INTRODUCTION TO PHILOSOPHY OF SCIENCE

Book I Page 3

 

3.16 Contemporary Pragmatist Semantics

 Philosophers’ reflection on the development of quantum physics occasioned development of the contemporary pragmatist philosophy. A fundamental postulate in the contemporary pragmatist philosophy of language is the rejection of the naturalistic thesis of the semantics of language and its replacement with the artifactual thesis that relativizes all semantics and ontology to linguistic context consisting of universally quantified beliefs. The rejection of the naturalistic thesis is not new in linguistics, but it is fundamentally opposed to the positivism that preceded contemporary pragmatism.

3.17 Pragmatist Semantics Illustrated

Consider the following analogy illustrating relativized semantics. Our linguistic system is analogous to a mathematical simultaneous-equation system. The equations of the system are a constraining context that determines the variables’ numerical values constituting a solution set for the equation system. If there is not a sufficient number of constraining equations, the system is underdetermined such that there are an indefinitely large number of possible numerical solution sets.

In pure mathematics numerical underdetermination can be eliminated and the system can be made uniquely determinate by adding related independent equations, so there are just as many equations as there are variables. Then there is one uniquely determined solution set of numerical values for the equation system.

When applying such a mathematically uniquely determined equation system to reality as in basic science or in engineering, the pure mathematics functions as the syntax for a descriptive language, when the numerical values of the descriptive variables are measurements. But the measurement values make the mathematically uniquely determined equation system empirically underdetermined due to measurement errors, which can be reduced indefinitely but never completely eliminated. Then even for a mathematically uniquely determined equation system admitting only one solution set of numerical values, there is still an infinitely large number of possible measurement values falling within even a narrow range of empirical underdetermination due to measurement errors.

When the simultaneous system of equations expresses an empirical theory in a test, and if its solution-set numerical values fall within the estimated range of measurement error in the corresponding measurement values produced in the test, then the theory is deemed not falsified. But if the solution-set numerical values are outside the estimated range of measurement error in the measurement values, then the theory is deemed to have been falsified by all who accept the test design and its execution.

The language system is like a mathematically underdetermined equation system having an infinitely large number of solution sets for the system. A set of logically consistent beliefs constituting a system of universally quantified related statements is a constraining context that determines the semantics of the descriptive terms in the belief system. This is most evident in an axiomatized deductive system. Like the equation system’s numerical values the language system’s semantics for any “semantical solution set”, as it were, are relativized to one another by the system’s universal beliefs and have definitional force. But the semantics conceptualizing sense stimuli always contains some vagueness. Due to this vagueness the linguistic system is empirically underdetermined and admits to an indefinitely large number of relativized semantical sets for the system. There is no uniquely determinate belief system of concepts.

This vagueness does not routinely manifest itself or cause communication problems so long as we encounter expected or familiar experiences for which our conventionalized beliefs are prepared. But the language user may on occasion encounter a new situation, for which the existing relevant conventional beliefs cannot take into account. In such new situations the language user must make some decisions about the applicability of one or several of the problematic terms in their existing beliefs, and then add some new beliefs or reject some currently accepted beliefs, if the decision about applicability is not simply ad hoc.

Adding more universally quantified statements to the belief system reduces this empirical underdetermination by adding clarifying information, but the residual vagueness can never be completely eliminated. Our semantics captures determinate mind-independent reality, but the cognitive capture with our semantics can never be exhaustive. There is always residual vagueness in our semantics. Vagueness and measurement error are both manifestations of empirical underdetermination. And increased clarity reduces vagueness as increased accuracy reduces measurement error.

Relativized semantics also has implications for ontology. Mind-independent recalcitrant reality imposes the empirical constraint that makes our belief systems contingent, and in due course falsifies them. Our access to mind-independent reality is by language-dependent relativized semantics, which signifies a corresponding ontology. Ontology is the cognitively apprehended aspects of the fathomless plenitude that is mind-independent reality as described by the relativized semantics. Thus there are no referentially absolute or fixed terms. Instead descriptive terms are always fuzzy, i.e., referentially indeterminate or as Quine says “inscrutable”, because their semantics is always empirically underdetermined.

