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Free will?
- Thread starter Skeptisch
- Start date
Ownership is only as credible as the usage of it implies within a given system. Maybe a martial claimed the moon a million years ago. I is just for reference.
PolyHedral
Superabacus Mystic
You assume, without proving so, that there is a single instant in which you make the choice.
Also, if you causality doesn't work, so why this is so in the context of light-cones. All other ideas of causality are approximations, estimates and wild guesses by comparison.
That was the point of the reference to classical and to quantum information theory. Both use randomness in order to make possible information processing, one through algorithms and the other through states. However, in each case randomness is used in order to give non-random "answers". If we equate the brain to a computer running algorithms (which we shouldn't), then random processes can (theoretically) be implemented during conceptualization in order for it to exist at all. Simplistically, we run "randomized" algorithms in order to construct "concepts" which are the foundations for (or even the entirety of) conscious action.
If there are quantum processes at play, then the states of neurons can (again, simplifying) use the inherent indeterminancy of quantum processes in order to again construct concepts. Either way, randomness is "used" to create nonrandom, deliberate states.
Self-governing, self-fabrication, and nonlinear (cyclical) causality are part of cellular behavior. Essentially, whether we are talking about a cell or an organism, functional components contribute to the state of the system, but cannot be abstracted from the activity of the system without significantly decreasing any ability to understand the state of the system. So, for example, cellular metabolism and repair are functional processes governed by components of the system (the cell), yet the states of the components responsible for these functional processes also (and at the same time) result from them. Metabolites are the "cause" of the function metabolism (i.e., the metabolic process as conceptual abstraction or model of a number of processes which form a functional whole), but this same function, which is the result of basically the entire cell, also affects the entire cell. The function is a product of coordinated cellular activity which is also a result of that function.
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You assume, without proving so, that there is a single instant in which you make the choice.
I was using another's terminology and method of description, not because I believe it is very accurate but because the last discussion involved addressing the "instant" some event like choice happened.
How is it so? From Rohrlich's contribution to the edited volume Probability in Physics (from Springer's edited series The Frontiers Collection, 2012): "Having redefined the axiom of nonlocality, we must now redefine also the axiom of causality. We cannot say, No action at a distance can be used to send signals, when action at distance is itself a signal. We can only say that the signal cannot be outside the forward light cone of the act of sending it. So we are back to relativistic causality" (p. 194). Rohrlich continues on a back-and-forth discussion about nonlocality, light cones, and causality, and concludes "This is jamming, within quantum mechanics! Hence the question of whether quantum mechanics is the unique theory reconciling causality and action at a distance remains open after all." (p. 199). Now, one can certainly disagree with Rohrlich on this and other points, but the idea that light cones somehow create an absolute basis for causility is simply not a generally accepted interpretation.
Skwim
Veteran Member
I agree, it's simply the reason some people accept it as true. Nothing more. Nothing less.
Glad to see you agreeing that your "choice" was caused, i.e. your "choice" was an effect of its cause.
And as we both know, it couldn't be other than what it was at that moment. If it could, then it would be an utterly random event: it had an equal possibility of not occurring as occurring.
So what is it that made you finally "choose" the food you did? I assume it wasn't a random event.
Sorry to disappoint, but apparently you missed the qualifiers. Even working within a reductionist, linear causal model (which neither reflects my view or the state of research in relevant fields), there are still many, many times when the only way you can reduce some phenomena to a series of causes or effects is completely abritrary and renders the whole exercise meaningless.
No, we both know that this is your view, and that it is your view despite the fact that you have stated:
When you believe something about the nature of reality, and your belief runs counter the state of research in fields relevant to that belief (and you aren't familiar with these fields to know what the state of research is or why), then that seems no different to me than any religious approach to the nature of reality: You may have some intuitive feel that you are right, and some intuitive feel that anything else is wrong, but your faith in your belief is enough to stick to it regardless of whatever research might say.
