Commensurability (philosophy of science)
Encyclopedia
Commensurability is a concept in the philosophy of science
. Scientific theories are described as commensurable if one can compare them to determine which is more accurate; if theories are incommensurable, there is no way in which one can compare them to each other in order to determine which is more accurate.
and Paul Feyerabend
both independently introduced the idea of incommensurability to the philosophy of science. In both cases the concept
came from mathematics
and in its original sense is defined as the absence of a common unit of measurement that would allow a direct and exact measurement of two variable
s, such as the prediction of the diagonal
of a square
from the relationship of its sides.
The central idea of this mathematical concept is not the impossibility of comparison but the absence of a common factor that can be expressed. Take the example of the diagonal of a square and the relationship with its sides. The ratio of the diagonal d of a square and its side l is immeasurable (it is irrational).
It is possible to demonstrate that d/l is not rational
by considering the opposite, in other words by looking for proof by contradiction. If a logical contradiction
is reached then the opposite is not true and incommensurability is demonstrated. In terms of logic
: if we want to demonstrate the proposition J, we assume that "not J" is true. Through logical deductions from "not J" we arrive at a contradiction. Then it can be concluded that "not J" is not true and therefore "J" must be true. This method is called reductio ad absurdum
.
proposed by followers of the received view of theories
. These include the famous thesis on the accumulation of scientific knowledge, which states that the body of scientific knowledge has been increasing with the passage of time. Both Kuhn and Feyerabend reject this thesis.
Another equally important thesis proposes the existence of a neutral language
of comparison which can be used to formulate the empirical
consequences of two competing theories. This would allow one to choose the theory with the greatest empirically verified contents - or the greatest content that is not falsified if the formulation is Popper
ian.
The idea at the root of this second thesis does not just relate to the existence of said language but also implies at least two further postulates. Firstly, this choice between theories presupposes that they can be intertranslated, for example between Theory T and its successor T’ – and in the case of Popper that T’ can be deduced from T. Secondly, it is assumed that the choice is always carried out under the same standards of rationality
.
In both cases the concept of incommensurability makes the viability of the thesis impossible. In the first, by showing that certain empirical consequences are lost between successive theories. In the second case, by confirming that it is possible to make a rational choice between theories even when they can not be translated into a neutral language. However, although the reasons for the introduction of these counter arguments, and the criticism from which they arise, are the same, the sense in which the coauthors use them are in no way identical. For this reason the idea of incommensurability will be discussed for each coauthor separately.
which has the underlying idea that the change in significance in the basic terms of a theory changes the totality of the terms of the new theory, so that there are no empirically common meanings between T and T’
Feyerabend is credited with coining the modern philosophical sense of "incommensurability," which lays the foundation for much of his philosophy of science. He first presented his notion of incommensurability in 1952 to Karl Popper
's LSE
seminar. Feyerabend argued that frameworks of thought, and thus scientific paradigms, can be incommensurable for three reasons. Included in the group was Elizabeth Anscombe, Peter Geach
, H.L.A. Hart and Georg Henrik von Wright
. Briefly put, Feyerabend's notion of incommensurability is as follows:
According to Feyerabend, the idea of incommensurability cannot be captured in formal logic, because it is a phenomenon outside of logic's domain.
then resolves problems by inventing theories that should be relevant and falsifiable, at least to a greater degree than any other alternative solution. Once an alternative theory is presented the critical phase commences regarding T’ which must answer the following questions: (a) why has theory T been successful up until now and (b) why has it failed. If the new theory T’ answers both questions then T is discarded.
That is, a new theory T’, in order to be an adequate successor to the refuted theory T, must have a collection of additional predictions regarding T (Class A), as well as a collection of successful predictions that coincide to a certain degree with the old theory (Class S). These Class S predictions constitute those parts of the new theory containing new truths and they therefore exclude a series of consequences of T, the failures in the old theory, which are part of the untrue (false) contents of the new theory (Class F).
Given this model
it is possible to construct relational statements between certain terms from T and from T’, which will be the basis for the comparison between the theories. This will allow a choice between the two in the light of their empirical contents. But, if we come across a theory T’ in which Class S is empty then the theories are incommensurable with each other.
However, Feyerabend clarifies this by stating that, incommensurability between T and T’ will depend of the interpretation given to the theories. If this is instrumental, every theory that refers to the same language of observation
will be commensurable. In the same way, if a realist
perspective is sought then it will favour a unified position which employs the most highly abstracted terms of whatever theory is being considered in order to describe both theories, giving a significance to the observational statements as a function of these terms, or, at least to replace the habitual use they are given.
It can be noted that the instrumentalist interpretation recognizes the existence of certain statements whose truth is not only dependent on the observational statements but also on the evaluation criteria they are subjected to, which are anchored in the theories. For example, to afirm the relational character of longitude
, this asseveration can not be decided solely using observational terms. Its truth value, in part, depends on the theory that establishes the sense in which the terms are used. In this case they relate to quantum mechanics
(QM) as opposed to classical mechanics
(CM). In this sense, the instrumentalist position only deals with the empirical consequences and leaves to one side the relationship that the concepts have with each other.
