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by Corry Shores
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[Quine, Two Dogmas of Empiricism, entry directory]
[The following is a paragraph by paragraph summary of the text. More analysis is still needed and will be updated when conducted. Proofreading is incomplete, so please forgive all my various mistakes. Material between brackets or between parentheses within brackets is my own and should not be trusted over the quotations, which themselves may contain typographical errors from their transcription. Please consult the original text in any case.]
Summary of
W. V. Quine
“Two Dogmas of Empiricism”
2
Definition
Brief summary (collecting those below):
(2.1) (Recall from section 1.12 that there is a first class of analytic statements that are “logically true”, because their denial presents a formal contradiction, as with “No unmarried man is married.” And recall from section 1.13 that there is a second class of statements that are thought to be analytic, because they can be rendered into logically true ones by means of a substitution of synonyms, as “No bachelor is married” can be rendered “No unmarried man is married” but substituting the synonyms “bachelor” and “unmarried man”.) Some feel that analytic statements of the second class can reduce into the first class by means of definition. For example, “bachelor” is defined as an “unmarried man,” thus we can thereby transform “No bachelor is married” to “No unmarried man is married.” Quine then wonders, on what basis can we establish such definitional equivalences? If our answer is, the dictionary, then we have a problem. The dictionary does not establish the equivalences. It only describes equivalences that are already found to be operable in a language. We still need to account for how these equivalences are established within linguistic behavior, independently of the lexicographer’s descriptions of it. (2.2) Even when other fields define terms, they often similarly do it by “affirming a relationship of synonymy antecedent to the exposition in hand” (25). (2.3) Normally synonymy is grounded in usage, and thus “Definitions reporting selected instances of synonymy come then as reports upon usage” (25). (2.4) Carnap however discusses a definitional activity, called explication, that is not merely a lexicographical reporting of pre-existing synonymies. When we explicate a term, we do not simply give a synonymous meaning to the term being defined (that is, to the “definiendum”). We instead improve upon it “by refining or supplementing its meaning” (25). However, even though this is not a report of a pre-existing synonymy, still, Quine argues, explication rests upon other pre-existing synonymies. (2.5) Even in cases where we have two alternative, non-synonymous definientia that are equally appropriate for explicating a given term (they may be interchangeable in one context but not in others) and where we choose one over the other and thus where we have by fiat (rather than by observation) a relation of synonymy that did not hold before, still this uses pre-existing synonymies. (2.6) Quine notes one example of definition not based on prior synonymies, namely, when we introduce “novel notations for purposes of sheer abbreviation. Here the definiendum becomes synonymous with the definiens simply because it has been created expressly for the purpose of being synonymous with the definiens” (26). Quine seems to suggest, however, that this meager instance is the only exception. (2.7) There are two kinds of economy in mathematical and logical systems. The nature of each counteracts the other. {1} Economy of practical expression. Here there are “distinctive concise notations for a wealth of concepts,” and it strives for “ease and brevity in the statement of multifarious relationships” (26). {2} Economy of grammar and vocabulary. Here what is first determined is a minimum of basic concepts. Then, a distinctive notation is assigned to them. On that basis, other more complex concepts can be formulated by combining the basic notations. In this case, because the basic elements are minimized, “it greatly simplifies theoretical discourse about the language, through minimizing the terms and the forms of construction wherein the language consists” (26). But it also has the impractical feature of requiring the more complex formulations to be rendered less economically. (Presumably in the first case, there are many more notations, which allow for the more complex ones to be rendered more economically. (2.8) To get the best of both economies, often they are combined as two related languages. The more “inclusive” one has complex grammar and vocabulary, but shorter messages, while the other, called “primitive notation” is more efficient with grammar and vocabulary. There are then rules to translate the formulations of the inclusive language into complexes of primitive notation. “These rules of translation are the so-|called definitions which appear in formalized systems. They are best viewed not as adjuncts to one language but as correlations between two languages, the one a part of the other” (26-27). (I wonder if it is something similar to object language and metalanguage. See Tarski.) (2.9) The relation that the definitions create between definiendum and definiens can be one of three sorts: {1} the definiens may paraphrase the definiendum in a way that preserves “a direct synonymy as of antecedent usage”; {2} the definiens may explicate the definiendum, thereby improving upon its antecedent usage; or {3} the definiendum may be a newly established notation therewith endowed with its own meaning. (2.10) Thus we see that with one rare exception (the introduction of new notation), definition depends upon prior synonymy when used in both formal and informal languages. (Recall that our present concern is grounding analyticity. We found in section 1 that under Kant’s conception, it means the sentence is true by meaning and independent of fact. Then we found that the notion of meaning was elusive and superfluous when considering extension. We next noted that while we have a formal way to define analyticity when the denial of the sentence presents an obvious self contradiction, like “No unmarried man is married,” we do not have such a formal grounding for converting other kinds of analytic statements into ones of that form, for example, “No bachelors are married.” We know that it has to do with synonymy. And we need a formal means to ground it. But as we have seen in this section, using definitions is not viable, because instead of being responsible for establishing synonymies, they instead are based on pre-existing synonymies. Thus we must look elsewhere for a way to ground synonymy.)
