25 Jul 2021

Quine (3) “Two Dogmas of Empiricism”, section 3, “Interchangeability”, summary

 

by Corry Shores

 

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[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”

 

 

3

Interchangeability

 

 

 

 

 

 

 

 

Brief summary (collecting those below):

(3.1) (Recall that in this paper, Quine is addressing two dogmas of empiricism, namely the analytic/synthetic distinction and reductionism (see section 0). We are now looking for a way ground analyticity. We found in section 1 that we cannot use the Kantian notion that it is based on meanings. We next looked at a formal grounding for it with a class of analytic statements where it can be formally defined as the denial rendering a self-contradiction, like “No unmarried man is married.” The problem was that there is another class of analytic sentences, like “No bachelor is married,” where its denial does not render an obvious self-contradiction. However, it is thought to be translatable into the first class by means of a synonymy of the terms “bachelor” and “unmarried man.” So we sought a way to ground this synonymy, so to ground all analytic statements of any kind. We found in section 2 that definitions will not suffice, because rather than establishing synonymies, they instead employ pre-existing ones. So) we are currently considering another way to ground synonymy, namely, “their interchangeability in all contexts without change of truth value; interchangeability, in Leibniz’s phrase, salva veritate” (27). This can even work for vague terms, so long as that vagueness matches in each context. (3.2) Yet, this does not work for “bachelor” and “unmarried man.” For instance, we cannot substitute “unmarried man” in for “bachelor,” in the phrase “bachelor of arts” or in the sentence “‘Bachelor’ has less than ten letters.” One solution for these cases is to treat them as longer forms constituting one word and stipulating that they cannot be broken down and have their parts be substituted. The problem with this approach is that it presupposes a conception of word, but we will put that issue aside for the moment. (3.3) What we need to now determine is how sufficient interchangeability salva veritate is to define synonymy. It would be insufficient if there are cases of nonsynonymous words that still fulfill the requirements for interchangeability salva veritate (interchangeable in all contexts without change of truth value). Quine notes that the synonymy in question here does not mean that when interchanged it has identical mental associations or poetic qualities. For, in fact, we will never find such cases of synonymy anyway. More precisely, the kind of synonymy we have in mind is cognitive synonymy. It will be more fully explicated throughout the essay. It is the sort of synonymy that allows an analytic statement (like “All Bachelors are unmarried men”) to be converted into logical truths (like “Unmarried men are unmarried men”) by means substituting synonyms. If we assume what analyticity is (even though in fact we are trying to ground it), we can define the cognitive synonymy of “bachelor” and “unmarried man” with the statement: (3) “All and only bachelors are unmarried men” is analytic. (Perhaps the idea here is that all cases of one are cases of the other, so nothing will be lost or gained by substituting them.) (3.4) We need still a definition of cognitive synonymy that does not presuppose analyticity, and we are currently considering as a possible candidate interchangeability salva veritate. To see that it works, recall first (3) “All and only bachelors are unmarried men.” We next consider (4) “Necessarily all and only bachelors are bachelors.” This is self-evidently true (if it were false, it would be a contradiction, perhaps). Next, we suppose that ‘bachelor’ and ‘unmarried man’ are interchangeable salva veritate, and by making the substitutions, we obtain (5) “Necessarily, all and only bachelors are unmarried men.” If we say that this is true, then we are saying that ‘bachelor’ and ‘unmarried man’ are synonymous, and thus that (3) “All and only bachelors are unmarried men” is analytic (perhaps because by means of an acceptable substitution, it can be rendered into the analytically true “All bachelors are bachelors” or “All unmarried men are unmarried men.” (3.5) Something that makes this proposal tricky is that it regards(4) “Necessarily all and only bachelors are bachelors” as analytic on account of the use of “necessarily”. (Perhaps this is because when it is necessary, it is impossible to not be so. Thus it fulfills the formal criterion of analyticity as its denial being a contradiction.) This means that we are dangerously close to circularity. We want to define analyticity, but we assume it with our use of “necessarily.” So is this a straightforward case of circularity? (3.6) Quine claims that it is not entirely circular but can be thought more of as “a closed curve in space” (29). (3.7) We need to specify the parameters of a language before we can adequately see interchangeability salva veritate operating in it. Quine stipulates a language with atomic sentences composed of predicates and variables and with rules to build up complex sentences using truth functions (truth functional connectives maybe) and quantification (among other features). This language can handle descriptions, class names, and singular terms. This sort of a language will be “extensional” because in it, “any two predicates which agree extensionally (i.e., are true of the same objects) are interchangeable salva veritate” (29). (3.8) (Recall from section 1.6 the example of predicates, “creature with a heart” and “creature with a kidney”. They might be alike in extension, but they are not alike in meaning. Quine now seems to say that these predicates are also not cases of cognitive synonymy. Thus we might gather that cognitive synonymy requires a similarity in meaning, which may not have been noted back in section 3.3 when he was first discussing it.) In an extensional language, we can interchange salva veritate ‘bachelor’ and ‘unmarried man’ , because they extensionally refer to exactly the same class of entities. But we can do the same for ‘creature with a heart’ and ‘creature with a kidney’. Thus, interchangeability salva veritate in an extensional language does not give us cognitive synonymy, which we need for grounding analyticity. It only can tell us that (3) “All and only bachelors are unmarried men” is true. (3.9) But as we saw in section 1, we need to equate the cognitive synonymy between words like ‘bachelor’ and ‘unmarried man’ with the analyticity of (3) “All and only bachelors are unmarried men” and not merely with its truth, which is all that extensionality can accomplish. (3.10) So we see that “interchangeability salva veritate, if construed in relation to an extensional language, is not a sufficient condition of cognitive synonymy” (30). And previously we saw that “If a language contains an intensional adverb ‘necessarily’ [...], then interchangeability salva veritate in such a language does afford a sufficient condition of cognitive synonymy; but such a language is intelligible only if the notion of analyticity is already clearly understood in advance” (30) (3.11) So we cannot first formally establish cognitive synonymy to then secondly ground analyticity, like we set out to do. Supposing we could firstly ground analyticity, then we could define cognitive synonymy fairly easily, however: “Singular terms may be said to be cognitively synonymous when the statement of identity formed by putting ‘=’ between them is analytic. Statements may be said simply to be cognitively synonymous when their biconditional (the result of joining them by ‘if and only if’) is analytic” (31). Furthermore, “we can describe any two linguistic forms as cognitively synonymous when the two forms are interchangeable (apart from occurrences within ‘words’) salva (no longer veritate but) analyticitate” (31). So let us return now to the problem of analyticity.

 

 

 

 

 

 

Contents

 

3.1

[Interchangeability Without Loss of Truth as Potential Ground for Synonymy]

 

3.2

[The Need to Define “Word”]

 

3.3

[Cognitive Synonymy as Fulfilling the Requirements for Interchangeability Salva veritate]

 

3.4

[Using “Necessarily” to Define Synonymy Indirectly in Terms of Analyticity]

 

3.5

[The Potential Circularity of Using “Necessarily” to Function for Analyticity]

 

3.6

[The Solution as Not Entirely Circular]

 

3.7

[Extensionality (in a Logically Formulated Language) as Interchangeability Salva veritate]

 

3.8

[Extensional Languages as Not Ensuring Cognitive Synonymy]

 

3.9

[Extensional Synonymy as Not Being Cognitive Synonymy and as Being Unable to Ground Analyticity]

 

3.10

[The Problems with Extensional Interchangeability Salva veritate and with “Necessarily”]

 

3.11

[Grounding Analyticity First as a Better Strategy]

 

Bibliography

 

 

 

 

 

 

 

Summary

 

3.1

[Interchangeability Without Loss of Truth as Potential Ground for Synonymy]

 

[(Recall that in this paper, Quine is addressing two dogmas of empiricism, namely the analytic/synthetic distinction and reductionism (see section 0). We are now looking for a way ground analyticity. We found in section 1 that we cannot use the Kantian notion that it is based on meanings. We next looked at a formal grounding for it with a class of analytic statements where it can be formally defined as the denial rendering a self-contradiction, like “No unmarried man is married.” The problem was that there is another class of analytic sentences, like “No bachelor is married,” where its denial does not render an obvious self-contradiction. However, it is thought to be translatable into the first class by means of a synonymy of the terms “bachelor” and “unmarried man.” So we sought a way to ground this synonymy, so to ground all analytic statements of any kind. We found in section 2 that definitions will not suffice, because rather than establishing synonymies, they instead employ pre-existing ones. So) we are currently considering another way to ground synonymy, namely, “their interchangeability in all contexts without change of truth value; interchangeability, in Leibniz’s phrase, salva veritate” (27). This can even work for vague terms, so long as that vagueness matches in each context.]