Or not:
Yes, I've been down this road before. When I explain it to you, you simply call it inaccurate and insist that "logic" makes your view necessarily true, when I quote and offer to give you references you say you won't (or can't) read them (even if I can get them to you for free), and when I demonstrate from technical literature (regardless of the field) that what you say is inconsistent with the relevant studies by specialists, I get:
There are a lot of words in what you say, and if I thought you were serious and believed everything you've written I might continue, but I don't, so
And frankly, having just spent enough time on another thread dealing with a dogmatic insistence that the theory of evolution disproves itself and a refusal to actually attempt to understand either errors concerning what the ToE actually is (compared to how the critic was portraying it) or the argument used, I'm not about to try to lead another horse to water (so to speak).
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Skwim
Veteran Member
Well, let's see. You said, "At the instant my choice is made, what caused it?" So here we have an event, your "choice," and this unknown cause you're concerned with; all of which denotes a cause:effect relationship. But now you seem to want to retract this admission, "Sorry to disappoint, but. . . ."
What's a person to think, LOM?What I think you're missing here is that no matter how an event arises, it doesn't do so out of thin air. And if it wasn't an absolutely random event then there had to be some other reason, and from where I sit causation is it. Now you may not be able to determine whether the horse came before the cart or not, or that they came at the same time, but they did come. And this coming had to be driven by something (the thin air proposition doesn't convince). Personally, I'm content with acknowledging either absolute randomness or cause as this something, or even a combination of the two, but if you have a fourth possibility I'm ready to listen. Just name and explain this other mechanism.
Good thing you said "so to speak" because I was about to take you literally.
But just to be clear here, you addressed me first, even trying to provoke me into replying to you. But feel free to skip out, I won't try to follow. And of course, as it still stands, freewill remains dead in the water. :dan:
methylatedghosts
Can't brain. Has dumb.
I feel like you have raised some very good points here, and I don't disagree. My simply-worded post was just to give some examples of what ideas might have been part of giving rise to the concept of democracy. You include here some examples of other concepts that could have been included. What I'm getting at, is that from a more deterministic point of view, there are concepts and ideas that can be added together to form entirely new ones. Kind of like in the way that flour, eggs and milk can be combined to make pancakes.
Now this is an entirely different thread, but I have written something vaguely related here: http://www.religiousforums.com/forum/3102702-post7.html
from http://www.religiousforums.com/forum/mysticism-dir/139557-what-if-god-like-color.html
I would argue that there is no objective observation, that there is no objective reality, that all information that is assimilated is necessarily subjective.
It was a rhetorical question.
An "event" is nothing more than our conceptualization of "process". You haven't any idea whether or not something can "rise" out of thin air (there are actually models in physics in which this happens), and the two frameworks which make up the sum total of human knowledge of "the laws of nature" are both counter-intuitive and do not seem to abide by what our experience tells us they should.
Your "logic" which by virtue of its almost unbelievably simplistic approach to reality, ignores both relativity and quantum mechanics. You state that "time is linear' only relativity says "time doesn't exist, but spacetime does and it is curved." You posit that all is effects and causes, but QM allows for effects without anything typically conceived of as a cause (because causation is local).
So, armed with your linear view of time which is inconsistent with "the laws of nature", and a linguistic reduction of everything into "cause and effect" based on the assertion that, well, you can't see how things could be different, you dogmatically insist that your conception of "event" and "cause" is somehow meaningfully descriptive of reality, despite admitting your lack of familiarity with physics and with philosophy.
The problem is that neither the "laws of nature" nor biological systems fit into your model in any meaningful way. Luckily, because your faith in your description is simply that, you don't have to deal with pesky things life falsification or evidence or (apparently) research.
I have pointed out again and again how your model fails, but as you don't need to (and can't) demonstrate how (for example) cellular processes can be reduced and all those silly biologists who adopted an entirely new framework (a systems approach) to deal with complexity that arises far more than could have been anticipated even a few decades ago are all wasting their time because, having failed to model even basic systems without loosing most of what makes models useful, they realized that complex systems do not conform to linear causation or reduction.
