CZ:Cold Storage/Plausible science
Introduction
During more than 25 centuries western thinking was dominated by the dualistic paradigm described by Aristotle's syllogism. A statement is true or false, exclusively one of both, and all of intellectual activity consists of evaluating, arguing or refuting the statement. This approach got a boost during Renaissance, where "cartesian" deductive logical and mathematical thinking was considered as the absolute requisite for any kind of scientific, "experimental", reliable thinking.
Apart from its contributions to deductive thinking, this approach is misleading in at least three of its explicitly or implicitly suggested conclusions:
(1) there is no category between true and false; (2) science and technology are making progress thanks to logical deductions and experimental procedures; (3) "sciences" which so far are unable to apply the exact, experimental procedure can't be rated as scientifically reliable, and remain in the realm of mythical, obscure, fictitious and unreliable thinking.
During the second part of the 20th century, after the umpteenth deception about the blessings of scientific progress, tentatives towards a more holistic, non-aristotelic approach of reality were launched. This trend is masterly pictured by authors as Fritjof Capra. Many approaches, from postmodernism to New Age, recommend a less dualistic, mutually-exclusive way of thinking. But up to now a central paradigm was not clearly defined. In this essay, integration is proposed as such a paradigm.
Definition
As defined elsewhere, integration can be defined as [1,2]
a process of combination of elements that, at first approach, seem to be incompatible or even conflictuous, but, after a bit of analysis and re-synthesis (leading to reformulation or re-orientation), prove to be rather complementary.
Symbolically this process could be represented by:
(A,B) Æ [A>>A'] & [B>>B'] Æ {A'B'}
where A en B are elements in their primary, "unintegrable" state, that are "retroduced" to their "essential core" [AÆA'] & [BÆB'], what makes them "integrable", and then combined into a new unity {A'B'}. Æ here means "to provoke a certain fact or transformation". and >>here means "to transform into". We use the three kinds of brackets in a different sense: (collection of elements), [process], {integration}.
We would like to introduce the function of Y (Psi) meaning "to be reduced to its essential core", so that:
Y(A) = A'
and v as the inverse function, the "eduction"
A = v(A')
so that A is an eduction of A', meaning that we can come from A' to A by making A' less general.
Likewise we propose to introduce the fundamental function W (Omega) to describe the integrative process in short:
W (A,B)= {A'B'}
To make the indication "a more integrative version" more precise than A' relative to A (A' meaning just "vaguely related to") we propose to introduce the index # meaning "more integrative".
Symbolically, the above statements can be written as
(A,B) Æ [A>>A#]& [B>>B#]Æ {A#B#}
Y(A) = A#
A = v (A#)
W (A,B) = {A#B#}
Assumptions
The paradigm of integration is based upon some assumptions, postulates, some of them conflictuous with the fundamental logical postulates.
1. The probability that a theory is completely true/false, is practically nill
The probability that a theory, an insight, a concept, a hypothesis, an idea, etc. is completed, completely exact and true, is practically inexistent. Each idea, etc. will probably be improved some day. So between "true" and "false" a third category has to be intercalated, being defined as "theories that are far more better than previous theories, but not as perfect as the final theory".
The classical, dualistic, aristotelian-cartesian categories:
In the integrative approach we discern three categories:
In practice, we could probably put all existing theories, concepts, etc., in the middle category, making both classical logical extreme categories obsolete, i.e. only existing as a theoretical concept, unless we're working with extremely simple data, e.g. natural numbers and other conventional concepts.
Inspired by the diagram, we could, perhaps, represent the presence of the plausibility factor, in discursive intellection, as forming an important part of a sort of continuum as follows:
"FPPPPPPPPPPPPPPPPPPT",
here "F" stands for "false", "P" stands for "more or less plausible" and "T" stands for "true".
The more an outlook is implausible, the closer it stands to the "F" or "false" end of the continuum, and the more an outlook is plausible, the closer it is the "T" or "true" end of the continuum. [Brian Cowan]
As the "plausibility" category is very extended, it seems useful to introduce a measure of plausibility (P). This measure can only be used in a relative sense, i.e. by comparing two or more theories.
Example. If we define TE as the Theories of Einstein, and TN as the Theories of Newton, we can state that:
P(TE) > P (TN)
Or: Y(TN) = TE
TN = v (TE)
As explained in the General Systems Theory, and Logics, knowledge of any rather complex system presents a progressive development: as with a spiral, each new experience or intellectual confrontation may lead to a more comprehensive conceptualization.
