Historicism, Entrenchment, and Conventionalism

Transcription

1 J Gen Philos Sci (2009) 40: DOI /s x Historicism, Entrenchment, and Conventionalism Nathaniel Jason Goldberg Published online: 19 December 2009 Ó Springer Science+Business Media B.V Abstract W. V. Quine famously argues that though all knowledge is empirical, mathematics is entrenched relative to physics and the special sciences. Further, entrenchment accounts for the necessity of mathematics relative to these other disciplines. Michael Friedman challenges Quine s view by appealing to historicism, the thesis that the nature of science is illuminated by taking into account its historical development. Friedman argues on historicist grounds that mathematical claims serve as principles constitutive of languages within which empirical claims in physics and the special sciences can be formulated and tested, where these mathematical claims are themselves not empirical but conventional. For Friedman, their conventional, constitutive status accounts for the necessity of mathematics relative to these other disciplines. Here I evaluate Friedman s challenge to Quine and Quine s likely response. I then show that though we have reason to find Friedman s challenge successful, his positive project requires further development before we can endorse it. Keywords Analytic-synthetic distinction A priori Carnap, R. Constitutive principles Conventionalism Entrenchment Friedman, M. Historicism Kuhn, T. Quine, W. V. Thomas Kuhn was once asked how his views fit into the so-called analytic-continental divide. Kuhn explained that in his formative years he had been exposed only to analytic philosophy s logical positivism. He then added: I think, in some sense or other, I can be described as in some part having reinvented that [Continental] tradition for myself (2002, p. 321). While I am unsure about the extent to which Kuhn reinvented the Continental tradition, he and others did introduce elements of that tradition into the analytic philosophy of science that facilitated the end of logical positivism. Here I focus on one such element. N. J. Goldberg (&) Department of Philosophy, Washington and Lee University, Lexington, VA 24450, USA goldbergn@wlu.edu

2 260 N. J. Goldberg I call it historicism. By this I mean the thesis that the nature of science (including mathematical science) is illuminated by taking into account its historical development. 1 I have two mutually reinforcing aims in this paper. The first is to illustrate how differing attitudes toward historicism color an important debate that Michael Friedman has recently initiated with (the shade of) Willard van Orman Quine. That debate concerns how to account for the necessity of mathematical claims relative to those in physics and the special sciences. 2 My second aim is to evaluate that debate. I proceed as follows. In 1 I consider how Quine appeals to an ahistoricist method to argue that though all knowledge is empirical, mathematics is entrenched relative to physics and the special sciences. For Quine, entrenchment accounts for the necessity of mathematical claims relative to those in physics and the special sciences. In 2 I consider the first of Friedman s two historicist objections to Quine. In 3 I provide reason to think that the objection succeeds. In 4 I discuss how Friedman appeals to historicism to argue that mathematical claims serve as principles constitutive of languages within which empirical claims in physics and the special sciences can be formulated and tested. For Friedman, these mathematical claims are not themselves empirical but conventional; their conventional, constitutive status accounts for their relative necessity. Embedded within Friedman s account is his second historicist objection to Quine, which I provide reason to think also succeeds. In 5 I consider ahistoricist objections that Quine would presumably have made against Friedman and show that none succeeds. In 6 I conclude that though we have reason to prefer Friedman s view to Quine s, Friedman s account of the relative necessity of mathematical claims requires further development before we can endorse it. 1 Quine on Ahistoricism and Entrenchment Though Quine flirts with historicism, 3 his method of accounting for the necessity of mathematical claims relative to those in physics and the special sciences is ahistoricist. It weds epistemic holism, according to which all statements in the total system of science are confirmed or revised together against experience, to entrenchment, according to which some of those statements, including those belonging to mathematics, are more central to our knowledge and so are relatively shielded from revision. Historical facts about the development of science do not come into play. 1 In the Continental tradition historicism traces to Herder (1970/1784) and Hegel (1981/1862). See Goldberg (2008) for discussion of historicism in semantics. 2 Friedman s side of the debate is part of his broader project of proposing a theory of conceptual change that does justice to the history of science. Friedman takes Quine s account of theory confirmation as his foil, and central to that account is Quine s grappling with the necessity of mathematical claims relative to those in physics and the special sciences. Friedman therefore grapples with that necessity also, which is why his broader project contains within it his alternative account of such necessity. 3 Consider Quine s assertion that as sciences advance uncritical assumptions are replaced by definitions. Hence what was once regarded as a theory about the world becomes reconstrued as a convention of language. Thus some flow from the theoretical to the conventional is an adjunct of progress in the logical foundations of any science (2004c/1936, p. 3). Regardless of whether he is right, Quine does realize that changes occur to theories during their historical development. Also consider Quine s observation that our scientific heritage (2006b/1951, p. 46) is relevant to contemporary theorizing. Finally, consider Quine s appeal to Neurath s boat which, if we are to rebuild it, we must rebuild plank by plank while staying afloat in it (1964, p. 3). The idea of rebuilding plank by plank presupposes a diachronic view of science, and such a view heeds changes in scientific theories from one historical era to another; cf. van Fraassen: We must accept that, like Neurath s mariner at sea, we are historically situated (2004, p. 139, my emphasis).

