Meaning, truth, and belief are sticky notions. They stick together

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Tolerating Semantics: Carnap’s Philosophical Point of View

Alan Richardson

“Meaning, truth, and belief are sticky notions. They stick together,” W.V. Quine once wrote (Quine 1981, 38). One large task of Quine’s philosophy was to pry them apart. Throughout modern philosophy, meaning and truth have been most intimately stuck together in the notion of the analytic judgment or proposition. That there are, at least in languages of suitable structures, sentences that are true as a matter of linguistic convention, that are true in virtue of the meanings of the words within them, was once a generally acknowledged truth, a happy meeting ground for empiricist and rationalist, realist and idealist, formalist and logicist. As we all know, Rudolf Carnap’s account of the analytic/synthetic distinction was, in fact, the location of Quine’s most celebrated solvent influence in unsticking meaning and truth. Quine’s views have had significant influence on philosophy, spawning generations of increasingly contented and self-assured naturalists, for example. Contemporary naturalism is a fascinating topic, but it is not the topic of this essay. If naturalism is the tremendous consequence, the fall of the analytic/synthetic distinction is the even more tremendous cause, and it is the pertinent topic to consider in a volume on Carnap’s philosophy.

The task of this essay is to revisit Carnap’s semantic program in order to ascertain what its philosophical point was meant to be. The essay argues against two towering figures of Harvard analytic philosophy–Quine and Hilary Putnam–to the conclusion that Carnap’s adherence to the analytic/synthetic distinction does not derive from his empiricism, much less his alleged verificationism. I hope to make plausible the view that for Carnap the analytic/synthetic distinction solves two problems at once: it answers long-standing methodological issues within his own philosophy of science regarding the place of mathematics in the system of knowledge, and it makes possible his technical vision for philosophy. I argue that Carnap’s use of formal semantics was motivated by two overarching concerns: the promulgation of a scientific philosophy given shape and precision as the logical syntax and formal semantics of artificial languages and a commitment to exhibiting the virtues of such a philosophical vision by defusing, rather than answering, the questions at the heart of the disputes over the foundations of mathematics and the place of mathematics in empirical knowledge.

The argument has five parts: First, I will rehearse some of Quine’s arguments against Carnap’s analytic/synthetic distinction, uncovering some of Quine’s interpretative presuppositions along the way. Second, I will briefly note some reasons to be chary of reading Carnap in the way Quine invites us to read him, some ways in which Quine’s interpretative framework raises more questions than it answers. Third, I will enunciate my own first principle of Carnap interpretation: take his Principle of Tolerance seriously. Fourthly, I will use this perspective to discuss Carnap’s early work on semantics, especially his monograph in the International Encyclopedia of Unified Science, “The Foundations of Logic and Mathematics” (Carnap 1939), and to present a place for Carnapian semantics rather at odds with Quine’s story. Finally, I will face one last embarrassment, one we can associate with Putnam, regarding my reading of Carnap.
1. From a Quinean Point of View: Carnap as Dogmatist
We all know that the analytic/synthetic distinction is, according to Quine (1980), both the more famous and the more derivative of the two dogmas of empiricism that he uncovered in 1951. Why is the analytic/synthetic distinction a dogma of empiricism, according to Quine? Quine’s chain of reasoning here is tight and compelling. Quine asks us to begin our understanding of Carnap’s philosophy by seeing Carnap as promoting a radical empiricist project: a desire for an empiricist criterion of meaningfulness that divides the meaningful from the meaningless, the scientific from the metaphysical. This criterion is also atomistic (or molecular), assigning the sentence as the primary vehicle of meaning. Thus, within the realm of the empirical, we conceive a radical reductionist project designed to show how each sentence of meaningful discourse can be translated into a sentence that speaks only of sensation. The meanings of empirical terms are then given in the chains of definition that link all meaningful discourse to experience. This is one place for the analytic sentence: The chains of definitions are the means to effect the translational reduction, not genuine claims about the world that themselves have to be reduced. Analyticity is, in this sense, an ineliminable means for producing the translational reduction.

There is an additional problem, however, that yields a second place for analyticity. Carnap’s project is meant to hive off the meaningless verbiage of metaphysics from the meaningful claims of science. But, what are we to do with mathematics? Here, Quine sees another motivation for analyticity. Mathematical claims cannot be dismissed as meaningless, even though they have no empirical import. The idea then is to ground mathematics not in empirical matters of fact, but in linguistic convention. All of logic and mathematics consists in expressions of conventions for the meanings of symbols and the logical consequences of such conventions. This solves the empiricist worry by showing that mathematics is a priori precisely because it is empty of content. Its certainty is not due to rational intuition into Plato’s heaven nor to the place of mathematics in constituting the world of experience, but is, rather, a sort of Pickwickian certainty, expressive wholly of choices we have made about what the signs we use will mean.