Three noteworthy consequences of the artifactual thesis of relativized semantics are:

-Rejection of the positivist observation-theory dichotomy,
       -Rejection of the positivist thesis of meaning invariance.
       -Rejection of the positivist analytic-synthetic dichotomy.

3.18 Rejection of the Observation-Theory Dichotomy

All descriptive terms are empirically underdetermined, such that what the positivists called “theoretical terms” are simply descriptive terms that are more empirically underdetermined than what the positivists called “observation terms”.

One of the motivations for the positivists’ accepting the observation-theory dichotomy is the survival of the ancient belief that science in one respect or another has some permanent and incorrigible foundation that distinguishes it as true knowledge as opposed to mere speculation or opinion. In the positivists’ version of this foundational agenda observational description is presumed to deliver this certitude, while theory language is subject to revision, which is sometimes revolutionary in scope. The positivists were among the last to believe in any such eternal verities as the defining characteristic of truly scientific knowledge.

More than a quarter of a century after Heisenberg said he could observe the electron in the Wilson cloud chamber, philosophers of science began to reconsider the concept of observation, a concept that had previously seemed inherently obvious. On the contemporary pragmatist view there are no observation terms that receive isolated meanings merely by simple ostension, and there is no distinctive or natural semantics for identifying language used for observational reporting. Instead every descriptive term is embedded in an interconnected system of beliefs, which Quine calls the “web of belief”. A relevant subset of the totality of beliefs constitutes a context for determining any given descriptive term’s meaning, and a unilingual dictionary’s relevant lexical entries are a minimal listing of a subset of relevant beliefs for each univocal term. Thus the positivists’ thesis of “observation terms” is rejected by pragmatists.

Quine said that all descriptive terms are empirically underdetermined, such that what the positivists called “theoretical terms” are simply descriptive terms that are more empirically underdetermined than what the positivists called “observation terms”. All descriptive terms lie on a continuum of greater or lesser degree empirical of underdetermination. Contemporary pragmatists view the positivist problem of the reduction of theoretical terms to observation terms as a pseudo problem.

3.19 Rejection of Meaning Invariance

The semantics of every descriptive term is determined by the term’s linguistic context consisting of a set of universally quantified statements believed to be true, such that a change in any of those contextual beliefs changes some component parts of the constituent terms’ meanings.

In science the linguistic context consisting of universally quantified statements believed to be true may include both theories awaiting empirical testing and law statements including test-design statements, which jointly contribute to the semantics of their shared constituent descriptive terms.

When the observation-theory dichotomy is rejected, the language that reports observations becomes subject to semantical change or what Feyerabend called “meaning variance”. For the convinced believer in a theory the statements of the theory contribute meaning parts to the semantics of descriptive language used to report observations, such that a revision of the theory changes part of the semantics of the relevant observational description.

3.20 Rejection of the Analytic-Synthetic Dichotomy

All universally quantified affirmations believed to be true are both analytic and empirical.

On the positivist view the truth of analytic sentences can be known a priori, i.e., by reflection on the meanings of the constituent descriptive terms, while synthetic sentences require empirical investigation to determine their truth status, such that their truth can only be known a posteriori. Thus to know the truth status of the analytic sentence “Every bachelor is unmarried”, it is unnecessary to take a survey of bachelors to determine whether or not any such men are currently married. However, determining the truth status of the sentence “Every raven is black” requires an empirical investigation of the raven bird population and then a generalizing inference.

On the alternative pragmatist view the semantics of all descriptive terms are contextually determined, such that all universally quantified affirmations believed to be true are analytic statements. But their truth status is not thereby known a priori, because they are also synthetic, i.e., empirical, firstly known a posteriori by experience. This dualism implies that when any universally quantified affirmation is believed to be empirically true, the sentence can then be used analytically, such that the meaning of its predicate offers a partial analysis of the meaning of its subject term. To express this analytic-empirical dualism Quine used the phrase “analytical hypotheses”.

Thus “Every raven is black” is as analytic as “Every bachelor is unmarried”, so long as both statements are believed to be true. The meaning of “bachelor” includes the idea of being unmarried and makes the phrase “unmarried bachelor” redundant. Similarly so long as one believes that all ravens are in fact black, then the meaning of “raven” includes the idea of being black and makes the phrase “black raven” redundant. In science an important reason for belief is empirical adequacy demonstrated by a nonfalsifying empirical test outcome.

