Explicating Formal Epistemology: Carnap’s Legacy as Jeffrey’s Radical Probabilism

Explicating Formal Epistemology: Carnap’s Legacy as Jeffrey’s Radical ProbabilismI Christopher F. French Department of Philosophy, Buchanan E370, 1866 Main Mall, Vancouver, BC Canada V6T 1Z1

Abstract Quine’s “naturalized epistemology” presents a challenge to Carnapian explication: why try to rationally reconstruct probabilistic concepts instead of just doing psychology? This paper tracks the historical development of Richard C. Jeffrey who, on the one hand, voiced worries similar to Quine’s about Carnapian explication but, on the other hand, claims that his own work in formal epistemology – what he calls “radical probabilism” – is somehow continuous with both Carnap’s method of explication and logical empiricism. By examining how Jeffrey’s claim could possibly be accurate, the paper suggests that Jeffrey’s radical probabilism can be seen as a sort of alternative explication project to Carnap’s own inductive logic. In so doing, it deflates both Quine’s worries about Carnapian explication and so also, by extension, similar worries about formal epistemology. Keywords: Rudolf Carnap, Richard Jeffrey, method of explication, protocol-sentence debate, radical probabilism 1. Introduction Rudolf Carnap repeatedly explained the philosophical significance of his technical work on probability and induction using the vocabulary of explications. Controversies between scientists, statisticians and philosophers concerning how to interpret probabilities, suggested Carnap, could be resolved by distinguishing between different explicanda; for example, between a frequency and logical concept of probability.1 Moreover, and on more than one occasion, Carnap explained how a particular explicandum could be clarified or even partially replaced with an adequate explicatum. In Carnap (1962b), first published in 1950, Carnap details how a logical concept of probability could be replaced with a quantitative, semantic concept of degree of confirmation. Shortly afterwards, in Carnap (1952), he goes on to show how a continuum of inductive methods can be characterized using a particular parameterization of confirmation functions, the λ-system. He was also concerned with showing how various probabilistic concepts, like the concepts of relevance and statistical estimation, could themselves be explicated in terms of confirmation functions – indeed, he even proposed various ways of likewise explicating semantic concepts of information and I

I thank the speakers from the 2013 workshop Formal Epistemology and the Legacy of Logical Empiricism at the University of Texas, Austin – especially Sahotra Sarkar and Thomas Uebel – and also Alan W. Richardson, S. Andrew Inkpen and Stefan Lukits for their comments and suggestions. Email address: [email protected] (Christopher F. French) 1 See Carnap (1945). Carnap also makes similar remarks about two other explicanda – the “objectivist” and the “subjectivist” or “personalist” interpretations of probability – in Carnap (1980), pp. 118-9. Preprint submitted to Elsevier

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entropy.2 Importantly, the aim of all this technical labor was to construct an inductive logic fit for explicating inductive reasoning in general, viz. reasoning which has at its conceptual core a particular explicandum: the logical concept of probability.3 Thus from the perspective of Carnap’s inductive logic as an explication project, providing a narrative about the legacy of logical empiricism for formal epistemology should be, it would seem, a fairly straightforward matter.4 This is especially so when we take into consideration Carnap’s various attempts to apply his work in inductive logic to descriptive and normative decision theory, e.g., as exemplified by his work on credence and credibility functions.5 Carnap’s work on decision theory in the 1950s, after all, was squarely situated within a tradition of interpreting probabilities in terms of betting quotients, a tradition which included several of Carnap’s peers.6 Indeed, the results of this tradition – which includes both what are now called “Dutch Book” arguments and the related concepts of regular probability functions and (strictly) coherent belief functions – are now familiar topics to formal epistemologists.7 Nevertheless, aside perhaps for a general consensus among formally minded philosophers that Carnap’s standard of technical rigor should be emulated, Carnap’s legacy is rarely spelled out in terms of inductive logic as an explication project.8 Rather, as an advocate of the logical interpretation of probability, Carnap is seen as requiring an in principle split between inductive logic – as a piece of logic or mathematics – and its empirical interpretation. However, it is precisely this split between the logical and the empirical which advocates for a naturalized epistemology, like Quine (1951; 1969), reject.9 Instead, Quine’s naturalized epistemologist would prefer to replace Carnap’s talk of rational reconstructions with the empirical findings of psychology. Quine thus not only repudiates Carnap’s use of formal tools to help clarify philosophical problems and concepts, but Quine similarly repudiates any use of formal tools – if not informed by the practices of some scientific community – to reconstruct epistemological problems and concepts. However, getting clear on exactly what is at stake between Carnap and Quine turns out to be a fairly subtle philosophical quandary.10 The purpose of this paper will not be to rehearse the Carnap-Quine debate. Instead, it aims to address the question of how formal epistemologists can understand their own formal work relative to these explication and naturalization frameworks. This paper provides an answer to this question by way of an historical and conceptual investigation of one of Carnap’s fellow collaborators, but also a former student and friend, Richard C. Jeffrey. In2

See chapters VI and IX of Carnap (1962b) for his work on concepts of relevance and estimation. For his work on information and entropy, see Carnap and Bar-Hillel (1952) and RC 80-15-01, respectively. The acronyms “RC” and “RCJ” refer to the Rudolf Carnap and Richard C. Jeffrey archives at the Archives for Scientific Philosophy at the University of Pittsburgh. Quoted by permission of the University of Pittsburgh. All rights reserved. 3 See Carnap (1953, 190) and Carnap (1963, 967). 4 “Formal epistemology” is understood here in a fairly broad sense, including not only formal problems from mainstream epistemology and philosophy of science, but also the foundations of decision, game and probability theory. 5 See Carnap (1962b, §§50-51; 1962a; 1963, 971 ff.; 1968; and 1971b). 6 For example, Kemeny (1955), Shimony (1955) and Savage (1954). See French (in progress) for the relevant historical details. 7 For a survey of the historical and philosophical issues concerning probability theory, see Galavotti (2005). 8 One exception is Maher (2010). 9 Although Quine never directly discusses Carnap’s work in inductive logic except in passing, Jeffrey (1994) is arguably correct in suggesting that Quine’s arguments about Carnap’s work on syntax and semantics also extend to Carnap’s inductive logic (852-3, 856-7). 10 See Creath (1991), Richardson (1997) and Stein (1992).