 

[ditto]

A natural suggestion, deserving close examination, is that the synonymy of two linguistic forms consists simply in their interchangeability in all contexts without change of truth value; interchangeability, in Leibniz’s phrase, salva veritate. Note that synonyms so conceived need not even be free from vagueness, as long as the vaguenesses match.

(27)

[contents]

 

 

 

 

 

 

3.2

[The Need to Define “Word”]

 

[Yet, this does not work for “bachelor” and “unmarried man.” For instance, we cannot substitute “unmarried man” in for “bachelor,” in the phrase “bachelor of arts” or in the sentence “‘Bachelor’ has less than ten letters.” One solution for these cases is to treat them as longer forms constituting one word and stipulating that they cannot be broken down and have their parts be substituted. The problem with this approach is that it presupposes a conception of word, but we will put that issue aside for the moment.]

 

[ditto]

But it is not quite true that the synonyms ‘bachelor’ and ‘unmarried man’ are everywhere interchangeable salva veritate. Truths which become false under substitution of ‘unmarried man’ for ‘bachelor’ are easily constructed with help of ‘bachelor of arts’ or ‘bachelor’s buttons’. Also with help of quotation, thus:

‘Bachelor’ has less than ten letters.

Such counterinstances can, however, perhaps be set aside by treating the phrases ‘bachelor of arts’ and ‘bachelor’s buttons’ and the quotation ‘ ‘bachelor’ ‘ each as a single indivisible word and then stipulating that the interchangeability salva veritate which is to be the touchstone of synonymy is not supposed to apply to fragmentary oc-|currences inside of a word. This account of synonymy, supposing it acceptable on other counts, has indeed the drawback of appealing to a prior conception of “word” which can be counted on to present difficulties of formulation in its turn. Nevertheless some progress might be claimed in having reduced the problem of synonymy to a problem of wordhood. Let us pursue this line a bit, taking “word” for granted.

(27-28)

[contents]

 

 

 

 

 

 

3.3

[Cognitive Synonymy as Fulfilling the Requirements for Interchangeability Salva veritate]

 

[What we need to now determine is how sufficient interchangeability salva veritate is to define synonymy. It would be insufficient if there are cases of nonsynonymous words that still fulfill the requirements for interchangeability salva veritate (interchangeable in all contexts without change of truth value). Quine notes that the synonymy in question here does not mean that when interchanged it has identical mental associations or poetic qualities. For, in fact, we will never find such cases of synonymy anyway. More precisely, the kind of synonymy we have in mind is cognitive synonymy. It will be more fully explicated throughout the essay. It is the sort of synonymy that allows an analytic statement (like “All Bachelors are unmarried men”) to be converted into logical truths (like “Unmarried men are unmarried men”) by means substituting synonyms. If we assume what analyticity is (even though in fact we are trying to ground it), we can define the cognitive synonymy of “bachelor” and “unmarried man” with the statement: (3) “All and only bachelors are unmarried men” is analytic. (Perhaps the idea here is that all cases of one are cases of the other, so nothing will be lost or gained by substituting them.)]

 

[ditto]

The question remains whether interchangeability salva veritate (apart from occurrences within words) is a strong enough condition for synonymy, or whether, on the contrary, some nonsynonymous expressions might be thus interchangeable. Now let us be clear that we are not concerned here with synonymy in the sense of complete identity in psychological associations or poetic quality; indeed no two expressions are synonymous in such a sense. We are concerned only with what may be called cognitive synonymy. Just what this is cannot be said without successfully finishing the present study; but we know something about it from the need which arose for it in connection with analyticity in Section I. The sort of synonymy needed there was merely such that any analytic statement could be turned into a logical truth by putting synonyms for synonyms. Turning the tables and assuming analyticity, indeed, we could explain cognitive synonymy of terms as follows (keeping to the familiar example): to say that ‘bachelor’ and ‘unmarried man’ are cognitively synonymous is to say no more nor less than that the statement:

(3) All and only bachelors are unmarried men

is analytic.4

(28)

4. This is cognitive synonymy in a primary, broad sense. Carnap (Meaning and Necessity, pp. 56ff.) and Lewis (Analysis of Knowledge and Valuation [La Salle, Ill., 1946], pp. 83ff.) have suggested how, once this notion is at hand, a narrower sense of cognitive synonymy which is preferable for some purposes can in turn be derived. But this special ramification of concept-building lies aside from the present purposes and must not be confused with the broad sort of cognitive synonymy here concerned.

(28)

[contents]

 

 

 

 

 

 

3.4

[Using “Necessarily” to Define Synonymy Indirectly in Terms of Analyticity]

 

[We need still a definition of cognitive synonymy that does not presuppose analyticity, and we are currently considering as a possible candidate interchangeability salva veritate. To see that it works, recall first (3) “All and only bachelors are unmarried men.” We next consider (4) “Necessarily all and only bachelors are bachelors.” This is self-evidently true (if it were false, it would be a contradiction, perhaps). Next, we suppose that ‘bachelor’ and ‘unmarried man’ are interchangeable salva veritate, and by making the substitutions, we obtain (5) “Necessarily, all and only bachelors are unmarried men.” If we say that this is true, then we are saying that ‘bachelor’ and ‘unmarried man’ are synonymous, and thus that (3) “All and only bachelors are unmarried men” is analytic (perhaps because by means of an acceptable substitution, it can be rendered into the analytically true “All bachelors are bachelors” or “All unmarried men are unmarried men.”]

 

[ditto]

What we need is an account of cognitive synonymy not presupposing analyticity – if we are to explain analyticity conversely with help of cognitive synonymy as undertaken in Section I. And indeed such an independent account of cognitive synonymy is at present up for consideration, viz., interchangeability salva veritate everywhere except within words. The question before us, to resume the thread at last, is whether such interchangeability is a sufficient condition for | cognitive synonymy. We can quickly assure ourselves that it is, by examples of the following sort. The statement:

(4) Necessarily all and only bachelors are bachelors

is evidently true, even supposing ‘necessarily’ so narrowly construed as to be truly applicable only to analytic statements. Then, if ‘bachelor’ and ‘unmarried man’ are interchangeable salva veritate, the result

(5) Necessarily, all and only bachelors are unmarried men

of putting ‘unmarried man’ for an occurrence of ‘bachelor’ in (4) must, like (4), be true. But to say that (5) is true is to say that (3) is analytic, and hence that ‘bachelor’ and ‘unmarried men’ are cognitively synonymous.

(28-29)

[contents]

 

 

 

 

 

 

3.5

[The Potential Circularity of Using “Necessarily” to Function for Analyticity]

 

[Something that makes this proposal tricky is that it regards(4) “Necessarily all and only bachelors are bachelors” as analytic on account of the use of “necessarily”. (Perhaps this is because when it is necessary, it is impossible to not be so. Thus it fulfills the formal criterion of analyticity as its denial being a contradiction.) This means that we are dangerously close to circularity. We want to define analyticity, but we assume it with our use of “necessarily.” So is this a straightforward case of circularity?]