In this same way Feyerabend comments that:
elaborated by Carnap and comments that the use of such abstract concepts leads to an impossible position, as «...theoretical terms receive their interpretation by being connected with an observational language and those terms are empty without that connection.» (Feyerabend, pp. 373). As before it follows that they can not be used to confer significance to the observational language as this observational language is its only source of significance, with which it is not possible to make a translation but only a restatement of the term.
Therefore Feyerabend considers that both the instrumentalist and the realist interpretations are flawed, as they try to defend the idea that incommensurability is a legitimately unsolvable idea with which to revoke the theses of the accumulation of knowledge and panrationalism
in science.
This leads to the following consideration: if each new theory has its own observational basis, within the meaning of the theoretical framework, how can we hope that the observations that are produced could eventually refute it. Further more, how can we actually recognize that the new position explains what it is supposed to explain or if it is deviating off into other areas and therefore how can the theories be definitively compared.
Feyerabend's answer to the first consideration lies in noting that the initial terms of a theory depend on the postulates of the theory and their associated grammatical rules, in addition, the predictions derived from the theory also depend on the underlying conditions of the system. Feyerabend doesn't explore the point further, but it can be assumed that if the prediction does not agree with the observation and if we have a high degree of confidence in the description that we have made from the initial conditions
than we can be sure that the error must be present in our theory and in its underlying terms.
In dealing with the second consideration Feyerabend asks «why should it be necessary to have a terminology
that allows us to say that two theories refer to the same experiment. This supposes a unificationist or possibly a realist aspiration, whose objective appears to be the truth, however, it is assumed that the theory can be compared under a criterion of empirical adequacy. Such an approach would build on the relationship established between the observational statement that describes the outcome of an experiment formulated for each theory independently, which is compared with the predictions that each theory posits. In this way the selection is made when a theory is an empirically better fit. If the objection to the possible deviation of the new theory is not answered it is irrelevant as often history has shown that in fact differing points of view change or modify their fields of application, for example the physics of Aristotle
and Newton
.»
Feyerabend uses this reasoning to try to shed light on one of Popper's arguments, which says that we are always able to change any statement, even those reference systems that guide our critical thinking. However, the two thinkers reach different conclusions, Popper assumes that it is always possible to make a criticism once the new criteria have been accepted, so the selection can be seen as the result of a rationality "a posteriori" to the selection. While, Feyerabend's position is that this solution is merely a verbal ornament whenever the standards are influenced by Popper's first world, the physical world, and they are not just developed in the third world. That is, the standards are influenced by the expectations of their originators, the stances they imply and the ways of interpreting the world they favour, but this is strictly analogous to the same process of the scientific revolution, that leads us to believe that the thesis of incommensurability can also be applied to standards, as is shown by the following asseveration:
Feyerabend states that the Popperian criticism is either related to certain clearly defined procedures, or is totally abstract and leaves others with the task of fleshing it out later with specific contents, making Popper's rationality a «mere verbal ornament». This does not imply that Feyerabend is an irrationalist but that he considers that the process of scientific change can not be explained in its totality in the light of some rationality, precisely because of incommensurability.
, who introduced it in his 1962 book, The structure of scientific revolutions
, in which he describes it as a universal property that defines the relationship between successive paradigm
s. Under this meaning incommensurability goes beyond the field of semantics and covers everything relating to its practical application, from the study of problems to the associated methods and rules for their resolution. However, the meaning of the term was continually refined throughout Kuhn's work, he first placed it within the field of semantics and applied a narrow definition, but later he redefined it in a taxonomic
sense, wherein changes are found in the relationships between similarities and differences that the subjects of a defining matrix draw over the world.
In The Structure of Scientific Revolutions Kuhn wrote that "when paradigms change, the world itself changes with them" (see esp. Chapter X of this book). According to Kuhn, the proponents of different scientific paradigms cannot fully appreciate or understand the other's point of view because they are, as a way of speaking, living in different worlds. Kuhn gave three reasons for this inability:
In a postscript (1969) to The Structure of Scientific Revolutions, Kuhn added that he thought that incommensurability was, at least in part, a consequence of the role of similarity sets in normal science. Competing paradigms group concepts in different ways, with different similarity relations. According to Kuhn, this causes fundamental problems in communication between proponents of different paradigms. It is difficult to change such categories in one's mind, because the groups have been learned by means of exemplars instead of definitions. This problem cannot be resolved by using a neutral language for communication, according to Kuhn, since the difference occurs prior to the application of language.