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deed, not only does Jeffrey, in several retrospective articles written in the 1970s and 1990s, motivate his own decision theory (viz. “radical probabilism”) against the backdrop of Carnap’s inductive logic but he also seems to share with Quine the idea that Carnap is committed to the empiricist dogma of reductionism; specifically, the reduction of experience to “sense data.”11 Nevertheless, Jeffrey also claims that his own technical project is not so much a rejection but as a further step in the development of logical empiricism, i.e., the movement, not its particular verificationist stage ca. 1929. (Jeffrey 1994, 863) So how exactly does Jeffrey, whose credentials amongst formal epistemologists need little introduction, understand his own project as a “development” of logical empiricism? By marshaling together the historical and conceptual details of Jeffrey’s own professional development, this paper provides an answer to this question. Although the following historical narrative will most likely not resolve much, if any, of the Quine-Carnap debate itself, it will be of interest to formal epistemologists generally sympathetic to both explication and naturalization projects. 2. Inductive Logic as an Explication Project In order to understand Jeffrey’s criticism of Carnap’s inductive logic, we first need to explain Carnap’s project – especially Carnap’s work on decision theory – in a bit more detail. The most straightforward way to do so is in terms of an analogy Carnap himself introduces between pure/applied inductive logic and mathematical/physical geometry. The analogy between inductive logic and geometry is as follows (also see Carnap 1971a, §4). “Pure,” or mathematical, geometry concerns both the provision of axioms, or postulates, and the derivation of theorems from those axioms. Different choices of axioms, for example, will determine whether it is possible to derive theorems about Euclidean or non-Euclidean geometrical spaces. “Applied,” or physical geometry, however, concerns the provision of rules, or rather procedures, for how “pure” geometry should be applied to physical space in the sense that those rules state how “pure” geometrical concepts should be used to measure physical magnitudes. These “applied” rules give a particular interpretation to the “pure” rules. A similar distinction between “pure” and “applied” rules holds for inductive logic. “Pure” inductive logic concerns the provision of logical rules which define confirmation functions, like c(h, e), over all the sentence (or proposition) pairs h and e from some logical language L . Ideally, Carnap is interested in confirmation functions that are “complete” in the sense that, for each pair h and e in L , it is a theorem of the metalanguage that for some probability value v, c(h, e) = v (see Carnap 1952, §17). By contrast, in “applied” inductive logic, Carnap tells us, the theorems are used for practical purposes, e.g. the determination of the credibility of a hypothesis under consideration in a given knowledge situation, or for the choice of a rational decision. (1971a, 104) For example, Carnap (1962b) discusses how different methodological rules may be chosen, as a matter of practical decision, for specifying the meaning, or rather the interpretation, of confirmation 11

See Jeffrey (1970; 1973; 1974; 1992a, 1994). Examples of Jeffrey’s radical probabilism include Jeffrey (1992a,b).

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functions.12 Specifically, such decisions determine how the theorems in a “pure” inductive logic based on ‘c’ are to be interpreted, for example, in terms of some credence function Cr relative to a system of bets or inductive dispositions (see Carnap 1962a; 1971b). Now the question arises, for Carnap, how exactly can such an interpreted ‘c’, call it Cr, help a person make rational decisions? First, we have to understand what it means to say that Cr provides an explication of inductive reasoning. Carnap takes it for granted that rational decision making depends, somehow, on a logical concept of probability. However, according to Carnap, because this probability concept, understood as an explicandum, is itself vague or inexact any theory of inductive reasoning will be inadequate until an adequate explication of this logical concept of probability is found (see Carnap 1945; 1962b, chapter II; 1953). Indeed, Carnap intends his work on inductive logic to provide an explicatum, or a partial replacement, of this logical concept of probability. As an illustration, suppose a scientist is certain, by a process of inductive reasoning, that the logical probability value 2/3 should be assigned to the hypothesis h given the evidence e but yet is uncertain how to adjust their expectations about h after encountering a new piece of evidence, e′ . Arguably, according to Carnap, the scientist can try to explicate their inductive practices by first deciding how to logically construct a “pure” inductive logic based on L and then provide an interpretation for L such that a credence function Cr is defined which best matches their inductive practices, e.g., by setting Cr(h, e) = 2/3. Once our scientist is satisfied that Cr adequately matches their inductive practices, at least to a certain extent, it seems reasonable for them to then assign the credence value Cr(h, e ∧ e′ ) to the hypotheses h given both e and e′ . In other words, our scientist can now give non-arbitrary reasons for adjusting their subjective expectations concerning whether or not that h based on the credence values given by Cr (relative to L ). This, in a nutshell, is Carnap’s qualified solution to the problem of induction (see the last sections of Carnap 1962a, 316-318; 1971b). Crucially for Carnap, the fixing of values for some credence function Cr need not rest on any a priori epistemological principle. Carnap clarifies his position in an unpublished manuscript, originally written as a reply to Lenz (1956), titled “How can induction be justified?”.13 On the first page of the manuscript, Carnap splits the question of how to justify induction into two separate questions: first, the “justification of the axioms of inductive logic” and second, “the justification of a choice of a single inductive method among those satisfying the axioms” (1). The first question requires the provision of “reasons” for why certain axioms should be included over others. In particular, Carnap argues that we may appeal to inductive reasoning itself for guidance about which axioms should be used to define an inductive logic (ibid., 4-6). Carnap, however, argues that this does not imply a vicious circularity because, in a way analogous with deductive logic and deductive reasoning, “it is not possible to convince a person X that there are good reasons for accepting a given axiom unless X is already capable of correct inductive reasoning, at least with respect to very simple cases” (ibid., 6-7).14 12

According to Carnap, logical probabilities as an explication are typically interpreted in at least three different ways: as betting quotients, estimations of some physical quantity, or in terms of the confirmation of hypotheses given one’s total evidence (see Carnap 1962b §§41, 44, 45B). Concerning practical decisions, see Carnap (1952), especially §18. 13 RC 082-07-01. 14 For the analogy between inductive and deductive reasoning see Carnap (1953, 189; 1962b, §§43, 45A; and 1968,

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The second problem, Carnap tells us in the manuscript, can be addressed in terms of the “degree of caution,” or “inductive inertia,” of a person (ibid., 12-13). Although Carnap’s discussion here is quick, he explains that these terms can be expressed in terms of betting quotients such that a change in inductive inertia corresponds to a change in the inductive method (represented by a particular confirmation function) an agent employs. An adequate confirmation function is one which is “reasonable” (and not necessarily more successful) in the sense above: its values are in agreement with one’s own “intuitive probability values” (ibid., 15). Thus, for Carnap, no “synthetic principle” is required to justify a confirmation function. Instead, once practical decisions are made concerning which axioms are reasonable to adopt, e.g. like an axiom for learning from experience, the second question of which confirmation function to choose is assessed by answering the question whether those functions satisfy our newly chosen axioms (ibid., 18-19). Indeed, Carnap later clarifies his position in the 1957 manuscript in a letter sent to his peers:15 I have not the aim of justifying inductive reasoning on a non-inductive basis, but the much more modest aim of helping somebody who has already accepted inductive reasoning to make this reasoning more consistent and systematic. (Carnap, May 27, 1957; RC 080-02-37) In conclusion, for Carnap, the point of inductive logic, at least in its applied stage, is to help clarify or systematize the inductive practices of a person who has already made the practical decision to represent those practices to themselves in terms of credence and credibility functions. 3. Jeffrey’s Criticism When Jeffrey attempts to explain Carnap’s project in the 1970s, he distinguishes between two different notions of “logical” he suggests are implicit in Carnap’s work on inductive logic. The first notion of logical corresponds fairly well to what Carnap calls a “pure” inductive logic. As Jeffrey explains, a functor ‘c’ is logical in this sense if it is defined from the sentences in the object language L to the real numbers in the unit interval such that, for any h and e in L , “it is a matter of calculation to determine the value” of c(h, e) and thus “no empirical investigation is needed” (1973, 300).16 Second, a confirmation function c – interpreted, for example, as a belief or credence function – is logical in the sense that the values of c will be in agreement with our inductive intuitions as they exist at the time when the program has been carried out. (emphasis in original; 1973, 301).17 266). 15 The letter is a dittoed copy, but judging from Carnap’s correspondence around the same time, it was presumably sent to Herbert Feigl and Carl Hempel. I have not found any evidence to suggest that Carnap sent it to Jeffrey; as far as I know they only first start written correspondence in June 1957. 16 Also see Jeffrey’s use of a network metaphor to explain this notion of logical (1974, 38-41). 17 Carnap uses the term “inductive intuitions” as a way to describe, arguably, the implicit inductive expertise or practice of a person, especially of scientists and not in the sense of providing some separate source of knowledge or insight (see Carnap 1968). Jeffrey takes some liberties with this moniker, for example, he extends its meaning to the description of our collective inductive “norms” (1973, 303).