3.21 Semantical Rules

A semantical rule is a universally quantified affirmation believed to be true and viewed in logical supposition in the metalinguistic perspective, such that the meaning of the predicate term displays some of the component part or parts of the meaning of the subject term.

The above discussion of analyticity leads immediately to the idea of “semantical rules”, a phrase also found in the writings of such philosophers as Rudolf Carnap and Alonzo Church but with different meanings. In the contemporary pragmatist philosophy semantical rules are statements in the metalinguistic perspective, because they are about language. And their constituent terms are viewed in logical supposition, because as semantical rules the statements are about meanings as opposed to nonlinguistic reality. Semantical rules are enabled by the complex nature of the semantics of descriptive terms. But due to psychological habit that enables prereflective linguistic fluency, meanings are experienced wholistically, and reflective semantical analysis is needed to appreciate their componential nature.

3.22 Componential vs. Wholistic Semantics

Semantical change had vexed the contemporary pragmatists, when they initially accepted the artifactual thesis of the semantics of language. When they rejected a priori analytic truth, many of them mistakenly also rejected analyticity altogether. And when they accepted the contextual determination of meaning, they mistakenly took an indefinitely large context as the elemental unit of language for consideration. They typically construed this elemental context as consisting of either an explicitly stated whole theory with no criteria for individuating theories, or an even more inclusive “paradigm”, i.e., a whole theory together with many associated pre-articulate skills and tacit beliefs. This wholistic (or “holistic”) semantical thesis is due to using the psychological experience of meaning instead of making semantic analyses that enable recognition of the componential nature of meaning.

On this wholistic view therefore a new theory that succeeds an alternative older one must, as Feyerabend maintains, completely replace the older theory including all its observational semantics and ontology, because its semantics is viewed as an indivisible unit. In his Patterns of Discovery Hanson attempted to explain such wholism in terms of Gestalt psychology. And following Hanson the historian of science Kuhn, who wrote a popular monograph titled Structure of Scientific Revolutions, explained the complete replacement of an old theory by a newer one as a “Gestalt switch”.

Feyerabend tenaciously maintained wholism, but attempted to explain it by his own interpretation of an ambiguity in Benjamin Lee Whorf’s thesis of linguistic relativity also known as the “Sapir-Whorf hypothesis” formulated jointly by Whorf and Edward Sapir, a Yale University Linguist. In his “Explanation, Reduction and Empiricism”, in Minnesota Studies in the Philosophy of Science and later in his Against Method Feyerabend proposes semantic “incommensurability”, which he says is evident when an alternative theory is not recognized to be an alternative. He cites the transition from Newtonian to Einstein’s relativity physics as an example of such incommensurability. The thesis of semantic incommensurability was also advocated by Kuhn, but he later revised the idea to admit partial or local incommensurability that enables “incommensurability with comparability”, but without successfully explaining how it can be partial.

Any wholistic semantical thesis including notably the semantic incommensurability thesis creates a pseudo problem for the decidability of empirical testing in science. It implies complete replacement of the semantics of the descriptive terms used for test design and observation. And complete replacement deprives the two alternative theories of any semantical continuity, such that their language cannot even describe the same phenomena or address the same problem. In fact the new theory cannot even be said to be an alternative to the old one, much less a more empirically adequate one. The empirical undecidability due to alleged semantical wholism would logically deny science both production of progress and recognition of its history of advancement. The untenable character of the situation is comparable to the French entomologist August Magnan whose book titled Insect Flight (1934) set forth an aerodynamic analysis proving that bees cannot fly. Bees do fly, and empirical tests do decide.

The thesis of componential semantics resolves the wholistic semantical muddle in the linguistic theses proffered by philosophers such as Kuhn and Feyerabend. Philosophers of science have overlooked componential semantics, but linguists have long recognized componential analysis in semantics, as may be found for example in George L. Dillon’s Introduction to Contemporary Linguistic Semantics. Some linguists use the phrase “lexical decomposition”. With the componential semantical thesis it is unnecessary to accept any wholistic view of semantics in philosophy much less any incommensurable discontinuity in language.

