# Conventionalism

The conventionalism ( Latin . Conventio "Convention") is within the philosophy of a direction from the theory goes that scientific knowledge and laws (moral laws) not in accordance with the nature of reality, but on conventions based.

Conventionalism as a current in the philosophy of science assumes that observational facts can be brought into a rational order by any alternative constructions. Even contradicting theories can always be brought into agreement with the observations; consequently, facts cannot provide an authority to test the validity of theories. If necessary, the conventionalist will achieve the desired agreement by introducing ad hoc hypotheses .

"The conventionalistically conceived laws of nature cannot be falsified by any observation, because only they determine what an observation, in particular what is a scientific measurement."

## Justification of conventionalism

The French mathematician and physicist Henri Poincaré is considered the founder of conventionalism . In his book La science et l'hypothèse he described a mental experiment to demonstrate the “indeterminacy” of the geometry of space.

He imagines a two-dimensional disc world on which all things begin to shrink equally at a distance from the center due to a universal force, i.e. are smaller the further they are from the center. The inhabitants of this world take on a different geometry of the room than can be observed by outsiders. This leads to two possible geometrical assumptions: those of the Euclidean and the Bolyai-Lobachevsky geometry . Conventionalism emphasizes that a decision in favor of one of the theories must be made and accepted as a convention, even though both theories are equivalent and even contradict each other. One theory is not more correct than the other, it is just more convenient ( plus commode ).

In relation to Euclidean geometry, this means that, for example, the scales of objects do not change and light rays propagate in a straight line, although other models are conceivable and do not contradict observations; They would simply not conform to our conventions and thought models. Synthetic geometric knowledge a priori in the sense of Kant is therefore not possible. With regard to arithmetic and logic, however, Poincaré is of the opinion that their statements are a priori and necessary, which is disputed by more radical conventionalists such as Rudolf Carnap . Even more radical positions were represented by Édouard Le Roy , for whom what we call reality is constituted by definitions that give names to the phenomena in an “ocean of images”, and Percy Williams Bridgman and Hugo Dingler with their theory of operationalism , according to which the meaning of a term are nothing more than a sequence of measurement operations that describe it.

## Poincaré's geometry of the discworld

Let Flatland be a two-dimensional disk with the fixed radius (thus this constructed world has a finite extent). Furthermore, there should be a universal force that causes all objects on this disk to begin to shrink with increasing distance from the center . This shrinking process follows the following law: An object with the 'true' length in the center has the length at a distance of . This principle applies to everything, regardless of material, shape, etc. Thus, the causative force for the Flatlander cannot be experienced or proven, since it and possible measuring devices (e.g. a cord or a measuring wheel) both shrink. ${\ displaystyle R}$${\ displaystyle M}$${\ displaystyle l}$${\ displaystyle r}$${\ displaystyle M}$${\ displaystyle l '= l \ cdot {\ tfrac {R ^ {2} -r ^ {2}} {R ^ {2}}}}$

If the Flatlanders wanted to try to determine the radius by using a string that was long , they would find the following: On the one hand, this string would have the length at the edge ( ) of the disc , on the other hand, they could never be Reach edge because the sum of any finite number of measurement steps - as the sum of the shrunk lengths - would always be less than . Thus they would come to the 'right' conclusion for them that their world is infinite. ${\ displaystyle M}$${\ displaystyle l}$${\ displaystyle r = R}$${\ displaystyle l '= l \ cdot {\ tfrac {R ^ {2} -r ^ {2}} {R ^ {2}}} = 0}$${\ displaystyle R}$

### Determination of the geometry

There is a simple possibility to determine the geometry of the room: You determine the ratio of the measured circumference to the measured diameter of a circle. If this ratio is equal , then it is Euclidean geometry, if it is greater than , it is BL geometry. ${\ displaystyle \ pi}$${\ displaystyle \ pi}$

