Determinism and uncertainly in the physical and social sciences

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                             Determinism and uncertainly in the physical and social sciences. 
 
 
                                               Introduction. 
 
 
         I would here like to present the influence of determinism in economics. Similar positions have 
born by the success of the physical theories and by the following transfer of the concepts to 
economics. In the Chapter 1 I explicate the historical back-ground related to the Marxism, as more 
coherent example to transfer the physical methods to the social sciences, next I pose a definition of 
determinism in according to the Laplace  interpretation by the Popper view. Next I talk about the 
neo-classical economy as a trial, I think successful, to introduce mathematical concepts in economy 
and not dialectical, in same time saving the notion of freedom against a strong determinism. 
             In the Chapter 2 I analyze the feed-back between mathematics and economics, often 
following the applications to the physics and biology. I sustain that so it exists a cultural flow such 
that the successes in a matter have results in other matters. Particullary, I observe as if the previews 
in economics must have a sufficiently exact form, so the mathematics can’t avoid an exit by an 
applicative view. Therefore it is interesting as the difference in physics between static and dynamic 
theory can be obtained in economics. 
           In the Chapter 3 I affirm that some new mathematical theories, for example the fractal 
geometry and the chaos theory, explicate the economic facts with a coherence better than physical 
determinism. 
               In the Chapter 4 I show as by a historical view it has been a relation between deterministic 
philosophy and research of social consent, but that the problems of a global society need open 
model. In the two appendix I pose an approach about the Colletti philosophical view and the 
Prigogine physics.
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                                        Chapter 1. 
 
A definition of indeterminism related to the neo-classical economy. 
 
 
1. Some initial considerations. 
 
       A general question born around the scientific and philosophic discussions has been the 
difference between determinism and uncertainly. After the successes of Newton physics it is tried to 
propose the determinism also in social sciences, generating wrong constructions as the URSS 
materialism, what have born applying to the economy and to the society the arguments of Marx and 
Lenin. It was about a mix of Hegelian dialectic elements and the Marxian deterministic pseudo-
scientism. It represents surely a complex vision what tried to include in certain structures the 
behaviour of particular phenomena. It was a trial  to study those phenomena in a systemic way 
learning by the interaction between several facts. 
   Popper, who has sustained in a strong way a polemics against the Hegelian-marxist theory in “The 
open society and its enemies”, admitted the importance of this construction what had into the more 
different social problems. Unfortunately this question is old as the philosophical thinking, because 
we found these steps already in Greek culture for example in the polemic between Socrates and the 
sophists. If the first sustained the ethical thesis why social behaviours should follow necessary these 
principles, the others preferred the free choices whose had been determined by real interests. But 
the authority principle inner to the Marxist theory is founded just on to see as needed its 
consequences once one has posed the hypothesis, a strong determinism what derives, more than 
from  to scientism, to the application of the Hegel idealism to the social theory. 
            In economics it is important as the theory of Jevons, Menger and Pareto has had different 
position from the Marxist materialism and, also if the first had a mathematical model, it have give a 
value to the individual choices. Bernstein showed that the Marxist thesis didn’t be true already the 
first part of XX century, on contrary they have gone in different direction respect to reality; 
therefore this theory shouldn’t finished historically into the working  class, but the democratic 
socialism must think in a new way it. In according to Bernstein the exit didn’t justify more the 
socialist method, because it was the steps for adapting to the reality to realize the movement, what 
determined the successes of the politics. 
         We can observe that if the determinism didn’t work more, the sociology accepted complex 
theories in economics, also in physics we can see in this century as the reality is evolutive and in 
few cases we use the Cartesian procedures. The relativity theory has left the fact that the physical 
law is deterministic, why Popper talks more about the falsification than the verify. 
           The quantum theory goes against the evidence and the chaos theory is placed between the 
determinism and the probability theory. In economics Arrow showed that it is impossible connect 
the democracy with the trial to unify the individual preferences; also who goes against this 
principle, as Rawls, poses himself into the open society. In Italy Colletti shows as to reduce the 
reality to the logics is an error that the Marxist theory derives from the Hegelian dialectics.  
     These are in few words the principal lines of thinking whose around I would like do an 
approach, talking about the fact that if the science found in itself a part of uncertainly, it not loses 
importance, but it further become better in several senses. It need to think that in the real world they 
are few cases to whose it is applied the linear differential equations theory, but we have more 
applications to the economy and to the biology of the chaos laws and of fractals.
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2. The determinism. 
 