The expression of the componential aspect of semantics most familiar to philosophers of language is the analytic statement. But the pragmatists’ rejection of the analytic-synthetic dichotomy with its a priori truth claim need not imply the rejection of analyticity as such. The contextual determination of meaning exploits the analytic-empirical dualism.

Therefore when there is a semantical change in the descriptive terms in a system of beliefs due to a revision of some of the beliefs, some component parts of the terms’ complex meanings remain unaffected, while other parts are dropped and new ones added. For empirical testing in science the component meaning parts that remain unaffected by the change from one theory to a later alternative one include those parts determined by the statements of test design shared by the two theories, even if the executable test design was formulated after the older theory was initially proposed. Therein is found the semantical continuity that enables empirical testing of alternative theories to be decidable.

Thus a revolutionary change in scientific theory, such as the replacement of Newton’s theory of gravitation with Einstein’s, has the effect of changing only part of the semantics of the terms common to both the old and new theories. It leaves the semantics supplied by test-design language unaffected, so Arthur Eddington could test both Newton’s and Einstein’s theories of gravitation simultaneously by describing the same celestial photographic observations in his 1919-eclipse test. Thus contrary to Feyerabend there is no semantic incommensurability between these theories. And contrary to Feyerabend there is there no historical evidence that the advocates of Einstein’s relativity theory had failed to recognize that Einstein’s theory is an alternative to Newton’s.

Readers wishing to know more about the philosophies of Kuhn, Feyerabend, and Eddington’s 1919-eclipse test are referred to BOOK VI below.

3.23 Componential Artifactual Semantics Illustrated

The set of affirmations believed to be true and predicating characteristics universally and univocally of the term “raven” such as “Every raven is black” are semantical rules describing component parts of the complex meaning of “raven”. But if a field ornithologist captures a red bird specimen that exhibits all the characteristics of a raven except its black color, he must make a decision. He must decide whether he will continue to believe “Every raven is black” and that he holds in his birdcage some kind of red nonraven bird, or whether he will no longer believe “Every raven is black” and that the red bird in his birdcage is a red raven. Thus a semantical decision must be made. Color could be made a criterion for species identification instead of the ability to breed, although many other beliefs would also then be affected, an inconvenience that is typically avoided as a disturbing violation of the linguistic preference that Quine calls the principle of “minimum mutilation” of the web of belief.

Use of statements like “Every raven is black” may seem simplistic for science (if not quite bird-brained). But as it happens, a noteworthy revision in the semantics and ontology of birds has occurred due to a five-year genetic study launched by the Field Museum of Natural History in Chicago, the results of which were reported in the journal Science in June 2008. An extensive computer analysis of 30,000 pieces of nineteen bird genes showed that contrary to previously held belief falcons are genetically more closely related to parrots than to hawks, and furthermore that falcons should no longer be classified in the biological order originally named for them. As a result of the new genetic basis for classification, the American Ornithologists Union has revised its official organization of bird species, and many bird watchers’ field guides have been revised accordingly. Now well informed bird watchers will classify, conceptualize and observe falcons differently, because some parts of the meaning complex for the term “falcon” have been replaced with a genetically based conceptualization. Yet given the complexity of genetics some biologists argue that the concept of species is arbitrary.

Our semantical decisions alone neither create, nor annihilate, nor change mind-independent reality. But semantical decisions may change our mind-dependent linguistic characterizations of mind-independent reality and thus the ontologies, i.e., the various aspects of reality that the changed semantics reveals.

3.24 Semantic Values

Semantic values are the elementary component parts distributed among the meaning complexes associated with the descriptive terms of a language at a point in time.

For every descriptive term there are several semantical rules with each rule’s predicate describing some component parts of the common subject term’s meaning complex. A linguistic system therefore contains elementary components of meaning complexes that are shared by many descriptive terms, but are almost never uniquely associated with any single term, because all words have dictionary definitions analyzing the lexical entry’s component parts. These elementary components may be called “semantic values”.

Semantic values describe the most elementary ontological features of the real world that are distinguished by a language at a given point in time, and are the smallest elements in any meaning complex at the given point in time. The indefinitely vast residual reality not captured by any semantic values and that the language user’s semantics is unable to signify at the given point in time constitutes the empirical underdetermination of the whole language at the given point in time.