Kuhn's thinking on incommensurability was probably in some part influenced by his reading of Michael Polanyi
who held that there can be a logical gap between belief systems and who also said that scientists from different schools, “think differently, speak a different language, live in a different world.” (Personal Knowledge,1958, p151).
by a localist and semanticist vision in which incommensurability is now defined as the relationship between two theories that are articulated in two languages that are not completely interchangeable, as Kuhn states in the following extract:
The above only prohibits one type of comparison, that which is carried out between the statements of these two theories in a one to one relationship. An idea that underlies this formulation is that translation implies symmetry
and transitivity
so that if theory T is translatable with theory T’, then T’ can be translated to T, and furthermore if there is a third theory T’’ and this can be translated to T’, then theories T and T’ cannot be incommensurable, as long as the transitive relationship and the symmetrical relationship assures that their statements can be compared one to another.
It should be noted that Kuhn did not deny that two incommensurable theories may have a common reference environment and in this sense he did not state that it was impossible to compare them, his thesis solely refers to the ability to translate the statements belonging to two theories in a one to one relationship, as is shown in the following passage:
This is relevant because it allow us to elucidate that Kuhn's sense of rationality
is linked to the ability to comprehend, and not to the same capacity for translation (Pérez Ransanz, 2000).
In the third stage of Kuhn's work the formulation of the thesis of incommensurability became refined in taxonomic
terms and is explained as a function of the change in the relations of similarity and difference between two theories. Kuhn declared that this change relates to the concepts of Class A not only because there is a change in the way of referring to the concepts but also because their underlying structure becomes altered, that is, the meaning changes - its intention - but also its reference. In this way Kuhn states that not all of the semantic changes are changes that lead to incommensurability, they are only those that, by being made in the basic categories, operate in a holistic manner meaning that all the relationships between these terms becomes altered. This uses taxonomic terms to define incommensurability as the impossibility to prove the taxonomic structures of two theories, an impossibility that is expressed as a necessarily incomplete translation of the terms.
, since, if the taxonomic categories are divisions in a logical sense then this implies that the relations established between these concepts and the rest are necessarily hierarchical. It is for exactly this type of relationship that the changes in categories are holistic, as the modification of a category necessarily implies the modification of the surrounding categories, which explains why once the change takes place the taxonomies can not be comparable - they are isomorphic.
This characterization was already present in Kuhn's writing along with remnants of semantic characterization, which he developed in full towards the end of the 1980s
in his taxonomic characterization. An advantage of this characterization is the belief that the criteria that allow the identification of a concept with its references are many and varied, so that a coincidence of criteria is not necessary for successful communication except for those categories that are implicated. Kuhn saw the relations between concepts as existing in a multidimensional space, the categories consist of partitions in this space and they must coincide between the communicators, although this is not the case for the criteria that establish a connection between this space and the associated reference.
. Translation is an almost mechanical activity which produces a Quinean translation manual that relates sequences of words in such a way that their truth values are conserved. However, the process of interpretation implies the development of translation hypotheses, which have to be successful when they allow external preferences to be understood in a coherent and meaningful way. Kuhn then rejected the idea of a universal translatability but not the principle of universal ineligibility, a distinction that is very important in understanding Kuhn's rejection of his critics, such as Popper
and Davidson
.
However, without a doubt the previous idea invites us to question how is it that we are able to interpret in the first place. Kuhn's solution consists in affirming that this is like learning a new language. How is it that we are able to learn a new language when we are confronted with a holistic change such as is implied by the notion of incommensurability? Kuhn's work suggests four aspects to this question:
that if the new theory deviates into new areas, this is not a problem of the theory, as often the conceptual progress leads to the disappearance and not to the refutation or resolution of the old questions.
Philosophy of science
The philosophy of science is concerned with the assumptions, foundations, methods and implications of science. It is also concerned with the use and merit of science and sometimes overlaps metaphysics and epistemology by exploring whether scientific results are actually a study of truth...
. Scientific theories are described as commensurable if one can compare them to determine which is more accurate; if theories are incommensurable, there is no way in which one can compare them to each other in order to determine which is more accurate.
Thesis
In 1962, Thomas KuhnThomas Kuhn
Thomas Samuel Kuhn was an American historian and philosopher of science whose controversial 1962 book The Structure of Scientific Revolutions was deeply influential in both academic and popular circles, introducing the term "paradigm shift," which has since become an English-language staple.Kuhn...
and Paul Feyerabend
Paul Feyerabend
Paul Karl Feyerabend was an Austrian-born philosopher of science best known for his work as a professor of philosophy at the University of California, Berkeley, where he worked for three decades . He lived a peripatetic life, living at various times in England, the United States, New Zealand,...
both independently introduced the idea of incommensurability to the philosophy of science. In both cases the concept
Concept
The word concept is used in ordinary language as well as in almost all academic disciplines. Particularly in philosophy, psychology and cognitive sciences the term is much used and much discussed. WordNet defines concept: "conception, construct ". However, the meaning of the term concept is much...
came from mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
and in its original sense is defined as the absence of a common unit of measurement that would allow a direct and exact measurement of two variable
Variable
Variable may refer to:* Variable , a logical set of attributes* Variable , a symbol that represents a quantity in an algebraic expression....
s, such as the prediction of the diagonal
Diagonal
A diagonal is a line joining two nonconsecutive vertices of a polygon or polyhedron. Informally, any sloping line is called diagonal. The word "diagonal" derives from the Greek διαγώνιος , from dia- and gonia ; it was used by both Strabo and Euclid to refer to a line connecting two vertices of a...
of a square
Square (geometry)
In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles...
from the relationship of its sides.