Here, too, Quine finds a motivation for analyticity in the sentence-by-sentence reductionism that is the second dogma of empiricism. Reductionism and verificationism ground sentence meaning in confirmation relations that ultimately link meaningful claims to experience. A translation into the language of sensation of a high-level scientific claim reveals its meaning by tying it to what can be directly known. But this process reveals the dual dependence of the truth of sentences on what they mean–how they are translated into sensation–and on what it the case–what the knowable facts of sensation are. Once we conceive of this dual dependence, however, and see it operating at the level of individual sentences, we can conceive of sentences for which the first component does all the work–sentences whose truth is guaranteed solely by what they mean. This is the linguistic doctrine of logical and analytic truth: they are true in virtue of the meanings of the words they contain.

This linguistic doctrine is given epistemological punch when combined with the verificationist theory of meaning. For this latter account ties meaning to confirmation and, hence, to epistemology. Mathematical claims are, then, true in virtue of meaning and, thus, true independently of the facts of experience. That is, in Quine’s famous phrase, the linguistic doctrine of logical (analytic, mathematical) truth and the verificationist theory of meaning combine to render analytic truths as those that are verified or confirmed come what may.

It is for these reasons that Quine invites us to see the analytic/synthetic distinction to be Carnap’s response to a pressing epistemological problem regarding logical and mathematical truth, given Carnap’s strict verificationist empiricism. The certainty of mathematics can only be guaranteed by draining mathematics of content and, thus, showing how mathematical claims can be verified regardless of the course of experience. Analyticity solves an epistemological problem without which Carnap’s empiricism would collapse–for want of an account of the certainty of mathematics–and slide inexorably into Quine’s own brand of empiricism in which mathematics is recognized to be epistemologically on a par with the higher reaches of empirical theorizing.

This latter is the conclusion that the arguments of “Two Dogmas” wants us to reach, but is not available to Carnap since his whole vision of philosophy as the mathematics of language itself requires that the analytic/synthetic distinction is well-founded. That is to say, Carnap needs the analytic in order not merely to solve an empiricist epistemological problem but also to make sense of his own account of philosophical work. No project that makes philosophy wholly a matter of analysis and explication makes sense if the logic-mathematical cannot be sharply distinguished from the empirical. This is why, once we accept Quine’s critique, we stand on the trembling ground of incipient naturalism, without any a priori element in knowledge and without, therefore, a distinctive and a priori method for philosophy.

This point of view regarding Carnap’s philosophy can be summarized in five points. First, Carnap’s primary philosophical commitment is to a strict empiricism that seeks to tie all knowledge claims via logically precise confirmation relations to experience. Second, in the service of this empiricism, Carnap engages in a translational reductionism with the sentence as the primary unit of meaningfulness. Third, this raises a striking epistemological difficulty regarding mathematics, which is, it seems, devoid of empirical content but not meaningless, but rather certain. Fourth, the answer to the problem is found in making precise a notion of truth in virtue of meaning, that is, of analyticity. Fifth, this solves the problem by combining with the verification criterion to yield the epistemologically satisfying outcome for the empiricist that mathematical certainty is ultimately understood as confirmation come what may, or, if you prefer, immunity from disconfirmation in light of experience, without any metaphysical or transcendental account of how it attains this immunity. The certainty of mathematics is as clear as meaning itself–and this is exactly the point at which Quine demurs.
2. Quine and Interpretative Truth
This is a tidy account of Carnap, one that serves to do with Carnap’s work what Quine most wants to do with it. Quine wants two things: For Carnap’s work to be the last best hope for foundationalist empiricism and for it to be refutable. In Quine’s interpretation of Carnap, empiricism does all the philosophical work. The empiricist epistemological question of the certainty of logical and mathematical truth leads to the need for a linguistic doctrine of such truth; if logical and mathematical truths are true in virtue of meaning, then those truths are not disconfirmable in light of experience and, thus, once we have adopted a logical and mathematical framework, we will never have a reason to give it up. This view of Carnap as first and foremost an empiricist has certain predictive consequences, however, and none of these is particularly well borne out in his writings. I will mention only three such consequences here.1

First, Quine is clear that reductionism is the source of the analytic/synthetic distinction.2 Thus, for Quine, Carnap’s move away from reductionism and verificationism while continuing to insist on the intelligibility and importance of the analytic is inexplicable. Indeed, Quine finds no motivation within Carnap’s philosophy for the move to reduction conditionals or any other of the more tenuous connections between theoretical and observational discourse that is the hallmark of Carnap’s work in philosophy of science from the mid-1930s. This Carnapian reaction to the failure of the project of the Aufbau, according to Quine, is based simply on a mistaken generosity of logical spirit that leads Carnap to think that there is something illuminating about a story of the introduction of higher level theoretical terms in science that does not show how they reduce to experience. For Quine, however, this last move “renounce[s] the last remaining advantage othat we supposed rational reconstruction to have over straight over psychology” (Quine 1969, p. 78), and leads him to ask why we would engage in make-believe stories about the introduction of theoretical terms in science rather than doing the empirical work to find out how they are in fact introduced. In Quine’s work, the Aufbau is the most epistemologically telling document in Carnap’s corpus, and Carnap’s mature work is a philosophically degenerating project.