 

[ditto]

Let us see what there is about the above argument that gives it its air of hocus-pocus. The condition of interchangeability salva veritate varies in its force with variations in the richness of the language at hand. The above argument supposes we are working with a language rich enough to contain the adverb ‘necessarily’, this adverb being so construed as to yield truth when and only when applied to an analytic statement. But can we condone a language which contains such an adverb? Does the adverb really make sense? To suppose that it does is to suppose that we have already made satisfactory sense of ‘analytic’. Then what are we so hard at work on right now?

(29)

[contents]

 

 

 

 

 

 

3.6

[The Solution as Not Entirely Circular]

 

[Quine claims that it is not entirely circular but can be thought more of as “a closed curve in space” (29).]

 

[ditto]

Our argument is not flatly circular, but something like it. It has the form, figuratively speaking, of a closed curve in space.

(29)

[contents]

 

 

 

 

 

 

3.7

[Extensionality (in a Logically Formulated Language) as Interchangeability Salva veritate]

 

[We need to specify the parameters of a language before we can adequately see interchangeability salva veritate operating in it. Quine stipulates a language with atomic sentences composed of predicates and variables and with rules to build up complex sentences using truth functions (truth functional connectives maybe) and quantification (among other features). This language can handle descriptions, class names, and singular terms. This sort of a language will be “extensional” because in it, “any two predicates which agree extensionally (i.e., are true of the same objects) are interchangeable salva veritate” (29).]

 

[ditto]

Interchangeability salva veritate is meaningless until relativized to a language whose extent is specified in relevant respects. Suppose now we consider a language containing just the following materials. There is an indefinitely large stock of one- and many-place predicates, mostly having to do with extralogical subject matter. The rest of the language is logical. The atomic sentences consist each of a predicate followed by one or more variables; and the complex sentences are built up of atomic ones by truth functions and quantification. In effect such a language enjoys the benefits also of descriptions and class names and indeed singular terms generally, these being contextually definable in known ways.5 Such a language can be adequate to classical mathematics and indeed to scientific discourse generally, except | in so far as the latter involves debatable devices such as modal adverbs and contrary-to-fact conditionals. Now a language of this type is extensional, in this sense: any two predicates which agree extensionally (i.e., are true of the same objects) are interchangeable salva veritate.

(29-30)

5. See, e.g., my Mathematical Logic (New York, 1940; Cambridge, Mass., 1947), sec. 24, 26, 27; or Methods of Logic (New York, 1950), sec. 37ff.

(29)

[contents]

 

 

 

 

 

 

3.8

[Extensional Languages as Not Ensuring Cognitive Synonymy]

 

[(Recall from section 1.6 the example of predicates, “creature with a heart” and “creature with a kidney”. They might be alike in extension, but they are not alike in meaning. Quine now seems to say that these predicates are also not cases of cognitive synonymy. Thus we might gather that cognitive synonymy requires a similarity in meaning, which may not have been noted back in section 3.3 when he was first discussing it.) In an extensional language, we can interchange salva veritate ‘bachelor’ and ‘unmarried man’ , because they extensionally refer to exactly the same class of entities. But we can do the same for ‘creature with a heart’ and ‘creature with a kidney’. Thus, interchangeability salva veritate in an extensional language does not give us cognitive synonymy, which we need for grounding analyticity. It only can tell us that (3) “All and only bachelors are unmarried men” is true.]

 

[ditto]

In an extensional language, therefore, interchangeability salva veritate is no assurance of cognitive synonymy of the desired type. That ‘bachelor’ and ‘unmarried man’ are interchangeable salva veritate in an extensional language assures us of no more than that (3) is true. There is no assurance here that the extensional agreement of ‘bachelor’ and ‘unmarried man’ rests on meaning rather than merely on accidental matters of fact, as does extensional agreement of ‘creature with a heart’ and ‘creature with a kidney’.

(30)

[contents]

 

 

 

 

 

 

 

3.9

[Extensional Synonymy as Not Being Cognitive Synonymy and as Being Unable to Ground Analyticity]

 

[But as we saw in section 1, we need to equate the cognitive synonymy between words like ‘bachelor’ and ‘unmarried man’ with the analyticity of (3) “All and only bachelors are unmarried men” and not merely with its truth, which is all that extensionality can accomplish.]

 

[ditto. (Perhaps the idea is the following, but I am not sure. For a sentence to be true, it need not be analytically true. To be analytically true, the sentence either has to either be one whose denial presents a self-contradiction, or be a sentence that can be rendered as such by substituting cognitively synonymous terms. In an extensional language, we can use substitutions and reference to extensions to demonstrate that ‘bachelor’ and ‘unmarried man’ can be interchanged without loss of logical truth and that (3) “All and only bachelors are unmarried men” is true. However, we have not established that (3) is analytic. I am not certain why. By substitution, we can render it “All and only unmarried men are unmarried men.” Perhaps we should consider a sentence like “Creatures with a heart are ones that (thereby) pump their blood through their circulatory system.” that experience stress when the heartrate goes above a certain threshold.” If we substitute “creatures with a kidney”, that might still be a true sentence, but we might not get an analytically true statement, (“Creatures with a kidney are ones that (thereby) pump their blood through their circulatory system.”) And maybe this will be because there is nothing about the kidney itself that directly suggests blood pumping, although the heart rather does, and also although the kidney is normally needed when pumping blood. If so, Quine’s notion of analyticity might be built on a notion of cognitive synonymy where the synonymous terms are ones that directly implicated, such that from the one we can directly derive the other, and not just indirectly by checking their extensions. As Quine noted before, the sameness of extensions can be for accidental reasons. This suggests possibly he still has intensional meaning in mind for cognitive synonymy, but we will  have to see.]

For most purposes extensional agreement is the nearest approximation to synonymy we need care about. But the fact remains that extensional agreement falls far short of cognitive synonymy of the type required for explaining analyticity in the manner of Section I. The type of cognitive synonymy required there is such as to equate the synonymy of ‘bachelor’ and ‘unmarried man’ with the analyticity of (3), not merely with the truth of (3).

(30)

[contents]

 

 

 

 

 

 

3.10

[The Problems with Extensional Interchangeability Salva veritate and with “Necessarily”]

 

[So we see that “interchangeability salva veritate, if construed in relation to an extensional language, is not a sufficient condition of cognitive synonymy” (30). And previously we saw that “If a language contains an intensional adverb ‘necessarily’ [...], then interchangeability salva veritate in such a language does afford a sufficient condition of cognitive synonymy; but such a language is intelligible only if the notion of analyticity is already clearly understood in advance” (30) ]

 

[ditto]

So we must recognize that interchangeability salva veritate, if construed in relation to an extensional language, is not a sufficient condition of cognitive synonymy in the sense needed for deriving analyticity in the manner of Section I. If a language contains an intensional adverb ‘necessarily’ in the sense lately noted, or other particles to the same effect, then interchangeability salva veritate in such a language does afford a sufficient condition of cognitive synonymy; but such a language is intelligible only if the notion of analyticity is already clearly understood in advance.

(30)

[contents]

 

 

 

 

 

 

3.11

[Grounding Analyticity First as a Better Strategy]

 

[So we cannot first formally establish cognitive synonymy to then secondly ground analyticity, like we set out to do. Supposing we could firstly ground analyticity, then we could define cognitive synonymy fairly easily, however: “Singular terms may be said to be cognitively synonymous when the statement of identity formed by putting ‘=’ between them is analytic. Statements may be said simply to be cognitively synonymous when their biconditional (the result of joining them by ‘if and only if’) is analytic” (31). Furthermore, “we can describe any two linguistic forms as cognitively synonymous when the two forms are interchangeable (apart from occurrences within ‘words’) salva (no longer veritate but) analyticitate” (31). So let us return now to the problem of analyticity.]