Incommensurability in mathematics
It is possible to demonstrate that d/l is not rational
Rational number
In mathematics, a rational number is any number that can be expressed as the quotient or fraction a/b of two integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer is a rational number...
by considering the opposite, in other words by looking for proof by contradiction. If a logical contradiction
Contradiction
In classical logic, a contradiction consists of a logical incompatibility between two or more propositions. It occurs when the propositions, taken together, yield two conclusions which form the logical, usually opposite inversions of each other...
is reached then the opposite is not true and incommensurability is demonstrated. In terms of logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
: if we want to demonstrate the proposition J, we assume that "not J" is true. Through logical deductions from "not J" we arrive at a contradiction. Then it can be concluded that "not J" is not true and therefore "J" must be true. This method is called reductio ad absurdum
Reductio ad absurdum
In logic, proof by contradiction is a form of proof that establishes the truth or validity of a proposition by showing that the proposition's being false would imply a contradiction...
.
Introduction of the term
The term commensurability was coined because of a series of problems that both authors found when trying to interpret successive scientific theories. Without doubt its implementation is better understood thanks to the critiques that both Kuhn and Feyerabend have made in response to certain thesesThesis
A dissertation or thesis is a document submitted in support of candidature for an academic degree or professional qualification presenting the author's research and findings...
proposed by followers of the received view of theories
Received view of theories
The received view of theories is a position in the philosophy of science that identifies a scientific theory with a set of propositions which are considered to be linguistic objects, such as axioms...
. These include the famous thesis on the accumulation of scientific knowledge, which states that the body of scientific knowledge has been increasing with the passage of time. Both Kuhn and Feyerabend reject this thesis.
Another equally important thesis proposes the existence of a neutral language
Standard language
A standard language is a language variety used by a group of people in their public discourse. Alternatively, varieties become standard by undergoing a process of standardization, during which it is organized for description in grammars and dictionaries and encoded in such reference works...
of comparison which can be used to formulate the empirical
Empiricism
Empiricism is a theory of knowledge that asserts that knowledge comes only or primarily via sensory experience. One of several views of epistemology, the study of human knowledge, along with rationalism, idealism and historicism, empiricism emphasizes the role of experience and evidence,...
consequences of two competing theories. This would allow one to choose the theory with the greatest empirically verified contents - or the greatest content that is not falsified if the formulation is Popper
Popper
Popper may refer to:* Jalapeño popper, a type of food* Poppers, the family of drugs that are a subset of a class of chemicals known as alkyl nitrites* Poppers, a brand of frozen food owned by Heinz...
ian.
The idea at the root of this second thesis does not just relate to the existence of said language but also implies at least two further postulates. Firstly, this choice between theories presupposes that they can be intertranslated, for example between Theory T and its successor T’ – and in the case of Popper that T’ can be deduced from T. Secondly, it is assumed that the choice is always carried out under the same standards of rationality
Rationality
In philosophy, rationality is the exercise of reason. It is the manner in which people derive conclusions when considering things deliberately. It also refers to the conformity of one's beliefs with one's reasons for belief, or with one's actions with one's reasons for action...
.
In both cases the concept of incommensurability makes the viability of the thesis impossible. In the first, by showing that certain empirical consequences are lost between successive theories. In the second case, by confirming that it is possible to make a rational choice between theories even when they can not be translated into a neutral language. However, although the reasons for the introduction of these counter arguments, and the criticism from which they arise, are the same, the sense in which the coauthors use them are in no way identical. For this reason the idea of incommensurability will be discussed for each coauthor separately.
Feyerabend's perspectives
Feyerabend locates incommensurability within a principle from the field of semanticsSemantics
Semantics is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata....
which has the underlying idea that the change in significance in the basic terms of a theory changes the totality of the terms of the new theory, so that there are no empirically common meanings between T and T’
Feyerabend is credited with coining the modern philosophical sense of "incommensurability," which lays the foundation for much of his philosophy of science. He first presented his notion of incommensurability in 1952 to Karl Popper
Karl Popper
Sir Karl Raimund Popper, CH FRS FBA was an Austro-British philosopher and a professor at the London School of Economics...
