertia, at a chosen time.

So the issue of determinism and free will, is how we approach and interpret Newton's first law.

I’m not arguing against any of that, merely distinguishing randomness from chaos as concepts. Determinism is the absence of randomness, not the absence of chaos. You could conceivably have a deterministic but chaotic system. Or a non-chaotic but indeterministic system. Or chaotic randomness, or non-chaotic determinism. They’re two separable things.

And yes, quantum phenomena are random, at least from any particular entangled observer’s point of view. (The math describing the evolution of the wavefunction itself is deterministic, it’s only at the supposed “collapse” of the wavefunction that anything random happens, and there’s disagreement about whether that collapse is a real thing that actually happens or only a shift in an observer’s perspective as they become entangled with the observed system.)

OK.

The salient point is that determinism is not found in classical physics but assumed — Banno

I think it's true that the hypothetical "if initial state is completely specified, then trajectory is completely specified" is true of the systems like the Galton's box I linked; if that's all someone means by determinism, I think it holds of the box. If they additionally assert "the initial state is completely specified in this Galton box", I don't think it holds of the box. At least, there's room for doubt.

Only partially a response to your last post in particular, but I am interested in this conversation (read & enjoyed the OP paper) and have some thoughts, but I want to make sure I'm following before bringing them in.

What you & @StreetlightX have been talking about, is it something like this?

-Within some local systems, the state of things at t=0 does determine a unique state at t=x. (i.e. there is only one possible state at tx, given t0)
-But the universe (or 'everything' or 'the one' or ' the total totality' etc )cannot be treated as a closed system where 'everything' is such and such at state 0, determining unique states at t=x
-What counts as a closed system always requires some sort of constituting 'carving' in order to foreground certain aspects, while ignoring others.
-That doesn't mean that the 'subject' or 'mind' or 'knowledge' is the ultimate ground for what happens in that system -things still happen as they do - but how you're tracking what's happening is based on how you've carved

-[less sure of this] if you're focused on deterministic systems, you're going to keep finding them, because that's where you're directing your attention.

Is that roughly right?

Looks right to me.

So, building on that, the part of the essay that most jumped out at me was this:

There is something to observe here, that lies under our noses. It is little attended to, and yet still so obvious as to seem trite. It is this: causality consists in the derivativeness of an effect from its causes. This is the core, the common feature, of causality in its various kinds. Effects derive from, arise out of, come of, their causes. For example, everyone will grant that physical parenthood is a causal relation. Here the derivation is material, by fission. Now analysis in terms of necessity or universality does not tell us of this derivedness of the effect; rather it forgets about that. For the necessity will be that of laws of nature; through it we shall be able to derive knowledge of the effect from knowledge of the cause, or vice versa, but that does not show us the cause as source of the effect. Causation, then, is not to be identified with necessitation. — Anscombe

I like this. I think it directs us back to how we first think of causes: something happens and we know it happened due to this other thing. It doesn't mean forensically establishing a necessary frame-by-frame progression, but simply recognizing that the presence of this led to that. That's it. How the one lead to the other depends on the case. Whether the one had to lead to the other also depends on the case.

I think learning to be attentive to how we actually encounter causality, leads to an epistemic humility that counteracts a prideful awareness of an epistemic ideal, never actually attainable. (The 'pride' is in offloading precision to a dream of total comprehension (absolute accounting) that you are at least aware of, while others operate blindly, not even aware of the dream) Like most things born out of pride, the awareness of an ideal lets us undercut others, while simultaneously undercutting ourselves (we are aware there is a 'deterministic order' and can rest on the laurels of having apprehended that). And I think that that kind of epistemic humility (there is no way to shatter the universe into a series of precise distributions of matter along a time axis) ultimately lets us track causes in a more effective way: If you drop the idea of a demon who could do it at a subatomic level, you have to simply look at how you see causes being responsible for certain effects. There is an art (and pragmatism) of understanding causality and there is no metaphysical reason to see that as mere 'folk' understanding of causation.

(Now obviously this can cut both ways (one can 'see' false causation, and that has historically happened a lot, and caused horrible things) so a methodology and an ethics of how ones casts causal relationships is still necessary, but dropping the metaphysical pretense at least clears the ground for going to work on that.)

You have to simply look at how you see causes being responsible for certain effects. There is an art (and pragmatism) of understanding causality and there is no metaphysical reason to see that as mere 'folk' understanding of causation. — csalisbury

Yeah exactly - 'look and see' being the empirical principle par excellence. I think it also makes more sense when it comes to the phenomenology of scientific - or other - investigation: we pay attention to what the system under investigation 'pays attention' to, where, even if we delineate what constitutes a 'system', we still need to follow it's lead. I'm very fond on these lines from Susan Oyama, whom always comes to mind when I deal with this stuff:

"For coherent integration to be accomplished, an investigator must do by will and wit what the [system] does by emerging nature: sort out levels and functions and keep sources, interactive effects, and processes straight. ... This is not to say that selection of variables must be random or that analysis is impossible. It is to suggest that guidance is more likely to come from the system under investigation than from some more abstract assumption ... Fine investigators have always been guided by good intuitions about what their phenomenon is "paying attention" to ... Scientific talent is partially a knack for reading one's particular system productively."