[The Unfeasibility of Grounding the Transformability of Sentences into Logically True Ones in Dictionary Entries]
[Other Fields’ Definitions as Doing the Same]
[Synonymy as Found in Usage]
[Carnap’s Explication as Also Being Based in Pre-Existing Synonymies]
[Cases of Selected Alternative Explications as Also Involving Pre-Existing Synonymies]
[Exception: Novel Abbreviatory Notations]
[Two Kinds of Economy in Mathematical and Logical Systems: Economy of Practical Expression and Economy of Grammar and Vocabulary]
[Coordinating Two Languages of Each Economy Using Definitions for Translation]
[Three Relations Between Definiendum and Definiens]
Summary
[The Unfeasibility of Grounding the Transformability of Sentences into Logically True Ones in Dictionary Entries]
[(Recall from section 1.12 that there is a first class of analytic statements that are “logically true”, because their denial presents a formal contradiction, as with “No unmarried man is married.” And recall from section 1.13 that there is a second class of statements that are thought to be analytic, because they can be rendered into logically true ones by means of a substitution of synonyms, as “No bachelor is married” can be rendered “No unmarried man is married” but substituting the synonyms “bachelor” and “unmarried man”.) Some feel that analytic statements of the second class can reduce into the first class by means of definition. For example, “bachelor” is defined as an “unmarried man,” thus we can thereby transform “No bachelor is married” to “No unmarried man is married.” Quine then wonders, on what basis can we establish such definitional equivalences? If our answer is, the dictionary, then we have a problem. The dictionary does not establish the equivalences. It only describes equivalences that are already found to be operable in a language. We still need to account for how these equivalences are established within linguistic behavior, independently of the lexicographer’s descriptions of it.]
[ditto. ]
There are those who find it soothing to say that the analytic statements of the second class reduce to those of the first class, the logical truths, by definition; ‘bachelor’, e.g., is defined as ‘unmarried man’. But how do we find that ‘bachelor’ is defined as ‘unmarried man’? Who defined it thus, and when? Are we to appeal to the nearest dictionary, and accept the lexicographer’s formulation as law? Clearly this would be to put the cart before the horse. The lexicographer is an empirical scientist, whose business is the recording of antecedent facts; and if he glosses ‘bachelor’ as ‘unmarried man’ it is because of his belief that there is a relation of synonymy between these forms, implicit in general or preferred usage prior to his own work. The notion of synonymy presupposed here has still to be clarified, presumably in terms relating to linguistic behavior. Certainly the “definition” which is the lexicographer’s report of an observed synonymy cannot be taken as the ground of the synonymy.
(24)
[Other Fields’ Definitions as Doing the Same]
[Even when other fields define terms, they often similarly do it by “affirming a relationship of synonymy antecedent to the exposition in hand” (25).]
[ditto]
Definition is not, indeed, an activity exclusively of philologists. Philosophers and scientists frequently have occasion to “define” a | recondite term by paraphrasing it into terms of a more familiar vocabulary. But ordinarily such a definition, like the philologist’s, is pure lexicography, affirming a relationship of synonymy antecedent to the exposition in hand.
