The document discusses how scientific knowledge and thinking have advanced in the 20th century due to the end of classical certainties. It describes how Ilya Prigogine addressed the end of certainty in concepts like time and causality. Werner Heisenberg's uncertainty principle showed that there are limits to human knowledge at the quantum level. Kurt Gödel's incompleteness theorems demonstrated the limitations of classical logic and that a system cannot prove itself consistent. The document argues that complex thinking is needed to develop a comprehensive understanding of scientific phenomena by integrating knowledge across disciplines through group work rather than individual specialization.

1. 1
ADVANCEMENT OF SCIENTIFIC KNOWLEDGE AND COMPLEX
THINKING
Fernando Alcoforado *
The end of certainty and the necessary connection between cause and effect, and the
inadequacy of the Cartesian method of dealing with science, contributed to the advent of
a profound crisis of classical thought in the scientific field that occurred during the
twentieth century. O fim das certezas (The end of certainty) (São Paulo: UNESP, 1996)
is the title of a book by Ilya Prigogine. In it, Prigogine addresses, among other things,
the end of certainty about the concept of time (and space), characteristic of the era of
rationalism of Descartes and Newton which did not conceive multiple time. Immanuel
Kant's Crítica da razão pura (Critique of Pure Reason) (Petrópolis: Vozes, 2010)
advocated the view that the time has only one dimension of time and fragments occur
successively one after another. This conception, which is linked to a vision of
rationalist, deterministic and Euclidean world, was subsequently modified. Concerning
Prigogine, he also addresses the irreversibility of time, through what he called
"dissipative structures" contrary to the law of conservation of matter.
Another factor that led to the end of certainties, in the sciences (and by extension in the
humanities as a whole), was questioning the theory of causality. Since Aristotle,
"knowing is knowing the cause". This assumption was made for many centuries, until
the late nineteenth century and early twentieth century. The first blow was struck by
David Hume, Scottish philosopher who showed we thought just by habit, and we said
we know the cause when we were doing the relation between something that happened
before with what came later, but without being able to demonstrate the necessary
connection between cause and effect (See the article David Hume published on the
website <http://www.filosofia.com.br/historia_show.php?id=81>). But causality took to
be sidelined for Science, which will only occur with the onset of quantum theory.
Particularly interesting is the discovery of the Uncertainty Principle, by Werner
Heisenberg. Even before the formulation of this principle, he discovered new
mathematical properties related to quantum physics. In March 1927, Heisenberg
published his famous Uncertainty Principle. In it, showed that in the quantum realm
there were certain pairs of properties of which, the more you know about a less you can
know about the other. The more we are able to measure the velocity of a particle, we are
less secure of his position; and the same happens with several other interconnected
quantities. In other words, there is a genuine limit, absolute, to human knowledge. This
was the final blow that Einstein feared from the beginning, when he realized that
quantum processes threatened causality.
Another development that will shake the world of certainties established is the failure of
classical logic, or Aristotelian, in explaining the real contradictions. For Aristotle, logic
is not a science but an instrument to correct thinking. The object of logic is the
syllogism which is nothing more than an argument consisting of propositions from
which we infer (draw) a conclusion. Thus, it is not giving value truth or falsity to
propositions (or sentences given premises) or the conclusion, but only to observe how it
was composed. It is a mediated reasoning that provides the knowledge of one thing
from other things (seeking, for your cause). The great obstacle in this sense was
triggered by the famous Gödel's Theorem, which shows that a system cannot justify
itself.