[And because it's on my mind - the kind of thing accords to what D&G call 'minor science', which is always a matter of "following the singularities of a matter", which they distinguish from "reproducing", which "implies the permanence of a fixed point of view that is external to what is reproduced: watching the flow from the bank".]

-But the universe (or 'everything' or 'the one' or ' the total totality' etc )cannot be treated as a closed system where 'everything' is such and such at state 0, determining unique states at t=x — csalisbury

Think you're mostly right. "Open" and "closed" don't mean quite that though. A closed system is one that isn't subject to any external net force or matter/energy transfer. Once the balls in the box are set in motion, it's a closed system (to a good approximation).

I like this. I think it directs us back to how we first think of causes: something happens and we know it happened due to this other thing. It doesn't mean forensically establishing a necessary frame-by-frame progression, but simply recognizing that the presence of this led to that. That's it. How the one lead to the other depends on the case. Whether the one had to lead to the other also depends on the case. — csalisbury

"Necessitation" is a tricky word, because "necessary" and its derivatives have very many different uses. An effect, by that name is a contingent event, so if it occurs it has been necessitated by its causes. But I think what misleads people is the idea that an event, as an effect, has one cause. Contingent events generally require the fulfillment of numerous conditions, all of which can be called causes of the event. So the idea of a one to one cause/effect relation is what ought to be scrutinized.

What we commonly call "the cause" of an event is one of many contributing factors, and it is only within a very specific (subjective) perspective, that it is designated as "the cause". The experimental process which attempts to fix initial conditions for repetition, and note consistency and inconsistency in the results, is not actually looking for the cause of the results per se. The cause of the results is more properly attributed to the fixing of the initial conditions. What the experimentation is looking for is the cause of differences, the degree of consistency in the results. If there is inconsistency in the results, we want to know "the cause" of the inconsistency. If the single variant factor, which leads to an inconsistent event can be identified, it becomes known as the cause of that event, the inconsistent event. But to designate this as "the cause" is to neglect the fact that the more substantive "cause" is the prerequisite fixing of the initial conditions in such a way so as to allow "the cause" to produce its effect.

Worth reading for context. A deterministic model of the Galton box; no randomness involved. Against Galton's idea that the collisions of balls with pins were "independent accidents" summing together (hence normal distribution). Against independence, because it seems that how a ball bounced last pin and the pins before it influences how it bounces next pin.

On reflection, I think that on topic arguments shouldn't really be concerning themselves with randomness vs determinism here; it's more regarding whether it's appropriate to consider the Galton box as an example of bounces following bounces as a matter of logical necessity in the wild. The central question for whether it's determined in that logical sense is whether a real Galton box can sensibly be modelled with infinite precision inputs. I don't think it's fundamentally about whether deterministic mathematical models are successful in providing insights about 'em (they are), it's regarding the relationship of a real Galton box to the "input completely specified => unique trajectory" implication.

I wanna have my cake and eat it to, really. I'd like to insist that "input completely specified => unique trajectory" applies to real Galton boxes since deterministic models of them work, but that nevertheless real Galton boxes do not have a specifying mechanism that enables anyone to do anything to them that pre-specifies any ball's initial conditions to sufficient precision for that mechanism's actions to collapse the outcome set to a unique hole for any given ball.

I also wanna insist that that isn't "just an epistemic limitation", it's built into the box that it cannot be manipulated in that way. Maybe for other boxes you can.

↪Banno A pseudorandom function is algorithmic. The decay of a radioactive isotope is not. Kenosha Kid back me up here. — Pfhorrest

Yes; but then you are going back to quantum phenomena to produce randomness.

What we in the article though is indeterminism in a classical system without reliance on quantum phenomena.

The salient point is that determinism is not found in classical physics but assumed. The article goes some way to showing that the assumption might be removed without cost. — Banno

I’m not arguing against any of that, merely distinguishing randomness from chaos as concepts. Determinism is the absence of randomness, not the absence of chaos. You could conceivably have a deterministic but chaotic system. Or a non-chaotic but indeterministic system. Or chaotic randomness, or non-chaotic determinism. They’re two separable things. — Pfhorrest

Typically chaotic systems are defined to be deterministic but nonlinear, nonlinear meaning that a small change in the input can yield a huge change in the output. The system described in the article is I think normally known as a chaos machine, because small changes in the initial conditions of the ball give rise to large changes in its final position. The article is also putting forward a epistemological means of accounting for those practical differences, so while the system is chaotic, the ball is epistemologically indeterministic as well, and using this to propose what I think is an ontological agnosticism about determinism.

That indeterminism does not depend on the chaotic nature of the system that exemplifies it, but obviously since linear systems would not be demonstrably different from Laplace's demon (i.e. differences in output would be as immeasurably small as the immeasurably small differences in input), it's apt to use a chaotic system to illustrate the point. Quantum mechanics is deemed ontologically indeterministic, although there are deterministic interpretations (Bohm theory) which are chaotic.