(24-25)
[Synonymy as Found in Usage]
[Normally synonymy is grounded in usage, and thus “Definitions reporting selected instances of synonymy come then as reports upon usage” (25). ]
[ditto]
Just what it means to affirm synonymy, just what the interconnections may be which are necessary and sufficient in order that two linguistic forms be properly describable as synonymous, is far from clear; but, whatever these interconnections may be, ordinarily they are grounded in usage. Definitions reporting selected instances of synonymy come then as reports upon usage.
(25)
[Carnap’s Explication as Also Being Based in Pre-Existing Synonymies]
[Carnap however discusses a definitional activity, called explication, that is not merely a lexicographical reporting of pre-existing synonymies. When we explicate a term, we do not simply give a synonymous meaning to the term being defined (that is, to the “definiendum”). We instead improve upon it “by refining or supplementing its meaning” (25). However, even though this is not a report of a pre-existing synonymy, still, Quine argues, explication rests upon other pre-existing synonymies.]
[ditto. Here by the way are some relevant passages by Carnap.
The task of making more exact a vague or not quite exact concept used in everyday life or in an earlier stage of scientific or logical development, | or rather of replacing it by a newly constructed, more exact concept, belongs among the most important tasks of logical analysis and logical construction. We call this the task of explicating, or of giving an explication for, the earlier concept; this earlier concept, or sometimes the term used for it, is called the explicandum; and the new concept, or its term, is called an explicatum of the old one. Thus, for instance, Frege and, later, Russell took as explicandum the term ‘two’ in the not quite exact meaning in which it is used in everyday life and in applied mathematics; they proposed as an explicatum for it an exactly defined concept, namely, the class of pair-classes [...] Many concepts now defined in semantics are meant as explicata for concepts earlier used in everyday language or in logic. For instance, the semantical concept of truth has as its explicandum the concept of truth as used in everyday language (if applied to declarative sentences) and in all of traditional and modern logic. [...] Generally speaking, it is not required that an explicatum have, as nearly as possible, the same meaning as the explicandum; it should, however, correspond to the explicandum in such a way that it can be used instead of the latter.
(Carnap 7-8)
(Note: I was not able to summarize Quine’s reasoning for his critical comments, because I am not sure what he means by “contexts.” But we can still work through it as best we can, just to start somewhere. And we can go line by line. “Any word worth explicating has some contexts which, as wholes, are clear and precise enough to be useful; and the purpose of explication is to preserve the usage of these favored contexts while sharpening the usage of other contexts.” Suppose we have a term we want to explicate. Let’s say it is “analog” maybe. Suppose we have a mathematically precise notion of the continuum of variables that compose something that is analog (see for instance Trask.) Perhaps Quine is saying that we have this context where the notion is precise, and then we want to achieve a similar level of precision in another context, for instance, when discussing the analog features of record albums (see for instance this entry). Next: “In order that a given definition be suitable for purposes of explication, therefore, what is required is not that the definiendum in its antecedent usage be synonymous with the definiens, but just that each of these favored contexts of the definiendum, taken as a whole in its antecedent usage, be synonymous with the corresponding context of the definiens.” Here I am really unsure what Quine means, but this is my guess. In the case of the analog contexts, we begin in the mathematical context which understands analog as a perfectly dense continuum of quantitative variation. Suppose we want to be sure that it is not understood like Russell’s continuum, which is made of an infinity of discrete parts, but rather we want it to be more like a Bergsonian sort of continuum (as with Duration), where it is made never of discrete parts but rather always with movements or transitions. Then, we explicate the notion of analog by placing it into the context of movements that are continuously variable, like the needle moving along the record groove. Perhaps, (and quite likely not, but I have no other guesses), Quine is saying that the contexts are synonymous, in the sense that it is the notion of the continuity of variation that makes analog, rather than being a composition of infinitely many static points all densely packed together. Thus perhaps (and again, probably not) Quine is saying that there is still a pre-existing synonymy between analog as a mathematical continuum of variation and as a mechanical continuous motion, because both were already thought to be equivalent, only now, the features of the mechanical context are brought to light in order to highlight certain features in the mathematical context.)]
