Thursday 5 January 2012

A letter from Kristor on Free Will and Determinism


This is excerpted from a letter by penfriend and commenter Kristor, in relation to:



The first thing I would say is that while the left and right brains may process their data using different sorts of algorithms, so that one half treats of things in terms of linear causal chains while the other treats of them in terms of holistic field superpositions [how different, really, is a vector sum from a field superposition, when push comes to shove?], nevertheless they must both be subject to ontological causal inputs from their pasts. I.e., however things might seem to be different to the two sides of the brain, the world as it impinges upon them causally must impinge upon both to the same ontological extent and via the same ontological mechanisms. The two halves of the brain do not, after all, inhabit different metaphysical causal orders.


So, any resolution of the seeming contradiction between freedom and causal order – for that is what we are talking about – must be made available to both of them, must cover both of them, equally. The resolution cannot be derived from the differences in the way that they treat data. The resolution must rescue all sorts of creatures from the contradiction.


Some related items that are of interest:


1.       The problem of the resolution of freedom with causal order is a department of the problem of the resolution of creaturely freedom with Divine foreknowledge/Providence. This is a clue that should point us in the direction of searching for an ultimate resolution in the reconciliation of the reality of time and temporality – which is to say, simply, causation and a causal order, things happening, and happening to each other, and affecting each other, and all coordinated – with the superordinate reality of eternity – which is to say, not Eleatic immobility, not the impossibility of motion, but rather the subsumption of all subsidiary, creaturely motions in the immense and singular Divine motion, or act.

2.       If there is causation, if there is happening, then reality cannot be continuous. If one thing is to cause another, then the causer and the caused must be different from each other, and disparate. If they are not truly disparate, they are then but one thing, and there is not properly speaking any causal relation between them, but rather a relation of unity. So this means that if there is a past that is going to have causal effect upon this present moment, that is going to influence this present moment, then that past and its events must all be different entities than this present moment. So that, if things do really happen, then they must happen quantally. Reality must be discontinuous if there are really events.

3.       Given a certain configuration of past events, given a cosmic history, It is possible for a current eventuating event that arises from them as its data to turn out a number of different ways that are lawfully related to them. There are a number of different ways that the probabilities implicit in the [wholly determined] Schrodinger equation may turn out, without escaping the constraints of that equation. What evolves deterministically, then, is the range of possible orderly outcomes of a given past set of events. The predetermination of a given event that is imposed upon it by its past, then, does not constrain it to only one possible outcome. If it did, there would be no sense in talking about “probabilities” or “outcomes.” For, if an event were wholly determined by its past, down to the last jot and tittle, why then it would be nothing but a feature of that past. It would not in that case be a real entity, a real event. The complete and utter predetermination of events is the elimination of events as an ontological category – and, thus, also an elimination of entities.

4.       Items 2 and 3 obtain with equal force whether we construe causation in a left-brained, linear fashion, as of the vector sum of particular interactions, or in a right-brained holistic fashion, as a superposition of fields. Again, what is the difference that makes a difference between a vector sum and a superposition of fields? Are these not merely different mathematical formalizations of the same basic notion: of causal inputs delivered to a locus in the extensive continuum from its past?     

5.       NB also that a vector sum or integral can be just as finally, teleologically oriented toward and ordered toward a strange attractor as a field.


So, whether we treat of causation using fields or vectors, we still face the problem of freedom versus predetermination. What then is the resolution? Put in terms of the Schrodinger equation, what is it that does the determination of what precisely will be the outcome of a given quantum situation? What is it that might prevent that outcome from being always and everywhere the one that is under the equation the most probable? I.e., how can there be more than one lawful outcome of a given step in the evolution of the equation?


The resolution, then, it seems to me, is provided by a distinction between the past of an event and the event itself. The past as past is fixed, determined, changeless (tace for the moment on backward causation mediated by prayer, that takes place in the supratemporal causal order). The past has to be just exactly, changelessly, what it is, in order to function as a completed set of data for the processes of the present moment of eventuation. If you are going to have inputs to the present, as yet unfinished moment of eventuation, then those inputs must be themselves finished. If they are not finished, then they just don’t yet fully exist to function for any subsequent events as causal inputs. It is, then, the past that is fixed, determined. The Schrodinger equation arising from a given past is determined because that past is determined.