I see no reason not to consider chaotic, indeterministic systems as well as chaotic deterministic ones. In that case, you would have to account for errors in the positions of each of the pegs too. I imagine the reason why chaotic systems are deemed to be deterministic is that no one has had cause to explore chaotic indeterminism; it's typically been one or the other.

Yes, but even aside from the measurement problem if quantum events are uncaused, then tiny divergences from initial conditions will add up over time to great divergences. What evidence can you adduce that no quantum events are uncaused? The only evidence I think is available to you to call upon is expert opinion and the expert consensus is that (at least some) quantum events are uncaused. — Janus

The expert consensus is also that QM and classical mechanics appear to contradict each other but they both work. The consensus also includes a need to unify both theories, or at least explain why one is so useful and incorrect, while the other is correct. I think that the unifying theory lies in explaining consciousness, as consciousness is a kind of measurement.

What effects do uncaused quantum events have on the macro-scale world? You'd think that all those "tiny divergences from initial conditions will add up over time to great divergences" would be observable at the macro scale, but what we observe is consistent - similar causes lead to similar events.

And we have experiences where we are ignorant of the causes - where it appears that there isn't a cause, but there is. You need to account for those kinds of experiences and the fact that it shows that uncaused appearances can be deceiving.

The salient point is that determinism is not found in classical physics but assumed — Banno

Them indeterminism is not found in QM, but assumed. And you seem to be agreeing that certain observations cause you to assume certain ideas.

The probability of one ball falling in any particular bin is given by the normal curve. — Banno

To your knowledge, Banno, has that ever been tested.

Lots of balls falling strike against each other and have different mass distributions to influence the fall...so the bell curve distribution is understandable.

But if one single ball...always the same ball...were carefully and systematically dropped, would it randomly create a bell curve...or will it favor one or two slots?

Just wondering.

Actually, I've done this myself - dropping balls one at a time, slowly, so that my students could see the curve build.

ever had an experience of any of the balls falling up, or out through the glass? Why do the balls fall only down?

You'd think that, all those

tiny divergences from initial conditions will add up over time to great divergences. — Janus

And you'd observe the behavior of the balls greatly diverging.

Banno
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↪Frank Apisa Actually, I've done this myself - dropping balls one at a time, slowly, so that my students could see the curve build. — Banno

Suggestion for what might be a doctoral level experiment, B.

Mark a ball with a red dot...and drop THAT INDIVIDUAL ball each time with the red dot in the same position at release...keeping the drop effort as similar as possible...

...and see if the randomness occurs.

That one ball...skewed slightly as every ball must be...might favor one or two adjacent slots.

Just an idea. Or maybe one you could pawn off to a serious student to attempt and report.

A simpler version of the same experiment:

Imagine a steel wedge on a table or floor, with a sharp hedge pointing upward ( like ^ ).

Drop vertically a light steel ball on the wedge edge. Sometimes the ball will end up falling right of the edge, sometimes left. If you drop the ball right on the edge each time, and long enough, logic dictates that it will fall on both sides a near equal number of times, 50-50.

Can anyone predict where the ball will fall next?

Does anyone suppose the ball could EVER bounce on top of the edge several times before settling there, in equilibrium exactly on top of the edge? Intuitively this seems impossible, and yet... if it were a perfectly round and homogenous ball falling exactly on a perfect wedge, that's exactly what the math says the ball will do...

So QM determines that determinism is impossible? — Harry Hindu

Might be more accurate to say that evidence suggests nondeterminism?

nonlinear meaning that a small change in the input can yield a huge change in the output. — Kenosha Kid

Roughly speaking, but needs elaboration. Not a definition of nonlinear in the strictly mathematical sense. And what is "small"?. For example:

Linear:
$f({{z}_{1}}+{{z}_{2}})=f({{z}_{1}})+f({{z}_{2}}),\text{ }f(\alpha z)=\alpha f(z)$
$f(z)=Mz,\text{ }M={{10}^{10}},\text{ }\varepsilon ={{10}^{-3}}\Rightarrow f(z+\varepsilon )-f(z)=M\varepsilon ={{10}^{7}}$

Nonlinear:
$f(z)=\frac{1}{z},\text{ }z=10,\text{ }\varepsilon =\frac{1}{10}\text{ }\Rightarrow \text{ }f(z+\varepsilon )-f(z)=.01$

What effects do uncaused quantum events have on the macro-scale world? — Harry Hindu

The world is one; it's not neatly divided into micro and macro scales. E.g. radioactivity, a quantic phenomenon, is an important cause of genetic mutations, which are an important driver of evolution.

n. Not a definition of nonlinear in the strictly mathematical sense. And what is "small"?. For example: — jgill

Wrote a post trying to explain some chaos concepts a while ago. Since you're a meteorologist I'd guess you probably already know it and are making a point regarding chaos being a buzzword most of the time, but just in case.