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Thus, according to Jeffrey, Carnap’s project will be a success if the functor ‘c’ is logical in the first sense and there is some function c which is logical in the second sense such that ‘c’ “denotes” c (301).18 In summary, Jeffrey understands Carnap’s project as an attempt to reconstruct most, if not all, of our inductive intuitions with a single, complete, function c. More specifically, Jeffrey claims that this project will only be successful because we have been able to apply that method on a broad front, thus developing and sharpening our inductive intuitions – creating them, one might every [sic] say – while at the same time narrowing the set of candidates for the role of c. (1973, 301) Jeffrey has basically two criticisms of this project. The first is that, although Jeffrey doesn’t doubt that Carnap’s project could, in principle, succeed, there is little reason to think it will happen anytime soon. Instead, Jeffrey suggests that our inductive practices and intuitions shift over time; specifically, that “our notion of what constitutes sensible decision making and what constitutes rational belief” is actually a matter of “cultural evolution” (1970, 171)19 But if our inductive practices and intuitions are not only disparate but are also constantly changing, or even “evolving,” why think we could ever find a single function c which would be in agreement – and remain in agreement – with our common inductive practices and intuitions? Radical probabilism is Jeffrey’s answer to this worry. He uses the metaphor of a quilt to characterize Carnap’s project as an idealized “seamless garment” which would fully capture our inductive practices with some set of necessary and sufficient conditions (1970, 170). By contrast, Jeffrey’s probabilism is only a “patch-work quilt” with “gaps” and “frayed edges” which signify a failure to uniquely codify many of our inductive intuitions or practices (169). What holds Jeffrey’s rags together, however, is “a beautiful cord – probabilistic coherence” (169). Specifically, Jeffrey places no requirements on how a new probability function should be updated from an old, regular, probability function besides that of regularity (and so strict coherence) (169).20 Jeffrey’s second criticism is a bit more difficult to pinpoint. Basically it concerns the rejection of the idea that the logical machinery of Carnap’s inductive logic can be nicely separated from the observational evidence accumulated by a person over time (e.g. see Jeffrey 1974, 48-9). In the 1990s, Jeffrey further clarifies his criticism of Carnap’s inductive logic by suggesting that that project has a dual commitment to “rationalism” and “empiricism”; namely, that there is “a purely 18

Of course, as Jeffrey points out, it could be the case that different persons have different, mutually exclusive, inductive intuitions, or practices. If so, the function ‘c’ may then denote several belief functions, c or c′ , each of which, for example, are in partial agreement with the inductive practices of different groups of scientists. One solution to this problem which Jeffrey suggests is available to Carnap is the Bayesian suggestion that experience will eventually “swamp out” the differences between initial confirmation functions, and so the differences between our inductive practices (1973, 302). 19 Also see Jeffrey’s discussion of ‘inductive temperament’ in (1973, 303) and the last section of Jeffrey (1973). 20 For the details of how regularity and coherence are mathematically related, see Shimony (1955). Technicalities aside, a probability function P(−) is regular if, for any H which does not logically imply a falsehood, P(H) > 0 (regular conditional probability is defined similarly). Coherence and strict coherence are different ways of explicating a “fair” betting system based on a P where the values of P are interpreted in terms of betting quotients. See Carnap’s 1955 UCLA lectures on inductive logic (reprinted as Carnap 1973) for how he understands the notions of regularity and (strict) coherence in the 1950s (especially pp. 273). For more on the technical details of the probability kinematics see chapter 11 of Jeffrey (1990) and Diaconis and Zabell (1982).

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rational, “logical” element, a priori probability assignment M characterizing the state of mind of a newborn Laplacean intelligence” and also a “purely empirical element, a comprehensive report D of all experience to date” (1994, 855). Together, these two commitments determine the experienced Laplacean intelligence’s judgmental probabilities, obtained by conditioning the “ignorance priori” M by the Prototokollsatz [sic] D. Thus M(H|D) is the correct probabilistic judgment about H for anyone whose experiential data base is D. (855) Jeffrey rejects Carnap’s empiricism in the sense that Jeffrey countenances no nice separation of D and M and importantly this rejection is informed by a certain idiosyncratic reading of the history of logical empiricism, especially of the protocol-sentence debate between Carnap and Neurath.21 Fortunately, what is of interest here is not so much what Neurath and Carnap actually said in the 1920s and 1930s, but what their North American peers understood the philosophical implications of that debate to be. In order to understand what is motivating Jeffrey’s worries about Carnap’s empiricism and inductive logic, we will shift our focus to some of the historical details about Jeffrey’s professional development. 4. Jeffrey’s Historical Background Jeffrey was no stranger to Carnap’s mature philosophical views concerning logical syntax and tolerance; nor was he a stranger to Carnap’s work on inductive logic. Indeed, between 1946 and 1952, Jeffrey completed his masters in philosophy at the University of Chicago under Carnap’s supervision and it was also at Chicago that Jeffrey sat in on Carnap’s seminars on inductive logic.22 After some time working as a research engineer at MIT’s Digital Computer and Lincoln Labs between 1952 and 1955, Jeffrey went on to get his doctorate degree at Princeton University between 1955 to 1957 (he was co-supervised by Carl Hempel and Hilary Putnam). Then, according to Jeffrey’s 1960 NSF proposal, after spending some time at Oxford University in England with a Fulbright grant, Jeffrey took advantage of an Office of Navy Research grant to become Carnap’s research assistant at UCLA in September 1958 and then again for the entire summer of 1959.23,24 However what is of interest to us in this paper are three sets of documents from 1956 to 1958: an unpublished 1956 draft of Jeffrey’s dissertation, the dissertation itself, completed in June 1957, and the correspondence between Carnap and Jeffrey, between June 1957 and February 1958, concerning Jeffrey’s dissertation. 4.1. The 1956 Dissertation Draft Jeffrey’s dissertation draft, titled “Epistemology without “the Given”: A Study in Radical Physicalism,” is important for two reasons.25 First, it provides a historical reconstruction of logical 21

See Uebel (2007) for a more historically and philosophically accurate treatment of Carnap and Neurath. For example, Jeffrey reports that he read Carnap (1937) in a class on logical syntax taught by Carnap at Chicago in 1948 (Jeffrey 2000, 3). Jeffrey’s masters thesis is located at RCJ, box 12, folder 1. 23 RC 083-07-02. 24 Another historical episode of interest which is not discussed here is Jeffrey’s involvement with Kurt G¨odel and Ethan Bolker while at Princeton’s Institute for Advanced Study. The eventual result of that work is Jeffrey’s 1965 The Logic of Decision. 25 I replace Jeffrey’s use of underlining words to indicate emphasis with italics. 22