Quine’s remarks on reduction conditionals and so on serve nicely to dismiss Carnap’s later work, but could invite a rethinking instead. That is, if, according to our interpretation of Carnap, one of his most salient and fundamental philosophical shifts seems unjustifiable, then we could pause to consider whether we have his motivations and commitments right in our interpretation. A more satisfying interpretation of Carnap would enable us to make sense of an interesting and, from a Quinean point of view, I would argue, inexplicable fact: At the very time Carnap first formulates an analytic/synthetic distinction that seems to him to be at all viable–that is, in Logical Syntax (Carnap 1937)–, he gives up translational reduction entirely. So, my first claim regarding proper interpretation of Carnap is that reductionism does not serve, for Carnap, to ground or motivate the analytic/synthetic distinction.

Second, if Quine were right, we ought to expect Carnap to present the analytic/synthetic distinction as part of an argument for empiricism, one showing how empiricism solves the problem of the a priority of mathematics and logic. Carnap nowhere in his writings clearly does that, however. Indeed, it is highly characteristic of Carnap’s work not to argue for empiricism at all. Certainly by the mid 1930s Carnap explicitly came to view empiricism not as a thesis at all and, a forteriori, then, not something for which an argument would be forthcoming. He viewed it, rather, as a commitment to set of the analytic tools in the reconstruction of science. Thus, in “Testability and Meaning,” Carnap (Carnap 1936/7) writes:

It seems to me that it is preferable to formulate the principle of empiricism not in the form of an assertion–“all knowledge is empirical” or “all synthetic sentences that we can know are based on (or connected with) experience” or the like–but rather as a proposal or requirement. As empiricists, we require that descriptive predicates and hence synthetic sentences are not admitted unless they have some connection with possible observation, a connection which has to be characterized in a suitable way. (§27)

This is a highly significant moment in Carnap’s thinking and indicates how for him, far from being a solution to an antecedent epistemological problem for an independently understandable philosophical commitment to empiricism, analyticity serves to first clarify and make sense of empiricism. First and most globally, note that this passage commits empiricists to a limited range of independently specified Carnapian formal languages, languages specifiable as languages only through and with the analytic/synthetic distinction drawn for them. Thus, the analytic must be specifiable prior to and independently of empiricism. Second, it is clear that for Carnap mathematics is analytic in all formal languages, not just in empiricist ones. This is because Carnap has no independent way of specifying “the mathematical”–he argued in Logical Syntax that no distinction had ever properly been drawn between the mathematical and the other logical signs of languages. Thus, by the time of Syntax, the notion of “mathematics” as an independently specifiable class of claims about which there are special problems not common to the problems of all analytic sentences has wholly dropped out of his thinking. You might, if you so desired, in an informal or formal metalanguage decide that a formal language did not have mathematics unless it contained at least, say, primitive recursive arithmetic (specified now in your metalanguage) but this is a conventional matter that bears no important philosophical weight. You would never find, however, that mathematics so specified was synthetic in any formal language. Finally, note that empiricism simply is not a thesis that has any justification–it is not a thesis at all and nothing could justify it. It is a proposal of or requirement regarding or commitment to a project of regimenting science in one way rather than another. These three points could be summarized as follows: Analyticity is not a dogma but a presupposition of empiricism for Carnap. This is because empiricism is a pragmatic commitment to the use of some languages as tools for the rational reconstruction of science and the very notion of a language depends upon an analytic/synthetic distinction. Indeed, we can put this point starkly by saying that the distinction between empiricist and non-empiricist approaches to science can only be made philosophically precise, on Carnap’s view, inside the project of syntax and semantics. If we wanted a slogan, we could say: Carnap was not trying to provide an empiricist semantics, but a semantics in which it could be said precisely what empiricism is.

Finally, if analyticity meant “immune from disconfirmation” for Carnap, then we should expect him to use the armament of his confirmation theory to specify the analytic sentences of a language. Far from this, the confirmation theory for a language is typically introduced through analytic sentences, through meaning postulates for the confirmation function, for example. In Logical Foundations of Probability (Carnap 1962), for example, analyticity or L-truth is defined roughly 200 pages before “degree of confirmation” is.