2. 2
At the International Congress of Mathematicians in Paris in 1900, the young and
brilliant David Hilbert, imbued with the current ideas presented an amazing paper
summarizing the 23 questions still "open", which, after resolved, would complete the
entire scope of mathematics. In 1931, when still in effect the proposed Hilbert to get the
full construction of the mathematical theory through formal logic, Gödel published his
work "On Undecidable Propositions", ending this expectation. The first incompleteness
theorem of Gödel appeared as "Theorem VI" in Gödel's article called On Formally
undecidable Propositions in Principia Mathematica and Related Systems I in which he
stated that "Any effectively generated theory capable of expressing elementary
arithmetic cannot be both consistent and complete. In particular, for any consistent
formal theory and actual output that proves certain basic arithmetic fact, there is an
arithmetical statement that is true but not provable in the theory" (Nagel, Ernest;
Newman, James R. A prova de Gödel (The proof of Gödel). Trad. Gita K. Ginsburg Sao
Paulo: Perspectiva, 1973).
In an increasingly complex world in which we live, the sciences continue to
compartmentalize information, by Cartesian way, which prevents them from developing
a comprehensive understanding of scientific phenomena. This problem will only be
solved with the use of complex thinking. This does not mean simply abandoning
disciplinary boundaries, or make more difficult task requiring the researcher to account
for all subjects. The researcher does not mean leaving your area of expertise, but it
forces him to work together recognizing that no one else can search alone. The
increasing complexity of the scientific issues of the contemporary era is leading to the
conviction that there can be only advance knowledge for group work among
researchers.
There is a widespread view in the society we live in that question about any issue
should be answered by the expert. It is very common, for example, the emergence of
economic issues that affect the life of a country or the world, the media seek an
economist for answers to questions asked. However, the economy's problems involve
several areas of knowledge, eg, political science, sociology, infrastructure, education,
health, among others that require the opinion of other experts to answer the questions
asked. The problems of the economy of a country or the world cannot be restricted to
issues that relate to economic growth, inflation, unemployment and other economic
variables. For proper understanding of the economic problems of a country or the world,
we need to hear the opinion of many experts, if possible, at a round table.
Unlike the thesis of the great economist John Maynard Keynes, the University seeks to
form, in general, the expert in economics, in the same way that the engineer specialist,
medical specialist, etc.. Keynes stated that "(...) the master economist must possess a
rare combination of talents. He must be mathematician, historian, statesman,
philosopher. Must understand symbols and express themselves with words. Must
contemplate the particular in terms of the general, and touch abstract and concrete in the
same flight of thought. Must study the present in light of the past for the purposes of the
future. No aspect of nature or human institutions must lie entirely outside his interest.
Should be objective and disinterested in a simultaneous manner; so distanced and
incorruptible as an artist and sometimes as near the earth as a politician "( Keynes, John
Maynard, Essays in biography, p. 140-141, apud Heilbroner, Robert. A história do
pensamento econômico. 6a ed. São Paulo: Nova Cultural, 1996, p. 265).

3. 3
In O pensar complexo (The complex thinking) (Rio: Garamond, 1999), Edgar Morin
says, to overcome the limitations of classical thought in the sciences, it is appropriate to
adopt the complex thinking that seeks to work between certainty and uncertainty. In
other words, researchers must not only work within the field of their expertise, but
interact with other areas of knowledge, since human knowledge is a whole, which is
more than the mere sum of its parts. Given this need for interaction, the research must
now operate in groups, and not only individually. Have the Bachelard said in its
complex O novo espírito científico (The new scientific spirit) (São Paulo: Abril Cultural,
1978): "Behold now guide theoretical thinking: the group".
Returning to Edgar Morin, who stated that complex thinking is not intended simply to
replace the old rationalist, deterministic thinking. Complex thinking is the thought that
strives to unite, not in confusion, but operating differentiations. Therefore, complex
thinking aims to stimulate communication between hitherto separate areas. Urge finish
this segmentation. You cannot get more disqualify callers, with arguments, saying that
they are from another area or discipline, not yours. Complex thinking indicates that the
philosopher, economist, sociologist, engineer, physicist, chemist or biologist, among
other experts, must also have, to some extent, knowledge of the area of other.
* Fernando Alcoforado , member of the Bahia Academy of Education, engineer and doctor of Territorial
Planning and Regional Development from the University of Barcelona, a university professor and
consultant in strategic planning, business planning, regional planning and planning of energy systems, is
the author of Globalização (Editora Nobel, São Paulo, 1997), De Collor a FHC- O Brasil e a Nova
(Des)ordem Mundial (Editora Nobel, São Paulo, 1998), Um Projeto para o Brasil (Editora Nobel, São
Paulo, 2000), Os condicionantes do desenvolvimento do Estado da Bahia (Tese de doutorado.
Universidade de Barcelona, http://www.tesisenred.net/handle/10803/1944, 2003), Globalização e
Desenvolvimento (Editora Nobel, São Paulo, 2006), Bahia- Desenvolvimento do Século XVI ao Século XX
e Objetivos Estratégicos na Era Contemporânea (EGBA, Salvador, 2008), The Necessary Conditions of
the Economic and Social Development-The Case of the State of Bahia (VDM Verlag Dr. Muller
Aktiengesellschaft & Co. KG, Saarbrücken, Germany, 2010), Aquecimento Global e Catástrofe
Planetária (P&A Gráfica e Editora, Salvador, 2010), Amazônia Sustentável- Para o progresso do Brasil e
combate ao aquecimento global (Viena- Editora e Gráfica, Santa Cruz do Rio Pardo, São Paulo, 2011)
and Os Fatores Condicionantes do Desenvolvimento Econômico e Social (Editora CRV, Curitiba, 2012),
among others.