But that doesn't make it any harder to describe anything and everything as either random, cause, or event. Someone actually turns water into wine, or raises the dead, or shoots lasers out of their eyes? Easy. Magic turns water to wine, so cause and effect. Reanimation is the cause behind those pesky zombies, so we're good there too. And as for lasers shooting out of one's eyes, well that's a mutation in the genes.
When you don't actually have any idea what kind of processes are involved in something like "choice", because you haven't studied the brain, complexity, neurobiology, etc., then it's easy to reduce everything to cause and effect because all you have to do is describe it that way. Meanwhile, those who want to understand how something like "choice" or "the laws of nature" actually work have to deal with how this reductionist and linear account just doesn't work when they use it to describe all the technical stuff you get to ignore my simply describing "cause" or "effect" and applying it when you don't know what's actually going on at all.
1) Your definition of "randomness" isn't consistent with the term as it is used formally. Informally, it's as useless as claiming everything results from a cause, or from magic, or from god. It's easy to describe when you don't have to show how it works.
2) Cause isn't a "mechanism". It's your vague description used to reduce actual mechanisms to fit your conception.
3) In reality, causality (to the extent it is meaningful) is often nonlinear. The "other mechanism" is the capacity for complex system to work as a whole:
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Follow up: Does recursive conditioning reinforce the belief in linear causality, and how can this conditioning (recursive causality?
) be broken?
PolyHedral
Superabacus Mystic
That should have been "show that it is so." Also, we can make spooky action at a distance disappear simply by reinterpreting QM to get rid of Copenhagen collapse. Everything else is transmitted by bosons, which travel at/slower than c.
Absolute Zero
fon memories
[youtube]pCofmZlC72g[/youtube]
Sam Harris on "Free Will" - YouTube
Sam Harris on "Free Will" - YouTube
Skwim
Veteran Member
Now I take conceptualization to be the exclusive property of sentient beings, be it a human or a giraffe. So assuming your claim is correct, then no event can take place if there is no being to conceptualize it. "No, there was no tree that fell in the woods, much less one that made a sound."LegionOnomaMoi said:
Please recall that I said, " Personally, I'm content with acknowledging either absolute randomness or cause as this something [the means by which an event occurs] , or even a combination of the two, but if you have a fourth possibility I'm ready to listen. Just name and explain this other mechanism."
Perhaps; but like almost everyone else on Earth I'm not schooled in the complexities of relativity and quantum mechanics, yet, I do know that neither are without controversy and criticism, so I am unwilling to accept any of your (you, having no verifiable credentials) claims for it ---being unable to judge their veracity. If they cannot be convincingly expressed or explained in layman's language then they'll have to remain a bust. Sorry if this disappoints, but that's the lay of the land.
So, I assume, you do have an "idea what kind of processes are involved in something like "choice," and can enunciate that mechanism in layman's terms. Or is this an impossibility?
By "your definition" I assume you mean "absolutely random." And, I have to ask which fields of science or philosophy are you referring to in which my definition of "randomness" isn't consistent with the term as it is used formally, because I know that in quantum mechanics its been asserted that true random events do occur. In any case, true or not, if an event isn't random it must have a reason (cause) for its existence. But if you know of something other than causation then please enlighten me. What is this other possible non-random, non-causal mechanism?
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I'm still not quite certain what you mean (my apologies), and part of this is that I'm not quite sure what "that" refers to when you say it should've been "show that it is so". I frequently get's caught up thinking about my responses or answers in posts, and thus frequently forget to insert a word or upon some editing don't finish the job or use wording that made sense to me at the time but not looking back. Having seen how easily this can derail a discussion (at least temporarily), I want to make sure I get this right. Here is what you said:
It seems to me that there are two places into which (with some alternate phrasing) you wished to put "show that it is so". The first might result in something like "if you show that causality is what you say it is", and the second might result in something like "show why this is so in the context of..."