And, therefore, it is the present moment that is free and – despite the constraints derived from its past, and formalized in the Schrodinger equation – not yet wholly determined.


What then feels to us like a unity of experience, a unification of disparate feelings in the integrity of the present moment – this unification being the matter of the binding “problem” – is just our present feeling of the feelings of past moments. A present moment is an integration and concrescence of impressions, feelings, of past events. And this is so whether we formalize the unification using vectors of particular interactions, or superpositions of fields.


[I got everything I have so far said from Whitehead. He doesn’t say it all explicitly, but it is all implicit in his metaphysics. Everything from here forward I got from Boethius, and Aquinas.]


Now notice that this is not the ultimate resolution of the problem. For, while we may so far have dealt with the problem of determinism versus free will by ascribing the former to the past and the latter to the present (and, a fortiori, to the future), we have not yet dealt with the problem of creaturely freedom versus Divine Providence.


To resolve that contradiction, we must transcend time altogether, and remember that temporal relations are characteristics of an eternal state of affairs that comprehends all events, whatever their spatiotemporal loci. That that state of affairs is eternal does not mean that the events that constitute it – i.e., the set of events that includes all events whatsoever, of whatever spatio-temporal locus in all actual causal orders, all worlds (in secula seculorum) – are not free. God’s eternal act is free, even though (being eternal) it is also necessary. So likewise with everything he knows, including all creaturely events. Everything that happens happens freely, even though it is eternally known, and thus necessary.


Thus the causal inputs of a temporal event are present to it only via the medium of the Divine Providence. It is God who forms the Receptacle for creaturely eventuation. He is the causal order, He the nexus. The past is real to the present, is “thingish” to the present, by virtue of its reality to God. We access the past via God; He is the medium of the causal influence of the past upon the present.


So Leibniz, Spinoza and Descartes were all right in ascribing to God in their various ways the ultimate function of relating and coordinating all events that, absent his provision of an ontological milieu for causal relations, would not – nay, could not – be related to each other at all. Things are orderly insofar as they are ordered in the Divine comprehension. And a thing that is not ordered in the Divine comprehension is not ordered at all.




PS: what Zeno disproved was the impossibility of motion and causation in a continuous state of affairs. Motion is not, however, paradoxical in a state of affairs that is discontinuous. In such a state of affairs, things can be really disparate, so that there can be a relation of motion between them. It is obvious that if events are continuous with each other then there cannot be motion between them, for there is in that case no disparity between them; and where there is no disparity there is only unity.


Newton and Planck both in different ways ratified Zeno. Planck’s quantum of action is the physical implementation of the Newtonian infinitesimal.


Bruce Charlton said...

Kristor takes the argument a step or two further or deeper than I think the early Greeks would have gone.

His argument seems rigorous and watertight to me (I can follow it although I could not have made it myself) - so the question is to what extent arguments of this type are compelling - and to what extent they are limited by their abstraction (hence their intrinsic selectivity and simplification)

My own preference, these days, is to use philosophy as a 'single step back' kind of procedure to reconcile spontaneous common sense in-your-face 'how things seem' with apparent contradictions and paradoxes. Rather as Plato did when trying to include both unchanging eternal reality (which is necessary for any knowledge to be real) and the change and time of this (commonsense) real world.

Plato answers this problem, but the extra step back of philosophy which Aristotle introduces answers problems arising from this Platonic perspective.

However, I am not convinced that it is necessary to deal with the problems of the Platonic perspective in a philosophical way - at that point we can admit to the mystery of things, and cease philosophy - because going down the path of further, two-steps-back philosophy brings further problems of its own.

Deep waters! This is related to my belief that (Platonic) Eastern Orthodoxy is more nearly right in its general approach than (Aristotelian) Roman Catholicism. I think Platonism gives us enough of the advantages of philosophy, without stepping onto the slippery slope of scholasticism (as I perceive it).