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positivism which, although absent in the 1957 dissertation, re-appears in a slightly altered form in Jeffrey’s reappraisal papers in the 1970s and 1990s.26 Second, Jeffrey’s idiosyncratic understanding of both physicalism and the debate between Carnap and Neurath on protocol sentences in this 1956 draft, arguably, motivates Jeffrey’s later radical probabilism. The purpose of the 1956 draft, according to Jeffrey, is to provide a theory of perception – cashed out in terms of probability and statistical information theory – as a “reconstruction” of knowledge without “the given” (2-4, 2-8).27 The first chapter, for example, discusses the historical development and reception of an “account of knowledge,” called “radical physicalism,” defended, Jeffrey argues, by both Carnap and Neurath (Preface i). Specifically, Jeffrey argues that Carnap and Neurath defend what Jeffrey calls the “consensus theory of truth,” which attempts an analysis of knowledge, including knowledge like this book is red, in abstraction from phenomenal experience (“the given”). It does not deny the existence of experience (nor does it assert it); it does deny the possibility of our communicating with each other about its qualities (as distinct from our communicating with each other about red books, etc.); and it holds that the epistemological foundations of science and of the more humble sorts of everyday knowledge can be given without mention of experience. (Preface ii) Indeed, Jeffrey sees Carnap’s Aufbau as a work in transition, from Mach’s positivism to Carnap and Neurath’s later physicalism, which is “concerned with an empiricist reconstruction of knowledge in the strictest sense, i.e., a reconstruction based only upon what is “given” in experience” (15,3). Moreover, the central link between Mach and logical positivism, according to Jeffrey, was a verificationist theory of meaning which states that “the meaning of a statement is a function of all the sense-experience that could verify it, where “sense-experience” refers to the given” (1-7,2). What interests Jeffrey, however, is that in the 1930s Carnap rejects this principal of verification and instead uses the tools of logical syntax to provide an account of scientific knowledge for which phenomenal statements can be reduced into physical statements without reference to “the given.” However, as Jeffrey understands the debate, Neurath clearly argues that only sentences and sentences, but not facts and sentences, can be meaningfully compared and analyzed (1-4). But then how do protocol sentences get their meanings in the first place? Jeffrey suggests a solution to this problem by highlighting two key passages, one from Carnap and the other from Neurath. First, Jeffrey quotes from Carnap (1932), where Carnap, responding to Zilsel, says that “the origin of protocol-sentences” is a problem for “descriptive semantics” (Translated by Jeffrey; Carnap 1932, 182; Jeffrey 1956 1-4,1 to 1-4,2). Of particular interest to Jeffrey is Carnap’s claim that the system of science is ultimately based on statements (namely the protocol-statements) which are not fashioned by logical operations but by a certain practical process, by learned reactions. (Translated by Jeffrey; Carnap (1932, 182-3); in Jeffrey 1956 1-4,2) 26

Unfortunately, for lack of space, a full account of all the facets of Jeffrey’s historical reconstruction will have to wait for another occasion. 27 I adopt the following convention when citing from Jeffrey’s 1956 draft: save for the Preface, “1-3,4” is a reference to page 4 of section 3 in chapter 1. The draft itself is actually a set of five different documents in RCJ folder 2 of box 12 and folders 04 and 16 in box 19. Some of the chapters and sections have multiple versions: in particular, chapter 4, titled “Observation without the Given,” has an alternative version, called “Observations,” which I denote by 4♯ below.

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What Jeffrey takes from this passage is that, for Carnap, “the question of which protocol-statements are actually made is not a philosophical one” but rather an empirical question belonging to “descriptive pragmatics, or science itself rather than meta-science” (1-4,2). Jeffrey turns next to the following passage from Neurath to suggest that protocol statements, as a whole, are revisable: [e]very new statement is to be confronted with the totality of existing statements which have already been brought into harmony with each other. A statement is called correct if it can be fitted in. What cannot be fitted in will be rejected as incorrect. (Translated by Jeffrey; Neurath (1931, 403); in Jeffrey 1956, 1-4,3) Now Jeffrey has a picture of knowledge. Thanks to Carnap’s project of logical syntax, scientific and ordinary knowledge can be “reconstructed” into physical protocol sentences without reference to any ineffable experiences. The meanings of the sentences are provided by the “learned reactions” of scientists. Neurath’s contribution is that sentences themselves can be modified as new statements are “brought into harmony” with each other. As Jeffrey puts it, “physicalists,” in contrast to philosophers like C. I. Lewis, attempt an account of knowledge in abstraction from the given, an account which would remain usable even if human beings – like electromechanical measuring instruments – produced their reports without the mediation of colors, sounds, etc. in the phenomenological sense. (1,7-2) This is an account of knowledge represented by a system of concepts, fitted together, with empirical inputs from the “learned reactions” of scientists. Jeffrey’s worry, however, is that this is all too vague: what could Neurath mean, for example, by these notions of “fitting” or “harmony”? Moreover, Jeffrey asks, how do I recognize the situation in which the appropriate move is to alter the previously accepted, “harmonious” system of statements rather than to reject a protocolstatement which has been newly uttered? (1-4,3) In other words, how does Jeffrey understand this suggestion that the meaning of protocol statements – statements which are themselves revisable – are to be fixed pragmatically, through the “learned reactions” of the scientist? Any tenable answer to this question, suggests Jeffrey, has to reject the idea – which he associates with C. I. Lewis – that some empirical statements, i.e., statements about direct observation, can never be doubted. For if that were the case, some empirical statements could never be revisable after all (1-7,3). Jeffrey’s solution is that phenomenological statements, in particular, are to somehow be reduced to physical statements using specific technical machinery, including Boolean algebras, probability theory and statistical information theory (see also 1-8 and 1-9 for more of Jeffrey’s philosophical arguments). It is with this technical machinery that Jeffrey suggests we can introduce an informal concept of “sign” which could function as a “tool” for “developing a theory of observation” (41,3). Talk of phenomenal experience, or “the given,” can then be replaced with talk of statements with different informational “sources,” where the “reliability” of the propositions associated with

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each statement could be cashed out in terms of probabilities (although, here, Jeffrey has in mind frequencies) (4-1,4-5).28 Jeffrey gives the following example to help illustrate his problem. Suppose a person who, while sailing, has to use a variety of physical indicators to try and determine which direction the wind is blowing. This, according to Jeffrey, amounts to the judgmental process of determining which factors – like the person’s sailing expertise and training, the “sensations on the back of the neck” or the direction that their cigarette smoke blows – are more or less “reliable” indicators of the direction of the wind (4♯ -2,1). However, Jeffrey argues that none of these indicators by themselves are perfectly reliable. Instead, says Jeffrey, “[a]n essential part of learning to judge wind direction is learning the relative reliabilities of the various indicators” (4♯ -2,1 to 4♯ -2,2). More specifically, the reliabilities of these indicators can influence each other, [c]onditionally upon the wind’s blowing from the west, there is rather high degree of belief in the proposition that cigarette smoke will blow to the east, that the west side of a wet finger will feel coldest, etc. (4♯ -2,2) I suggest that we should treat this introduction of the “reliability” terminology as Jeffrey’s attempt to have a more psychologically realistic account of knowledge than what Jeffrey calls “radical physicalism.” Specifically, it is with this notion of “reliability” that Jeffrey explains Carnap’s talk of “learned reactions.” For Jeffrey, by attaching reliabilities to propositions of events, i.e., to protocol statements, he sees himself as clarifying the vision of physicalism he attributes to both Carnap and Neurath. Importantly, as we will see in the next section, Jeffrey later modifies his views yet again so that reliabilities, which for Jeffrey are judgments, are understood in terms of assignments of subjective probabilities. 4.2. Probability Kinematics How exactly Jeffrey gets from talking about “reliabilities” to subjective probabilities is a complicated question. An answer can be found once we attend to certain philosophical details from both Jeffrey’s official 1957 dissertation and his correspondence with Carnap from 1957 to 1958.29 Interestingly, in the 1957 dissertation, gone is Jeffrey’s earlier historical discussions of logical positivism and the protocol-sentence debate. It is instead replaced with a discussion of two problems: first, how the problem of learning can be generalized to a particular kind of conditionalization, which he later calls a “probability kinematics”; and second, how universal generalizations, viz. laws, can have non-zero confirmation values.30 We will only be concerned with this first problem.31 28