With that in mind, there are somethings which I think need to be addressed for the sake of clarity, because either I wasn't clear at some point, or I misunderstood you, or whatever.
1) What do you mean by "causality doesn't work?" In other words, it seems you are saying that I am denying causation exists at all, or at least that it fails in such a way that it is a meaningless concept.I don't believe either of these. However, I also don't believe (and here I think most cosmologists, philosophers, etc., would agree with me) that "causation" exists in the way even something like velocity does, but it does exist in the way that things like "future" or "past" or "event" do. And while I am uncertain whether or not causality is a meaningful term applied to any and all processes or "events", even if it is not so universal, it remains a meaingful term and useful model for just about everything. What I would absolutely disagree with is the idea that we can always reduce causation to a linear, discrete set of causes behind some effect.
I have used cellular processes (in particular metabolism) to illustrate the problem such reduction, because one finds this example quite often in computational and/or systems biology. The reason for this is the enormous influence of Rosen's work (whence comes the example) on current approaches to biology. As It may be useful here for me to borrow another's simplified version, I'll use Mikulecky's contribution to a recent volume in the edited series Mathematical and Computational Chemistry. His paper ("The circle that never ends: Can complexity be made simple?" in Complexity in Chemistry, Biology, and Ecology; Springer, 2005) is, I think, perhaps the simplest and clearest.
First, most of mathematics, we have a function/mapping from one set to another:
f: A -> B
"where f is the process that takes input A and output B...The system Rosen uses for an example is the Metabolism-Repair or [M,R] system. The process, f, in this case stands for the entire metabolism goin on in an organism...The transition, f, which is being called metabolism, is a mapping taking some set of metabolites, A, into some set of products, B. What are the members of A? Really everything in the organism has to be included in A, and there has to be an implicit agreement that at least some of the members of A can enter the organism from its environment. What are the members of B? Many, if not all, of the memebers of A since the transitions in the reduced system are all strung together in the many intricate patterns or networks that make up the organism's metabolism. It also must be true that some members of B leave the organism as products of metabolism...In the context developed so far, the mapping, f, has a very special nature. It is a functional component of the system we are developing. A functional component has many interesting attributes. First of all, it exists independent of the material parts that make it possible. Reductionism has taught us that every thing in a real system can be expressed as a collection of material parts. This is not so in the case of functional components...Fragmentability is the aspect of systems that can be reduced to their material parts leaving recognizable material entities as the result. A system is not fragmentable is reducing it to its parts destroys something essential about that system. Since the crux of understanding a complex system had to do with identifying the context dependent functional components, they are by definition, not fragmentable". (pp.103-108; emphasis added; italics in original)
Mikulecky continues (and, for the sake of simplicity, I actually took a lot out, concentrating on his conclusions) on a topic of interest to you: organisms are non-computable. However, unfortunately I think that would be a bit to far off topic.
More importantly, all of consciousness and cognition are (to use Mikulecky's words) "functional components". In other words, they cannot be reduced to the various cellular activities within and between neurons.
2) I'm still not sure what you intend by reference to light cones. Do they (or at least could they) relate to causality? Of course. But only in a rather specific way. For the sake of simplicity, I'll use a non-technical explanation (i.e., no math or formalism):
"Correspondingly, the light-cone, as ordinarily understood, constrains relations of cause and effect. According to the conventional wisdom, what happens at a given event can only be affected by what happens within, or on the surface of, the past light-cone of that event, and can only affect what happens within, or on the surface of, the corresponding future light-cone." (from p. 45 of Lockwood's The Labyrinth of Time; Oxford University Press, 2005).