Maybe it is simply a matter of the fact that anything more complex than Plato is incomprehensible to the inexpert? Plato stands at about the limit of common sense, and is perhaps about as far as humans were 'meant' to go?

Valkea said...

Kristor, what do you say about string theory; it says that quantum probabilities are produced by deterministic processes in the same way that two right angled swinging pendulums produce probabilities, and that reality (particles and the four forces) is an illusion of continuous generation of "surfaces" and "membranes" by the moving strings and coiled strings? Thus, according to string theory particles and the four forces are "pure geometry", whatever it ultimately is. Nobody knows what the strings really are, and no strings, "surfaces" and "membranes" has ever been detected directly or indirectly because of too high energy requirements, although the theory has opened new avenues, and to some extent mathematically and geometrically explained old unsolved problems, like black holes as "fuzzy balls" as big as the event horizons; quantum particle-field dualism; the combination of gravitation and quantum mechanics; a single geometrical cause and explanation for the four forces and multiplicity of particles; illusionary nature of quantum action-at-the-distance, e.g. when photons are send to opposite directions at the same time by the same light source; rebounding nature of the Planck's constant, the smallest possible size of energy quanta, thus impossibility of black hole singularities and infinite masses etc.; etc.

Anonymous said...

Is determinism really incompatible with free will? At this point one might ponder the concept of deterministic chaos: if the assumption is taken that the laws which govern reality are indeed deterministic, but the sets upon which these laws operate might be varied infinitesimally and the consequent behaviour would be totally different (compared to the sets not being altered), then randomness might be reconciled with determinism.

If Heisenberg's principle of uncertainty is taken to be a fundamental principle of nature (that is to say, quantities like momentum and precise location of a particle or energy and time cannot be known in detail at the same time) then it might turn out in the following way: the "white noise" of the system (which must occur in a system where some form of sampling takes place, i.e. where a continuous function (which would be the underlying eternity, unity) is broken down into values that are both discontinous in time as well as in the associated value of the function) alters the values in such a way that the resulting output is utterly different to the one that occurs without noise.

For example, let us think about the logistic map which is a very simple relation characterised by the following equation: x_{n+1} = r*x_{n}*(1-x_{n}), 0 < r <= 4; n = 0,1,2,...
The logistic map maps the interval [0,1] onto itself. Between r=3.5699... and r=4 deterministic chaos takes place: minimal variations of r lead to a very different output (the logical map might be used for example to simulate the growth of a population of animals where r is the supply of food). The output is predictable if all necessary values are known with perfect precision. By taking into account the principle that nature can never be known and measured with ever increasing accuracy, determinism in effect becomes an integral part of chaos. As our material self is subject to the laws of nature but is fundamentally corrupted by noise which by principle is random, the deterministic processes of our brain might yield random results obtained in deterministic ways. Material determinism does not necessary mean that free will is impossible. It rather strengthens free will. Deterministic chaos that accompanies some nonlinear equations which govern the physical world is thus a fundamental part of nature. It might explain the sheer diversity of living objects and forms, and at the same time explain how this diversity could develop although only a couple of laws (and not infinitely many) govern nature. It is the symbiosis of randomness and determinism.

By the way, I have been reading your blog for quite a while: this way I want to thank you for your great thoughts that often provoked heated discussions within myself.


Kristor said...

@ Valkea: String theory is cool, but I’m not sure it’s science. That doesn’t mean I think it’s false, but that I think that it may just be that it’s not susceptible to experimental falsification. This is what I understand “pure geometry” to indicate: a pure geometry is a geometry that is not a geometry of a given physical domain, but that is rather a geometry of a type of physical being as such. And you can’t do an experiment on being as such. So, this would make string theory a theory in applied mathematics, I guess. And that would make it a department of metaphysics.

