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Kuhn’s
second reason is that incommensurability is due to
semantical or lexicon restructuring.
Kuhn’s initial statement of this reason is
found in his “Commensurability, Comparability,
Communicability” in the section titled “The
Invariants of Translation.”
Here he distinguishes and describes two
characteristics of language:
1.
Co-referencing.
This means that two users of the same
language can employ different criteria for
identifying the referents of its descriptive terms.
Co-referencing requires that each user
associate each descriptive term with a cluster of
criteria including contrast sets of terms.
He adds that the sets of terms must be
learned together by interpretation, and that this
having to learn them together is the holistic aspect
essential to local incommensurability.
2.
Structures of criteria. For each language user a
referencing term is a node in a lexical network,
from which radiate labels for the criteria he uses
in identifying the referents of the nodal term.
Those criteria tie some terms together and at
the same time distance them from other terms, thus
building a multidimensional structure within the
lexicon. That
structure mirrors aspects of the structure of the
world, which the lexicon can be used to describe,
and it also simultaneously limits the phenomena that
can be described with the lexicon.
If anomalous phenomena arise, their
description and possibly even their recognition will
require altering some part of the language, thereby
restructuring the previously constitutive linkages
between terms.
In discussing translation Kuhn says that homologous
structures mirroring the same world may be fashioned
using different sets of criterial linkages.
What such homologous structures preserve is
the taxonomic categories of the world and the
similarity/difference relationships between them. Different languages impose different structures on the world,
and what members of the same language community
share is homology of lexical structures, in which
the taxonomic structures match. The invariants of
translation are matching co-referential expressions
and identical lexical structures.
Translation is impossible if taxonomy cannot
be preserved, to provide both languages shared
categories and relationships.
And when translation is impossible,
interpretation, i.e. language acquisition, is
required. Finally revolutionary developments in
science are those that require taxonomic change,
i.e. change in lexical taxonomic structure thus
producing incommensurability.
In his
“The “Road Since Structure” (1991) also
reprinted in Road Since Structure Kuhn states that the lexical taxonomy might be
called a conceptual scheme, which is not a set of
beliefs, but rather an operating mode of a mental
module prerequisite to having beliefs, a module that
supplies and bonds what is possible to conceive. He also says that the taxonomic module is prelinguistic and
possessed by animals.
In this respect he calls himself a
post-Darwinian Kantian, because like the Kantian
categories the lexicon supplies preconditions of
possible experience, while unlike Kantianism the
lexicon can and does change.
And he adds that underlying these changes
there must be something stable and permanent that is
located outside space and time that like Kant’s Ding
an sich is ineffable, inscrutable, and
indiscernible.
In “Road
Since Structure” and in “Afterwords” Kuhn
elaborates further on his idea of lexicon with his
thesis of kind words or taxonomic terms, the
vocabulary terms contained in the lexicon, and he
states that they have two properties: 1) they are
identifiable by their lexical characteristics,
notably their occurrence with an indefinite article,
and 2) they are subject to what Kuhn’s no-overlap
principle, which is that no two terms with the kind
label may overlap in their referents, unless they
are related as species to genus.
For example the meanings of “male” and
“horse” may overlap, but not those of
“horse” and “cow.”
Kuhn
illustrates his thesis of taxonomic terms and his
principle of no overlap in the language of the
Copernican revolution.
He says that the content of the Copernican
statement “planets travel around the sun” cannot
be expressed in a statement that invokes the
celestial taxonomy of the Ptolemaic statement
“planets travel around the earth”, and that the
difference between the two statements is not simply
a matter of fact.
The term “planet” appears in both
statements as a kind term, and the two kind terms
overlap in membership without either containing all
the celestial bodies contained in the other (a
genus-species relation), such that there is a change
in taxonomic categories that is fundamental.
But Kuhn believes that such overlap could not
endure, and says that a redistribution of
individuals among natural kinds with its consequent
alteration of features salient to reference, is the
central feature of the episodes he calls
revolutions. Kind
words supply the categories prerequisite to
description of and generalization about the world.
Periods in which a speech community deploys
overlapping kind words end in one of two outcomes:
1) one meaning entirely displaces the other or 2)
the community divides into two groups.
In the resolution of scientific revolutions
the former outcome occurs as a result of the crisis
phase. And
in the specialization and speciation of new
disciplines the latter outcome occurs.