This is basically just "classical" causation with relativity thrown in. It provides no basis for grounding causality (taking it from metaphysics and philosophy into "regular physics"), any more than locality does. Any definition of causality entails particular consequences concerning the way objects and processes can interact or have an affect upon one another. Light-cones aren't "ideas" or definitions or models of causality, but instead follow necessarily from an already constructed model. That is, having defined causality as X (therefore framing the ways in which interactions can occur), relativity tells us that X can be involved in some activity happing in B, but that it cannot in C.
Also, I quoted that paper from Probability in Physics not because I intended to show that there are those who disagree that light cones in some sense "define" causation (because, as I said above, one cannot derive causality using light cones; rather, a model of causality must already exist which can then at best be altered). It was because even granting that light cones are often considered as redefining, altering, and/or constraining causality (and not as defining casuality nor as providing some firm foundation), we don't find a general agreement in the literature how (if it all) this "constraining" relates to causality.
Not so simply as that, I'd say. There are certainly no shortages of explanations for nonlocal correlations, but as these are not only theoretically grounded but experimentally produced, any interpretation necessarily changes the restriction in "classical" causation of spatio-temporal proximity. Simply put, however one wishes to interpret the formalism and explain empirical observations, things are going on in some space-like region which are related to other actities in some other, disconnected place in this space-like region, and there is no way to explain this by using "classical" causation.
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PolyHedral
Superabacus Mystic
AFAIK, closed time-like curves don't exist. Therefore, causation should be a one-directional chain of cause-and-effect over the time-scales we care about. I'm asking you to phrase any objection to this in terms of light-cones, because at the moment, you (and the people you are citing) seem to be using the complexity of biological systems to hand-wave what precisely leads to what, and I don't see your logic as valid.
So far so good.
Oh no, you can't do that! A is an immutable set, and an inherent part of f! (Because everything is immutable in math, and a function with a domain other than A is not, and cannot be, f.) In order for A to vary, then you must define an entire series of sets and functions - a single one doesn't suffice, because mutating objects do not exist in mathematics.
We run into the same issue here. Also, it is the implication above, "everything in the organism has to be included in A", that A is a set of molecules. (Those being things "in the organism") However, the reasoning doesn't appear to be coherent under that interpretation - certainly, it is not at all clear what f is actually describing.
Since we've derived the function entirely from the properties of parts that are material, (...I think. It's not clear :sarcastic) this is not true.
Causality can be coherently defined mathematically as a function mapping universe-configurations to other universe-configurations, which may be what the author was going for. However, it is not what he said.
Since Mikulecky just apparently reduced conciousness and cognition to maths, you've actually shot yourself in the foot - computers should be better at this than neurons are.
I do not know what you are asking. Every region contains a configuration of energy, and each configuration's "future(s)" - including how that configuration expands into space - are defined by the laws of physics, so by induction, we have defined the "future(s)" for the entire universe.
Importantly, the laws of physics posits a number of interactions but all of them are limited to propagating at c or less. This means we can use lightcones which expand/contract at precisely c as a short-cut for what region affects a given point in spacetime, and what region that event can then go on to influence.
(I say futures, because quantum produces something we do not normally think of as a single future, but is nonetheless consistent.)
Sure there is - multiple-universe QM does it perfectly fine, for instance. (Because the quantum particles must move at less than c, and there is no propagation faster than light, because there is no wavefunction collapse.)
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Orias
Left Hand Path
We have will, but its not free. There is a cost for every exchange, for every transmutation.
During certain moments of transition, and perhaps negotiation, there is an action that we do "freely" (opening a door, building a house, etc etc.). In between is the action, which is reinforced with the energy (the will, thought, desire, etc etc.) that is necessary in all exchanges, and even the non-physical invocations.
That's because you are confusing sets with their elements. To illustrate:
Within a given forest, we might have a number of different kinds of trees, some which look quite different than others. We may also have other plants, including bushes. Some bushes may look more like what most people imagine when they think of a tree, while on the other hand some trees may seem more like bushes.