As one would except from a draft of a dissertation chapter, Jeffrey’s exposition of observation, reliabilities and experience in both versions of chapter four are not clear; one clue as to how all this fits together, however, comes earlier in the dissertation where he considers a causal account of “sensation” for which “observable = measurable physical magnitude. Here observation becomes identical with receipt of information” (1-8,2). 29 Jeffrey finished the final draft in June 1957 and received his doctorate in October 1957 (RC 083-07-02). 30 As far as I know, it is only in a letter, dated the 28th of February 1958, sent to Hempel, Putnam and Carnap on the topic of the 1957 dissertation – which also contained a manuscript written by Jeffrey called “On Changing One’s Betting Function: Probability Kinematics” – that Jeffrey first calls his new method of conditionalization a “probability kinematics” (RC 084-04-44 and RCJ box 12, folder 4). 31 In order to solve the second problem, Jeffrey adopts, in chapter V, Carnap’s λ-system from Carnap (1952). However, there turns out to be a fatal technical flaw discovered by Savage and Kemeny, which went unnoticed by Carnap and Jeffrey and so Jeffrey quickly abandons this part of the dissertation (see Jeffrey 1990, 212).

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Normal conditionalization, e.g. as found in Carnap (1962a), works basically as follows. Let e0 , ..., et , ... be a sequence of new observations of some phenomenon for times 0, ..., t, ... and let Et be the the total evidence for an agent at time t (i.e. the conjunction, ‘e0 ∧ · · · ∧ et ’). Then if mEt is the current belief function of the agent at time t, the agent is to update their beliefs for any proposition h in light of the observation et+1 using the following equation, mEt+1 (h) =

mEt (h ∧ Et+1 ) . mEt (Et+1 )

(1)

Here, mEt+1 is the agent’s new belief function, in Carnap’s terminology the agent’s new initial credence function, viz. mEt conditional on Et+1 . Jeffrey’s problem with conditionalization, however, is that the new evidence, Et+1 , must be treated as if it were known with certainty, i.e., mEt+1 (Et+1 ) = 1. In a June 10, 1957 letter to Carnap, Jeffrey explains that the aim of the first half of his dissertation is to provide “an alternative proposal in which one takes explicit account of the “reliability” of the evidence” (2).32 Jeffrey relies on the fact that if a probability measure is regular, then it is strictly coherent and stipulates that, at any given time, the agent’s belief function should be regular. Then Jeffrey defines the belief function for an agent at some time over a particular domain; namely, the set S of propositions (closed under the operations of negation and disjunction) which are intended to represent all the possible opinions the agent can have. Let p be the proposition that the event described by Et+1 has already occurred and suppose that p is in S . Then the agent, if they are rational, should change their mind from m, conditional on p, for any other proposition q in S , to any other regular belief function m1 which satisfies the following equation, (Jeffrey 1957, 63) m1 (q) = a · m p (q) + (1 − a) · m¬p (q).

(2)

Here, a represents the credence an agent assigns to q given that p may have already happened. The new belief function, m1 (q), is then given by the weighted sum of m restricted to the partition {p, ¬p} with weights a and 1 − a. What is new is that as long as m1 remains regular, the agent is free to adjust their confidence in p on the fly, so to speak, by setting the value of a themselves. 4.3. The Carnap-Jeffrey Correspondence Aspects of the Carnap-Jeffrey correspondence are already well-known (Jeffrey 1974 re-prints parts of it). Nevertheless, it is useful to discuss portions of the text because, first, Jeffrey did not reproduce important details from his correspondence (viz. his talk of explications) and, second, it will be useful to stress some continuities between the 1956 draft and the correspondence. In a letter dated July 17, 1957, Carnap responds to Jeffrey’s June 10th letter by revealing that Jeffrey’s work reminded Carnap of a problem he struggled with both in the 1940’s and later in the early 1950’s when he collaborated with Kemeny at Princeton’s Institute for Advanced Studies (see French, in progress). Carnap acknowledges, for example, that normal conditionalization is an oversimplification (July 17, 1). Carnap instead suggests that it may be possible to represent the changes in an agent’s beliefs as a list of ordered pairs of sentences ei and coefficients bi (∈ (0, 1)) as E = {e1 , b1 ; . . . , ei , bi ; . . .} (ibid., 2). Interpreting the e-sentences as sequential evidential statements, Carnap lets b1 represent “the certainty of e1 merely on the basis of an observational experience, 32

Except were noted otherwise, the Carnap-Jeffrey correspondence can be found in RCJ box 12, folder 3.

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without regard to any inductive relation to earlier observations” (ibid., 2). And so similarly for all the b’s: each bi represents the agent’s certainty in ei without regard to any earlier inductive relations. Carnap then states that the problem is to define a credence function, cr(h, E), only in terms of the bi coefficients and “the values c(h, −) with respect to the ei or combinations of such” (ibid., 2). Nevertheless even after discussing the problem with Hempel, Helmer, Kemeny and Putnam, Carnap reports to Jeffrey that he never found a satisfactory solution. The difficulty, suggests Carnap, is that it is by no means obvious “how to determine the value of cr(e1 , E)” (ibid., 2). The value cannot simply be b1 , says Carnap, because the value must also take into account the inductive influence on e1 of the other sentences in E, and this influence is not taken into account in the number b1 . (ibid., 2) Not only must Carnap find the right combination of factors from E to define cr(e, E), there is no guarantee that any satisfactory answer will be found. Hence the reason for Carnap’s initial interest: he thought that Jeffrey’s a’s could be the same as his b’s. However, Carnap realizes that the values of the a’s are fixed after the agent has experienced Et+1 , so Jeffrey’s a’s couldn’t possibly used to determine what value should be assigned to cr(h, E). But if this is so, Carnap asks Jeffrey, what is the rule of application which your theory would give to [the agent - CFF] A for the determination of the new value a1 for the sentence e1 ? (ibid., 3) That is, what reasons does Jeffrey have for assigning the value a1 to e1 ? Carnap then discusses two kinds of problems concerned with the justification of induction which echo his earlier discussions about the problem of induction from his recent 1957 manuscript. Carnap tries to clarify his worry to Jeffrey by describing what “any practicable system of inductive logic must give to A”; namely, (1) rules for choosing a function m as the initial belief function [...]; and (2) rules for A to determine the rational change of his belief function step for step on the basis of new observations which he makes. (ibid., 3) For it seems like Jeffrey, according to Carnap, leaves rules of type (2) implicit: the a’s are chosen ad-hoc by the agent. But for Carnap, this seems to side-step the entire point of inductive logic, i.e., to provide explicit rules to an agent for how to assign values to a credence function. Jeffrey, in a letter dated September 4th, 1957, does agree that, under special circumstances – including the condition that “E reports all the observational experience the person has ever had which is relevant to the e’s” – his a’s would then be the same as Carnap’s b’s in the sense that there is some function cr(ei , E), defined in terms of the b’s, which equals Jeffrey’s a’s.33 However, as Jeffrey points out, these conditions rarely hold. For this reason, Jeffrey suggests that instead of trying to define his a’s in terms of Carnap’s b’s, perhaps the reverse is more appropriate. In particular, Jeffrey argues that his a’s are actually “measurable by observing the believer’s behavior” in terms of betting quotients and in this sense Carnap’s b’s are actually the “higher theoretical terms, relative to the a’s” (Sept. 4, 1). Jeffrey then invokes Carnap’s own notion of explication to re-phrase the problem at hand: 33

A discussion of these conditions will take us too far afield; although for the interested reader, they are conditions i-iii on page 1.