 

[ditto]

The effort to explain cognitive synonymy first, for the sake of deriving analyticity from it afterward as in Section I, is perhaps the wrong approach. Instead we might try explaining analyticity somehow without appeal to cognitive synonymy. Afterward we could doubtless derive cognitive synonymy from analyticity satisfactorily enough if desired. We have seen that cognitive synonymy of ‘bachelor’ and ‘unmarried man’ can be explained as analyticity of (3). The same explanation works for any pair of one-place predicates, of course, and it can be extended in obvious fashion to many-place predicates. Other | syntactical categories can also be accommodated in fairly parallel fashion. Singular terms may be said to be cognitively synonymous when the statement of identity formed by putting ‘=’ between them is analytic. Statements may be said simply to be cognitively synonymous when their biconditional (the result of joining them by ‘if and only if’) is analytic.6 If we care to lump all categories into a single formulation, at the expense of assuming again the notion of “word” which was appealed to early in this section, we can describe any two linguistic forms as cognitively synonymous when the two forms are interchangeable (apart from occurrences within “words”) salva (no longer veritate but) analyticitate. Certain technical questions arise, indeed, over cases of ambiguity or homonymy; let us not pause for them, however, for we are already digressing. Let us rather tum our backs on the problem of synonymy and address ourselves anew to that of analyticity.

(30-31)

6. The ‘if and only if’ itself is intended in the truth functional sense. See Carnap, Meaning and Necessity, p. 14.

(31)

[contents]

 

 

 

 

 

 

 

 

 

 

 

 

Bibliography:

Quine, W. V. “Two Dogmas of Empiricism.” The Philosophical Review 60, no. 1 (1951): 20–43.

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Quine (2) “Two Dogmas of Empiricism”, section 2, “Definition”, summary

 

by Corry Shores

 

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[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.)

 

 

 

 

 

 

Contents

 

2.1

[The Unfeasibility of Grounding the Transformability of Sentences into Logically True Ones in Dictionary Entries]

 

2.2

[Other Fields’ Definitions as Doing the Same]

 

2.3

[Synonymy as Found in Usage]

 

2.4

[Carnap’s Explication as Also Being Based in Pre-Existing Synonymies]

 

2.5

[Cases of Selected Alternative Explications as Also Involving Pre-Existing Synonymies]

 

2.6

[Exception: Novel Abbreviatory Notations]

 

2.7

[Two Kinds of Economy in Mathematical and Logical Systems: Economy of Practical Expression and Economy of Grammar and Vocabulary]

 

2.8

[Coordinating Two Languages of Each Economy Using Definitions for Translation]

 

2.9

[Three Relations Between Definiendum and Definiens]

 

 

 

Bibliography

 

 

 

 

 

 

 

Summary

 

2.1

[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)

 

[contents]

 

 

 

 

 

 

2.2

[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)

[contents]

 

 

 

 

 

 

2.3

[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)

[contents]

 

 

 

 

 

 

2.4

[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)

[contents]

 

 

 

 

 

 

2.5

[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)

[contents]

 

 

 

 

 

 

2.6

[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)

[contents]

 

 

 

 

 

 

2.7

[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)

[contents]

 

 

 

 

 

 

2.8

[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)

[contents]

 

 

 

 

 

 

 

2.9

[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)

[contents]

 

 

 

 

 

 

2.10

[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)

[contents]

 

 

 

 

 

 

 

Bibliography:

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.

.

 

 

.

24 Jul 2021

Quine (1) “Two Dogmas of Empiricism”, section 1, “Background for Anayticity”, summary

 

by Corry Shores

 

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[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”

 

 

1

“Background for Anayticity”

 

 

 

 

 

 

 

 

 

Brief summary (collecting those below):

(1.1) There are forerunners to Kant’s analytic/synthetic judgment distinction. {1a} Hume’s relations of ideas, which are logically certain (because their contraries imply contradictions), as for example mathematical equations, and {1b} matters of fact, which are probable, because their contraries are not contradictions, as for example ‘the sun will rise tomorrow’. (Enquiry 4.2) {2a}  Leibniz’ truths of reason, which are necessary because their opposite is impossible, and {2b} truths of fact, which are contingent, because their opposite is possible. (Monadology 33, Philosophical Texts p.272) Morton White shows that the definition of analyticity as “Analytic statements are those whose denials are self-contradictory” is insufficient, because there are cases of denials that render contradictions, but it is not a syntactical case of “A and not-A;” for instance “All men are rational animals” would be denied as “It is not the case that all men are rational animals” (or “Some men are not rational animals”). (1.2) For Kant, an analytic statement is one that “attributes to its subject no more than is already conceptually contained in the subject. (20) Quine notes two problems with this definition: {1} it is limited only to statements in a subject-predicate form (and presumably there are analytic statements not of this form, but Quine does not mention any here) and {2} its notion of containment remains only at a metaphysical level (perhaps because it is not defined formally). Quine sees Kant’s intent and redefines Kant’s analyticity as “a statement is analytic when it is true by virtue of meanings and independently of fact.” (21) We turn now to the notion of meaning used here. (1.3) Meaning cannot be mere reference, because there are cases where two different names name the same thing, but each name has a different meaning, as for instance Frege’s ‘Evening Star = Morning Star’. As the two names are not identical in meaning, this statement is not analytic. (In fact, the meaning of ‘the evening star’ is almost the opposite of the meaning of ‘morning star’.) Also the identity made between the two is a statement of fact that is demonstrated through astronomical observation. (Thus it does not fulfill either of the Kantian requirements that an analytic statement be “true by virtue of meanings and independently of fact.”). (1.4) Another example of a case where equated names do not render an analytic statement is Russell’s “Scott is the author of Waverley.” (1.5) Even with abstract terms, like number values,  we still have this problem, as “9” and “the number of planets” names one and the same abstract entity (the number value of nine), but the equation of the two is not analytic; for, observation was needed to make that equation, and a reflection on their meanings is insufficient to. (1.6) A general term or predicate does not name an entity, but it is true of an entity or entities, or of none. The extension of a general term is that class of all entities that a general term is true of. With singular terms, we distinguished its meaning from its extension (Evening Star and Morning Star have the same extension, the planet Venus, but different meanings); similarly, we must do the same for general terms. So for example, the general terms “creature with a heart” and “creature with a kidney” may have an identical extension (supposing all creatures with the one organ also in fact have the other), but they are not alike in meaning. (1.7) We sometimes contrast intension (or meaning) and connotation with extension or denotation. (1.8) Aristotle’s notion of essence was a forerunner for what we now call intension (meaning). Aristotle distinguishes the essential from the accidental, so for humans, it is essential to be rational, but it is accidental to have two legs. Quine notes a problem. Consider a human person. They will be both rational and two-legged. Quine observes however that we may classify this person either as a human or a biped. Insofar as they are a human, their rationality is essential and their bipedalism is not. But insofar as they are a biped, their two-leggedness is essential and their rationality is not. (Here Quine claims that we are dealing with meanings rather than essences. We might say under a doctrine of essences that for some particular individual person, their rationality is essential and their bipedalism is not. However, under a doctrine of meanings, for this individual’s predicates of being rational and bipedal, it cannot be said that one of them is essential and the other is not. For, by the same reasoning that we would use to designate one over the other, we may equally use it to designate the other over the first. (We might say, “here is a human,” and take their rationality as essential; or, for the same person, we might say, “here is a biped” and take their two-leggedness as essential. This is because in that case we are concerned with meanings (of “human” and of “biped”) rather than with the entity itself’s proper essence).) “Things had essences, for Aristotle, but only linguistic forms have meanings. Meaning is what essence becomes when it is divorced from the object of reference and wedded to the word.” (22) (1.9) In a theory of meaning, we would need to explain what kind of objects meanings are. They seem to be ideas. For semanticists, they are mental ideas. For others, they are Platonic ideas. But these characterizations are not sufficient because such entities are too elusive to erect “a fruitful science about them.” (22) Some things are often not clear about such entities: {1} whether we have two or one; and {2} when linguistic forms are synonymous or not. (1.10) But once we distinguish a theory of meaning from a theory of reference, we can then think of meanings just in terms of synonymy of linguistic forms and the analyticity of statements. (1.11) We began wondering how to define analyticity. (We saw in the Kantian conception that it can be understood as being true by meanings and independently of fact. See 1.2. We distinguished meaning from extension. Then we found that meanings are hard to define and unnecessary when we have extension.) We now no longer consider a “special realm of entities called meanings.” (23) That means we must find other ways to understand analyticity. (1.12) Statements that are often considered analytic in philosophy are generally of two types. {1} Ones that are logically true, for instance (1) No unmarried man is married. (This is true no matter what the interpretations are of the terms. It is formally true.) (1.13) {2} The other kind of analytic statements are ones that can be rendered into a logically true format by substituting synonyms. For example, (2) “No bachelor is married” can be rendered “No unmarried man is married” but substituting the synonyms “bachelor” and “unmarried man”. Yet, we do not have a proper (formal?) characterization of these kinds of analytic statements, especially since we do not have a (formal?) definition of synonymy. Thus we do not have an adequate (formal?) characterization of analyticity. (1.14) Carnap defines analyticity in the following way. We begin by assigning all the truth values to every atomic statement in a language. Each complete combination of assignments for all the atomic sentences is what he calls a “state description.” We can then compositionally build up the complex statements of the language using logical means, with their truth values being computable based on logical laws. A statement is analytic when it is true under every state description. Since a state description is like a possible world (it is one combination of facts), this can be seen as following Leibniz’ notion of being true in all possible worlds. (Quine then explains a problem with this conception: if the language has extralogical synonym-pairs, such as ‘bachelor’ and ‘unmarried man’, then statements like “All bachelors are married” will turn out to be synthetic rather than analytic. Thus) “The criterion in terms of state-descriptions is a reconstruction at best of logical truth.” (24) (1.15) Yet, Carnap’s main concern was clarifying probability and induction, not analyticity, which is our concern, “and here the major difficulty lies not in the first class of analytic statements, the logical truths, but rather in the second class, which depends on the notion of synonymy.” (23)