Similarly, if analytic meant “true in virtue of meaning” one would expect that analytic sentences would be specified through a notion of meaning introduced in the semantic metalanguage. But this is not how Carnap proceeds. Throughout his semantic period, and certainly early on in it, his specification of analytic sentences is, roughly and nontechnically, this: A sentence, S, of language L is L-true in L if and only if the truth in L of S is a consequence (in the metalanguage) of the Tarski truth definition for L. No notion of meaning is employed in this specification; all talk of meaning is informal, heuristic, elucidatory talk that is rendered precise in formal semantics, where no such language is employed. This is exactly how Carnap proceeds in, for example, Meaning and Necessity (Carnap 1956, p. 10), where he first gives an informal “convention” for L-truth in terms of truth in virtue of meaning and then gives a formal definition in which all such talk is expunged in favour of talk of state-descriptions (which are even syntactically specifiable).3

In a slogan, we might say that for Carnap, translation into the formal mode of speech is the very process of throwing away the ladder, that is, the very process of coming to see what is properly philosophical aright. But this translation into the formal mode of speech always expunges from consideration the notions that Quine posits as Carnap’s deepest philosophical commitments. My suggestion is that we take Carnap’s own views seriously here and consider what his philosophy looks like when we do.
3. From Dogmatic to Tolerant Readings of Carnap
Quine’s Carnap is a very traditional philosopher–he is simply a technically competent empiricist. If Hume had had logic, he would have been Carnap. What empiricism is, for Quine, is evident–it is a commitment to the claim that all significant discourse stands in confirmation relations with experience. It is interesting that for Quine experience is a naturalistic notion and confirmation relations become, if only problematically so, causal. Thus, for example, his specification of the underdetermination of theory by evidence in “Epistemology Naturalized” (Quine 1969, p. 83) becomes a causal underdetermination of verbal output by sensory input. Contrast this with Carnap: For Carnap, both “experience” and “confirmation relations” are terms of traditional epistemology that participate in the vagueness and lack of specification of such terms generally. Thus, Carnap would not even know what he was asked to commit to if asked to sign a loyalty oath to Quinean empiricism. Carnap’s characteristic philosophical move is to take such unspecified commitments and to render them precise through logic. One can imagine Carnap trying to make sense of Quine’s position in roughly the following way: Perhaps Quine means that empiricists are committed to using formal languages in which the predicates in the protocol sublanguages stand in a close logical relation (which must be specified!) to observation and within which all other descriptive predicates stand in tighter or looser logical relations to the observation predicates, allowing the definition, therefore, of a confirmation function that tracks their distance from the empirical base. Consider a language, L, for example, he might go on to say, with the following analytic sentences, including meaning postulates for the confirmation function, and the following observational protocol sublanguage. Quine, he might ask, is this an empiricist language in your sense of empiricism?

Such “ways of going on” are what is most characteristically Carnapian. From his earliest publication, the published version of his doctoral thesis, Der Raum (Carnap 1922), Carnap returned again and again to a position that he came to designate as “tolerance” in philosophy (Carnap 1937, p. 51): Philosophical controversies tend to be puzzling and seem to go nowhere, not because the issues involved are so deep as to render these disputes harder than all others, but because they were so confused. The confusion in a sense indicates a certain depth–the question whether there are numbers is in some sense deeper than the question as to whether, for example, seventeen is a number. What is deep here, according to Carnap, is not, however, the theoretical issue at stake, but rather the real import of the discussion; that import was so deep that the disputants themselves missed it. What they missed is that their question only seems to be about objects (numbers) but is really, if misleadingly, about the language they speak. In Carnap’s late vocabulary, it is an external question of choice of linguistic framework, not a question of a thesis formulated in a framework.

Why is this “tolerance”? Because it moves the dispute from the ineffable grounds of philosophical argumentation regarding the very being of things to the practical grounds of choice of an instrument for speaking about the world. Thus, it is tolerant in two ways: First, alternative philosophical positions do not divide into the true and the false, but into the more well-suited for this purpose and the more well-suited for that purpose. (People tend to be tolerant of different tools. No one refutes a screwdriver by using a hammer, and no one feels compelled to use a screwdriver to drive in a nail by the truth of screwdrivers and the falsity of hammers.) Second, we may come to see, if we adopt this perspective, that our purposes may well, in the realm of knowledge, be different. You may, for example, be keen on giving physics as much mathematics as it might want and in a simple form; I, on the other hand, wary of potential contradiction, may play my language games close to my vest, and adopt a constructivist language for mathematics. We might even come more carefully to delimit our purposes and to discover that our own language forms are inexpedient given our purposes. What we cannot do, however, is argue for our purposes as if we were arguing for a theoretical claim.4