The lexicon of various members of a speech
community may vary in the expectations that the
lexicons induce, but they must all have the same
structure or else mutual incomprehension and
breakdown of communication will result.
What is involved in incommensurability -
different lexical structure - can only be exhibited
ostensively by pointing out examples, it cannot be
articulated, i.e. expressed linguistically.
The term
“incommensurability” is also central to the
philosophy of Paul Feyerabend, and neither
Feyerabend nor Kuhn had claimed priority for its
use. In
his autobiographical interview Kuhn claims to have
used it independently.
In his “Commensurability, Comparability,
Communicability” Kuhn relates his use of the term
to Feyerabend’s.
He stated that his use of
“incommensurability” was broader than
Feyerabend’s, while Feyerabend’s claims are more
sweeping. Kuhn
noted that each was led to use the term by problems
encountered in interpreting scientific texts, that
both were concerned to show that the meanings of
scientific terms and concepts such as “force”,
“mass”, “element” and “compound”, often
changed with changes in the theories that contained
them, and that when such theory changes occur it is
not possible to define all
the terms of one theory into the vocabulary of the
other. In
a footnote Kuhn adds that he restricted
incommensurability to a few specific terms.
Kuhn said Feyerabend restricted
incommensurability to language, while Kuhn initially
spoke also of differences in methods, problem-field,
and standards of solution.
Later in comparing his views with
Feyerabend’s, Kuhn modified his original idea of
incommensurability with his thesis of local
incommensurability.
Kuhn's
Philosophy of Science
Of the four basic questions in philosophy of
science (the aim of science, scientific discovery,
scientific criticism, and scientific explanation)
his philosophy is almost exclusively concerned with
the aim of science and its implications for
criticism. Though a historian of science Kuhn, had
written his Structure
of Scientific Revolutions for philosophers of
science, and he was disappointed to find that they
did not receive it sympathetically.
In response to criticism by philosophers he
modified and evolved his philosophy several times
over succeeding decades.
His thesis is twofold:
Firstly in the normal science phase the
consensus paradigm or theory assumes institutional
status, and that therefore scientists’ conformity
to the consensus view becomes the aim of science and
criterion for scientific criticism. The conventionally recognized criteria for empirical
criticism are subordinate to this institutionalized
criterion of conformity to the prevailing paradigm,
and scientific progress is understood in these
terms.
Secondly in the revolutionary phase, which is
incidental to the conscious aim of science, semantic
incommensurability between old and new successive
theories makes the revolutionary transition such
that empirical criteria for theory choice cannot
apply. In
response to critics’ questions about the
possibility of scientific criticism of revolutionary
new theories he later developed his thesis of local
incommensurability, which enables incommensurable
theories to be compared conceptually and empirically
by means of the common vocabulary that somehow falls
outside of the range of incommensurability. However,
within the area of incommensurable vocabulary the
language of the new theory must be learned by
multiple ostensive demonstrations and/or by
approximate paraphrase.
Then in response to philosophers’ demand
that he supply a linguistic analysis explaining his
incommensurability thesis, he evolved his position
substantially in the decades following Structure
of Scientific Revolutions.
The result of his linguistic analysis is his
two reasons for incommensurability: The first is
that the language of the new theory contains
descriptive semantics incorporating features of the
world not recognized by the earlier preceding
theory. The
second is that the contextual determination of the
descriptive terms in the statements of a theory
results in a restructuring of those terms, the
“lexicon” of “kind words” i.e. common nouns,
when those same terms are carried into the context
of the new succeeding theory.
Kuhn
mentions little about the topic of scientific
discovery. He
says that he disagrees with Hanson’s thesis that
there is a logic for scientific discovery, and Kuhn
prefers to speak of the circumstances of discovery.
He makes no comments about the nature of
scientific explanation. Consider next Feyerabend’s
philosophy of science and specifically his theses of
meaning variance and semantic incommensurability.
Nagel
and Feyerabend on Meaning Variance
Semantic incommensurability is a special case
of the more general semantic phenomenon that
Feyerabend calls "meaning variance", the
phrase that he uses to refer to semantic change.
Accordingly it is instructive to consider
firstly Feyerabend's thesis of meaning variance.
This thesis is argued in his
"Explanation, Reduction, and Empiricism"
in Minnesota Studies in the Philosophy of Science (1962), where he
opposes it to the contrary thesis of meaning
invariance, which he finds characteristic of the
Logical Positivist philosophy and specifically of
the views of Carl Hempel and Ernest Nagel.