 

 

 

 

 

Contents

 

1.1

[Forerunners of Kant’s Analytic/Synthetic Distinction in Hume and Leibniz. M. White’s Account for the Inadequacy of Defining Analyticity as Denial Rendering a Contradiction]

 

1.2

[Reformulation Kant’s Notion of Analyticity as Being True by its Meanings and Independently of Fact]

 

1.3

[Meaning as Not Referential Naming]

 

1.4

[Russell’s “Author of Waverley” as Another Example of an Identifying Naming Statement That Is Not Analytical]

 

1.5

[Abstract Terms as Also Having This Problem (“9” and “The Number of Planets”)]

 

1.6

[Meaning and Extension for General Terms (“Creature with a Heart” and “Creature with a Kidney”]

 

1.7

[Intention (Meaning)/Connotation Vs. Extension/Denotation]

 

1.8

[Aristotle’s Essence as Being Similar to Meaning, but Not Identical]

 

1.9

[Difficulty in Defining What Kind of Entities Meanings Are]

 

1.10

[Defining Meaning as Superfluous]

 

1.12

[Logically True Analytic Statements]

 

1.13

[Statements Made Logically True by Substitutions]

 

1.14

[Carnap’s Definition of Logical Truths (Analyticity)]

 

1.15

[Turning Instead to Analyticity From Synonymy]

 

Bibliography

 

 

 

 

 

 

 

Summary

 

1.1

[Forerunners of Kant’s Analytic/Synthetic Distinction in Hume and Leibniz. M. White’s Account for the Inadequacy of Defining Analyticity as Denial Rendering a Contradiction]

 

[There are forerunners to Kant’s analytic/synthetic judgment distinction. {1a} Hume’s relations of ideas, which are logically certain (because their contraries imply contradictions), as for example mathematical equations, and {1b} matters of fact, which are probable, because their contraries are not contradictions, as for example ‘the sun will rise tomorrow’. (Enquiry 4.2) {2a}  Leibniz’ truths of reason, which are necessary because their opposite is impossible, and {2b} truths of fact, which are contingent, because their opposite is possible. (Monadology 33, Philosophical Texts p.272) Morton White shows that the definition of analyticity as “Analytic statements are those whose denials are self-contradictory” is insufficient, because there are cases of denials that render contradictions, but it is not a syntactical case of “A and not-A;” for instance “All men are rational animals” would be denied as “It is not the case that all men are rational animals” (or “Some men are not rational animals”).]

 

[We are dealing with the first dogma (see section 0.1), which is that truths are distinctly either: {1a} synthetic, meaning that they they are grounded in fact, or they are {1b} analytic, meaning that they grounded in meanings independently of matters of fact. Hume made the distinction between relations of ideas and matters of fact (recall from his Enquiry concerning Human Nature, Section 4, part 2 that we have knowledge either of {1} relations of ideas, which are logically certain (because their contraries imply contradictions), as for example mathematical equations, or we have knowledge of {2} matters of fact, which are probable, because their contraries are not contradictions, as for example ‘the sun will rise tomorrow’ (for, it is not a contradiction to think, ‘the sun will not rise tomorrow’). We trust such conclusions regarding matters of fact, because we come to have knowledge of causal relations governing such regularities. And this causal knowledge is obtainable only through experience. Leibniz makes a similar distinction between truths of reason and truths of fact: “There are also two kinds of truths, those of reasoning and those of fact. The truths of reasoning are necessary and their opposite is impossible; the truths of fact are contingent, and their opposite is possible. When a truth is necessary, its reason can be found by analysis, resolving it into simpler ideas and simpler truths until we reach the primitives.” (Monadology 33, Philosophical Texts p.272) Kant’s analytic and synthetic judgment distinction is similar to both of these (we examine it below). Quine notes how Morton White claims that “Analytic statements are those whose denials are self-contradictory.” (324) Here White is presenting this as an anti-intensional view that he is critical of. This is not sufficient, White says, because in many cases of a denied formulations that intuitively present a contradiction, there is no syntactically obvious contradiction. For example, “All men are rational animals” would be denied as “It is not the case that all men are rational animals” or as converted to “Some men are not rational animals.” But here we do not have a syntactical contradiction of the form “A and not-A.” Thus, defining analyticity as resulting in a contradiction when denied does not suffice, because we still need a formal account of contradiction (for these cases where it is not syntactically apparent.)]

Kant’s cleavage between analytic and synthetic truths was foreshadowed in Hume’s distinction between relations of ideas and matters of fact, and in Leibniz’s distinction between truths of reason and truths of fact. Leibniz spoke of the truths of reason as true in all possible worlds. Picturesqueness aside, this is to say that the truths of reason are those which could not possibly be false. In the same vein we hear analytic statements defined as statements whose denials are self-contradictory. But this definition has, small explanatory value; for the notion of self-contradictoriness, in the quite broad sense needed for this definition of analyticity, stands in exactly the same need of clarification as does the notion of analyticity itself.2 The two notions are the two sides of a single dubious coin.

(20)

2. See White, op. cit., p. 324.

(20)

[contents]

 

 

 

 

 

 

1.2

[Reformulation Kant’s Notion of Analyticity as Being True by its Meanings and Independently of Fact]

 

[For Kant, an analytic statement is one that “attributes to its subject no more than is already conceptually contained in the subject. (20) Quine notes two problems with this definition: {1} it is limited only to statements in a subject-predicate form (and presumably there are analytic statements not of this form, but Quine does not mention any here) and {2} its notion of containment remains only at a metaphysical level (perhaps because it is not defined formally). Quine sees Kant’s intent and redefines Kant’s analyticity as “a statement is analytic when it is true by virtue of meanings and independently of fact.” (21) We turn now to the notion of meaning used here.]