For Carnap, this tolerance (interestingly, given the title of Quine’s “Two Dogmas of Empiricism”) contrasts with dogmatism. Carnap makes this contrast explicit in the essay that must have given Quine the impetus to write “Two Dogmas”–the essay, “Empiricism, Semantics, and Ontology” (Carnap 1956, pp. 205-221). At the end of that essay, Carnap writes (Carnap 1956, p. 221):

To decree dogmatic prohibitions of certain linguistic forms instead of testing them by their success or failure in practical use, is worse than futile; it is positively harmful because it obstructs scientific progress.... Let us grant to those who work in any special field of investigation any form of expression which seems useful to them; the work in the field will sooner or later lead to the elimination of those forms which have no useful function. Let us be cautious in making assertions and critical in examining them, but tolerant in permitting linguistic forms.5
4. Putting Tolerance to Work: Semantics and Foundations of Mathematics
I want briefly to turn now to two points raised in Carnap’s Encyclopedia monograph (Carnap 1939) in order to show how characteristic such tolerance is in Carnap’s work and to give a sense of what issues regarding mathematics he was genuinely interested in. The first point concerns the proper philosophical understanding of the standpoint of tolerance itself; the second point concerns the principal use to which Carnap put tolerance.

On the first point, tolerance is often understood to be a crude conventionalism regarding logical truth. Given this interpretation, we should be especially interested in the section of the monograph that asks the question “Is logic a matter of convention?” (§12). If tolerance is conventionalism about logic, one might expect this to be a short section, basically saying “Yes.” This is not what Carnap does, however. Rather, he divides the issue and finds a sense of the question in which the answer is yes and a sense of the question in which the answer is no. In essence, his discussion proceeds as follows: Logical systems consist of, on the one hand, a syntactic calculus and, on the other, a semantics. Since there are these two parts, the question of conventionality of logic is under-specified. We might be asking about the choice of the syntactic rules in advance of the interpretation or only subsequently to an interpretation of the logical symbols. If the rules of the syntactic calculus are chosen first and then a semantical system is added onto it as an interpretation, then, of course, the rules of the calculus are freely chosen and, in the appropriate sense, conventional. On the other hand, if the rules of the semantical system are chosen first, then in this sense the “meanings” of the logical particles are fixed and the rules of the syntactic calculus are severely constrained. Carnap, in this sense, views the question of the conventionality of logic not as a philosophical issue upon which he takes an important stand, but as a philosophical issue that his work clarifies. His strategy is to use the standpoint of tolerance and technical tools of logic to clarify the issue of conventionality of logical truth.

On the second point, in this monograph, as elsewhere, Carnap’s principal use of tolerance occurs in his discussions of the foundations of mathematics. Here, the tolerant attitude has two characteristic moments. First, he seeks to clarify the issues and, thus, to defuse disputes in the foundations of mathematics. Once we see that what is at stake is not truth, but a choice of logical structures, a good deal of the saber-rattling of, for example, Brouwer-style intutitionism just goes away. Rather than staking a claim to the truth about mathematics, an appropriately tolerant intuitionist will simply present a constructivist logical system, perhaps indeed will come to use Carnap’s own Language One from Logical Syntax. Second, notwithstanding this attempt to overcome the standard wrangling over “foundations,” Carnap’s tolerance also, somewhat surreptitiously, invokes an advantage of logicism over formalism and intuitionism; in Carnap’s eyes, logicism had the good sense always to put questions of the role of mathematics in empirical knowledge at the forefront of its concerns (cf. Carnap 1937, §82). This is always Carnap’s concern also, one intimately connected in his mind with the advantages of his tolerant attitude. Thus, he writes in §12 of the Encyclopedia monograph, regarding the variety of logical systems then being formulated and discussed:

The task is not to decide which of the different systems is “the right logic” but to examine their formal properties and the possibilities for their interpretation and application in science. It might turn out that a system deviating from the ordinary form will turn out to be useful as a basis for the language of science.

This stress on application in science is most strikingly illustrated in the monograph in his discussion of geometry in §§21-22. Here we see the way in which Carnap takes the lessons of the development of relativity theory to require an analytic/synthetic distinction. Why is this? For two reasons: First, the very distinction that Einstein draws between mathematical and physical geometry must be made precise and is made precise by Carnap in the distinction between logical and physical interpretations of geometrical calculi. Mathematical geometers, on Carnap’s view, exhibit tolerance; they neither play with uninterpreted symbols nor worry about some ineffable mathematical “truth.” Mathematical truth is guaranteed by logical models of geometrical systems and those logical models are available for many such systems. In essence, then, the logical models of geometrical sentences when embedded in well-defined axiom systems explains mathematical tolerance: all the systems have the appropriate notion of truth and there is nothing to choose if pure mathematics is all we care about. Physical geometers care about physical truth. Even here though, and this is the second point, Carnap wants to claim a space for a version of geometrical conventionalism in the manner of Poincaré. This requires a second place for the analytic: a place for co-ordinative definitions that connect heretofore uninterpreted geometrical calculi to independently specifiable physical processes like light rays. So, tolerance underwrites physical conventionalism for Carnap, and physical conventionalism explains the unique epistemological role of analytic sentences that first give physical significance to pure mathematical terms such as “geodesic.”