's LSE
London School of Economics
The London School of Economics and Political Science is a public research university specialised in the social sciences located in London, United Kingdom, and a constituent college of the federal University of London...
seminar. Feyerabend argued that frameworks of thought, and thus scientific paradigms, can be incommensurable for three reasons. Included in the group was Elizabeth Anscombe, Peter Geach
Peter Geach
Peter Thomas Geach is a British philosopher. His areas of interest are the history of philosophy, philosophical logic, and the theory of identity.He was educated at Balliol College, Oxford...
, H.L.A. Hart and Georg Henrik von Wright
Georg Henrik von Wright
Georg Henrik von Wright was a Finnish philosopher, who succeeded Ludwig Wittgenstein as professor at the University of Cambridge. He published in English, Finnish, German, and in Swedish. Belonging to the Swedish-speaking minority of Finland, von Wright also had Finnish and 17th-century Scottish...
. Briefly put, Feyerabend's notion of incommensurability is as follows:
- The interpretation of observations is implicitly influenced by theoretical assumptions. It is therefore impossible to describe or evaluate observations independently of theory.
- Paradigms often have different assumptions about which intellectual and operational scientific methods result in valid scientific knowledge.
- Paradigms can be based on different assumptions regarding the structure of their domain, which makes it impossible to compare them in a meaningful way. The adoption of a new theory includes and is dependent upon the adoption of new terms. Thus, scientists are using different terms when talking about different theories. Those who hold different, competing theories to be true will be talking over one another, in the sense that they cannot a priori arrive at agreement given two different discourses with two different theoretical language and dictates.
According to Feyerabend, the idea of incommensurability cannot be captured in formal logic, because it is a phenomenon outside of logic's domain.
Theories
In 1989, Feyerabend presented an idea informed by Popper's critical rationalism whereby "investigation starts with a problem. The problem is the result of a conflict between an expectation and an observation, which, in its turn, is formed by the expectation." (Feyerabend, 1989; pp. 96). Scientific methodologyMethodology
Methodology is generally a guideline for solving a problem, with specificcomponents such as phases, tasks, methods, techniques and tools . It can be defined also as follows:...
then resolves problems by inventing theories that should be relevant and falsifiable, at least to a greater degree than any other alternative solution. Once an alternative theory is presented the critical phase commences regarding T’ which must answer the following questions: (a) why has theory T been successful up until now and (b) why has it failed. If the new theory T’ answers both questions then T is discarded.
That is, a new theory T’, in order to be an adequate successor to the refuted theory T, must have a collection of additional predictions regarding T (Class A), as well as a collection of successful predictions that coincide to a certain degree with the old theory (Class S). These Class S predictions constitute those parts of the new theory containing new truths and they therefore exclude a series of consequences of T, the failures in the old theory, which are part of the untrue (false) contents of the new theory (Class F).
Given this model
Scientific modelling
Scientific modelling is the process of generating abstract, conceptual, graphical and/or mathematical models. Science offers a growing collection of methods, techniques and theory about all kinds of specialized scientific modelling...
it is possible to construct relational statements between certain terms from T and from T’, which will be the basis for the comparison between the theories. This will allow a choice between the two in the light of their empirical contents. But, if we come across a theory T’ in which Class S is empty then the theories are incommensurable with each other.
However, Feyerabend clarifies this by stating that, incommensurability between T and T’ will depend of the interpretation given to the theories. If this is instrumental, every theory that refers to the same language of observation
Observation
Observation is either an activity of a living being, such as a human, consisting of receiving knowledge of the outside world through the senses, or the recording of data using scientific instruments. The term may also refer to any data collected during this activity...
will be commensurable. In the same way, if a realist
Philosophical realism
Contemporary philosophical realism is the belief that our reality, or some aspect of it, is ontologically independent of our conceptual schemes, linguistic practices, beliefs, etc....
perspective is sought then it will favour a unified position which employs the most highly abstracted terms of whatever theory is being considered in order to describe both theories, giving a significance to the observational statements as a function of these terms, or, at least to replace the habitual use they are given.
It can be noted that the instrumentalist interpretation recognizes the existence of certain statements whose truth is not only dependent on the observational statements but also on the evaluation criteria they are subjected to, which are anchored in the theories. For example, to afirm the relational character of longitude
Longitude
Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes and seconds, and denoted by the Greek letter lambda ....
, this asseveration can not be decided solely using observational terms. Its truth value, in part, depends on the theory that establishes the sense in which the terms are used. In this case they relate to quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
(QM) as opposed to classical mechanics
Classical mechanics
In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...
(CM). In this sense, the instrumentalist position only deals with the empirical consequences and leaves to one side the relationship that the concepts have with each other.