3 Historicism, Entrenchment, and Conventionalism 261 How is his holism-cum-entrenchment supposed to work? Because of his commitment to holism, Quine agrees with Pierre Duhem (1991/1906) that if theory T, composed of statements S 1, 2,, n, entails prediction P, and experimentation results in *P, then a scientist can take any statement S i in the theory to be false provided that she makes appropriate truth-value assignments elsewhere. 4 Such latitude elucidates what Quine takes the structure of a theory at the most basic level to be. For Quine can allow the scientist this latitude in revision only if a theory is structured as one large conjunction of statements. Quine explains: Suppose an experiment has yielded a result contrary to a theory currently held in some natural science. The theory comprises a whole bundle of conjoint hypotheses, or is resoluble into such a bundle. The most that the experiment shows is that at least one of these hypotheses is false; it does not show which. It is only the theory as a whole that admits of evidence or counter-evidence. And how wide is a theory? Legalistically, one could claim that evidence counts always for or against the total system, however loose-knit, of science (2006a/1970, p. 5, my emphasis). 5 Quine goes on to explain, however, that some of the relations between arithmetic and mathematics generally, on the one hand, and physics and the special sciences, on the other hand, are asymmetric: [S]uppose from a combined dozen of our theoretical beliefs a scientist derives a prediction in molecular biology, and the prediction fails (p. 7). Quine s holism counts this against the total system of science. The scientist can therefore take any belief to be false if she makes appropriate truth-value assignments among the rest. Nonetheless, Quine continues, the scientist should scrutinize for possible revision only the half dozen beliefs that belonged to molecular biology rather than tamper with the more general half dozen having to do with logic and arithmetic (p. 7). For, as Quine explains elsewhere, tampering with beliefs belonging to arithmetic in particular would reverberate excessively through the rest of science (2004d/1991, p. 59) while tampering with those belonging to molecular biology would not. As Quine puts it elsewhere still, mathematics infiltrates all branches of our system of the world (2004b/1992, p. 15) while molecular biology does not. And the scientist is guided in her revision by the [virtue of] conservatism (2006b/1951, p. 46; 1964, p. 20) or maxim of minimum mutilation (2004b/1992, pp ; 2004d/1991, p. 59; 2006a, p. 7), counseling that she revises those statements whose revision would cause the fewest changes elsewhere. Quine concludes: [W]e have here an explanation of mathematical necessity itself. It resides in our unstated policy of shielding mathematics by exercising our freedom to reject other beliefs instead (2004b/1992, p. 15). Quine seems in these passages to be making two related points. The first concerns a more nuanced understanding of the structure of science than initially suggested. Ultimately, on Quine s view, the total system of science has two structures. There is the coarse conjunctive structure of the system as a whole. This is reflected in the confirmation holism that Quine and Duhem both embrace. Then there is the fine-grained inferential structure reflected in the asymmetries between certain beliefs. Those asymmetries are responsible for the reverberations that only some revisions, like those concerning arithmetic, would cause. Suppose that an arithmetic belief, that one plus one equal two, is taken to be false. On Quine s view, every molecular-biological belief concerning the number of ions, 4 Quine s (2004b/1992, pp ) agreement with Duhem is explicit. 5 See Quine (1975/1968, p. 79; 2004b/1992, pp ) for other statements of his conjunctive holism. See DeRosa and Lepore (2004), Dummett (1993, p. chap. 17), Fodor and Lepore (1992, p. chap. 2), Friedman (2001, part 1, chap. 2), and Glock (2003, p. 77) for commentary.

