Conventionalism

The conventionalism (latin conventio: " Convention " ) is in philosophy a direction that emanates from the thesis that scientific findings are not based on conformity with the nature of reality, but on conventions.

" The conventionalist conceived laws of nature are falsifiable by any observation, because only they determine what is an observation, which is particularly a scientific measurement. " (Karl Popper, Logic of Scientific Discovery )

Conventionalism in the philosophy of science assumes that observational facts can be brought by any structures in a rational order. A specific theory can always be brought into agreement with the observations; consequently can not give facts reviewing body for the validity of theories. If necessary, obtain the conventionalist the desired compliance by means of introducing ad hoc hypotheses.

The conventionalism in the philosophy of language asserts, logical and linguistic rules are only convention.

Philosophical currents that are attributable to the mathematical formalism, also have conventionalist tendencies.

Generally

As the founder of conventionalism is true of the French mathematician and physicist Henri Poincaré. In his book Science and Hypothesis, he described a thought experiment to demonstrate the " vagueness " of the true geometry of space.

He imagines a two-dimensional Discworld ( Flatland ), to which all things on the basis of a universal force alike begin to shrink from the center at a distance, and are therefore smaller the farther away they are from the center. The inhabitants of this world ( Flatlander ) thus take on a different geometry of space, as can be observed for outsiders. This leads to two possible assumptions geometry: the Euclidean and Bolyai - Lobachevsky geometry. Emphasizes Conventionalism that needs to be made ​​a decision for one of the theories and adopted as a convention, although both theories are equivalent.

In terms of Euclidean geometry, this means that, for example, do not change the standards of objects to each other and the light beams propagate in a straight line, although other models are conceivable and do not contradict the observations; You would only do not meet our conventions and modes of thought.

Flatland

Be Flatland a two-dimensional disk with fixed radius R ( thus this constructed world has a finite extension ). Furthermore, it should exist a universal force that causes all objects begin to decline on this disc with increasing distance from the center M. This shrinking process follows the following case law: An object with the ' true ' length l in the center is at a distance r from M is the length. This law applies to all, regardless of material, shape, etc.. Thus the force causing the Flatlander is not perceptible or detectable, as they possible and measurement devices (eg, a string, or a measuring wheel) shrink alike.

Determination of the radius

If the Flatlander now wanted to try to determine the radius by using a cord that in M has length l, they would thereby establish the following: On the one hand, this line would be at the edge of the disc have the length, on the other hand they could never the reach the edge, since the sum of any finite number of measuring steps would always be smaller than R. Thus they came to the for her 'right' conclusion that their world has an infinite expansion.

Determining the geometry

To determine the geometry of space, there is an easy way: Determine the ratio of the measured circumference to diameter of a circle measured. When this ratio is the same, it is Euclidean geometry, if it is greater than to BL geometry.

The Flatlander now measure a circle c whose center should lie in M, and whose real diameter D is chosen so that the size of an object ( in this case, the measuring line ) corresponds to this circle constant exactly half that it has in M. The scope of c, they would get is thus exactly twice as large as the real extent C. When measuring the diameter, the length of the measuring line corresponds only exactly on the circle, ie at the beginning and end of the measurement, exactly half. In the region between them is always greater than half. Thus, the measured diameter d is less than twice as large as the actual diameter D. It follows now for the ratio of c to d that the flatlander would come to the result of and would conclude, consequently, that their world a Bolyai Lobachevsky geometry is based. This finding contradicts the fact that there is indeed a disc in the Euclidean plane with their world.