If string theory is indeed a pure geometry, then the fact that no one knows what the strings really are is just what we should expect, because a pure geometry is by definition basic. The Calabi-Yau volumes and strings of the theory are not themselves physical, because if they were, they would then themselves stand in need of explication (in which case, string theory would not be a theory of everything physical – it would not be an ultimate theory). We are asking for such an explication when we ask, “what are strings and Calabi-Yau volumes, *really*?” If string theory is a pure geometry, then the answer has to be, “they are axioms of physical reality, and do not themselves therefore have any physical reality; their reality is purely mathematical.” This does not, NB, mean that they are unreal, or even that they are not concrete; it means only that they are not *physical.* Indeed, it is traditional to argue that mathematical reality is *more* real, *more* concrete than physical reality.

Drawing an analogy to computer science, asking what strings and Calabi-Yau volumes really are may be like asking what computer language binary code is written in. The question is a fundamental misprision. Binary is *just math.* Likewise, string theory may be *just math.*

Drawing an analogy to computer science, asking what strings and Calabi-Yau volumes really are may be like asking what computer language binary code is written in. The question is a fundamental misprision. Binary is just math. Likewise, string theory may be just math.

Kristor said...

@VLAI: What you describe as deterministic chaos does not seem to me to be truly deterministic; nor is it truly chaotic. A truly deterministic system could evolve along only one path, and so it would not really be proper to speak of it as a “system” that “evolved;” properly speaking, it would be a motionless unity. A truly chaotic state of affairs is likewise not a system at all, and cannot properly be said to evolve.

Your logistic map is an instance of what John Holland calls a Constrained Generating Procedure, or CGP: a system that transforms inputs into a constrained set of outputs. CGPs are orderly, and generate orderly outputs, but they do not constrain the set of outputs to the point that there is only one allowable output, given the inputs.

NB that noise and disorder are not instances of chaos. They are characteristics of otherwise orderly phenomena. You can’t get pure noise or pure disorder, because pure noise and pure disorder would be, like chaos, pure non-being. Noise is a feature of an orderly signal; disorder is a feature of a state of affairs that is at least a little bit orderly (even in a situation of immaculate heat death, there is a remnant of order: intra-molecular, intra-atomic, etc.). Take away the signal altogether, and there would be no noise; take away the basic order implicit in being as such, and you take away all disorder as well.

NB also that freedom is not a form of chaos. It is not a derogation of order. Rather, it is a product of order. Freedom – the possibility of true optionality, of true alternatives – supervenes upon the constraint of sheer, untrammelled possibility. If simply anything might happen, without any limit or constraint of any kind, then if x should happen, it could not have come to pass because an entity chose it; rather, it could only be that x happened *for no reason at all.*

None of this is to disagree with your suggestion that your logistic map shows how an ordered system can exhibit degrees of freedom. It does.

Further, I agree with you that Heisenberg’s Uncertainty Relation specifies the ineradicable bit of sampling error in our apprehension of the materially determined – i.e., ontologically complete and definite, and therefore apprehensible – past. The only way to know another thing perfectly and without any uncertainty whatsoever is to be that other thing; in which case, the thing known is not other, at all, but only oneself. Thus if an instant of knowledge or experience is really to exist as a disparate thing, it must be different from the instants that constitute its past, and that are the data of its experience. How different? For our causal order, the answer is given by the Planck length, which measures both the minimum amount of action and being, and also the greatest amount of knowledge or information it is possible for one particular thing to have of another.

Valkea said...

Ok. At some point physicists have no other choice, but to describe mathematically in simple terms what they "see".

My two guesses:

Mathematics might be ultimately too simple, too reduced and too "perfect" to describe strings or whatever underlies particles and forces. Too much have been taken away from numbers, too many qualities. One can describe equally well 1 particle, 1 cow, 1 car and 1 universe with number one. This is a huge advantage at the beginning when delving deeper into physics, but at some point, maybe at the level of strings, 1 and other numbers contain so much more than the said numbers, that they are not enough, not even when adding to the numbers increasingly more complex auxiliary mathematical descriptions, themselves suffering from the same simplicity. This in addition to the quantum uncertainty.

String theory, if it is right, increases first mathematical certainty, i.e. determinism, in relation to quantum theory, but later, if it will be somehow possible to indirectly study strings, new uncertainties will arise.