4 262 N. J. Goldberg molecules, cells, or anything else would then need to be reconsidered, for any such belief would depend on the belief that one plus one equal two. Conversely, on his view, falsifying every belief belonging to molecular biology need not falsify any belief belonging to arithmetic. Even if everyone is wrong about the number of different kinds of bases in DNA, say, and wrong too about all other particular molecular-biological convictions, one s arithmetic beliefs can remain untouched. Errors in molecular biology can be localized to molecular biology itself, because unlike arithmetic that discipline does not infiltrate the rest of science. Quine has the consequences of just such fine-grained structural asymmetries in mind when he calls arithmetic entrenched relative to molecular biology. Quine s notion of entrenchment therefore amounts to something like this: QUINEAN ENTRENCHMENT: a is entrenched relative to b iff the total system of science is structured so that falsifying b falsifies fewer claims than falsifying a does. To see how entrenchment is meant to account for the relative necessity of arithmetic and mathematics generally, consider the second point that Quine apparently has in mind in those passages above. It concerns not the structure of science but the way in which scientists should respond to the fine-grained structure specifically: if they have to falsify a or b, then (ceteris paribus) they should falsify b. More specifically, for Quine, scientists should avoid falsifying mathematical claims because doing so would reverberate excessively throughout the total system of the world, forcing other changes in that system also. This in turn would disturb the ease with which science is conducted. For Quine, therefore, mathematical claims are necessary not in any traditional sense of being truths of reason, being true in all possible worlds, being unrevisable, or holding with apodictic certainty. Insofar as it makes sense to speak of them as necessary at all, their necessity is pragmatic and relative. It is pragmatic because though when faced with a failed prediction scientists could in principle falsify any claim in the total system of science, they should in practice shield mathematical claims from revision. They should exercise their freedom to reject other beliefs instead (2004b/1992, p. 15). Science is more easily carried out when we mete out falsity as little as possible. The necessity of mathematical claims is relative because scientists should be less willing to revise them than they would claims in physics and the special sciences. Mathematical claims should be protected relative to those in physics and the special sciences. Regardless Quine takes himself to have accounted for mathematical necessity itself. 2 Friedman s Objections to Quine Friedman presents two historicist objections to Quine s method of accounting for the necessity of mathematical claims relative to those in physics and the special sciences. First, the history of science shows that certain mathematical claims have not always been entrenched relative to these others in the first place. Insofar as the nature of science is illuminated by its historical development, entrenchment cannot consistently do the work that Quine requires. I consider this objection below. Second, Friedman s own method of accounting for the relative necessity of mathematical claims itself better accounts for the historical development of science. I consider that objection in 4 when evaluating Friedman s positive project. 6 6 Though Friedman does not offer the ahistoricist objection that the coarse conjunctive structure of theories demanded by Quinean confirmation holism is incompatible with the fine-grained asymmetries required for Quinean entrenchment relations, see Dummett (1993, chap. 17) and Glock (2003, pp ) for versions of this objection and Quine (2006b/1951, p. 42) and Sher (1999) for responses.