Different languages have different semantics and therefore display different ontologies. Where the semantics of one language displays semantic values not contained in the semantics of the other, the languages are said to be semantically incommensurable. Translation is therefore made imprecise.

A science at different times in its history may also have semantically incommensurable language, when the later version contains semantic values not contained in the earlier. But such incommensurability is rare, because it is routinely possible to resort to what Hanson called “phenomenal seeing”. And incommensurability does not occur in scientific revolutions understood as theory revision, because the revision is a reorganization of pre-existing information. When incommensurability occurs is it at times of discovery occasioning articulation of new semantic values due to new observations.

3.25 Univocal and Equivocal Terms

The definitions of descriptive terms such as common nouns and verbs in a unilingual dictionary function as semantical rules. Implicitly they are universally quantified logically, and are always presumed to be true. Usually each lexical entry in a large dictionary such as the Oxford English Dictionary offers several different meanings for a descriptive term, because terms are routinely equivocal. Language economizes on words by giving them several different meanings, which the fluent listener or reader can distinguish in context. Equivocations are the raw materials for puns. There is always at least one semantical rule for the meaning complex for each univocal use of a descriptive term, because to be meaningful, the term must be part of the linguistic system of beliefs. If the use is conventional, it must be capable of a lexical entry in a dictionary, or else recognized by some clique as an argot.

A descriptive term’s use is univocal, if no universally quantified negative categorical statement accepted as true can relate any of the predicates in the several universal affirmations functioning as semantical rules for the same subject term. Thus if two semantical rules have the form “Every X is A” and “Every X is B”, and if it is also believed that “No A is B”, then the terms “A” and “B” symbolize parts of different meanings for the term “X”, and “X” is equivocal. Otherwise “A” and “B” symbolize different parts of the same meaning complex associated with the univocal term “X”.

A definition in a unilingual dictionary functions as a semantical rule. But the dictionary definition is only a minimal description of the meaning complex of a univocal descriptive term, and it is not the whole description. Univocal terms have many semantical rules, when many characteristics can be predicated universally to a given subject. Thus there are multiple predicates that universally characterize ravens, characteristics known to the ornithologist, and which may fill a paragraph or more in his ornithological reference book.

Descriptive terms can become, as it were, partially equivocal through time, when some parts of the term’s meaning complex are unaffected by a change of defining beliefs, while other parts are simply dropped as archaic or are replaced by new parts contributed by new beliefs. In science this partial equivocation occurs when one theory is replaced by another newer one due to a test outcome, while the test designs for both theories remain the same. A term common to old and new theory may remain univocal only with respect to the parts contributed by the test-design language.

3.26 Signification and Supposition

Supposition enables identifying ambiguities not due to differences in signification that make equivocations, but instead are ambiguities due to differences in relating the semantics to its ontology.

The signification of a descriptive term is its meaning, and terms with two or more alternative significations are equivocal in the sense described in Section 3.25. The signification of a univocal term has different suppositions, when it describes ontology differently due to its having different functions in the sentences containing it.

Historically the subject term in the categorical proposition is said to be in “personal” supposition, because it references individual entities, while the predicate term is said to be in “simple” supposition, because the predicate signifies attributes without referencing any individual entities manifesting the attributes. For this reason the predicate in the categorical proposition is not logically quantified with any syncategorematic terms such as “every” or “some”. For example in “Every raven is black” the subject term “raven” is in personal supposition, while the predicate “black” is in simple supposition. So too for “No raven is black”.

Unlike semantical rules that describe signification, the supposition of descriptive terms in object language depends only on the rôle of the terms in a statement containing them and not on the truth of the statement. Thus the suppositions of the subject and predicate terms respectively are the same in the statement “Every raven is orange”, which is believed to be false, as they are in the statement “Every raven is black”, which is believed to be true.

Both personal and simple suppositions are types of “real” supposition, because they are different ways of talking about extramental reality. They operate in expressions in object language and thus describe ontologies as either attributes or the referenced individuals characterized by the signified attributes. Real supposition is contrasted with “logical” supposition, in which the meaning of the term is referenced in the metalinguistic perspective exclusively as a meaning, i.e., only semantics is referenced and not extramental ontology. For example in “Blackness is a component part of the meaning of raven”, the terms “raven” and “blackness” in this statement are in logical supposition. Similarly to say in explicit metalanguage “‘Every raven is black’ is a semantical rule” to express “Black is a component part of the meaning of raven”, is again to use both “raven” and “black” in logical supposition.

