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by Corry Shores
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[Quine, Two Dogmas of Empiricism, entry directory]
[The following is a paragraph by paragraph summary of the text. More analysis is still needed and will be updated when conducted. Proofreading is incomplete, so please forgive all my various mistakes. Material between brackets or between parentheses within brackets is my own and should not be trusted over the quotations, which themselves may contain typographical errors from their transcription. Please consult the original text in any case.]
Summary of
W. V. Quine
“Two Dogmas of Empiricism”
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)
[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]
[Reformulation Kant’s Notion of Analyticity as Being True by its Meanings and Independently of Fact]
[Meaning as Not Referential Naming]
[Russell’s “Author of Waverley” as Another Example of an Identifying Naming Statement That Is Not Analytical]
[Abstract Terms as Also Having This Problem (“9” and “The Number of Planets”)]
[Meaning and Extension for General Terms (“Creature with a Heart” and “Creature with a Kidney”]
[Intention (Meaning)/Connotation Vs. Extension/Denotation]
[Aristotle’s Essence as Being Similar to Meaning, but Not Identical]
[Difficulty in Defining What Kind of Entities Meanings Are]
[Defining Meaning as Superfluous]
[Logically True Analytic Statements]
[Statements Made Logically True by Substitutions]
[Carnap’s Definition of Logical Truths (Analyticity)]
[Turning Instead to Analyticity From Synonymy]
Summary
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
[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)
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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