       I give the Popper definition of determinism. He made it from Laplace theory which in 
according to the universe is compounded by little bodies; on everyone it exists the Newton dynamic 
laws. If we could know the system state at a certain time, we determine the system evolution. But 
for doing that Laplace considered the existence of a metaphysical  knowledge; he admitted the 
action of a devil who can construct the differential equations whose rule the system once he knows 
the initial conditions. The existence of this devil in fact don’t suppose religious hypothesis, but he is 
only a super-scientist who can preview with a difficult calculation every future event. 
           This trust in predictive capacities it had born from the success of the Newton laws in physics 
whose allow to study the body movements; the bodies have mass and the movement happens in a 
force field. But the same Newton dynamics for resolving the simplest problem, that of two bodies, 
utilized the approximation method. If the bodies don’t be two, but three, the calculation became 
very difficult and the linear analysis is too weak for the solution. 
         By that it needs, also if one wouldn’t get out the determinism, to accept an uncertainly in the 
measures, which can be considered small or not, if we accept or not the Heisenberg indetermination 
principle. Popper thinks to confute the Laplace hypothesis with a Hadamard theorem, who found 
that in a physical space, given an interval very small, it contains always closed orbits and asyntotic 
curves. But he sustains that it exists the difficulty to pass from a physical law to affirmations about 
the universe structure, because his scientific theory is of certain type.   
            The Newton theory can be accepted until it is showed incoherent whit the relativity, which is 
considered better. Therefore the Laplace strong determinism is against the individual freedom; 
Popper resolves very good this question whit the difference between a World 2 (sensations, 
emotions) and a World 3 (theories). A strong determinism doesn’t allow the possibility of the art 
productions, that is also the Mozart music could be predict from body physical considerations. But 
it is an object of World 3 what has influences from World 2. 
         Also in logical mathematics we can pose the question if it exists a method able to show all 
true theorems; that is false for the Godel theorem, who found a true proposition what we can’t 
show. The question if the mathematic is deterministic goes out the our objectives, because we 
defined the determinism the automatic imposition of the mathematical laws to the physical and 
social back-ground. But the question born by Godel theorem poses the problem about the 
subjectivity or objectivity of mathematics. That is, the researcher imposes his axioms to the theory 
what he studies or he find a theorem in the same way a explorer find a geographic region? 
      We see that if Bernstein in sociology wanted a return to Kant, also the mathematics after Godel 
can’t avoid a similar path. Kant believed that determinism was true in physics, because he 
considered the Newton laws true a priori; that is different by his big trust in the freedom and in the 
human products. By contrary, he considered true the synthetic hypothesis a priori, but the Kant 
theory remains fundamental in the philosophical evolution of Western thinking, just for the 
importance of individual choices. In according to Kant, the physical determinism gives to single his 
ethic responsibilities, but also it makes stronger the choice capacity of a person. 
         In according to Popper the existence of mental products, whose can interact by the norms of 
the evolution of the science and the philosophy, is a important proof what refutes the possibility to 
preview events in a deterministic way. A strong polemic has been sustained by Popper against the 
historicism, that is the trial to apply the physical theories to the social sciences. The historicism in 
according to Popper is represented by the open society enemies, Hegel and Marx, who use the old 
Plato theory where the idealistic thinking imposes itself to the reality. 
         This polemic is honest for a trust in the human ratio, what, conscious of its limits, sustains  an 
action able to reconstruct the back-ground, thinking the consequences of that, but with the capacity 
to accept the reaction of the reality. I would like define a historical prospective where, considering