5 Historicism, Entrenchment, and Conventionalism 263 Friedman begins his first objection by offering the following historical analysis of Newtonian physics. 7 According to Friedman, Newtonian physics divided into three components: (a) a form of mathematics, the calculus; (b) conceptions of force and mass embodied in his three laws of motion; and, (c) a universal law of nature, the law of universal gravitation. He then argues contra Quine: When Newton formulated his theory of gravitation, for example, the mathematical part of his theory, the new calculus, was still quite controversial to such an extent, in fact, that Newton disguised his use of it in the Principia in favor of traditional synthetic geometry. Nor were Newton s three laws any better entrenched, at the time, than the law of universal gravitation (2001, p. 39, notes suppressed, his emphasis). Friedman concludes: since we are dealing with deep conceptual revolutions in both mathematics and mathematical physics, entrenchment and relative resistance to revision are not appropriate distinguishing features at all (p. 40). Though Friedman is not explicit about this, his notion of entrenchment differs from Quine s in two ways. First, Friedman thinks that to see whether a claim is entrenched one must take into account the historical circumstances during which the theory in which the claim occurs developed. Thus Friedman observes that when Newton formulated his theory of gravitation, the calculus was still quite controversial and Newton s laws of motion were [not] any better entrenched, at the time, either. While Quine s notion of entrenchment concerns relations between claims independent of historical context, on Friedman s view historical context is key. Second, Friedman treats entrenchment as a measure of community acceptance. He is concerned with whether a particular set of claims was controversial at a particular time. Presumably a claim would be controversial at a time if in conflict with the accepted theories of a particular historical era of which that time was a part, since only then would we be dealing with the deep conceptual revolutions that Friedman envisions. While Quine s notion of entrenchment is purely structural, concerning asymmetries within science, on Friedman s view community acceptance is key. Moreover, these two differences are connected. For Friedman, because entrenchment is relative to the theories of particular historical communities of scientists, whether members of those communities accept a claim as entrenched will be indicative of its being entrenched. Contra Quine, structural relations between claims will not be so indicative except to the extent that they inform community acceptance. Hence Friedman s notion of entrenchment amounts to something like this: FRIEDMANIAN ENTRENCHMENT: a is entrenched relative to b at time t iff a is more accepted by members of the scientific community (based on the theories of the particular historical era of which t is a part) at t than b is. 8 7 His discussion of Newtonian physics occurs in Friedman (2001, pp , 39 40, 75 77), most of which repeats in Friedman (2002a, pp ) and (2002b, pp ). As I consider in 6, Friedman also discusses special and general relativity (2001, pp , 61 63, 77 80, 83 4, 86 99; 2002a, pp ; 2002b, pp , ; 2008a), quantum mechanics (2001, pp. 120 ), modern chemical theory (2001, pp ), and evolutionary biology (2001, pp ). Nonetheless Friedman s discussion of Newtonian physics represents his view generally. 8 Friedmanian entrenchment therefore resembles Goodman s (2005/1955) notion of entrenchment.

6 264 N. J. Goldberg Because Friedman so construes entrenchment to disqualify Quine s use of it, he has no accompanying pragmatic point about how scientists should respect entrenchment relations. Friedman accounts for the necessity of mathematical claims relative to those in physics and the special sciences elsewhere. Now that we have seen how Friedman s notion of entrenchment differs from Quine s, we can focus on how Friedman uses that notion in his first historicist objection to Quine, also contained in the above passage (2001, pp ). Given what Friedman says above and what we have considered, we can formalize Friedman s objection thus: P 1 : If entrenchment is a historically relative property, then in Newton s day (a) was not entrenched relative to (c). P 2 : Entrenchment is a historically relative property. C: In Newton s day (a) was not entrenched relative to (c). Quine, however, generally privileges mathematical claims like those contained in the calculus. On his view, mathematics including the calculus just is entrenched relative to physics and the special sciences. Quine would therefore maintain that (a) is entrenched relative to (c) in Newton s day and our own. There is no historical relativization. Hence if C follows, then Friedman has successfully objected to Quine s use of entrenchment to account for the relative necessity of mathematical claims. Now Quine has two rejoinders to Friedman. He can deny P 1 on the grounds that Friedman gets the history wrong. The calculus did not relate to the universal law of gravitation in Newton s day as Friedman claims that it did. Or he can deny P 2 on the grounds that entrenchment is not historically relative. Quine can even go so far as to grant that regardless of whether Friedman s notion of entrenchment is historically relative, his is not; so Friedman simply changes the topic. Next we turn to P 1 and P 2 themselves. Considering those premises in the context of Quine s rejoinders shows that we have reason to think that Friedman s objection succeeds. 3 Reason to Think Friedman s Objection Succeeds P 1 claims that if entrenchment is a historically relative property, then in Newton s day (a) the calculus was not entrenched relative to (c) the universal law of gravitation. The truth of P 1 therefore depends on whether Friedman s historical analysis is correct. It is. For (a) the calculus, (b) Newton s laws of motion, and (c) the universal law of gravitation were all revolutionary advance in Newton s day. Newton co-discovered the calculus. Further, though his laws of motion and universal law of gravitation had antecedents in René Descartes mechanical philosophy, Newton broke with Descartes view that rest and motion were fundamentally different states. He also broke with Descartes by urging that change of direction and change of speed were fundamentally the same phenomenon, viz., acceleration. All three elements of the Newtonian synthesis were revolutionary as Friedman maintains. If entrenchment is a historically relative property, then in Newton s day (a) was entrenched relative to (c). P 1 is true. Quine, as well as anyone else, would be wrong to deny it. P 2, which claims that entrenchment is a historically relative property, is more contentious. Its truth depends on whether Friedman is correct in endorsing historicism generally and treating entrenchment as historically relative specifically. If he is, then Quine cannot account for the necessity of mathematical claims relative to those in physics and the special sciences in at least this case. We then have reason to reject his account altogether.