 

[ditto. Here are some relevant passages from Kant’s Critique of Pure Reason:

On the difference between analytic and synthetic judgments.

In all judgments in which the relation of a subject to the predicate is thought […], this relation is possible in two different ways. Either the predicate B belongs to the subject A as something that is (covertly) contained in this concept A; or B lies entirely outside the concept A, though to be sure it stands in connection with it. In the first case I call the judgment analytic, in the second synthetic. Analytic judgments (affirmative ones) are thus those in which the connection of the predicate is thought through identity, but those in which this connection is thought without identity are to be called synthetic judgments. One could also call the former judgments of clarification and the latter judgments of amplification, since through the predicate the former do not add anything to the concept of the subject, but only break it up by means of analysis into its component concepts, which were already thought in it (though confusedly); while the latter, on the contrary, add to the concept of the subject a predicate that was not thought in it at all, and could not have been extracted from it through any analysis; e.g., if I say: “All bodies are extended,” then this is an analytic judgment. For I do not need to go outside the concept that I combine with the word “body” in order to find that extension is connected with it, but rather I need only to analyze that concept, i.e., become conscious of the manifold that I always think in it, in order to encounter this predicate therein; it is therefore an analytic judgment. On the contrary, if I say: “All bodies are heavy,” then the predicate is something entirely different from that which I think in the mere concept of a body in general. The addition of such a predicate thus yields a synthetic judgment.

Now from this it is clear: 1) that through analytic judgments our cognition is not amplified at all, but rather the concept, which I already | have, is set out, and made intelligible to me; 2) that in synthetic judgments I must have in addition to the concept of the subject something else (X) on which the understanding depends in cognizing a predicate that does not lie in that concept as nevertheless belonging to it.

In the case of empirical judgments or judgments of experience there is no difficulty here. For this X is the complete experience of the object that I think through some concept A, which constitutes only a part of this experience. For although I do not at all include the predicate of weight in the concept of a body in general, the concept nevertheless designates the complete experience through a part of it, to which I can therefore add still other parts of the very same experience as belonging to the former. I can first cognize the concept of body analytically through the marks of extension, of impenetrability, of shape, etc., which are all thought in this concept. But now I amplify my cognition and, in looking back to the experience from which I had extracted this concept of body, I find that weight is also always connected with the previous marks. Experience is therefore that X that lies outside the concept A and on which the possibility of the synthesis of the predicate of weight B with the concept A is grounded.

(Kant, Critique of Pure Reason, 130-131)

]

 

Kant conceived of an analytic statement as one that attributes to its subject no more than is already conceptually contained in the subject. | This formulation has two shortcomings : it limits itself to statements of subject-predicate form, and it appeals to a notion of containment which is left at a metaphorical level. But Kant’s intent, evident more from the use he makes of the notion of analyticity than from his definition of it, can be restated thus : a statement is analytic when it is true by virtue of meanings and independently of fact. Pursuing this line, let us examine the concept of meaning which is presupposed.

(20-21)

[contents]

 

 

 

 

 

 

1.3

[Meaning as Not Referential Naming]

 

[Meaning cannot be mere reference, because there are cases where two different names name the same thing, but each name has a different meaning, as for instance Frege’s ‘Evening Star = Morning Star’. As the two names are not identical in meaning, this statement is not analytic. (In fact, the meaning of ‘the evening star’ is almost the opposite of the meaning of ‘morning star’.) Also the identity made between the two is a statement of fact that is demonstrated through astronomical observation. (Thus it does not fulfill either of the Kantian requirements that an analytic statement be “true by virtue of meanings and independently of fact.”).]

 

[ditto]

We must observe to begin with that meaning is not to be identified with naming, or reference. Consider Frege’s example of ‘Evening Star’ and ‘Morning Star’. Understood not merely as a recurrent evening apparition but as a body, the Evening Star is the planet Venus, and the Morning Star is the same. The two singular terms name the same thing. But the meanings must be treated as distinct, since the· identity ‘Evening Star = Morning Star’ is a statement of fact established by astronomical observation. If ‘Evening Star’ and ‘Morning Star’ were alike in meaning, the identity ‘Evening Star = Morning Star’ would be analytic.

(21)

[contents]

 

 

 

 

 

 

1.4

[Russell’s “Author of Waverley” as Another Example of an Identifying Naming Statement That Is Not Analytical]

 

[Another example of a case where equated names do not render an analytic statement is Russell’s “Scott is the author of Waverley.”]

 

[ditto. It seems Sir Walter Scott wrote Waverley anonymously, and published certain subsequent writings under “the author of Waverley.” (see here and here) And “His identity as the author of the novels was widely rumoured, and in 1815 Scott was given the honour of dining with George, Prince Regent, who wanted to meet ‘the author of Waverley’’.” (source for this quote) Here are some relevant passages from Russell’s “On Denoting”:

If we say “Scott is the author of Waverley,” we assert an identity of denotation with a difference of meaning.”

(483)

If a is identical with b, whatever is true of the one is true of the other, and either may be substituted for the other in any proposition without altering the truth or falsehood of that proposition. Now George IV. wished to know whether Scott was the author of Waverley; and in fact Scott was the author of Waverley. Hence we may substitute Scott for the author of “Waverley,” and thereby prove that George IV. wished to know whether Scott was Scott. Yet an interest in the law of identity can hardly be attributed to the first gentleman of Europe.

(485)

Quine’s point might seem to be the following. George IV knew about the author of Waverley, and he may have even known Sir Walter Scott. But neither name is contained in the other.]

Again there is Russell’s example of ‘Scott’ and ‘the author of Waverley’. Analysis of the meanings of words was by no means sufficient to reveal to George IV that the person named by these two singular terms was one and the same.

(21)

[contents]

 

 

 

 

 

 

1.5

[Abstract Terms as Also Having This Problem (“9” and “The Number of Planets”)]

 

[Even with abstract terms, like number values,  we still have this problem, as “9” and “the number of planets” names one and the same abstract entity (the number value of nine), but the equation of the two is not analytic; for, observation was needed to make that equation, and a reflection on their meanings is insufficient too.]

 

[ditto]

The distinction between meaning and naming is no less important at the level of abstract terms. The terms ‘9’ and ‘the number of planets’ name one and the same abstract entity but presumably must be regarded as unlike in meaning; for astronomical observation was needed, and not mere reflection on meanings, to determine the sameness of the entity in question.

(21)

[contents]

 

 

 

 

 

 

1.6

[Meaning and Extension for General Terms (“Creature with a Heart” and “Creature with a Kidney”]

 

[A general term or predicate does not name an entity, but it is true of an entity or entities, or of none. The extension of a general term is that class of all entities that a general term is true of. With singular terms, we distinguished its meaning from its extension (Evening Star and Morning Star have the same extension, the planet Venus, but different meanings); similarly, we must do the same for general terms. So for example, the general terms “creature with a heart” and “creature with a kidney” may have an identical extension (supposing all creatures with the one organ also in fact have the other), but they are not alike in meaning.]

 

[ditto]

Thus far we have been considering singular terms. With general terms, or predicates, the situation is somewhat different but parallel. Whereas a singular term purports to name an entity, abstract or concrete, a general term does not; but a general term is true of an entity, or of each of many, or of none. The class of all entities of which a general term is true is called the extension of the term. Now paralleling the contrast between the meaning of a singular term and the entity named, we must distinguish equally between the meaning of a general term and its extension. The general terms ‘creature with a heart’ and | ‘creature with a kidney’, e.g., are perhaps alike in extension but unlike in meaning.

(21-22)

[contents]

 

 

 

 

 

 

1.7

[Intention (Meaning)/Connotation Vs. Extension/Denotation]

 

[We sometimes contrast intension (or meaning) and connotation with extension or denotation.]

