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Gödel, Popper and the empirical

Scientific hypotheses are "generalizations". They have the form

"For all x: x ε P".

generalizations differ from subjective-particulate single-statements you can make about again because of his personal life experience is limited, such as the country lore about the weather.
example of such a universal statement:

Adam said:

For all swans:

'this swan' ε know.

claims expressed colloquially Adam also: swans are always white feathers, and implied he says: there are no swans green, red, blue or black feathers.
How Adam say that? The philosopher Karl Raimund Popper says: Adam's allowed to, just so it can not forbid him, thoughts are free, Adam only makes use of his natural liberty. Only when someone proves to him that he is wrong in his assertion, he may, as a scientific statement say no more. In order to distinguish
science of just-so-therefore-talk, the scientist before Popper puts an additional task: he must be a method by which one can verify this claim empirically, that is, that they could prove to be incorrect.


is how such a "falsification" a general universal statement or hypothesis?


- "All swans" is, without exception, all the swans. So make Bedam, Cedam, Dedam, ... on to find a single counter-example to Adams to überpdüfen claim, thereby possibly refute. This is in our example, no lab, no statistical calculations, without complicated measuring equipment without Large Hadron Collider.

Bedam points to this:

Adam is right, the swan is white.
His claim is still legitimate.

Cedam points to this:

Adam is right, the swan is white.
(And divine, as at that)
His claim is still legitimate.

Dedam shows this:

Adam: Ooops ... I give my statement on
- IF that is really a swan!
(it might in that example to an incarnation of the devil, or who knows what else act ...)

Evidence that it is the black bird "really" a "Swan", it must run on a deeper level be. The level at which the alleged universal statement about the swans had been founded, the level of the feature was "color of the feathers." That this is not the decisive characteristic level of definitional criteria for the general concept "Swan" was delivered just demonstrated - which features one defined but this bird? At the moment of falsification breaks us off this word - now we know not what we are talking about. If we want to use the word "swan" on - and the real distinction of a species - we must find a new level of definition that allows both black and white copies. For this we have to change - on a deeper level feature. You have to know what you talking about after the falsification has the recent general term "swan" rocked.

So what is the necessary and sufficient criterion for feature "Swan", if not for the springs? This seems, in this example not to be more problematic: biologists tell us that criterion can be the mating ability of this black swan with a white swan, it may also be eg a Genvergleich. As a result, a characteristic can be determined by the general term "Swan" is set and the empirical allows the color variety of this species. This all seems plausible - but beware! We use here a Previous knowledge, this is a problem in this trivial example. Quite differently, this issue arises in unknown areas of research.

So much for the famous Popper Falsifikationstheorie.

Is this sufficient critical rationalism as a method of science?
The requirement that a "new feature level" for the valid falsification of a general universal statement must be connotes, is commonly overlooked you. The real philosophical problem is that this is the feature level, just as in Russell's set theory, like a Matryoshka pulled out of the larger. What kind of relationship to each other this feature levels? Are there causal relationships? If it Classifications relationships? Easily provides thereby a naive reductionism: the economy is based on the psychology, physiology, psychology, physiology, chemistry, chemical physics is based on ... until the brilliant idea that today's economic crisis by "theory could be derived from everything from the Big Bang ... This means that out of the situation of a successful falsification out you stumble innocently into a naive idea of order in the world, into a metaphysical ontology.

But modern science but just wanted to say goodbye to the metaphysics, right?

Later in his Life came Popper to argue with the idea that straight from alleged general generalizations are taken from a type of individual, almost metaphysical sphere, the "third world" of ideas, intellectual and cultural artifacts, today one could say, from the Google universe . There, they carry ideas selective struggle for survival, so to speak, the Google-ranking ... A question for thought is subject to the hypothesis of the Third World and the Faslsifikationstheorie? What would be the method that would be to subject this hypothesis Falsifikationsversuchen?
But it was precisely this problem of hierarchical levels of the general concepts to their solution in the first half 20th wanted to escape philosophers, logicians, mathematicians, - century was fought - and those of Popper, such as the members of the Vienna Circle. Or Popper has displaced the problems be?

The Critical rationalism - a solution that does not work - and why Gödel's fault ...
We have a situation: a claim that is not, as generally valid claim may be. It has something to do with the concept of truth - because the words "That's true," yes we can commit someone else to give us our faith and entprechennd Claim to act.