Furthermore just to use “Every raven is black” as a semantical rule in order to exhibit its meaning composition without actually saying that it is a semantical rule, is also to use the sentence in the metalinguistic perspective and in logical supposition. The difference between real and logical supposition in such use of a sentence is not exhibited syntactically, but is pragmatic and depends on the intention of the writer or speaker. Whenever a universally quantified affirmation is used in the metalinguistic perspective as a semantical rule for analysis in the semantical dimension, both the subject and predicate terms are in logical supposition. Lexical entries in dictionaries are in the metalinguistic perspective and in logical supposition, because they are about language and are intended to describe meanings.

In all the above types of supposition the same univocal term has the same signification. But another type of so-called supposition proposed incorrectly in ancient times is “material supposition”, in which the term is referenced in metalanguage as a linguistic symbol in the syntactical dimension with no reference to a term’s semantics or ontology in object language. An example is “’Raven’ is a five-letter word”. In this example “raven” does not refer either to the individual real bird or to its characteristics as in real supposition or to the universal concept of it as in logical supposition. Thus material supposition is not supposition properly so called, because the signification is different. It is actually an alternative meaning and thus a type of semantical equivocation. Some philosophers have used other vocabularies for recognizing this equivocation: Stanislaw Lesńiewski’s “use” (semantics) vs “mention” (syntax) and Rudolf Carnap’s “material mode” (semantics) vs “formal mode” (syntax).

3.27 Aside on Metaphor

A metaphor is a predication to a subject term that is intended to include only selected parts of the meaning complex conventionally associated with the predicate term, so the metaphorical predication is a true statement due to the exclusion of the remaining parts in the predicate’s meaning complex that would make the metaphorical predication a false statement.

In the last-gasp days of decadent neopositivism some positivist philosophers invoked the idea of metaphor to explain the semantics of theoretical terms. And a few were closet Cartesians who used it in the charade of justifying realism for theoretical terms. The theoretical term was the positivists’ favorite hobbyhorse. But both realism and the semantics of theories are unproblematic for contemporary pragmatists. In his “Posits and Reality” Quine said that all language is empirically underdetermined, and that the only difference between positing microphysical entities (like electrons) and macrophysical entities (like elephants) is that the statements describing the former are more empirically underdetermined than those describing the latter. Thus contrary to the neopositivists the pragmatists admit no qualitative dichotomy between the positivists so-called observation terms and their so-called theoretical terms.

As science and technology advance, concepts of microphysical entities like electrons are made less empirically underdetermined, as occurred for example with the development of the Wilson cloud chamber. While contemporary pragmatist philosophers of science recognize no need to explain so-called theoretical terms by metaphor or otherwise, metaphor is nevertheless a linguistic phenomenon often involving semantical change and it can easily be analyzed and explained with componential semantics.

It has been said that metaphors are both true and false. In a speaker or writer’s conventional or “literal” linguistic usage the entire conventional meaning complex associated with a univocal predicate term of a universal affirmation is operative. But in a speaker or writer’s metaphorical linguistic usage only some selected component part or parts of the entire meaning complex associated with the univocal predicate term are operative, and the remaining parts of the meaning complex are intended to be excluded, i.e., suspended from consideration and ignored. If the excluded parts were included, then the metaphorical statement would indeed be false. But the speaker or writer implicitly expects the hearer or reader to recognize and suspend from consideration the excluded parts of the predicate’s conventional semantics, while the speaker or writer uses the component part that he has selected for describing the subject truly.

Consider for example the metaphorical statement “Every man is a wolf.” The selected meaning component associated with “wolf” that is intended to be predicated truly of “man” might describe the wolf’s predatory behaviors, while the animal’s quadrupedal anatomy, which is conventionally associated with “wolf”, is among the excluded meaning components for “wolf” that are not intended to be predicated truly of “man”.