Together with Paul Oppenheim, Carl Hempel set
forth the nomological-deductive thesis of scientific
explanation in "Logic of Explanation" in Philosophy
of Science (April, 1948), and a later statement
by Hempel is given in chapters five and six of his
Philosophy of Natural Science (1966).
Nagel set forth his thesis of reduction in
chapter eleven of his Structure of Science (1961). Hempel
and Oppenheim emphasize the logical-deductive nature
of scientific explanation, while Nagel addresses
more explicitly the semantical aspect of theoretical
explanation and reduction. Since the semantical aspect is at the center of Feyerabend's
thesis of meaning variance, a brief consideration of
Nagel's discussion of the reduction of theories is
in order, to understand what Feyerabend is opposing.
As it happens, Nagel might also be said to
have a thesis of meaning variance, but his view of
semantical change is not the same as Feyerabend's.
Initially the Logical Positivist interest in
reduction was part of the Unity of Science program.
When it became evident that this program is
unmanageably ambitious, the reductionist program was
limited to the characteristically Logical Positivist
problem of relating theoretical terms in theories to
an observation language.
This type of reduction is accomplished by
what Carnap called "reduction sentences",
what Hempel called "bridge principles",
and what Nagel calls “coordinating definitions”
and “correspondence rules.”
Nagel is in the Logical Positivist tradition,
but his treatment of logical reduction is somewhat
less programmatic and more closely related to
episodic developments in the history of science.
He is more interested in those cases in the
history of science, in which a relatively autonomous
theory is absorbed by or logically reduced to some
other more inclusive theory, a type of development
that he believes is a recurrent feature of the
history of modern science.
In this type of episode the set of
theoretical statements or experimental laws, as the
case may be, that is reduced to another theory is
called the "secondary science", while the
theory to which the reduction is effected is called
the "primary science".
Reductionism is a type of explanation in
science, and Nagel explicitly defines it as the
explanation of a theory or of a set of experimental
laws established in one area of inquiry by a theory
formulated in some other domain.
He is principally interested in those types
of reduction in which concepts are required for
describing phenomena in one area that were not
formerly employed in the other area, even when the
two areas were described with the same vocabulary.
He refers to this type of reduction as a
heterogeneous reduction, because it describes a
qualitative dissimilarity between the phenomena in
the domains of the two theories involved in the
reduction. On
the other hand a reduction without different
vocabulary and describing a qualitative similarity
is what he calls a homogeneous reduction.
Nagel finds only the heterogeneous type to be
problematic.
Nagel employs a theory of meaning in which a
descriptive term may have as many meanings as there
are explications.
He illustrates his thesis in his examination
of the heterogeneous reduction of thermodynamics to
statistical mechanics and of the semantics of the
term "temperature", as that term's meaning
is affected by the successful reduction.
Even before the reduction is made, there is
much to be said about the semantics of the terms
involved, because a term such as
"temperature" has several meanings
resulting from overtly performed instrumental
operations. Nagel exemplifies the multiple meanings
of the term "temperature" by noting that a
person who understands temperature in terms of an
ordinary mercury thermometer, would have difficulty
understanding what is meant by a temperature of
fifteen thousand degrees, if he also knew that no
mercury thermometer could be used to measure such an
extreme temperature.
But if the person had studied physics, he
would know that the term "temperature" in
physics has a broader application from a more
embracing set of rules of usage describing other
measurement procedures. Nagel references Bridgman's
idea of operationalist definitions, and states that
such rules of usage are explications aimed at
specifying the meanings of descriptive expressions
such as "temperature" in terms of other
observable ones, which in any given context must be
traced to certain descriptive expressions that are
selected to be observable primitive expressions. It is noteworthy that in Nagel's theory of semantical
specification as in Bridgman's, each such
specification describing an alternative measurement
procedure constitutes a cognitively distinct meaning
of the observation term.
Yet these multiple meanings are not unrelated
equivocations, since the diverse measurement
procedures will yield the same measurement values
where more than one is deemed applicable.
Thus the term is empirically
unambiguous while at the same time it is cognitively
equivocal. Nagel extends Bridgman's semantical
thesis for observation terms to theoretical terms.