How to transform a baseless assertion that is in a true, universal claim? How do you establish truth?
This problem had been the late 19 Century and mathematics. But we had the problem not only in mathematics but in all the sciences. The old metaphysics had lost its credibility, the numbers were now no longer, as in the Pythagorean tradition, independent entities with mythical properties, but only words. What do these number words? This is crucial for the whole of mathematics, including for example whether a physicist to the calculations may rely on a nuclear power plant. The mathematician Leopold Kronecker had formulated the problem: "The whole numbers has made the Lord, everything else is the work of man." Science will, however, after their claim, not rely on the wisdom of God, which is accessed by faith. Science wants to know everything yourself.
Unlike Kronecker (who is himself an early precursor of the so-called "constructivism" in mathematics, as he then was implemented by Paul Lorenzen) were tried, as a result of the formalistic way. This means that in the context of formal systems, based solely on the formal logic should prove possible for the truth originally generated by unsubstantiated claims, the axioms. Thus, it was hoped, could be the question: "what are the natural numbers?" get around, which would result in this formal, purely logical system then. For the other sciences are called such efforts "scientific theory".

This could reach that you are not in a social context, a dialogue on "empirical" truth must be some evidence. It could be on the dialogue, ie not on the production of the dialogical symmetry and drive like the individualist discourse of power of social transitivity. (See blog "Words provide music "). If the proof of the truth of an assertion also individualistic, just by Lonely logical thinking within his own head, then you may face with full permission by the so individualistic developed possession of the truth 'rational' obligations .. others say this is a basic idea of the so-called "methodological individualism" That play these theoretical efforts, specializing in the field of mathematics, does not matter - if it succeeds in theories justified only formally, it is possible also in other areas of methodologically sound knowledge.

But the efforts of several Decades have been in vain.
Almost every new attempt to solve this problem, experienced, barely invented, his ruin.

The English philosopher, logician and mathematician Bertrand Russell destroyed with the "Russell's antinomy" the inventor of modern logic, Gottlob Frege, the Good Hope, it is the foundation of mathematics from the formal logic by a 'naive' set theory succeeded.

Russell presented the paradox that is from the village barber who shaves all who do not shave themselves. Problem: the needs of the barber shave himself not fit in this rule - ie, the village barber who shaves?.

Russell himself would solve the problem by - in order to remain in his image - hired an additional barber who shaves those in other villages that do not shave themselves, then shave all but those who do not shave themselves ... . So he designed a "type theory", a hierarchical gradation of such rules. In level 1, you talk about the origins of art, in stage 2 you talk about the stage 1 and their contents, but not on the stage 2 itself, in stage 3 tells us about the items that are level 2 and level 1 but not on the level 3 itself, etc. .. (You can see the structure of argument in social transitivity: the elite make the rules plebs, but not to themselves, see blog "Words with Music) The theories be nested as Matrjoschkas.

It remained unclear whether the extensive amount of teaching from the Russell's "Principia Mathematica" self-contained, is consistent. The question of consistency and completeness is the lifeblood of any formal logical theory. If these two conditions are not met, you could 'prove' the theory of everything Any - and prove who else can not prove anything, "quodlibet ex falsum. For what you put into it in the formal theory are so completely arbitrary, unproven axioms. So, after the detection of internal consistency and the completeness of a formal theory can be used to produce this true statements.

The mathematician David Hilbert had announced its comprehensive "Hilbert program" with which he was honored to provide the necessary evidence for Russell's "Principia Mathematica" with a meta-mathematics - but hardly the ink had dried, to be published student Kurt Gödel's "incompleteness theorem".

Gödel's Incompleteness Theorem This states that a formal axiomatic theory NEVER can with their own arguments with their own language means also prove that she herself is both fully consistent - that the two necessary conditions are met, a formal theory to theory making. One can either prove the completeness or the consistency - but not both.
It is about the question of the generality of statements. A statement is universally valid if and only if it is formally provable - that is the starting position. Generality is stated: Truth. But it is about such statements, which are first asserted arbitrarily, and then only under a system of formal conclusions as consistent with all other statements that can produce this system to be proven. The consistency of a statement with the other statements is evidence of the truth (with respect to this system), this implies the universal validity of a statement. From an incomplete system, however, all possible statements are derived again without opposition - there is then worthless because arbitrary.