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This question is not factual; it asks for an explication, and might be rephrased: “How shall we define the b’s in such a way that they will adequately explicate that component of the rational observer’s belief in the e’s which corresponds to what he has seen with his own eyes?” (ibid., 1) In a letter dated November 14th, 1957, Jeffrey further tries to clarify his approach to Carnap’s problem. First, Jeffrey acknowledges that Carnap is right to emphasize the importance of choosing a confirmation function. Nevertheless, Carnap, says Jeffrey, relies too heavily on the claim that “as experience accumulates it makes less and less difference which m-function you started with, as long as it is a regular m-function” (Nov. 14, 1). In practice, only a finite amount of evidence is ever obtainable. Second, Jeffrey has serious doubts that it is possible to reduce evidential statements into a list of ordered pairs like E. Here is how Jeffrey now understands the problem: I don’t really see how to explicate the way in which E could be used to get a rational belief function, because I really don’t see how to explicate the b’s in E, ... . [sic] the observer’s actual degrees of belief in the a’s will include the effects of cross-inductions with other observations and beliefs, and I do not see how to distill, out of a set of actual beliefs, the purely observational components. (Worse yet, b is not only to be purely observational, but it must be based purely on the observation on the basis of which the observer recorded a as a protocol statement.) (ibid.,1) It is tempting to equate this talk of “cross-inductions” with Jeffrey’s earlier discussion in the 1956 draft of differing “reliabilities” for different sources of information. Moreover, in the next paragraph, Jeffrey further elaborates on this point using language similar to the 1956 draft, the trouble is with the myth that the observer writes down protocol statements as a way of recording his observational experience. Something of this sort does go on, at least sometimes, but it’s a rather special case to which we need no longer confine ourselves. (2) Jeffrey then goes on to cite the Neurath “harmony” and Carnap “learned reaction” passages from the 1956 draft (ibid., 2). The solution to Neurath’s “apparent paradox” that statements cannot be compared with facts is that “the function of this comparison with fact has already been performed when the protocol statement is recorded” (ibid., 2). Jeffrey then cites Carnap’s “learned reactions” passage mentioned above to suggest that protocol-statements should not be understood as single statements, but rather as “as a whole probability distribution” representing these “learned reactions” (ibid., 3). Lastly, Jeffrey suggests that the acquisition of protocol statements by an observer could be understood in pragmatic terms. Namely, “one might try regarding the scientific observer as the sort of object that science studies” where the agent is represented “as a Turing machine which is connected to models of sense-organs” and even suggests that one represent the agent’s “desires” with pay-off matrices and the “beliefs” of the machine as “certain dispositions to respond” (ibid., 3). In a letter dated the day after Christmas, 1957, Carnap reports that he “is overwhelmed right now with proofreading on two books in addition to the pressure of the Schlipp volume” (Dec. 13

26, 1). For this reason, his response to both of Jeffrey’s letters is unfortunately rather laconic. In response to the September 4th letter, Carnap still retains some hope that his b’s could be explicated in terms of Jeffrey’s a’s. But more to the point, Carnap returns to the original question he asked to Jeffrey in July: “which rule does your inductive logic give to the observer in order to determine when and how he should made a change according to your method?” (ibid., 2). As Carnap points out, even normal conditionalization, though idealized, “gives at least a clear rule for these idealized situations” (ibid., 2). Jeffrey’s equation, weighted by some a, provides no rules for which value should be assigned to a which means any number of regular probability functions could be chosen as m′ , relative to the value of a. But then how could Jeffrey’s equation possibly be used to guide decision making? Carnap also presses Jeffrey on the idea that the b’s are behaviorally measurable: “this [concerns] only the factual question of the actual belief of A in ei ” whereas “A desires to have a rule which tells him what is the rational degree of belief” (ibid., 2). Unfortunately, Carnap only quickly responds in the postscript to Jeffrey’s second letter from November 14th. Carnap agrees that Jeffrey is correct about “Neurath’s paradoxical denial of the comparison of sentences and facts,” an issue which Carnap says he addressed in Carnap (1935).34 Moreover, it should also come to little surprise that Carnap agrees with Jeffrey’s suggestion that a scientific observer could be represented as a machine: it “seems to me very helpful” (Nov. 14, 3). Carnap is even hopeful that his b’s somehow could be inputs for the machine, namely as coefficients which “[depend] only on the circumstances of the observation” (ibid., 3). Jeffrey responds to Carnap in a letter dated January 16th, 1958. There, Jeffrey agrees that in some idealized cases, like in physics, it may be possible to find adequate rules for the determination of Carnap’s b’s (Jan. 16, 1-2). However, Jeffrey argues that “if one thinks of the observer as consisting of the human being together with a certain amount of apparatus,” which Jeffrey calls observation in the ‘broad’ sense, then the situation is much more complicated, especially if the science involved is not physics (ibid., 3). Nevertheless, Jeffrey claims that “Empiricists have usually tried to isolate the empirical element, i.e., the observational element, by analyzing “observations” in the broad sense into observations in the narrow sense plus theory” (ibid., 3). Specifically, in physics, the interactions between the observer and what is being observed can be neglected, but not so in psychology and so Jeffrey claims that, in general, “I expect that if we study only those situations in which such reduction [from the broad to the narrow sense of observation - CFF] is possible, we are apt to get a distorted notion of meaning” (ibid., 3).35 4.4. Jeffrey’s Retrospective Take on Carnap’s Empiricism What did Jeffrey take from his correspondence with Carnap? Fortunately, we can turn to what Jeffrey says on the matter himself. First, in Jeffrey (1974), he admits that he perhaps overemphasizes the “static” aspects of Carnap’s work in order to emphasize his own, dynamical, account. Carnap, according to Jeffrey, was perfectly happy to lay down rules for defining a family of confirmation functions in some logical language based on a parametrization of that language, e.g. as “adjustable constants” fixed by the number of primitive predicates (and their interpretation) in the language (46-7). For Jeffrey, this is what distinguished Quine from Carnap. Carnap had no qualms 34

Whether Carnap does or not is a question outside the scope of this paper; although see Uebel (2007, 336-340). Although Jeffrey’s correspondence with Carnap, both professional and personal, lasts until Carnap’s death in 1970, I have found no further discussion by either party of these letters in the Pittsburgh archives. 35