A listener or reader may or may not succeed in understanding the metaphorical predication depending on his ability to select the applicable parts of the predicate’s semantics tacitly intended by the issuer of the metaphor. But there is nothing arcane or mysterious about metaphors, because they can be explained in literal (i.e., conventional) terms to the uncomprehending listener or reader. To explain the metaphorical predication of a descriptive term to a subject term is to list explicitly those affirmations intended to be true of that subject and that set forth just those parts of the predicate’s meaning that the issuer intends to be applicable.

The explanation may be further elaborated by listing separately the affirmations that are not viewed as true of the subject, but which are associated with the predicated term when it is predicated conventionally. Or these may be expressed as universal negations stating what is intended to be excluded from the predicate’s meaning complex in the particular metaphorical predication, e.g., “No man is quadrupedal.” In fact such negative statements might be given as hints by a picaresque issuer of the metaphor for the uncomprehending listener.

A semantical change occurs when the metaphorical predication becomes conventional, and this change to conventionality produces an equivocation. The equivocation consists of two literal meanings: the original one and a derivative meaning that is now a dead metaphor. As a dead man is no longer a man, so a dead metaphor is no longer a metaphor. A dead metaphor is a meaning from which the suspended parts in the metaphor have become conventionally excluded to produce a new “literal” meaning. Trite metaphors, when not just forgotten, metamorphose into new literals, as they become conventional.

3.28 Clear and Vague Meaning

Meanings are more or less clear and vague, such that the greater the clarity, the less the vagueness. Vagueness is empirical underdetermination, and can never be eliminated completely, since our concepts can never grasp reality exhaustively. But vagueness in the semantics of a descriptive term is reduced by the addition of universal affirmations and/or negations accepted as true, to the list of the term’s semantic rules with each rule having the term as a common subject. The clarification is supplied by the semantics of the predicates in the added universal affirmations and/or negations.

Adding semantical rules increases clarity by elaboration. Thus if the list of universal statements believed to be true are in the form “Every X is A” and “Every X is B”, then clarification of X with respect to a descriptive predicate “C” consists in adding to the list either the statement in the form “Every X is C” or the statement in the form “No X is C”. Clarity is thereby added by elaborating the meaning of “X”.

Adding semantical rules that relate any of the univocal predicates in the semantical rules for the same subject increases clarity by increasing coherence. Thus if the predicate terms “A” and “B” in the semantical rules with the form “Every X is A” and “Every X is B” are related by the statements in the form “Every A is B” or “Every B is A”, then one of the statements in the list can be logically derived from the others. Awareness of the deductive relationship and the consequent display of structure in the meaning complex associated with the term “X” makes the complex meaning of “X” more coherent, because the deductive relation makes it more semantically integrated. And the coherence also supplies a psychological satisfaction. Clarity is thereby added by exhibiting semantic structure in a deductive system.

These additional semantical rules relating the predicates may be negative as well as affirmative. Additional universal negations offer clarification by exhibiting equivocation. Thus if two semantical rules are in the form “Every X is A” and “Every X is B”, and if it is also believed that “No A is B” or its equivalent “No B is A”, then the terms “A” and “B” symbolize parts of different meanings for the term “X”, and “X” is equivocal. Clarity is thereby added by the negation.

3.29 Semantics of Mathematical Language

The semantics for a descriptive mathematical variable is determined by its context consisting of universally quantified statements believed to be true including mathematical expressions in both theory language proposed for testing and test-design language presumed for testing.

Both test designs and theories often involve mathematical expressions. Thus the semantics for the descriptive variables common to a test design and a theory may be supplied in part by mathematical expressions, such that the structure of their meaning complexes is partly mathematical. The semantics-determining statements in test designs for mathematically expressed theories may include mathematical equations, measurement language describing the subject measured, the measurement procedures, the metric units and any employed apparatus.

Some of these statements may resemble 1946 Nobel-laureate physicist Percy Bridgman’s “operational definitions”, because the statements describing the measurement procedures and apparatus contribute meaning to the descriptive term. But contrary to Bridgman, and as Carnap says in his Philosophical Foundations of Physics, each of several operational definitions for the same term does not constitute a separate definition for the term’s concept for the measured subject, thereby making the term equivocal. Likewise pragmatists say that descriptions of different measurement procedures contribute different parts to the univocal meaning of the descriptive term, unless the different procedures produce different measurement values, where the differences are greater than the estimated measurement error in the same range of measurement.


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