The aim of the thought experiment

With this thought experiment Poincaré wanted to show that only the combination of geometry and physics can predict observations. This follows from the assumption that a geometry as such can make no prediction about the world. Now Fits the result of an attempt not to the corresponding forecast, so therefore either geometry or physics must be modified so that an agreement can be reached. If the geometry of a room has been set by convention, so must the physics (ie, the experiment or the measurement method) to be changed. Now can the people of this Discworld do not realize that all things shrink when they move away from the center, so its measurement method is wrong, but not the geometry itself. The Flatlander could for example the Pythagorean theorem simply by refuting that he must carry out to measure the length of the sides of a triangle in different places. But then is not the Pythagorean theorem wrong, but it must act an external force that affects the length measurement. This must be universal, that is, that they, no matter how they are arranged all things and what properties they have influenced in the same way. So it is not detectable for the inhabitants of this world. It can be seen that the physics can be changed ( by the introduction of a universal force), the geometry is not. And thus we interpret our observations always so that they match the geometry. Poincaré is firmly convinced that the true geometry of a space can not be detected by an experiment, but that it only shows which best suits the circumstances.

Different perspectives

There are two equal possibilities to explain the geometrical relationships in this world:

It follows that any geometry can be considered valid only if the assumptions ( here: objects shrink or not shrink ) can be selected accordingly. We ourselves are in the same position as the Discworld inhabitants. Also, we can not say by what geometry to our room where we live can really describe. We can only say that Euclidean geometry fits to our observations. However, it is pure convention that this geometry is valid.

General interpretation

In general it can thus be stated that the experiments and related observations allow two interpretations:

This raises the question of whether the search for the true geometry is an epistemological or ontological problem. So there is a real geometry that we just can not see, but with the can explain all observations, or is there ultimately perhaps no real facts on the basis of a true geometry can be found?

Example of interpretation

Assuming one occupational pen the angle sum of a triangle with optical means and would see that they would not follow 180 °. Now there are two possible interpretations:

From these two interpretations is therefore clear that we can not say at what is right. Both interpretations do not contradict the observations. But it now expects that physics is variable and the simplest geometry (in this case, the Euclidean ) is assumed, one would opt for the first possible interpretation.

Another Example

Using its interpretation of the theory of relativity, which was co-developed Poincaré, his conventionalism can illustrate perhaps especially provocative: Shorten the case of very fast movements only the rulers or the geometry? " Flows " a deflected by the gravitational field of the sun beam through the curved space or space will remain the "straight"? Poincaré 's response: It's convention! The relativistic curvature is in fact just as curvature of the light beam geodesic - about the fact that it is deflected by a gravitational field - and not necessarily apprehended as curvature of a geometric line. The " metrics " of the field equations are therefore not necessarily geometric metrics (see notes for discussion protophysics vs. Relativity theory in physics proto ). In this respect, the question remains whether the real geometry is Euclidean or non-Euclidean, open to the conventionalist Poincaré.

The conventionalist critique of Karl Popper

For Karl Popper conventionalism is logically and practically always feasible as a scientific theory. For the traditionalist, in the case of a " crisis of science" always the observations by changing the measurement methods reinterpreted.

This does not correspond to the methodology of empirical science, as Popper has proposed in the Logic of Scientific Discovery. Then to experience new science experience or overturn of observational hypotheses, systematically carry this into account, that for such refutations should always be sought and asked for consequences for each theory involved in the failure of an experiment. Redefining theoretical terms or the rescue of observations by auxiliary hypotheses therefore rejects Popper from a conventionalist twist or immunization strategy.

Just conventionalism provided, however, Popper against the logical positivism ( Vienna Circle ) the justification that its own methodology of the empirical sciences is necessary. Because the definition of conventionalism can not logically cognition, but only by methodological decisions (namely, how to have re jump in the case of conflicting observational results with the theory ).

Stegmüller has presented an attempt to interpret the theory change after Thomas S. Kuhn historically, by means of set-theoretic structures. He is critical of Popper's methodology, they summarize scientific statements of law as universal and existential sentences, and ignores the fact that about the physics formulate their claims in mathematical structures. According to the structuralist point of view of physical theories, as Stegmüller proposing is no longer sensible to say that parts of a core theory could be refuted by empirical observations. For example: No one has ever given, as empirical data would have to be designed to falsify Newton's second law.

The controversy thus basically boils down to the following questions to: 1 the extent to which the separation of synthetic and analytic statements is always strictly feasible, and second that theories can only be tested as a whole always being in an empirical failure had never known, to which part of the theory, or test the fault lies ( Duhem - Quine thesis ).