It might be argued that the methodological lessons of relativity theory–the distinction between pure and applied geometry and conventionalism within applied geometry–that Carnap exploits are actually misreadings of the methodology of relativity theory. It might further be argued that even if these are appropriate methodological lessons from relativity theory, they cannot block Quine’s objections to the analytic/synthetic distinction–that is, they are not lessons that can be adequately made precise through the technicalities of Carnap’s metalogical work.6 I do not have the space to rebut or even discuss these issues here. My current point regarding Carnap’s point of view here is motivational for Carnapian philosophy, not argumentative within it: If you adopt Quine’s point of view, of course, you will not grant Carnap his uses of relativity theory or the logical resources he uses to make those lessons precise and transportable. But, I argue, Carnap himself had no independent and informal philosophical commitments that would allow him to render philosophical judgement on the methodological lessons of the best theories of current exact science. That is, Carnap both took for granted and sought philosophically to comprehend and advance the conceptual techniques of the exact sciences, for they are the locus of best knowledge for him. Another point of view in philosophy might raise objections to distinctions such as Einstein’s distinction between pure and applied geometry–perhaps Quinean naturalist empiricism can make no such distinction. Carnap’s own view is that it is not his business directly to argue against such philosophers but to offer a different vision of and project for philosophy from theirs. His project is predicated on the presumption that what has worked in science cannot be dismissed in philosophy.

In sum, my view–one that owes a good deal to Richard Creath (1991)–of the mature Carnap is as conceptual engineer. An appropriate stance to take in the interpretation of his work is not to attempt to uncover his deepest philosophical commitments but to strive to understand just how deeply his anti-philosophical commitments go. My view is that he looks to the formalization inherent in the best scientific theorizing not as a source of interesting problems to solve for, nor triumphs to exclaim from within, an antecedent and informal empiricist perspective. Rather, Carnap’s lessons are historical and formal: the epistemic success of the exact sciences is revealed in their history and is due more to the precision and power of formal and mathematical techniques and how they are deployed in empirical knowledge than to any other aspect of such science. Carnap sought to understand that process through the introduction of the self-same techniques and the self-same tolerance of formally precise linguistic forms in philosophy that one finds in the exact sciences themselves. This precision can then for the first time make tolerably clear what someone is committed to in being committed to, for example, empiricism.
5. Coda: Tolerance, Conventionalism, and Verificationism
This conclusion regarding Carnap’s work may seem a happy one, especially for anyone who shares Carnap’s enthusiasm for formal techniques and indifference to choosing sides in the debates of the philosophers. There is one final way to worry this view, a worry perhaps most strikingly expressed by Putnam in his Reason, Truth, and History (Putnam 1981), in a section given over to arguing that positivism is self-refuting. The self-refutation argument is, as they always are, disarmingly simple: The verification principle of meaning is neither analytic nor verifiable and is, thus, by its own lights, meaningless. In considering an objection to his argument, Putnam writes (1981, p. 112):

The positivists, I will be reminded, conceded that the verification principle was ‘cognitively meaningless’. They said it was a proposal and as such was neither true nor false. But they argued for their proposal, and such arguments were (and had to be) non-starters.

To this passage, he appends a footnote that says in part (1981, p 112n4):

The most interesting view was that of Carnap. According to Carnap, all rational reconstructions are proposals. The only factual questions concern the logical and empirical consequences of accepting this or that rational reconstruction.... The conclusion he drew was that in philosophy one should be tolerant of divergent rational reconstructions. However, the Principle of Tolerance, as Carnap called it, presupposes the Verifiability Principle. For the doctrine that no rational reconstruction is uniquely correct or corresponds to the way things ‘really are’, the doctrine that ‘all external questions’ are without cognitive sense[,] is just the Verification Principle. To apply the Principle of Tolerance to the Verification Principle itself would be circular.