So one needs, besides the proof of consistency, even the proof of the completeness of this system, you will receive the claim to universal validity of the derived statement maintained. Both evidence must be inerhalb the system, not from without, not from a different system. Because this would even be considered until, by another, and so on and so on, ad infinitum. Matryoshka system.

Godel's incompleteness theorem has one, still not fully recognized explosive power for all "axiomatic" sciences. "Axiomatic" are all theories that start with any of these "definitions", and then to derive further conclusions. Let's go to the university library through the ranks of various Browse Departments and in the textbooks, then we observe: it is made virtually everywhere, especially in the social sciences..

is this is neglected, that Godel's incompleteness theorem final and definitely destroyed all hope of ever confined to a formalist methodology of unjustified initial assertions (axioms) truths, or even empirically confirmable truths, statements about the world as they generate outside can. The "Erlanger school" has only just for a few sciences offered a solution (logic, mathematics, physics, chemistry). Unfortunately, this is

consequence of the incompleteness not in science theory and methodology incorporated - and this is the task of a truly free science from metaphysics. Instead, it mystifies you: about the world as an "Eternal Golden Braid" (see Douglas R. Hofstadter: Gödel, Escher, Bach)) Such self-referential loops are aesthetically beautiful - "we Fahrner Fahrner. fahrn on the highway, then we turn on the radio, from the speaker it sounds: we Fahrner, fahrn fahrn on the highway "but hardly suitable for an argumentative reason.

This hard blow Godel against the "logical positivism" was the starting point, from which designed Popper his Falsifikationstheorie . His idea: If you have to say can not prove the truth of an assertion, then one may, out of sheer plausibility, resourcefulness and life experience, what you will, to the falsity of this assertion.

Earlier, Popper argued in a famous controversy with the philosopher and logician Rudolf Carnap. Carnap had to present Gödel's incompleteness theorem by also shipwrecked with his attempt, the (formal) logical structure of the world. " Incidentally, Wittgenstein on Godel's sentence affected his philosophy changed and complete - nothing but only a few years and thought thoroughly.

Carnap tried it now again with "physicalism". The basic idea is that physicalism by log records as closely as possible to take an observation of the real, physical things (who, when, how long has etc. "out there" was closely monitored). For these - in order provability and accountability well documented - Individual observations should be formed by "induction" general statements and general concepts, so to speak, the raw material of Sciences. This one takes a series of individual statements: This swan here is white, and that there is white swan, and the swan over there is white, AND ... AND ... It combines many individual statements with AND - and generalized. How many individual statements? Well, perhaps until as when asleep counting sheep. From the AND-connection of many individual statements then create the logical quantifier "ALL". Is it just because you "ALL" introduces the sentence, speaking of a general universal statement? (This occurred Popper, when he logged the data on the individuals in the "log records" and then emphasized "basic principles" language.)

fact is this induction, generalization, only at a finite, countable number of individuals, such as: "applies to all swans on our village pond:
'this swan' ε white"

The quantifier ALL can be replaced by a concrete number, eg "seven". Because the amount of animals we are talking about, is countable, we can always go back to the situation in which we eigeführt the predictor "Swan", taught or learned. "At that time I told you, this is a swan, therefore, look closely, it is true , which is a swan!"

We are looking for but after the way a general term for a potentially infinite set of individuals to establish, for an "unlimited communication community". We also want tomorrow, tomorrow, or on vacation in a distant country can, while watching a large water bird tell our child: "Look, this is a swan." And this claim should be able to claim to be true .

It is therefore an opportunity to make true statements - as in everyday life, so in science.

As long as the Godel's incompleteness theorem is not the necessary consequence will be considered if Thus the axiomatic-formalist methodology of science will be kept (as in economics), then you have to do without the generally scientifically substantiated claim to truth. this happening for example in systems theory and 'radical constructivism' - instead of "truth" one prefers to speak of feasibility, "viability". . The truth is the invention of a liar "for example, H. von Foerster titled his book for social theory, this means that the Widerspruchssfreiheit sufficient for the feasibility, if one is assertive and on the" completeness ", ie to take into account interests of ALL can give members of a social system. So the question of truth is stripped back to the question whether a self-appointed elite can impose their particular interests against the rest of society.

it any wonder when the economic policy in accordance with the political feasibility and feasibility of the power to the wealthy districts determined?

public in thinking and reasoning also means thinking and reasoning to the public.
science is not without ethics, which is already implemented in the concepts of science, a methodologically immanent ethics of science Generalization of the self.