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about making linguistic stipulations in the form of explications and in this sense Carnap was a voluntarist or engineer, (for a similar passage which emphasizes the engineering aspect, see Jeffrey 1994, 853) [Carnap] was a linguistic revisionist, and quite unabashed about it. He was not given pause by the fact that the distinction between primitive and defined terms is vacuous in connection with natural languages. He was prepared to impose and police such distinctions as part of the business of reconstructing languages closer to the mind’s desire. The instrument which he sought to forge was a unit consisting of a language and a c-function, fused. It was no part of his claim that either element now lies ready to hand, fully formed. (47) Jeffrey himself embraces a kind of voluntarism when he suggests that his own radical probabilism does not demand that one start out with a fully defined confirmation function nor that all evidential sentences need to be fully translated into some logical language (but instead they can be left to the determination of the analogues of Jeffrey’s a’s in the probability kinematics) (47-8). Nevertheless, although Jeffrey thinks Carnap’s empiricism is “unworkably simplistic,” he doesn’t suggest that Carnap’s project was somehow doomed to fail because of Carnap’s commitment to empiricism. Rather, Jeffrey remarks, “[i]t may be that, had he lived longer, he would have solved the problem, and it may be that some else will solve it yet”; however, Jeffrey acknowledges that his “own certain sense of plausibility leads me off on a different tack” (49). But so how exactly do Carnap and Jeffrey part ways? 5. Back to Quine, Jeffrey and Jeffrey’s Carnap Quine famously criticized logical empiricism for being dogmatically committed to both a sharp analytic/synthetic distinction and the reduction of evidential statements to something like sense data. Jeffrey does not share the first of these worries. Indeed, in the 1956 draft, Jeffrey points to two passages from §82 of Carnap (1937) which seem to imply that, for Carnap, not only can logical rules be modified but that no single hypotheses can be tested by itself (1-3). Moreover, Jeffrey gets Carnap right with the first sense of “logical.” According to Jeffrey, the functor ‘c’ itself is, for Carnap, a semantic concept defined over some object language. Once a definition has been chosen, the value of c(h, e) is analytic in the sense that its value can be determined (if only partially) in virtue of the logical properties of the object language and the meaning of h and e alone. Something similar is also true for Jeffrey: the probability calculus itself, defined for example over propositions represented by a sigma algebra, is “logical” in a similar sense. Instead, where Carnap and Jeffrey differ is with the second sense of “logical.” Carnap could understand, for example, Jeffrey’s claim that: (A) in order for ‘c’ to “denote” some credence function c, the interpretation of c must first be in agreement with (at least) a non-empty set of our collective inductive practices, as the conjunction of two different claims. Namely, both (B) the explicatum c of the logical concept of probability (the explicandum) is adequate only if the right kind of logical and methodological rules are chosen which define ‘c’ and (C) the chosen methodological rules adequately reflect the inductive practices of some community of scientists in the sense that those rules answer the second question about the justification of induction from Carnap’s 1957 manuscript. 15

Suppose that Jeffrey’s (A) is a plausible reconstruction of Carnap’s (B) and (C). Jeffrey’s worry can then be recast as a worry about (C): that we won’t be able to find an inductive logic which will be completely adequate. This argument, however, won’t faze Carnap. After all, for Carnap, inductive logic is an explication of inductive reasoning and Carnap does not appeal to any antecedent notion of a “correct” explicatum, but only better or worse explicata. Jeffrey’s second sense of “logical,” on the other hand, implies otherwise. This is where, I would suggest, Jeffrey is mistaken: the success of Carnap’s project does not depend on there being a “correct” interpreted ‘c’. Carnap, after all, is not worried about factual questions of belief formation. Returning back to Quine, both Jeffrey and Quine seem to agree that Carnap’s alleged commitment to a kind of reductionism of scientific knowledge to observations won’t work. Observation sentences, for Quine, are precisely the ones that we can correlate with observable circumstances of the occasion of utterance or assent, independently of variations in the past histories of individual informants. They afford the only entry to a language. (1969, 89) Such sentences get their meaning from verification, but verification, for Quine, is an empirical process. Thus the boundaries between philosophy and science, especially between philosophy and psychology, are blurred (89-90). As we have seen above, Jeffrey shares similar worries about the origin of meaningful observation sentences. What is of philosophical interest, however, is that Jeffrey does not feel any pressure to follow Quine in rejecting explications, or more broadly, in rejecting the use of formal tools to help clarify and better systematize the foundations of science.36 For example, Jeffrey (1994) summarizes Quine’s argument as roughly the claim that “surface irritations” – or what experience becomes for Quine’s web of belief metaphor – cannot be captured, without remainder, with protocol statements (852-3). Indeed, Jeffrey’s understanding of Quine’s worry here seems to be similar to the kind of worry Jeffrey expressed in the Carnap-Jeffrey correspondence. Namely, that Jeffrey preferred his a’s over Carnap’s b’s because, basically, our inductive practices are too complicated (e.g., because an explanation of these practices requires a “broader” theory of observation) to be faithfully transformed into evidential statements with a few formal equations. That is the upshot of Jeffrey’s correspondence with Carnap: there’s no obvious way to define Jeffrey’s a’s in terms of Carnap’s b’s. So, as Jeffrey suggests in his 1957 November letter, why not treat instead the a’s as primitive? Indeed, why do we need the b’s at all? The idea that experience cannot simply be reconstructed as a long conjunction of protocol-statements, each treated as if it were believed with certainty, begins with the 1956 draft. There, Jeffrey takes seriously the idea that protocol statements, as used in practice, are determined by some kind of empirical conditioning. But there is then no simple, non-circular, way to reconstruct the process of this conditioning in terms of the meaning relations between more “privileged” protocol statements. Instead, for Jeffrey, an agent has to supply their own subjective expectations or degrees of belief in order to formalize learning from experience. This is what equation (2) is meant to capture: the kinematics, but not the origins, of learning from experience.37 36

Quine, after all, tells us that “[e]pistemology is concerned with the foundations of science” (1969, 69). See Field (1978), Garber (1980) and chapter 11 of Jeffrey (1990), especially page 183, for discussion about how the probability kinematics should be interpreted. 37

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The crucial interpretive thesis is this. Putting aside the question of whether he provides an historically accurate account of Carnap’s work on inductive logic, instead of rejecting Carnap’s “constructivism” along with Quine, Jeffrey suggests that his a’s give a psychologically more realistic, or less-idealized, explication of inductive reasoning than do Carnap’s b’s (or, for that matter, normal Bayesian conditionalization). Indeed, the entire point of Jeffrey’s a’s is to provide a technical way for agents to represent their inductive judgments about some new observational event, as a matter of choice or convention, because there is no easy way to specify the rules required to adequately reconstruct their evidential judgments in terms of Carnap’s e’s and b’s. It is then in this sense that Jeffrey can understand his own work in decision theory as being continuous with logical empiricism. Namely, when it comes to the problem of learning from experience, Jeffrey’s probability kinematics provides an alternative explication project to Carnap’s inductive logic. Carnap, on the one hand, prefers to construct explications for which only a single explicatum is provided – like a concept of degree of confirmation – from which other related concepts – like concepts of estimation, information or entropy – can then be defined.38 Jeffrey, on the other hand, is more interested in explicata constructed specifically for agents; that is, concepts which agents can actually use, so to speak, on the spot. In Jeffrey (1994), Jeffrey explains the trajectory of his views from Carnap’s own “probabilism” to Jeffrey’s radical probabilism, where Jeffrey’s a’s are now expressed in an even more technically sophisticated way (i.e. as Bayes factors):39 As I see it, radical probabilism delivers the philosophical goods that logical empiricists reached for over the years in various ways. Carnap got close, I think, with his idea of a “logical” c-function encoding meaning relations, but I’d radicalize that probabilism twice, cashing out the idea of meaning in terms of skilled use of observations to modify our probabilistic judgments, and cashing that out in terms of Bayes’ [sic] factors. Carnap’s idea of an “ignorance” prior cumulatively modified by growth of one’s sentential data base is replaced by a pragmatical view of priors as carriers of current judgment, and of rational updating in light of experience as a congeries of skills like those of the histopathologist. (emphasis in original; 862) The inductive expertise of the histopathologist, the “justification” she gives for the setting of her Bayes factors, argues Jeffrey, “is a mish-mash including the sort of certification attested by her framed diploma and her reputation among relevant cognoscenti” (861-2; also see Jeffrey 1992b). This goes some way to explaining, for example, the precise sense in which Jeffrey says he would “put Carnap’s voluntarism to broader judgmental use” (Jeffrey, 1994, 848). For Jeffrey, Carnap’s voluntarism concerns the freedom required to construct any inductive logic. Although he ultimately parts way with Carnap’s project, Jeffrey still retains Carnap’s engineering sensibilities in the sense that he is worried about “whether we can fabricate useful probabilistic proxies for whatever it is we have in mind” (848). It is tempting to think that this is the same problem Jeffrey stumbled upon in 1956 when he discussed the sailing boat problem above: how should an agent 38