This view presents the principle of tolerance, which I have taken to be fundamental to Carnap’s philosophy, as derivative of another and more problematic principle, the Verification Principle. I limit myself to a few brief comments in rebuttal. First, Putnam is wrong about Carnap’s claims about the verification criterion. Carnap never said the criterion is a proposal and, therefore, cognitively meaningless. It is a category mistake to call proposals cognitively meaningful or meaningless. Cognitive meaningfulness applies to sentences in languages, not to proposals for the adoption of languages. Moreover, Carnap was quite clear (in, for example, Carnap 1934) that the verification criterion, once proposed and adopted (he himself was against the proposal by the mid 1930s) become an analytic truth of the semantic metalanguage. That is, the verification criterion for a given object language, L, is a meaning postulate for “meaningful in L” in the semantic metalanguage, ML, and thus is analytic in ML, as you could find out by ascending to a semantic metametalanguage, MML, and giving a truth definition in MML of ML.

Second, Putnam’s claim that Tolerance just is the principle of verification is surely not right. Claiming this makes Carnap quite a curious figure for, just as the analytic/synthetic distinction, the principle of tolerance was first clearly enunciated exactly when Carnap gave up verificationism in his own reconstructions of science. Given that among the rational reconstructions meant to be tolerated were non-verificationist reconstructions, Putnam’s interpretation seems to have gotten off on the wrong foot. The reason why it has gotten off on the wrong foot is interesting and allows us to draw one last lesson from Carnap’s work. For Putnam’s account of tolerance here, as Thomas Ricketts (1994) has shown, conflates conventionalism and tolerance; Carnap’s logico-semantic tolerance is not a version of conventionalism in the manner of Poincaré, however.

The notion of convention that we might associate with Poincaré begins with a specification of “maters of fact” and then proceeds to argue that the matters of fact in principle leave certain classes of claims indeterminate; adoption of those claims is then conventional. Thus, if the matters of fact of geometrical experience of nature consist solely of point-coincidences, the most that those matters of fact determine of the geometrical structure of the physical space is its topology (perhaps even just its local topology), and, hence, the metric of physical space is a convention. The matters of fact underdetermine our choice of metrical structure. Logical “convention” in Carnap’s sense is not this, but something more thorough-going. For there is no linguistic-framework transcendent notion of “matter of fact” that can be fixed and relative to which logical structure varies freely. On the contrary, the notion of “matter of fact” is given only internal to a linguistic framework and on the basis of the analytic/synthetic distinction for that framework. It is in this sense that the analytic (for a given language) is not explained by an antecedent notion of “independence from matters of fact” but first renders tolerably precise the factual/conventional distinction (relative to that framework) itself.

Putnam’s remarks indicate that his Carnap is a conventional conventionalist: fixing “the way things really are” does not fix the language you speak. Thus, the structure of a linguistic framework goes beyond the “totality of the facts” in just the way, according to Poincaré, the metrical geometry of space goes beyond the facts of physical geometry. But, as we just indicated, “the way things really are” and “the totality of the facts” are metaphysical notions that cry out for clarification and not at all terms that Carnap uses in specifying tolerance or linguistic frameworks. He is not concerned to show that language choice is not factual via an argument that trades in a linguistic-framework transcendent notion of factuality. It is in this sense that Carnap’s tolerance maintains a sort of Kantian transcendental flavour: linguistic frameworks do not regiment independently given framework-independent facts; they first induce a proper notion of factuality. The metaphysical terms in which Putnam explains Carnap’s philosophy are not appropriate to it.

There is an historical suggestion in all this with which I shall end: Quine and Putnam both view themselves as pragmatists and as deeply opposed to Carnapian philosophy. My suggestion is that Quine (1980) took himself to be offering the anti-thesis to Carnap’s thesis, while Putnam (1981) offers himself as a synthetic Aufhebung to the thesis of Carnap and the anti-thesis of Feyerabend. Carnap, however, always the deflationist, offers no Hegelian narrative of the history of philosophy, but rather offers only a tool for doing a new philosophy. Standing in the Hegelian historiographic tradition of Deweyan pragmatism, Quine and Putnam argue over the appropriate task of philosophy; Carnap, in my story, appears as a Nietzschean heir and prodigal, offering us not philosophy with a hammer but philosophy on the model of a hammer.

Carnap, Rudolf. 1922. Der Raum: Ein Beitrag zur Wissenschaftslehre. Berlin: Reuther & Reichard.

Carnap, Rudolf. 1936/1937. Testability and Meaning. Philosophy of Science 3: 419-71; 4: 1-40.

Carnap, Rudolf. 1937. The Logical Syntax of Language. London: Kegan Paul, Trench, Trubner.

Carnap, Rudolf. 1939. Foundations of Logic and Matematics. Chicago: University of Chicago Press.

Carnap, Rudolf. 1956. Meaning and Necessity. 2d Ed. Chicago: University of Chicago Press.

Carnap, Rudolf. 1962. Logical Foundations of Probability Theory. 2d Ed. Chicago: University of Chicago Press.