So you walk into a forest with a good diversity of trees, bushes, and other plants. You happen to be one of the foremost botanists in the world, and can recognize everything in this forest. No matter how much a tree may look like it might be something else, or something else might look like a tree, every time you see a tree you know that it is a tree.
Nothing you see, however, is "tree". They belong to the category "tree" (or, alternatively, are elements of the set "tree"). That category or set is an abstraction. Every one of its elements are a part of physical reality. The category itself, however, is merely conceptual.
In a real sense, the foundation of conscious thought is the ability to construct abstract, "fuzzy" categories into which elements (even novel ones) can considered members of.
Conceptualization involves both the construction of categories and the classification of elements into these.'
An "event" is a particular conceptual entity, and humans classify a particular set of elements (things we call events) as belonging to this category. However, while we do the same with trees, although the classification schema (or set, or category) is an abstraction, the elements or instances are not: whether I look out my window and call this things growing in my yard a "tree" or call it a "fwap", it's still there. Events, however, have no such instantiations. The category "event" consists of fuzzy, nebulous classifications of specific "events", each of which is mostly an arbitrarily derived conceptualization of material reality in some space through or in some time.
For example, I can the conquest of England in 1066 an important "event" in history as easily as I can call the instant of some orbital change in an atoms electrons an "event". The same is true of the big bang, the beginning of life, the invention of the telephone, etc.
Asserting that events are conceptualizations doesn't entail any ontological claims. However, the nature of this conceptual category and the incredible variety of the things which are classified as members make any cavalier use of it a serious problem for any model of reality. It has a great deal of use in communication (saying, for example, that the growth of a merchant class caused a monumental shift in the organization of societies is unproblematic as far as its use of the word "cause" because it need only have descriptive, explanatory power for a singular "event", and need not be a generalization applied to reality). But the ability for words like "cause" or "event" convey information about pretty much any situation (or any activity over an arbitrary timespan) means only that the meaningful units of language are (often extremely) flexible.
I do recall. The problem is that the question is phrased in such a way as to make any answer fundamentally inaccurate. It's like asking "I am fine with saying that there are only 4 elements (earth, fire, water, and air), but if you want to add another, just explain what it is". The question is phrased such that certain things which are not true are assumed.
You have a model of causality which has no (at least readily) identifiable relation to physics and instead relies on polysemy and linguistic flexibility. It's a closed discourse universe- unfalsifiable because the nature of language and the terms can be used to describe anything, including miracles and magic.
This is why even Aristotle identified different "types" of causes, and why philosophers do so today as well.
You need only look up things like "efficient cause", "material cause", "sufficient cause", etc., to realize that simply stating "it's all causes and effects" is incorrect. As for the idea that "time is linear" I'm willing to bet wikipedia talks about spacetime curvature.
Perhaps the best way to answer is through the following:
1) There are ways that one can explain the mechanisms in layman's terms with an acceptable loss of accuracy. The problem is that it would take a few hundred pages.
2) As an undergrad, several psychology courses involved reading textbooks which either dealt with or focused on neurons. Even senior level courses, however, so simplified how neurons are involved in cognition, behaviour, etc., that it isn't much of a stretch to say they were all wrong. A course on behavioral neuroscience, for example, might include a textbook that gives a pretty detailed explanation about the parts of neurons and areas of the brain which are thought to be related to this or that. However, all of my own and all I've seen since (helping undergrads) give the impression that neurons have a threshold which, if reached, will generate an "all-or-nothing" electrical "signal", the basic unit of neural information. This isn't true. Not only that, one could make the argument (and it has been made) that the entirety of this description is wrong. So why is it there? Probably for multiple reasons, but among them are 1) nobody is quite sure how spike trains, which are more like the "basic unit" of information, actually "work", and 2) the actual models of neural signaling necessarily require a fairly strong background in mathematics.
In quantum information theory, the "randomness" is the basis for computation. So if "choice" meant either determinism or random processes or both, then the brain too could use the randomness in QM to process information.