 

[ditto]

Confusion of meaning with extension, in the case of general terms, is less common than confusion of meaning with naming in the case of singular terms. It is indeed a commonplace in philosophy to oppose intension (or meaning) to extension, or, in a variant vocabulary, connotation to denotation.

(22)

[contents]

 

 

 

 

 

 

1.8

[Aristotle’s Essence as Being Similar to Meaning, but Not Identical]

 

[Aristotle’s notion of essence was a forerunner for what we now call intension (meaning). Aristotle distinguishes the essential from the accidental, so for humans, it is essential to be rational, but it is accidental to have two legs. Quine notes a problem. Consider a human person. They will be both rational and two-legged. Quine observes however that we may classify this person either as a human or a biped. Insofar as they are a human, their rationality is essential and their bipedalism is not. But insofar as they are a biped, their two-leggedness is essential and their rationality is not. (Here Quine claims that we are dealing with meanings rather than essences. We might say under a doctrine of essences that for some particular individual person, their rationality is essential and their bipedalism is not. However, under a doctrine of meanings, for this individual’s predicates of being rational and bipedal, it cannot be said that one of them is essential and the other is not. For, by the same reasoning that we would use to designate one over the other, we may equally use it to designate the other over the first. (We might say, “here is a human,” and take their rationality as essential; or, for the same person, we might say, “here is a biped” and take their two-leggedness as essential. This is because in that case we are concerned with meanings (of “human” and of “biped”) rather than with the entity itself’s proper essence).) “Things had essences, for Aristotle, but only linguistic forms have meanings. Meaning is what essence becomes when it is divorced from the object of reference and wedded to the word.” (22)]

 

[ditto]

The Aristotelian notion of essence was the forerunner, no doubt, of the modern notion of intension or meaning. For Aristotle it was essential in men to be rational, accidental to be two-legged. But there is an important difference between this attitude and the doctrine of meaning. From the latter point of view it may indeed be conceded (if only for the sake of argument) that rationality is involved in the meaning of the word ‘man’ while two-leggedness is not; but two-leggedness may at the same time be viewed as involved in the meaning of ‘biped’ while rationality is not. Thus from the point of view of the doctrine of meaning it makes no sense to say of the actual individual, who is at once a man and a biped, that his rationality is essential and his two-leggedness accidental or vice versa. Things had essences, for Aristotle, but only linguistic forms have meanings. Meaning is what essence becomes when it is divorced from the object of reference and wedded to the word.

(22)

[contents]

 

 

 

 

 

 

 

1.9

[Difficulty in Defining What Kind of Entities Meanings Are]

 

[In a theory of meaning, we would need to explain what kind of objects meanings are. They seem to be ideas. For semanticists, they are mental ideas. For others, they are Platonic ideas. But these characterizations are not sufficient because such entities are too elusive to erect “a fruitful science about them.” (22) Some things are often not clear about such entities: {1} whether we have two or one; and {2} when linguistic forms are synonymous or not. ]

 

[ditto]

For the theory of meaning the most conspicuous question is as to the nature of its objects: what sort of things are meanings? They are evidently intended to be ideas, somehow – mental ideas for some semanticists, Platonic ideas for others. Objects of either sort are so elusive, not to say debatable, that there seems little hope of erecting a fruitful science about them. It is not even clear, granted meanings, when we have two and when we have one; it is not clear when linguistic forms should be regarded as synonymous, or alike in meaning, and when they should not. If a standard of synonymy should be arrived at, we may reasonably expect that the appeal to meanings as entities will not have played a very useful part in the enterprise.

(22)

[contents]

 

 

 

 

 

 

1.10

[Defining Meaning as Superfluous]

 

[But once we distinguish a theory of meaning from a theory of reference, we can then think of meanings just in terms of synonymy of linguistic forms and the analyticity of statements.]

 

[ditto]

A felt need for meant entities may derive from an earlier failure to appreciate that meaning and reference are distinct. Once the theory of meaning is sharply separated from the theory of reference, it is a short step to recognizing as the business of the theory of meaning | simply the synonymy of linguistic forms and the analyticity of statements; meanings themselves, as obscure intermediary entities, may well be abandoned.

(22-23)

[contents]

 

 

 

 

 

 

1.11

[Abandoning Meaning for Defining Analyticity]

 

[We began wondering how to define analyticity. (We saw in the Kantian conception that it can be understood as being true by meanings and independently of fact. See 1.2. We distinguished meaning from extension. Then we found that meanings are hard to define and unnecessary when we have extension.) We now no longer consider a “special realm of entities called meanings.” (23) That means we must find other ways to understand analyticity.]

 

[ditto]

The description of analyticity as truth by virtue of meanings started us off in pursuit of a concept of meaning. But now we have abandoned the thought of any special realm of entities called meanings. So the problem of analyticity confronts us anew.

(23)

[contents]

 

 

 

 

 

 

1.12

[Logically True Analytic Statements]

 

[Statements that are often considered analytic in philosophy are generally of two types. {1} Ones that are logically true, for instance (1) No unmarried man is married. (This is true no matter what the interpretations are of the terms. It is formally true.)]

 

[ditto]

Statements which are analytic by general philosophical acclaim are not, indeed, far to seek. They fall into two classes. Those of the first class, which may be called logically true, are typified by:

(1) No unmarried man is married.

The relevant feature of this example is that it is not merely true as it stands, but remains true under any and all reinterpretations of ‘man’ and ‘married’. If we suppose a prior inventory of logical particles, comprising ‘no’, ‘un-’, ‘not’, ‘if’, ‘then’, ‘and’, etc., then in general a logical truth is a statement which is true and remains true under all reinterpretations of its components other than the logical particles.

(23)

[contents]

 

 

 

 

 

1.13

[Statements Made Logically True by Substitutions]

 

[{2} The other kind of analytic statements are ones that can be rendered into a logically true format by substituting synonyms. For example, (2) “No bachelor is married” can be rendered “No unmarried man is married” but substituting the synonyms “bachelor” and “unmarried man”. Yet, we do not have a proper (formal?) characterization of these kinds of analytic statements, especially since we do not have a (formal?) definition of synonymy. Thus we do not have an adequate (formal?) characterization of analyticity.]

 

[ditto]

But there is also a second class of analytic statements, typified by:

(2) No bachelor is married.

The characteristic of such a statement is that it can be turned into a logical truth by putting synonyms for synonyms; thus (2) can be turned into (1) by putting ‘unmarried man’ for its synonym ‘bachelor’. We still lack a proper characterization of this second class of analytic statements, and therewith of analyticity generally, inasmuch as we have had in the above description to lean on a notion of “synonymy” which is no less in need of clarification than analyticity itself.

(23)

[contents]

 

 

 

 

 

1.14

[Carnap’s Definition of Logical Truths (Analyticity)]

 

[Carnap defines analyticity in the following way. We begin by assigning all the truth values to every atomic statement in a language. Each complete combination of assignments for all the atomic sentences is what he calls a “state description.” We can then compositionally build up the complex statements of the language using logical means, with their truth values being computable based on logical laws. A statement is analytic when it is true under every state description. Since a state description is like a possible world (it is one combination of facts), this can be seen as following Leibniz’ notion of being true in all possible worlds. (Quine then explains a problem with this conception: if the language has extralogical synonym-pairs, such as ‘bachelor’ and ‘unmarried man’, then statements like “All bachelors are married” will turn out to be synthetic rather than analytic. Thus) “The criterion in terms of state-descriptions is a reconstruction at best of logical truth.” (24)]

 