Carnap, Rudolf. 1967. Logical Structure of the World. Berkeley and Los Angeles: University of California Press.

Carnap, Rudolf. 1987. On the Task of the Logic of Science. In Unified Science: The Vienna Circle Monograph Series Originally Edited by Otto Neurath, edited by B. MacGuiness, 46-66.

Creath, Richard. 1991. Every Dogma Has Its Day. Erkenntnis 35: 347-389.

Friedman, Michael. 1999. Tolerance and Analyticity in Carnap’s Philosophy of Mathematics. In Reconsidering Logical Positivism, 198-233. Cambridge: Cambridge University Press.

Putnam, H. 1981. Reason, Truth and History. Cambridge: Cambridge University Press.

Quine. W. V. 1969. Epistemology Naturalized. In Ontological Relativity and Other Essays, 69-90. New York: Columbia University Press.

Quine, W. V. 1980. Two Dogmas of Empiricism. In From a Logical Point of View, 3d Ed., 20-46. Cambridge, MA: Harvard University Press.

Quine, W. V. 1981. On the Very Idea of a Third Dogma. In Theories and Things, 38-42. Cambridge, MA: Harvard University Press.

Richardson, Alan. 1997. Two Dogmas About Logical Empiricism: Carnap and Quine on Logic, Epistemology, and Empiricism. Philosophical Topics 21: 145-168.

Ricketts, Thomas. 1994. Carnap’s Principle of Tolerance, Empiricism, and Conventionalism. In Reading Putnam, edited by P. Clark and B. Hale, 176-200. Oxford: Blackwell.

Ricketts, Thomas. 1996. Carnap: From Logical Syntax to Semantics. In Origins of Logical Empiricism, edited by R. Giere and A. Richardson, 231-250. Minneapolis: University of Minnesota Press.

Ryckman, Thomas. 1992. P(oint) C(oincidence) Thinking: The Ironical Attachment of Logical Empiricism to General Relativity (and Some Lingering Consequences). Studies in History and Philosophy of Science 23: 471-493.

1i. A more fulsome account along these lines is provided in Richardson (1997).

2ii. That Quine claims the dogmas to be “at root identical” might suggest that he views their relations as symmetric and be taken to be an objection to the claim in the text. But, the claim about their radical identity occurs at the end of a long argument in which the need for analyticity is explained as a consequence of reductionism. Analyticity and reductionism are both rooted in reductionism.

3. The best introduction to Carnap’s mature understanding of analyticity is Ricketts (1996). On Ricketts’s story, Quine comes out dialectically ahead of Carnap on semantic matters. There are, on Ricketts’s account, deep issues regarding the extent to which Carnap’s reconstructive project in philosophy of science requires a descriptive semantics and pragmatics that cause Carnap’s philosophy ultimately fall to Quinean objections. I cannot follow Ricketts here. On my reading of Carnap, the forensic reconstruction of past or present science is less important than the introduction of formal languages for future science. In that context, what matters is not observable behaviour but semantic commitment to a language. I recognize, however, that Ricketts is owed more of an answer than I have here given him.

4. That is, Carnap wishes us to be tolerate both of tools, given purposes, and of purposes themselves. But, of course, you may tolerate my use of a hammer to drive in nails if I am hanging portraits of great philosophers in the hallway, but not if I am driving nails into the skulls of kittens. Is the tolerance of purposes tantamount then to the claim that there no arguments against killing kittens by driving nails through their skulls? Carnap’s own philosophical interests and competencies were not in the moral domain, but I think his general attitude is this: Yes, there are such arguments but those arguments are only non-question-begging if they are based on higher-level and shared moral purposes. Someone can be argued out of driving nails through kittens’ skulls if he can see that his moral purposes are not served by doing that. In a radical case where there are no such shared purposes there is no argument in the pragmatically important sense–no argument that will have persuasive force. Where persuasive force runs out, other force begins. Happily, these cases seem, in fact, to be relatively rare in the moral domain. Perhaps there are no epistemological or methodological disputes in which there are no shared purposes–certainly, Carnap never seemed to worry about a radical relativism in matters epistemic.

5. Clearly, it is Quine who is being discussed here: Quine’s philosophical rejection of modal logic is a clear exemplar of the dogmatism Carnap here decries.

6. The former strategy, although applied more to Reichenbach than to Carnap, is a strategy one can associate with Thomas Ryckman (1992). The latter strategy is the strategy of Friedman (1999). Friedman and I differ on deep issues regarding whether Carnap can successfully adopt the standpoint of tolerance if his technical definitions of analyticity do not work. My remarks in this essay are motivated by the desire to show that tolerance is the pragmatic foundation for Carnap’s work and cannot be disrupted by technical issues, but in themselves they do not suffice to rebut Friedman.

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