In this same way Feyerabend comments that:
Realist objections
In relation to realist objections, Feyerabend returns to an argumentArgument
In philosophy and logic, an argument is an attempt to persuade someone of something, or give evidence or reasons for accepting a particular conclusion.Argument may also refer to:-Mathematics and computer science:...
elaborated by Carnap and comments that the use of such abstract concepts leads to an impossible position, as «...theoretical terms receive their interpretation by being connected with an observational language and those terms are empty without that connection.» (Feyerabend, pp. 373). As before it follows that they can not be used to confer significance to the observational language as this observational language is its only source of significance, with which it is not possible to make a translation but only a restatement of the term.
Therefore Feyerabend considers that both the instrumentalist and the realist interpretations are flawed, as they try to defend the idea that incommensurability is a legitimately unsolvable idea with which to revoke the theses of the accumulation of knowledge and panrationalism
Panrationalism
Panrationalism holds two premises true:# A rationalist accepts any position that can be justified or established by appeal to the rational criteria or authorities.# He accepts only those positions that can be so justified....
in science.
This leads to the following consideration: if each new theory has its own observational basis, within the meaning of the theoretical framework, how can we hope that the observations that are produced could eventually refute it. Further more, how can we actually recognize that the new position explains what it is supposed to explain or if it is deviating off into other areas and therefore how can the theories be definitively compared.
Feyerabend's answer to the first consideration lies in noting that the initial terms of a theory depend on the postulates of the theory and their associated grammatical rules, in addition, the predictions derived from the theory also depend on the underlying conditions of the system. Feyerabend doesn't explore the point further, but it can be assumed that if the prediction does not agree with the observation and if we have a high degree of confidence in the description that we have made from the initial conditions
Material conditional
The material conditional, also known as material implication, is a binary truth function, such that the compound sentence p→q is logically equivalent to the negative compound: not . A material conditional compound itself is often simply called a conditional...
than we can be sure that the error must be present in our theory and in its underlying terms.
In dealing with the second consideration Feyerabend asks «why should it be necessary to have a terminology
Terminology
Terminology is the study of terms and their use. Terms are words and compound words that in specific contexts are given specific meanings, meanings that may deviate from the meaning the same words have in other contexts and in everyday language. The discipline Terminology studies among other...
that allows us to say that two theories refer to the same experiment. This supposes a unificationist or possibly a realist aspiration, whose objective appears to be the truth, however, it is assumed that the theory can be compared under a criterion of empirical adequacy. Such an approach would build on the relationship established between the observational statement that describes the outcome of an experiment formulated for each theory independently, which is compared with the predictions that each theory posits. In this way the selection is made when a theory is an empirically better fit. If the objection to the possible deviation of the new theory is not answered it is irrelevant as often history has shown that in fact differing points of view change or modify their fields of application, for example the physics of Aristotle
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
and Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
.»
Theory selection
The above implies that the process of choosing between theories does not obey a universal rationality. Feyerabend has the following view regarding whether the absence of a universal rationality constitutes an irrational position:Feyerabend uses this reasoning to try to shed light on one of Popper's arguments, which says that we are always able to change any statement, even those reference systems that guide our critical thinking. However, the two thinkers reach different conclusions, Popper assumes that it is always possible to make a criticism once the new criteria have been accepted, so the selection can be seen as the result of a rationality "a posteriori" to the selection. While, Feyerabend's position is that this solution is merely a verbal ornament whenever the standards are influenced by Popper's first world, the physical world, and they are not just developed in the third world. That is, the standards are influenced by the expectations of their originators, the stances they imply and the ways of interpreting the world they favour, but this is strictly analogous to the same process of the scientific revolution, that leads us to believe that the thesis of incommensurability can also be applied to standards, as is shown by the following asseveration:
Feyerabend states that the Popperian criticism is either related to certain clearly defined procedures, or is totally abstract and leaves others with the task of fleshing it out later with specific contents, making Popper's rationality a «mere verbal ornament». This does not imply that Feyerabend is an irrationalist but that he considers that the process of scientific change can not be explained in its totality in the light of some rationality, precisely because of incommensurability.
Kuhn's perspectives
The second coauthor of the thesis of incommensurability is Thomas KuhnThomas Kuhn
Thomas Samuel Kuhn was an American historian and philosopher of science whose controversial 1962 book The Structure of Scientific Revolutions was deeply influential in both academic and popular circles, introducing the term "paradigm shift," which has since become an English-language staple.Kuhn...
, who introduced it in his 1962 book, The structure of scientific revolutions
The Structure of Scientific Revolutions
The Structure of Scientific Revolutions , by Thomas Kuhn, is an analysis of the history of science. Its publication was a landmark event in the history, philosophy, and sociology of scientific knowledge and it triggered an ongoing worldwide assessment and reaction in — and beyond — those scholarly...