There is also, however, a variant type of definitional activity which does not limit itself to the reporting of pre-existing synonymies. I have in mind what Carnap calls explication – an activity to which philosophers are given, and scientists also in their more philosophical moments. In explication the purpose is not merely to paraphrase the definiendum into an outright synonym, but actually to improve upon the definiendum by refining or supplementing its meaning. But even explication, though not merely reporting a pre-existing synonymy between definiendum and definiens, does rest nevertheless on other pre-existing synonymies. The matter may be viewed as follows. Any word worth explicating has some contexts which, as wholes, are clear and precise enough to be useful; and the purpose of explication is to preserve the usage of these favored contexts while sharpening the usage of other contexts. In order that a given definition be suitable for purposes of explication, therefore, what is required is not that the definiendum in its antecedent usage be synonymous with the definiens, but just that each of these favored contexts of the definiendum, taken as a whole in its antecedent usage, be synonymous with the corresponding context of the definiens.
(25)
[Cases of Selected Alternative Explications as Also Involving Pre-Existing Synonymies]
[Even in cases where we have two alternative, non-synonymous definientia that are equally appropriate for explicating a given term (they may be interchangeable in one context but not in others) and where we choose one over the other and thus where we have by fiat (rather than by observation) a relation of synonymy that did not hold before, still this uses pre-existing synonymies.]
[ditto. (Note: I again cannot explain this meaning, as I do not have a precise conception of what he means by the synonymy of contexts.)]
Two alternative definientia may be equally appropriate for the purposes of a given task of explication and yet not be synonymous with each other; for they may serve interchangeably within the favored contexts but diverge elsewhere. By cleaving to one of these definientia rather than the other, a definition of explicative kind generates, by fiat, a relationship of synonymy between definiendum and definiens which did not hold before. But such a definition still owes its explicative function, as seen, to pre-existing synonymies.
(25)
[Exception: Novel Abbreviatory Notations]
[Quine notes one example of definition not based on prior synonymies, namely, when we introduce “novel notations for purposes of sheer abbreviation. Here the definiendum becomes synonymous with the definiens simply because it has been created expressly for the purpose of being synonymous with the definiens” (26). Quine seems to suggest, however, that this meager instance is the only exception.]
[ditto]
There does, however, remain still an extreme sort of definition which does not hark back to prior synonymies at all; viz., the explicitly conventional introduction of novel notations for purposes of sheer abbreviation. Here the definiendum becomes synonymous with the definiens simply because it has been created expressly for the purpose of being synonymous with the definiens. Here we have a really transparent case of synonymy created by definition; would that all species of synonymy were as intelligible. For the rest, definition rests on synonymy rather than explaining it.
(26)
[Two Kinds of Economy in Mathematical and Logical Systems: Economy of Practical Expression and Economy of Grammar and Vocabulary]
[There are two kinds of economy in mathematical and logical systems. The nature of each counteracts the other. {1} Economy of practical expression. Here there are “distinctive concise notations for a wealth of concepts,” and it strives for “ease and brevity in the statement of multifarious relationships” (26). {2} Economy of grammar and vocabulary. Here what is first determined is a minimum of basic concepts. Then, a distinctive notation is assigned to them. On that basis, other more complex concepts can be formulated by combining the basic notations. In this case, because the basic elements are minimized, “it greatly simplifies theoretical discourse about the language, through minimizing the terms and the forms of construction wherein the language consists” (26). But it also has the impractical feature of requiring the more complex formulations to be rendered less economically. (Presumably in the first case, there are many more notations, which allow for the more complex ones to be rendered more economically.]