The Flatlanders now measure a circle whose center should be in, and whose real diameter is chosen so that the size of an object (in this case the measuring line) on this circular line is exactly half that it has in. The girth they would get is exactly twice the real girth . When measuring the diameter, however, the length of the measuring cord only corresponds exactly to the circular line, i.e. at the beginning and at the end of the measurement, exactly half. In the area in between it is always greater than half. Thus, the measured diameter is less than twice as large as the real diameter . From this it follows for the relation of to that the Flatlanders would have arrived at the result of and would consequently conclude that their world is based on a Bolyai-Lobachevsky geometry. This result contradicts the fact that your world is actually a disk in the Euclidean plane. ${\ displaystyle k}$${\ displaystyle M}$${\ displaystyle D}$${\ displaystyle M}$${\ displaystyle c}$${\ displaystyle C}$${\ displaystyle d}$${\ displaystyle D}$${\ displaystyle c}$${\ displaystyle d}$${\ displaystyle {\ frac {c} {d}}> \ pi}$

### Goal of the thought experiment

With this thought experiment, Poincaré wanted to show that only a combination of geometry and physics can predict observations. This follows from the assumption that geometry as such cannot predict the world. If the result of an experiment does not match the associated prediction, either the geometry or the physics must be changed so that a match can be achieved. If the geometry of a room has been determined by convention, the physics (i.e. the experiment or the measurement method) must be changed. If the inhabitant of this Discworld cannot recognize that all things shrink as soon as they move away from the center, then his measuring method is wrong, but not the geometry itself. The Flatlander could e.g. B. refute the Pythagorean theorem simply by having to measure the lengths of the sides of a triangle at different locations. But then the Pythagorean theorem is not wrong, but an external force must act that influences the length measurement. This must be universal, which means that it influences all things in the same way, regardless of how they are made and what properties they have. So it is undetectable for the inhabitants of this world. This shows that physics can be changed (by introducing a universal force), but geometry cannot. And so we always interpret our observations in such a way that they agree with the geometry. Poincaré firmly believes that an experiment cannot reveal the true geometry of a room, but only shows which one best suits the given circumstances.

### Different perspectives

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

1. Euclidean geometry applies, objects shrink
2. The Bolyai-Lobachevsky geometry applies, the objects have constant lengths

From this it follows that every geometry can be regarded as valid if only the assumptions (here: objects shrink or do not shrink) are selected accordingly. We ourselves are in the same position as the Discworld dwellers. We also cannot say by which geometry our space in which we live can really be described. We can only say that Euclidean geometry fits our observations. However, it is by convention that this geometry applies.

### General interpretation

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

1. Realistic interpretation: The geometry of a room is determined, but we cannot recognize it, because there are always some universal and therefore undetectable forces that can make the geometry of the room be different from how we perceive it
2. Anti-realistic interpretation: the geometry of a room is indefinite. That is, there is no such thing as an objective geometry that is true. All geometries are therefore equally true.

So the question arises whether the search for true geometry is an epistemological or an ontological problem. So does a true geometry exist that we just cannot recognize, but with which all observations can be explained, or are there ultimately no real facts at all on the basis of which a true geometry can be found?

### Example for interpretation

Suppose you measured the sum of the angles of a triangle by optical means and observed that it did not result in 180 °. Now there are two possible interpretations:

1. Realistic interpretation: keep the Euclidean geometry and make the assumption that the rays of light do not propagate in a straight line
2. Anti-realistic interpretation: keep the assumption that rays of light propagate in a straight line and reject Euclidean geometry.

It follows from these two possible interpretations that we cannot actually say what is correct. Both interpretations do not contradict the observations. But if one now assumes that physics can be changed and the simplest geometry (in this case the Euclidean) is assumed, one would opt for the first possible interpretation.

### Another example

Using the example of his interpretation of the theory of relativity , which Poincaré helped to develop, his conventionalism can perhaps be illustrated in a particularly provocative way: When moving very quickly, do only the rulers shorten or also the geometry? Does a light beam deflected by the gravitational field of the sun “flow” through the curved space or does the space remain “straight”? Poincaré answers: It is convention! The relativistic curvature can only be understood as the curvature of the light beam geodesics - for example because it is deflected by a gravitational field - and not necessarily as the curvature of a geometric straight line. The “metrics” of the field equations are therefore not necessarily geometric metrics (see notes on the discussion of protophysics vs. relativity theory in protophysics ). In this respect, the question of whether the real geometry is Euclidean or non-Euclidean remains open to the conventionalist Poincaré .

## Karl Popper's criticism of conventionalism

For Karl Popper , conventionalism as a philosophy of science is logically and practically always feasible. In the event of a “scientific crisis”, the conventionalist can always reinterpret the observations by changing the measurement method.