, in which he describes it as a universal property that defines the relationship between successive paradigm
Paradigm
The word paradigm has been used in science to describe distinct concepts. It comes from Greek "παράδειγμα" , "pattern, example, sample" from the verb "παραδείκνυμι" , "exhibit, represent, expose" and that from "παρά" , "beside, beyond" + "δείκνυμι" , "to show, to point out".The original Greek...
s. Under this meaning incommensurability goes beyond the field of semantics and covers everything relating to its practical application, from the study of problems to the associated methods and rules for their resolution. However, the meaning of the term was continually refined throughout Kuhn's work, he first placed it within the field of semantics and applied a narrow definition, but later he redefined it in a taxonomic
Taxonomy
Taxonomy is the science of identifying and naming species, and arranging them into a classification. The field of taxonomy, sometimes referred to as "biological taxonomy", revolves around the description and use of taxonomic units, known as taxa...
sense, wherein changes are found in the relationships between similarities and differences that the subjects of a defining matrix draw over the world.
In The Structure of Scientific Revolutions Kuhn wrote that "when paradigms change, the world itself changes with them" (see esp. Chapter X of this book). According to Kuhn, the proponents of different scientific paradigms cannot fully appreciate or understand the other's point of view because they are, as a way of speaking, living in different worlds. Kuhn gave three reasons for this inability:
- Proponents of competing paradigms have different ideas about the importance of solving various scientific problems, and about the standards that a solution should satisfy.
- The vocabulary and problem-solving methods that the paradigms use can be different: the proponents of competing paradigms utilize a different conceptual network.
- The proponents of different paradigms see the world in a different way because of their scientific training and prior experience in research.
In a postscript (1969) to The Structure of Scientific Revolutions, Kuhn added that he thought that incommensurability was, at least in part, a consequence of the role of similarity sets in normal science. Competing paradigms group concepts in different ways, with different similarity relations. According to Kuhn, this causes fundamental problems in communication between proponents of different paradigms. It is difficult to change such categories in one's mind, because the groups have been learned by means of exemplars instead of definitions. This problem cannot be resolved by using a neutral language for communication, according to Kuhn, since the difference occurs prior to the application of language.
Kuhn's thinking on incommensurability was probably in some part influenced by his reading of Michael Polanyi
Michael Polanyi
Michael Polanyi, FRS was a Hungarian–British polymath, who made important theoretical contributions to physical chemistry, economics, and the theory of knowledge...
who held that there can be a logical gap between belief systems and who also said that scientists from different schools, “think differently, speak a different language, live in a different world.” (Personal Knowledge,1958, p151).
Phases
Given his changing definition of incommensurability Pérez Ransanz has identified three phases in Kuhn's work, or at least in how it deals with this concept. As we have seen above the first phase was seen in The Structure of Scientific Revolutions (SSR) and it is characterized by an overall vision that is applied to paradigms. This perspective was replaced in the 1970s1970s
File:1970s decade montage.png|From left, clockwise: US President Richard Nixon doing the V for Victory sign after his resignation from office after the Watergate scandal in 1974; Refugees aboard a US naval boat after the Fall of Saigon, leading to the end of the Vietnam War in 1975; The 1973 oil...
by a localist and semanticist vision in which incommensurability is now defined as the relationship between two theories that are articulated in two languages that are not completely interchangeable, as Kuhn states in the following extract:
The above only prohibits one type of comparison, that which is carried out between the statements of these two theories in a one to one relationship. An idea that underlies this formulation is that translation implies symmetry
Symmetry
Symmetry generally conveys two primary meanings. The first is an imprecise sense of harmonious or aesthetically pleasing proportionality and balance; such that it reflects beauty or perfection...
and transitivity
Transitivity
-In grammar:* Intransitive verb* Transitive verb, when a verb takes an object* Transitivity -In logic and mathematics:* Arc-transitive graph* Edge-transitive graph* Ergodic theory, a group action that is metrically transitive* Vertex-transitive graph...
so that if theory T is translatable with theory T’, then T’ can be translated to T, and furthermore if there is a third theory T’’ and this can be translated to T’, then theories T and T’ cannot be incommensurable, as long as the transitive relationship and the symmetrical relationship assures that their statements can be compared one to another.
It should be noted that Kuhn did not deny that two incommensurable theories may have a common reference environment and in this sense he did not state that it was impossible to compare them, his thesis solely refers to the ability to translate the statements belonging to two theories in a one to one relationship, as is shown in the following passage:
This is relevant because it allow us to elucidate that Kuhn's sense of rationality
Rationality
In philosophy, rationality is the exercise of reason. It is the manner in which people derive conclusions when considering things deliberately. It also refers to the conformity of one's beliefs with one's reasons for belief, or with one's actions with one's reasons for action...
is linked to the ability to comprehend, and not to the same capacity for translation (Pérez Ransanz, 2000).
