DECISION UNDER UNCERTAINTY AND THE BAYESIAN BRAIN: A NOTE ON THE CONCEPT OF DETERMINISM

In a previous post [here] it was addressed the issue of bayesian modality of information processing into the brain. 
The main purpose was focused on the biological palusibility of the bayesian approach in decision making under uncertainty as reported by several authors in books and in leading journals of neuroscience. 
Now let's see an elucidation on  the concept of determinism. It has different meanings [see also]:

1. Causal Determinism (or Nomological Determinism) states that all events have a cause and effect therefore future events are explained (caused) by past and present events combined with the laws of nature.  
2. Logical Determinism is the notion that all propositions (i.e. assertions or declarative sentences), whether about the past, present or future, are either true or false. 
3. Environmental Determinism considers that the physical environment, rather than social conditions, determines culture.
4. Biological Determinism relies on the thesis that all behaviour, belief and desire is genetically fixed.
5. Theological Determinism is the belief that there is a God who determines all that humans will do, either by knowing their actions in advance (predestination) or by decreeing their actions in advance. (see also the Jansenism theology).
6. Emergentism (or Generativism) argues that free will does not exist, because all the actions and behaviors are just a realization and interaction of a deterministic process, that is, a finite set of rules. 

According to the Newtonian physics a set of fixed, knowable laws rule the universe, therefore once the initial conditions of the universe have been established, then the rest of the history of the universe follows inevitably. Any uncertainty was always a term that applied to the accuracy of human knowledge about causes and effects, and not to the causes and effects themselves.

Since the beginning of the 20th Century, quantum mechanics has revealed previously hidden aspects of events, and Newtonian physics has been shown to be merely an approximation to the reality of quantum mechanics (at atomic scales, for instance, the paths of objects can only be predicted in a probabilistic way).
Some argue that quantum mechanics is still essentially deterministic; some argue that it just has the appearance of being deterministic; some that quantum mechanics negates completely the determinism of classical Newtonian mechanics.

I considered the approach of Wolgang Pauli to the determinism-dilemma. He wrote [1]: 

The simple idea of deterministic causality must, however, be abandoned and replaced by the idea of statistical causality. [1] 

Actually, "the concept of causal relation have been modified because of the advances in the physics: it has been found necessary to abandon the idea of deterministic causality and substitute in its stead relations that are only determined with a certain level of probability" [2].  

The Bayesian use of the word probability refers to a form of reasoning and not to a factual statement. Used in that sense, assigning a probability to an event expresses a rational judgment on the likelihood of that single event, based on the information available at that moment. Note that one is not interested here in what happens when one reproduces many times the ‘same’ event, as in the objective approach, but in the probability of a single event.

Probabilities enter situations where our knowledge is incomplete and Bayesian methods allow us to make the most rational predictions in those situations. 

Now, suppose we want to explain some phenomenon when our knowledge of the past is such that this phenomenon could not have been predicted with certainty. That knowledge, although partial, is sufficient to ‘explain’ that phenomenon if we would have predicted it using Bayesian computations and the information we had about the past. That notion of ‘explanation’ incorporates, of course, as a special case, the notion of explanation based on laws. Also, it fits with our intuition concerning, for example, the coin-tossing situation: being ignorant of any properties of the coin leads us to predict a fraction of heads or tails around one-half.
Hence, such a result is not surprising or, in other words, does not “need to be explained”, while a deviation from it requires an explanation. 

A basically similar form of explanation is used in macroscopic physics, for example when one wants to account for the second law of thermodynamics, the law of increase of entropy. We do not know all the microstates of, say, a gas; nor do we know their evolution.
But we can assign, in a Bayesian way, a probability distribution on microstates, given some information that we have on the initial macrostate of the system. Since, for each microstate, the deterministic evolution leads to a well-defined evolution of the macrostate, we can, in principle, compute the probability, relative to our initial distribution on the microstates, of a given macrostate. If it happens that the one which is overwhelmingly probable coincides with the one which is observed, then one can say that the latter has indeed been accounted for by what we knew on the initial macrostate and by the above reasoning [3].

Therefore, the probabilistic (bayesian) laws play a major role in front of conditions which drive the system outside of the "comfortable" perfect cause-effect scheme (at micro and macro-level). 

1 C. McGinn, (1998). Problems in Philosophy : the Limits of Enquiry, Blackwell, Oxford. 

2. Jean Bricmont, Determinism, Chaos and Quantum Mechanics

3 In fact, a similar type of explanation is used in the theory of evolution, as was noted already in 1877 by C. S. Peirce: “ Mr. Darwin proposed to apply the statistical method to biology. The same thing has been done in a widely different branch of science, the theory of gases. Though unable to say what the movements of any particular molecule of gas would be on a certain hypothesis regarding the constitution of this class of bodies, Clausius and Maxwell were yet able, eight years before the publication of Darwin’s immortal work, by the application of the doctrine of probabilities, to predict that in the long run such and such a proportion of the molecules would, under given circumstances, acquire such and such velocities; that there would take place, every second, such and such a relative number of collisions, etc.; and from these propositions were able to deduce certain properties of gases, especially in regard to their heat relations. In like manner, Darwin, while unable to say what the operation of variation and natural selection in any individual case will be, demonstrates that in the long run they will, or would, adapt animals to their circumstances.” [C. S. Peirce, (1877). The fixation of belief, Popular Science Monthly 12, 1.]

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