However, this does not correspond to the methodology of empirical science as suggested by Popper in the logic of research . According to this, empirical science of new experience or the refutation of observation hypotheses should systematically take into account the fact that such refutations should always be sought and, if an experiment fails, the consequences for the theory involved should also be asked. The redefinition of theoretical terms or the rescue of observations through auxiliary hypotheses therefore rejects Popper as a conventionalistic turn or immunization strategy .

Conventionalism in particular provided Popper with the reasoning behind logical positivism ( Vienna Circle ) that a separate methodology of the empirical sciences was necessary. The demarcation from conventionalism cannot be made epistemologically, but only through methodological decisions (namely about how to deal with the theory in the event of contradicting observational results).

Wolfgang Stegmüller has presented an attempt to historically interpret the change in theories following Thomas S. Kuhn , using set-theoretical structures. In doing so, he criticizes Popper's methodology, it understands scientific statements of law as universal and existential propositions and thus misunderstand that physics, for example, formulate its claims in mathematical structures. According to the structuralist view of physical theories, as proposed by Stegmüller, it no longer makes sense to say that parts of a theory core could be refuted by empirical observations. For example: Nobody has ever stated how empirical data would have to be in order to falsify Newton's second law.

The controversy basically boils down to the following questions: 1. To what extent the separation of synthetic and analytical statements is always strictly feasible, and 2. Whether theories can only be tested as a whole - whereby in the case of an empirical failure it is never known which part of the theory or the test conditions the error lies ( Duhem-Quine thesis ).

## Use of the term in other sciences

Conventionalism in the philosophy of language claims that logical and linguistic rules are only semantic conventions. This view was directed against the thesis that words as images have a natural relationship to the object presented. Ferdinand de Saussure developed conventionalism further in modern linguistics .

Philosophical currents that can be assigned to the mathematical formalism also show conventionalistic tendencies.

Conventionalism in ethics refers to a theory that assumes that moral principles and judgments are not based on the nature of things or human nature, but rather on social conventions and habits (e.g. John Niemeyer Findlay ).

Social constructivism is a more modern variant of conventionalism .

## literature

• Henri Poincaré: Science et méthode. Flammarion, Paris 1908 ( Bibliothèque de philosophie scientifique ).
• Henri Poincaré: Dernières pensées. Flammarion, Paris 1913 ( Bibliothèque de philosophie scientifique ).
• Clark Glymour: Thinking Things Through. An Introduction to Philosophical Issues and Achievements. MIT Press, Cambridge MA et al. 1992, ISBN 0-262-07141-X ( A Bradford book ).
• Wesley C. Salmon : Space, Time and Motion. A Philosophical Introduction. Second edition, revised. University of Minnesota Press, Minneapolis MN 1980, ISBN 0-8166-1044-5 .
• Nick Huggett (Ed.): Space from Zeno to Einstein. Classic Readings with a Contemporary Commentary. MIT Press, Cambridge MA et al. 1999, ISBN 0-262-08271-3 ( A Bradford book ).
• Karl R. Popper : The two basic problems of epistemology. Edited by Troels Eggers Hansen on the basis of Mss. From the years 1930–1933. 2nd improved edition. Mohr, Tübingen 1994, ISBN 3-16-145774-9 ( The Unit of Social Sciences 18).

## Individual evidence

1. Victor Kraft : The Problem of Induction. Journal of general philosophy of science. 1, 1970, pp. 80f.
2. ^ Karl R. Popper: Logic of Research. 8th edition. JCB Mohr (Paul Siebeck), Tübingen 1984, p. 48.
3. ^ Henri Poincaré: Science and Hypothesis. Leipzig: Teubner 1904, p. 51.
4. Édouard Le Roy: Science et philosophy. 1899.
5. Formulated somewhat more drastically: "One decided to hold on to certain ideas, come what may, and the result was of course the survival of these ideas." ( Paul Feyerabend : Wider den Methodenzwang. Sketch of an anarchist epistemology. Frankfurt 1976, p. 64 )
6. Wolfgang Stegmüller: A combined analysis of the theory dynamics. in: Gerard Radnitzky, Gunnar Andersson: Requirements and limits of science. Tübingen 1981, p. 277 ff.
7. Wolfgang Stegmüller: A combined analysis of the theory dynamics. in: Gerard Radnitzky, Gunnar Andersson: Requirements and limits of science. Tübingen 1981, p. 299