In the third stage of Kuhn's work the formulation of the thesis of incommensurability became refined in taxonomic
Taxonomy
Taxonomy is the science of identifying and naming species, and arranging them into a classification. The field of taxonomy, sometimes referred to as "biological taxonomy", revolves around the description and use of taxonomic units, known as taxa...
terms and is explained as a function of the change in the relations of similarity and difference between two theories. Kuhn declared that this change relates to the concepts of Class A not only because there is a change in the way of referring to the concepts but also because their underlying structure becomes altered, that is, the meaning changes - its intention - but also its reference. In this way Kuhn states that not all of the semantic changes are changes that lead to incommensurability, they are only those that, by being made in the basic categories, operate in a holistic manner meaning that all the relationships between these terms becomes altered. This uses taxonomic terms to define incommensurability as the impossibility to prove the taxonomic structures of two theories, an impossibility that is expressed as a necessarily incomplete translation of the terms.
Taxonomic characterization
Taxonomic characterization allowed Kuhn to postulate his no-overlap principlePrinciple
A principle is a law or rule that has to be, or usually is to be followed, or can be desirably followed, or is an inevitable consequence of something, such as the laws observed in nature or the way that a system is constructed...
, since, if the taxonomic categories are divisions in a logical sense then this implies that the relations established between these concepts and the rest are necessarily hierarchical. It is for exactly this type of relationship that the changes in categories are holistic, as the modification of a category necessarily implies the modification of the surrounding categories, which explains why once the change takes place the taxonomies can not be comparable - they are isomorphic.
This characterization was already present in Kuhn's writing along with remnants of semantic characterization, which he developed in full towards the end of the 1980s
1980s
File:1980s decade montage.png|thumb|400px|From left, clockwise: The first Space Shuttle, Columbia, lifted off in 1981; American President Ronald Reagan and Soviet leader Mikhail Gorbachev eased tensions between the two superpowers, leading to the end of the Cold War; The Fall of the Berlin Wall in...
in his taxonomic characterization. An advantage of this characterization is the belief that the criteria that allow the identification of a concept with its references are many and varied, so that a coincidence of criteria is not necessary for successful communication except for those categories that are implicated. Kuhn saw the relations between concepts as existing in a multidimensional space, the categories consist of partitions in this space and they must coincide between the communicators, although this is not the case for the criteria that establish a connection between this space and the associated reference.
Reluctance
An important clarification that should be made, and which constantly appears in Kuhn's writing, is his reluctance to equate translation and interpretation, a comparison that Kuhn attributes to the analytical tradition of philosophyPhilosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
. Translation is an almost mechanical activity which produces a Quinean translation manual that relates sequences of words in such a way that their truth values are conserved. However, the process of interpretation implies the development of translation hypotheses, which have to be successful when they allow external preferences to be understood in a coherent and meaningful way. Kuhn then rejected the idea of a universal translatability but not the principle of universal ineligibility, a distinction that is very important in understanding Kuhn's rejection of his critics, such as Popper
Popper
Popper may refer to:* Jalapeño popper, a type of food* Poppers, the family of drugs that are a subset of a class of chemicals known as alkyl nitrites* Poppers, a brand of frozen food owned by Heinz...
and Davidson
Donald Davidson (philosopher)
Donald Herbert Davidson was an American philosopher born in Springfield, Massachusetts, who served as Slusser Professor of Philosophy at the University of California, Berkeley from 1981 to 2003 after having also held teaching appointments at Stanford University, Rockefeller University, Princeton...
.
However, without a doubt the previous idea invites us to question how is it that we are able to interpret in the first place. Kuhn's solution consists in affirming that this is like learning a new language. How is it that we are able to learn a new language when we are confronted with a holistic change such as is implied by the notion of incommensurability? Kuhn's work suggests four aspects to this question:
- Firstly, in order to carry out such an assimilation it is necessary that the complementary vocabularyVocabularyA person's vocabulary is the set of words within a language that are familiar to that person. A vocabulary usually develops with age, and serves as a useful and fundamental tool for communication and acquiring knowledge...
is easily understood. - Secondly, definitions must fulfill a minimal role, it is the paradigmatic examples that introduce the use of the new concepts, in such a way that an ostensive or stipulative component is essential.
- Thirdly, class concepts cannot be learnt in isolation, but in relation to a series of contrast sets.
- Fourthly, the process of learning involves the generation of expectations, which are the basis of the projectability of the class terms, in such a way that in their turn they form the basis of, among other things, inductive inferences. And lastly, as the criteria for relating the class and its reference vary, this forms the way of learning the subject matter.
Conclusion
It can be concluded that Kuhn's idea of incommensurability, despite its various reformulations, manages to seriously problematize both the idea of accumulation of a neutral language as well as of the very idea of a neutral language, without falling into irrationalism nor stating that the common reference level is irrelevant. An idea that differentiates him from Feyerabend who states in books such as Problems of Empiricism and Against MethodAgainst Method
Against Method is a book by Paul Feyerabend. In this work, Feyerabend argues that science is an anarchic enterprise. In the context of this work, the term anarchy refers to epistemological anarchy...
that if the new theory deviates into new areas, this is not a problem of the theory, as often the conceptual progress leads to the disappearance and not to the refutation or resolution of the old questions.