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General Science
Is reductionism intrinsically limited?
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Is reductionism intrinsically limited?
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learningalways
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Is reductionism intrinsically limited?
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20/10/2015 18:55:59 »
Reductionism, parsimony is deeply rooted in modern scientific thinking. It is the principle that a reduced set of axioms/properties are enough to "explain" reality, that any aspect of reality can be "reduced" to this finite set of properties by applying logic inference rules.
This obviously is the direct emulation of the same approach used first in Mathematics with the axiomatic method.
This axiomatic "thinking" had a maximal exponent in the axiomatization program promoted by the German mathematician David Hilbert in the first years of the 20th century. The goal of this ambitious program was to build precise axiomatic systems for all branches of mathematics, once an axiomatic system was build, the "theorems/properties" of the given branch can be obtained by "algorithmically" applying inference rules to the axioms. In principle a computer can be programmed to do just that and today such programs do exist.
But the Hilbert axiomatization program was shown to have intrinsic limitations by the Godel incompleteness theorems of the 1930's.
These results proved mathematically that any finite axiomatic system for the natural numbers is always "incomplete": in the sense that there are always properties of the natural numbers that can not be reduced to the given finite set of axioms, these properties can be considered as "emergent" properties, properties that are not reducible/explainable using the predefined set of axioms.
Now reality can be considered as a Model, the ultimate and richest of any model. Any serious mathematical model of any aspect of reality will contain in it at the very least the natural numbers. That automatically place that model in the context of the Godel incompleteness theorems. This means that there are going to be properties in that model that can not be reduced/explained by the preexisting assumed known properties/axioms of that model, the model will be intrinsically incomplete. Emergent properties will always be there.
Reductionism is intrinsically flawed.
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Last Edit: 20/10/2015 21:51:47 by learningalways
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puppypower
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Re: Is reductionism intrinsically limited?
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Reply #1 on:
21/10/2015 13:31:09 »
It is not so much that reductionism is flawed, but rather reductionism is a work in progress. As new or emergent properties appear, it will become necessary to redefine the phenomena with different base parameters. For example, the earth was the center of the universe. As data appeared, this was change to the sun, etc. It changed, but remained reduced to a one liner.
If we get rid of reductionism, what that means is the status quo will become a science dogma. From this never changing center, one will need to add band-aids, get overly complicated, until the majority of people will have to take the word of a small minority, since only they can follow the overly complex.
Reductionism prevents dogmatic bureaucracy, by constantly requiring a new way to simplify, so more people can play. More people playing means more innovation and more self policing in terms of future reductionism.
Say we all decided to remove reductionism; hypothetically, at the theory that the earth was the center of the universe. The data that suggested the sun was the center is manipulated as an addendum to the earth center theory using a complex math trick. This will work and can lead to predictive results, but simplicity is lost in favor of a science oligarchy. If we simplify/reduce and say sun is the center, now even children can play; from the mouths of babes.
The tax code is extremely complicated, to where you may need to hire people to do your taxes. This is good for jobs and good for those who can work the complex system in their favor, but most people are vulnerable, due to lack of working knowledge. If we reduced the tax code to one side of 9 1/2' X 11 piece of paper, then everyone can play in the same league.
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Colin2B
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Re: Is reductionism intrinsically limited?
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Reply #2 on:
21/10/2015 22:23:29 »
I think it is an error of reasoning and understanding to link the scientific method to Godel's theorems and reductionism in this way.
Modern scientific methods are not dependant on the limitations which Godel identified. In particular:
Science does not seek to prove anything. This is discussed in other threads on this forum, but see the following video for details "The science of physics is not about 'proving' anything by Alan Guth "
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Scientific method uses observations, measurements, and classification of items and phenomena and tries to identify the relationships that govern them. Using these relationships to make predictions about their behaviour which can be tested by experiment.
Modern science, particularly physics, uses a systems approach to study the interrelationship of components. Axioms are taken as baseline assumptions only, ready to be reevaluated in the light of new data.
Because each hypothesis is tested against its ability to predict the behaviour of the system via observed results it does not rely on absolute proof.
Modern physics does not deal with modelling reality, only with what we observe. Neither does it deal with certainty, only with the probability of outcomes.
I think your views of science in this and other threads are out of date.
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Re: Is reductionism intrinsically limited?
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