He gives as examples of theoretical
explications of "temperature", the
explication in the science of heat with the help of
statements describing the Cournot cycle of heat
transformation, and therefore in terms of such
theoretical primitives as perfect nonconductors,
infinite heat reservoirs and infinitely slow volume
expansions.
Nagel emphasizes that while the term
"temperature" is explicated in the science
of heat in terms of both theoretical and
observational primitives, it is not the case that
the term understood in the sense of the first
explication is cognitively synonymous with
"temperature" construed in the sense of
the second.
This is one way in which the thesis of
multiple meanings serves the Logical Positivist
well: the Positivist does not want the meanings of
observation terms to be contaminated with the
meanings of theoretical terms.
It is therefore important to him that the set
of meanings supplied by the various theoretical
explications and the set supplied by the
observational explications be separate and distinct.
The thesis that multiple explications do not
result in cognitive synonymy but rather in
empirically unambiguous cognitive equivocation, thus
enables him to say that even when a revolutionary
new theory is developed, it will produce a new set
of theoretical explications but will not revise the
set of observational explications.
In this way there is room for meaning
variance in the theoretical meanings, and yet there
is also room for meaning invariance in the
observational meanings.
It is interesting that Nagel's approach is
different from Carnap's, because the latter
distinguishes theoretical terms as having incomplete
semantics, such that theoretical terms could change
their meanings by becoming more complete even in a
heterogeneous reduction. Carnap did not employ any thesis of empirically unambiguous
equivocation like Nagel; Nagel is more faithful to
Bridgman.
Nagel next considers the formal conditions
for a heterogeneous reduction.
In the reduction of thermodynamics to
statistical mechanics the Boyle-Charles' law is made
a logical consequence of the principles of
mechanics, when these principles are supplemented by
a hypothesis about the molecular constitution of a
gas, a statistical assumption about the motions of
molecules, and a postulate concerning the
experimental notion of temperature with the mean
kinetic energy of the molecules.
Nagel sets forth two formal conditions for
the reduction: the condition of connectability and
the condition of derivability. The first condition requires that assumptions be introduced
which postulate suitable relations between what is
signified by a descriptive term (e.g.
"temperature") in the secondary science,
and traits represented by theoretical terms already
present in the primary science (e.g. the kinetic
energy of molecules).
The second condition, the condition of
derivability, requires that together with the above
mentioned assumptions all the laws of the secondary
science including those containing the connected
terms, must be logically derivable from the
theoretical premises and their associated
coordinating definitions in the primary science.
The coordinating definitions or
correspondence rules, as Nagel also calls them, have
the same functions as Carnap’s reduction sentences
and Hempel’s bridge principles.
By whatever name, these are the sentences
that connect theoretical terms occurring in a theory
with the observation terms in the empirical
statements the theory explains deductively.
Both the primary and secondary theories
involved in a reduction are presumed to have
whatever coordinating definitions they need before
the reduction is effected.
When both of these conditions are satisfied,
the reduction can be effected, and the experimental
and theoretical laws of the secondary science are
made logical consequences of the theoretical
assumptions including the coordinating definitions
of the primary science.
After his discussion of the formal
conditions, Nagel extends his semantical thesis of
multiple meanings to reduction.
After the reduction of thermodynamics to
statistical mechanics is accomplished, the term
"temperature" can be explicated in terms
of the mean kinetic energy of molecules, and it
thereby acquires still another meaning.
This is the outcome of satisfying the
condition of connectability.
He explicitly denies that the connection made
by the assumptions employed in the reduction are
logical connections between established meanings of
expressions, because the assumptions would then
assert that there is either a synonymy or a one-way
entailment in the relation to a theoretical
expression in the primary science.
Nagel maintains that the connecting
assumptions are initially conventions that merely
assign the additional meaning, and which later
become empirical statements, because further
development of the theory makes it possible to
calculate the temperature of the gas in some
indirect fashion from experimental data other than
the temperature value obtained by actually measuring
the temperature of the gas.
He rejects as unwitting double talk the
objection to his thesis that the reduction occurs
due to a redefinition of the term
"temperature". He maintains that the term "temperature" cannot be
cognitively synonymous with the phrase "mean
kinetic energy of molecules".
He says that the terms in each of the two
sciences have meanings unambiguously fixed by
codified rules of usage or by established procedures
appropriate to each discipline, and that these
established meanings are not lost or changed as a
result of the reduction.
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