[ditto. (Note: I did not understand Quine’s objection. According to Quine, a statement is analytically true (L-true) in a system if it is true in all possible state-descriptions. It is L-false if its negation is L-true, meaning that the statement does not hold in any state description.  The sentence is L-determinate if it is either L-true or L-false. And it is L-indeterminate or factual (synthetic) if it is not L-determinate, meaning that there is at least one state-description in which it holds and at least one in which it does not hold. (See Carnap block quotes below.) Now, suppose two cases. {1} In our system, we have a way to derive formulas based on meaning, so in worlds where ‘John is a bachelor’ is true, then in that same world, ‘John is married’ is false (and vice versa). That would presumably make ‘All bachelors are married’ false in every state description. That would make ‘All bachelors are married’ L-false, and thus L-determinate. As such, it would not be synthetic. Yet, Quine claims it makes it synthetic. I did not understand why yet. (I can only see it working if it is both true and false that John is a bachelor and both true and false that John is married.) However, it also would not be analytic, because it is not true in all worlds. {2} In the second case, Quine says we do not have such sentences with mutually dependent truth values. But does he mean we cannot have both “bachelor” and “married” in the same world? What kind of a language would we have without terms that imply opposite meanings? Would it be just a formal system of symbols? Or is he saying that we do have ‘John is a bachelor’ and ‘John is married’ , but the truth of the one does not entail the falsity of the other? Still, that would not make “All bachelors are married” analytic, because there would still be worlds where we assign ‘John is a bachelor’ as true and ‘John is married’ as false. Thus still “All bachelors are married” would not hold in every possible world (state description). So I am not sure what Quine’s objection is here yet.)  Below are some relevant passages from Carnap’s text.

In order to speak about expressions in a general way, we often use ‘Ai’, ‘Aj’, etc.,  for expressions of any kind and ‘Si’, ‘Sj’, etc., for sentences ...

(Carnap 4. Note: here and below, the bold “A” should instead be Mathematical Bold Fraktur Capital A; and the Bold “S” should be Mathematical Bold Fraktur Capital S)

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 [...]; other logicians have proposed other explicata for the same explicandum. 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.

The L-terms (‘L-true’, etc.) which we shall now introduce are likewise intended as explicata for customary, but not quite exact, concepts. ‘L-true’ is meant as an explicatum for what Leibniz called necessary truth and Kant analytic truth. We shall indicate here briefly how this and the other L-terms can be defined.

(Carnap 7-8)

A class of sentences in S1 which contains for every atomic sentence either this sentence or its negation, but not both, and no other sentences, is called a state-description in S1 , because it obviously gives a complete description of a possible state of the universe of individuals with respect to all properties and relations expressed by predicates of the system. Thus the state-descriptions represent Leibniz' possible worlds or Wittgenstein's possible states of affairs.

It is easily possible to lay down semantical rules which determine for every sentence in S1 whether or not it holds in a given state-description. That a sentence holds in a state-description means, in nontechnical terms, that it would be true if the state-description (that is, all sentences belonging to it) were true. A few examples will suffice to show the nature of these rules: (1) an atomic sentence holds in a given state-description if and only if it belongs to it; (2) ~Si holds in a given state-description if and only if Si does not hold in it; (3) Si Sj, holds in a state-description if and only if either Si holds in it or Sj or both; ...

(Carnap 9)

Our concept of L-truth is, as mentioned above, intended as an explicatum for the familiar but vague concept of logical or necessary or analytic truth as explicandum. This explicandum has sometimes been characterized as truth based on purely logical reasons, on meaning alone, independent of the contingency of facts. Now the meaning of a sentence, its interpretation, is determined by the semantical rules (the rules of designation and the rules of ranges in the method explained above). Therefore, it seems well in accord with the traditional concept which we take as explicandum, if we require of any explicatum that it fulfil the following condition:

2-1. Convention. A sentence Si is L-true in a semantical system S if and only if Si is true in S in such a way that its truth can be established on the basis of the semantical rules of the system S alone, without any reference to (extra-linguistic) facts.

This is not yet a definition of L-truth. It is an informal formulation of a condition which any proposed definition of L-truth must fulfil in order to be adequate as an explication for our explicandum. Thus this convention has merely an explanatory and heuristic function.

How shall we define L-truth so as to fulfil the requirement 2-1? A way is suggested by Leibniz' conception that a necessary truth must hold in all possible worlds. Since our state-descriptions represent the possible worlds, this means that a sentence is logically true if it holds in all state-descriptions. This leads to the following definition:

2-2. Definition. A sentence Si is L-true (in S1) =Df  Si holds in every state-description (in S1).

(Carnap 10)

2-3. Definitions

a. Si  is L-false in (S1) =Df ~Si is L-true.

[...]

d. Si is L-determinate (in S1) =Df Si  is either L-true or L-false.

[...]

2-4. Si is L-false if and only if Si does not hold in any state-description.

(Carnap 11)

We have seen that our concept of L-truth fulfils our earlier convention 2-1. Therefore, according to the definition 2-3d, a sentence is L-determinate if and only if the semantical rules, independently of facts, suffice for establishing its truth-value, that is, either its truth or its falsity. This suggests the following definition, 2-7, as an explication for what Kant called synthetic judgments. The subsequent result, 2-8, which follows from the definition, shows that the concept defined is indeed adequate as an explicatum.

2-7. Definition. Si is L-indeterminate or factual (in S1) =Df   Si  is not L-determinate.

2-8. A sentence is factual if and only if there is at least one state-description in which it holds and at least one in which it does not hold.

(Carnap 12)

]

In recent years Carnap has tended to explain analyticity by appeal to what he calls state-descriptions.3 A state-description is any exhaustive assignment of truth values to the atomic, or noncompound, statements of the language. All other statements of the language are, Carnap assumes, built up of their component clauses by means of the familiar logical devices, in such a way that the truth value of any complex statement is fixed for each state-description by specifiable logical laws. A statement is then explained as analytic when it comes out true under every state-description. This account is an adaptation | of Leibniz’s “true in all possible worlds.” But note that this version of analyticity serves its purpose only if the atomic statements of the language are, unlike ‘John is a bachelor’ and ‘John is married’, mutually independent. Otherwise there would be a state-description which assigned truth to ‘John is a bachelor’ and falsity to ‘John is married’, and consequently ‘All bachelors are married’ would turn out synthetic rather than analytic under the proposed criterion. Thus the criterion of analyticity in terms of state-descriptions serves only for languages devoid of extralogical synonym-pairs, such as ‘bachelor’ and ‘unmarried man’: synonym-pairs of the type which give rise to the “second class” of analytic statements. The criterion in terms of state-descriptions is a reconstruction at best of logical truth.

(23-24)

3. R. Carnap, Meaning and Necessity (Chicago, 1947), pp. 9ff.; Logical Foundations of Probability (Chicago, 1950), pp. 70ff.

(23)

[contents]

 

 

 

 

 

1.15

[Turning Instead to Analyticity From Synonymy]

 

[Yet, Carnap’s main concern was clarifying probability and induction, not analyticity, which is our concern, “and here the major difficulty lies not in the first class of analytic statements, the logical truths, but rather in the second class, which depends on the notion of synonymy.” (23)]

 

[ditto]

I do not mean to suggest that Carnap is under any illusions on this point. His simplified model language with its state-descriptions is aimed primarily not at the general problem of analyticity but at another purpose, the clarification of probability and induction. Our problem, however, is analyticity; and here the major difficulty lies not in the first class of analytic statements, the logical truths, but rather in the second class, which depends on the notion of synonymy.

(24)

[contents]

 

 

 

 

 

 

Bibliography:

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.

 

Kant, Immanuel. Critique of Pure Reason. Edited and translated by Paul Guyer and Allen W. Wood. Cambridge: Cambridge University, 1998.

 

Leibniz, Gottfried. “Monadology.” In Philosophical Texts, edited and translated by Richard Francks and Roger Woolhouse, 267–81. Oxford: Oxford University, 1998.

 

Russell, Bertrand. “On Denoting.” Mind 14, no. 56 (1905): 479–93.

 

White, Morton. “The Analytic and the Synthetic: An Untenable Dualism.” In John Dewey: Philosopher of Science and Freedom. a Symposium, edited by Sidney Hook, 316–30. New York: Dial, 1950.

 

 

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