[ditto]
In logical and mathematical systems either of two mutually antagonistic types of economy may be striven for, and each has its peculiar practical utility. On the one hand we may seek economy of practical expression: ease and brevity in the statement of multifarious relationships. This sort of economy calls usually for distinctive concise notations for a wealth of concepts. Second, however, and oppositely, we may seek economy in grammar and vocabulary; we may try to find a minimum of basic concepts such that, once a distinctive notation has been appropriated to each of them, it becomes possible to express any desired further concept by mere combination and iteration of our basic notations. This second sort of economy is impractical in one way, since a poverty in basic idioms tends to a necessary lengthening of discourse. But it is practical in another way: it greatly simplifies theoretical discourse about the language, through minimizing the terms and the forms of construction wherein the language consists.
(26)
[Coordinating Two Languages of Each Economy Using Definitions for Translation]
[To get the best of both economies, often they are combined as two related languages. The more “inclusive” one has complex grammar and vocabulary, but shorter messages, while the other, called “primitive notation” is more efficient with grammar and vocabulary. There are then rules to translate the formulations of the inclusive language into complexes of primitive notation. “These rules of translation are the so-|called definitions which appear in formalized systems. They are best viewed not as adjuncts to one language but as correlations between two languages, the one a part of the other” (26-27). (I wonder if it is something similar to object language and metalanguage. See Tarski.)]
[ditto]
Both sorts of economy, though prima facie incompatible, are valuable in their separate ways. The custom has consequently arisen of combining both sorts of economy by forging in effect two languages, the one a part of the other. The inclusive language though redundant in grammar and vocabulary, is economical in message lengths, while the part, called primitive notation, is economical in grammar and vocabulary. Whole and part are correlated by rules of translation whereby each idiom not in primitive notation is equated to some complex built up of primitive notation. These rules of translation are the so-|called definitions which appear in formalized systems. They are best viewed not as adjuncts to one language but as correlations between two languages, the one a part of the other.
(26-27)
[Three Relations Between Definiendum and Definiens]
[The relation that the definitions create between definiendum and definiens can be one of three sorts: {1} the definiens may paraphrase the definiendum in a way that preserves “a direct synonymy as of antecedent usage”; {2} the definiens may explicate the definiendum, thereby improving upon its antecedent usage; or {3} the definiendum may be a newly established notation therewith endowed with its own meaning.]
[ditto]
But these correlations are not arbitrary. They are supposed to show how the primitive notations can accomplish all purposes, save brevity and convenience, of the redundant language. Hence the definiendum and its definiens may be expected, in each case, to be related in one or another of the three ways lately noted. The definiens may be a faithful paraphrase of the definiendum into the narrower notation, preserving a direct synonymy as of antecedent usage; or the definiens may, in the spirit of explication, improve upon the antecedent usage of the definiendum; or finally, the definiendum may be a newly created notation, newly endowed with meaning here and now.
(27)
[The Conclusion Being That Definitions Are Inadequate to Ground Synonymy (And Thus Analyticity)]
[Thus we see that with one rare exception (the introduction of new notation), definition depends upon prior synonymy when used in both formal and informal languages. (Recall that our present concern is grounding analyticity. We found in section 1 that under Kant’s conception, it means the sentence is true by meaning and independent of fact. Then we found that the notion of meaning was elusive and superfluous when considering extension. We next noted that while we have a formal way to define analyticity when the denial of the sentence presents an obvious self contradiction, like “No unmarried man is married,” we do not have such a formal grounding for converting other kinds of analytic statements into ones of that form, for example, “No bachelors are married.” We know that it has to do with synonymy. And we need a formal means to ground it. But as we have seen in this section, using definitions is not viable, because instead of being responsible for establishing synonymies, they instead are based on pre-existing synonymies. Thus we must look elsewhere for a way to ground synonymy.)]
[ditto]
In formal and informal work alike, thus, we find that definition – except in the extreme case of the explicitly conventional introduction of new notations – hinges on prior relationships of synonymy. Recognizing then that the notion of definition does not hold the key to synonymy and analyticity, let us look further into synonymy and say no more of definition.
(27)
Quine, W. V. “Two Dogmas of Empiricism.” The Philosophical Review 60, no. 1 (1951): 20–43.
Carnap, Rudolf. Meaning and Necessity: A Study in Semantics and Modal Logic. Chicago: University of Chicago, 1947.
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