Here I have in mind a similar discussion by Carnap concerning his preference for his own work on estimation functions – where only one fundamental choice is required, a choice of a confirmation function – over the more traditional, but piece-meal, methods in statistical inference (1962b, 514; also see pg. 232). 39 For any two evidential statements A and B, the Bayes factor for a new probability function Pnew and old function Pold , is Pnew (A) : Pnew (B)/Pold (A) : Pold (B) (Jeffrey 1994, 862).

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represent their judgments about the reliabilities of the different sources of information in order to make an informed decision about which direction the wind is blowing? The technical machinery is more sophisticated in 1994 than in 1956, but the general learning problem remains the same. As Jeffrey later puts the point: The question is whether it’s feasible and desirable for us to train ourselves to choose probabilities or odds or Bayes factors, etc., as occasions demand, for use in our practical and theoretical deliberations. The question is not whether we are natural Bayesians but whether we can do Bayesianism, and, if so, whether we should. For Carnap, this last is the practical question: whether, after due consideration, we will. (emphasis in original; 1994, 848) 6. Conclusion In summary, Jeffrey presents us with two separate projects the formal epistemologist could take on. First, there is the Carnapian project of providing an explication of a concept, like analyticity, probability or rationality. This project comes in two stages. In the first stage, one proposes logical rules which define the explicatum such that those rules, to some extent, capture how we use the explicandum in practice. For the second stage, one proposes rules stating how to use the explicatum in some empirical or idealized context. Importantly, in the process of carrying out both of these stages, if our own practices are modified so they become more explicit, all the better. However, for Carnap, both of these stages have a practical component: there is no “in principle” correct way to choose these rules. Indeed, explications are to be understood as a kind of conceptual engineering, where one is free to use – as a matter of practical decision – formal tools in order to craft satisfactory concepts (e.g. see Creath 2009; French, in progress). Jeffrey’s own project collapses these two stages. For Jeffrey, aside from the probability calculus, there is no need to provide a complete set of logical rules which will determine how belief functions should be defined. Moreover, the only constraint Jeffrey places on new belief functions is that they be coherent: no additional rules or restrictions need apply. Thus, whereas Carnap wished to make inductive logic, as an explication of inductive reasoning, as explicit as possible, Jeffrey leaves the choice of how to represent certain judgments, as subjective probabilities, up to the agent. Whereas Carnap’s voluntarism operates at the level of making practical decisions about which rules to choose in two separate stages – choices which are required before inductive logic can be used to help aid decision making – Jeffrey’s voluntarism is at the level of letting a person decide for themselves how to continuously represent their judgments in a Bayesian manner. The upshot for formal epistemology, and for scientific philosophy in general, is this. Jeffrey’s radical probabilism isn’t necessarily continuous with any particular logical empiricist thesis. Rather, it is continuous with Carnap’s method of explication, as a process of making our inductive concepts and judgments explicit. If Jeffrey is right, empiricist dogmas aside, no dilemma is engendered when we use formal tools to help represent and clarify inductive reasoning while simultaneously holding that psychology provides an important source of information regarding what our inductive practices are. Naturalism, or pragmatism, in Jeffrey’s sense, is thus consistent with Carnapian explication. Indeed, radical probabilism can be explained as a sort of explication project itself; namely, as our scientific knowledge increases and we gradually learn more about ourselves, we can adjust, or better: engineer, how to best formally represent our inferential judgments to 18

ourselves. In conclusion, whereas Carnap held out for a more detailed explication of our inductive practices, Jeffrey preferred to adopt the technical tools already at our disposal to try and explicate – in real time – inductive reasoning. Carnap, R. (1932). Erwiderung auf die Vorstehenden Aufs¨atze von E. Zilsel und K. Duncker. Erkenntnis 3, 177–188. Carnap, R. (1936). Wahrheit und Bew¨ahrtung. Actes du Congr`es International de Philosophie Scientifique, 18–23. Carnap, R. (1937). Logical Syntax of Language. Trans. by A. Smeaton. Kegan P. Trench Trubner and Co. Ltd., London. Carnap, R. (1945). The Two Concepts of Probability: The Problem of Probability. Philosophy and Phenomenological Research 5(4), 513–532. Carnap, R. (1952). The Continuum of Inductive Methods. University of Chicago Press, Chicago. Carnap, R. (1953). Inductive Logic and Science. In Proceedings of the American Academy of Arts and Sciences, Volume 80, pp. 189–197. Carnap, R. (1962a). The Aim of Inductive Logic. In E. Nagel, P. Suppes, and A. Tarski (Eds.), Logic, Methodology and Philosophy of Science, pp. 303–318. Stanford University Press, Stanford. Carnap, R. (1962b). Logical Foundations of Probability (2nd ed.). University of Chicago Press, Chicago. Carnap, R. (1963). Replies and Systematic Expositions. V. Probability and Induction. In P. A. Schilpp (Ed.), The Philosophy of Rudolf Carnap, pp. 965–998. Open Court, La Salle. Carnap, R. (1968). Inductive Logic and Inductive Intuition. In I. Lakatos (Ed.), The Problem of Inductive Logic, Volume 51, pp. 258–314. Amsterdam, North-Holland. Carnap, R. (1971a). A Basic System of Inductive Logic, Part I. In R. Carnap and R. C. Jeffrey (Eds.), Studies in Inductive Logic and Probability, Vol. I, pp. 33–165. University of California Press, Los Angeles. Carnap, R. (1971b). Inductive Logic and Rational Decisions. In R. Carnap and R. C. Jeffrey (Eds.), Studies in Inductive Logic and Probability, Vol. I, pp. 5–31. University of California Press, Los Angeles. Carnap, R. (1973 [1955]). Notes on Probability and Induction. Synthese 25(3-4), 269–298. Carnap, R. and Y. Bar-Hillel (1952). An Outline of a Theory of Semantic Information. Technical report, Research Laboratory of Electronics, MIT. Creath, R. (1991). Every Dogma Has Its Day. Erkenntnis 35(1-3), 347–389.

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