E1(A) Æ a1
a1 + E2(A) Æ a2
a2 + E3(A) Æ a3
generally described as
an-1 + En(A) Æ an
A is a phenomenon, a part of reality to be conceptualized. E is an experience and/or an intellectual communication. E(A) is an experience with phenomenon A , and E1(A), E2(A)... are consecutive experiences. a1, a2, ..., anare consecutive visions, hypotheses about phenomenon A , becoming progressively more integrative. A cyclic scheme could also represent this procedure:
This means that at each given moment, each concept may become more complete, more realistic, more comprehensive, more integrative.
The historically most significant example is the theory of Newton, improved by Einstein. This example is particularly striking because during centuries the theories of Newton were quoted as the illustration par excellence of scientific, aristotelic-cartesian thinking. Let's take Newton's Law of the Addition of Speeds:
Einstein proposed an elaborated formula:
This means that at relatively slow speeds (v << c), the denominator practically equals 1, so we find back Newton's formula. But at high speeds the denominator increases, making the total speed significantly lower than what Newton predicted, and limiting even the maximal speed at the speed of light, c. Newton's formula appears to be a reduction a simplification of Einstein's elaborated formula, but at "normal" speeds on earth it was impossible to discover the inaccuracy of Newton's "simple" formula.
2. The 'complements' operator - the non-existence of contradictions
As there exists more than one category of exactness, the opposition and mutual exclusion of two statements (about the same phenomenon) that are not similar or reduceable to each other, disappear. Besides the fundamental categories equals (=) and is unequal (<>) we should like to introduce a third, much more useful operator: complements (¿)
Where in the traditional approach statements as
psychoanalysis <> behaviourTheory science <> religion theoryOfNewton <> unexplainableEvidence
seem very justified, in an integrative approach they are... false, because:
psychoanalysis ¿ behaviourTheory science ¿ religion theoryOfNewton ¿ unexplainableEvidence
Hence:
W (psychoanalysis, behaviourTheory, ...) = integrativePsychology W (science, religion, ... ) = hyperphysics W (theoryOfNewton, unexplainableEvidence ) = theoryOfEinstein
("Hyperphysics" being the name that Teilhard and Wildiers used as the scientific label for their evolutionary, cosmic and integrative approach).
This second postulate can be formulated another way: the probability that in two statements, which seem mutually exclusive of paradoxical, one is true and the other is false, is much lower than the probibility that both pseudo-conflicting statements are complementary, i.e. true in certain circumstances. Practically speaking: all so called contradictions are most probably complements.
3. An integrative theory is more plausible than its non-integrative elements
The degree of plausibility increases with integration, at least if no logical errors are made. This can be explained by the fact that the plausibility of the integrative view is at least as high of the plausibility of the most plausible of its complementary elements.
So we can state that
P(A#) > P(A)
and, more in detail, if:
W (A1, A2 , A3 , ...) = A# then: P(A#) > P(A1) P(A#) > P(A2) P(A#) > P(A3) ...
This has a very important consequence: to achieve the highest possible plausibility, one has to integrate. Or, otherwise stated, the Plausibility is the highest with theories that take into account the greatest number of phenomena, the greatest number of arguments.
Graphically represented:
A "proof" based upon the integration paradigm can be made by arguing, mathematically or logically, that the former, non-integrative theories can be reached by an eduction (v) of the integrative theory.
If
W (A1, A2 , A3 , ...) = A#
then the maximal plausibility for A# (replacing the obsolete concepts true and exact) is reached when
A1 = v (A#) A2 = v (A#) A3 = v (A#)
i.e. if we can (d)educe each elementary theory from the integrative, by restricting the conditions of applicability or observation. This is a proof, in the scientific meaning of the word, that the integrative theory is (more) true (preferably: plausible) than the non-integrative ones.
This edutive operation can easily be done with Einstein's theory about the addition of velocity, that mathematically can reduced to Newton's formula by putting v as extremely low, so that the denominator practically equals 1, and can be removed in the formula.
Implications. This third assumption has many important implications for science in general, especially for these sciences that are seemingly (still) inaccessible for the exact-scientific method. These consequences apply as well to the curriculum of the studies, as to the structure of scientific papers. In another article we will extend on that topic.