1) Why must it have a cause? And unless you believe the universe always was, then what caused the universe? Or, if you think the universe is uncaused, why must it be the only example?
2) Circular causality. Complex systems are capable of producing functional properties which act on these systems such that the functional properties and the system are both causes and effects at the same time. For an explanation, see my last post.
General relativity suggests the possibility of closed timelike curves (CTCs), while special relativity prohibits it. The issues, however, are:
1) Technically, the central issue concerns superluminal signals, but more than one specialist has written about the "vague" ways in which signaling is defined, which make debating the possibilities of CTCs and whether they violate SR difficult (and tend to create study after study about the hypothesized properties which may or may not exist in what is a hypothesized constraint to begin with).
2) Not only is there an issue with defining what constitutes a "signal", but also how, why, and in what way CTCs might (or might not) violate SR. See, e.g,. Closed Timelike Curves via Postselection: Theory and Experimental Test of Consistency:
Abstract: "Closed timelike curves (CTCs) are trajectories in spacetime that effectively travel backwards in time: a test particle following a CTC can interact with its former self in the past. A widely accepted quantum theory of CTCs was proposed by Deutsch. Here we analyze an alternative quantum formulation of CTCs based on teleportation and postselection, and show that it is inequivalent to Deutsch’s. The predictions or retrodictions of our theory can be simulated experimentally: we report the results of an experiment illustrating how in our particular theory the “grandfather paradox” is resolved."
(I chose this one because there is a free copy available)
M3) This concerns relativistic models, not necessarily QM (where we get into what "entanglement" actually is or is not). The problem here is well-known because the problem is the unknowns. Most of QM is formalism and the relationship between this formalism and reality is unknown (see e.g., Plotnitsky's paper "On physical and mathematical causality in quantum mechanics" in the journal Physica E Vol. 42)
4) In contrast to CTCs and all the unknowns, biological systems lend themselves to a great deal more actual empirical study. And here we have a problem:
The amount of research in biology alone (apart from the above, see e.g., "From exact sciences to life phenomena: Following Schrödinger and Turing on Programs, Life and Causality" published in Information and Computation vol. 207) represents a rather serious problem for reductionism, but when we get to neurobiology and consciousness, the "leaders" of the movement towards fundamentally indeterministic systems and mechanisms in the brain which allow for a form of "free will" are primarily physicists.
I can't tell if you are joking or seriously asserting the above.
f is not just a notational device used to describe an abstract mapping, but to represent a literal function: metabolism. Unlike QM, cellular processes can (in general) be observed. The problem is thay are extremely difficult to model. This is because (unlike programs run on computers), they are fuzzy systems with functions that aren't well-defined and don't seem to fit into linear causal models.
The material "parts" create a functional process or processes which are independent of any of them but are produced and affected by all of them.
He (actually they, in that this began with Rosen but hardly stopped there, instead largely creating a new framework for biology) did not mean that. Causality can certainly be "defined mathematically". I can define it as 3. Or 42. The issue is the relationship between the operations and symbolism and reality. The problem with well-defined functions in this case is the fuzzy boundaries (providing they exist at all) between the domain and image.
Here's the problem: you've objected to the use of ill-defined functions and so forth in the mathematical description, because (I think this is why) they are incompatible with computation theory. The mathematical formalism you object to is the way it is not because of Mikulecky's poor quantitative reasoning abilities, but for the same reason we find similar functions, schematics, and so forth elsewhere in systems biology, neuroscience, etc.: we can either make the mathematical descriptions such that a computer deal with them, which means we loose most of what's going on in our "model", or we can depict and describe as formally as possible what so far we have no idea how to model using a computer and which may (according to one's interpretation of various proofs) be impossible to run on any Turing-equivalent machine.
You're going to need to be more specific, as extra dimensions, multiverse theories, and so forth are not only diverse, but also do exactly what I said: deal with space-like nonlocality by constructing some alternative model, not by "restoring" locality.
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