7 Historicism, Entrenchment, and Conventionalism 265 I believe that Friedman is correct here also. Though I know no conclusive argument for P 2, I can offer two reasons in support of it. First, Quine should himself treat entrenchment as historically relative. Quine is the archetypal naturalist. He maintains that philosophy is informed by and continuous with our best empirical theories. 9 Now careful analyses of episodes in the history of science count as some of those theories. The history of science is an empirical discipline, and Quine (1998, p. 49) himself identifies history as a science. No naturalist should ignore scientific findings when devising her views. But then Quine should not ignore the history of science when devising his own views in the philosophy of science. And these include views concerning whether certain claims were entrenched relative to others. Quine should therefore follow Friedman in regarding historical circumstances as relevant when determining entrenchment, a property central to Quine s theory about the structure and practice of science. Further, the alternative to historicism is to ignore the historical realities of how a theory was promulgated and focus on a rational reconstruction of how different elements of the theory relate instead. It is to remove science from its historical context and place it in a rationally reconstructed one. Yet Quine himself calls rational reconstruction makebelieve (1975/1968, p. 75) precisely because it is at odds with naturalism. It ignores Quine s view that philosophy should be informed by and continuous with our best empirical theories. Having written: Better to discover how science is in fact developed and learned than to fabricate a fictitious structure to a similar effect (p. 78), Quine should appeal to those disciplines whose job is to discover how science is in fact developed and learned. And those disciplines include psychology, to which he (especially 1964, chap. 2, and 1975/1968) does appeal, and the history of science, to which he does not. As Michael Tsou explains when urging that not Quine but Friedman has naturalism on his side, Quine cannot do justice to the nature of scientific knowledge in the domain of mathematical physics (Tsou 2003, p. 585) because his holism-cum-entrenchment does not mirror historical events. Certain claims that Quine says are entrenched actually were not, and at no point did scientists in fact test the whole of science when they were testing particular predictions of particular theories as Quine, from his rationally reconstructed perspective, says they did. Tsou concludes: [I]t is not a challenge to [Friedman] to provide an ad hoc reconstitution of mathematical physics in Quinean terms. But rational reconstruction just is an ad hoc reconstitution. Quine offers it not because it matches actual facts, but because it promises to vindicate his view that mathematics is not conventional but empirical. It allows him to reconstruct the history of science so that he can always understand mathematical claims as tested holistically against experience, regardless of whether any actually were. Quine s own notion of entrenchment implicates rational reconstruction precisely because it takes science out of its historical context and is part of his a reconstitution of mathematical physics and scientific theories generally. Ironically Friedman s competing notion of entrenchment is more in line with Quine s naturalism. Ironically, therefore, though Friedman does in a sense change the topic on Quine by invoking a different notion of entrenchment, the changed topic should have been Quine s all along. Hence Quine should endorse P See Fogelin (1997, 2004) for discussion of Quine s naturalism. 10 Brown highlights one aspect of Kuhn s historicism by noting that Kuhn s claim is that in order to understand and evaluate scientific theory choice we must attend to the scientific process as well as the scientific product (2005, p. 160, his emphasis). If Quine s naturalism pushes him toward historicism, then Quine too would have to attend to the process as well as the product. And that process is distinct from any rational reconstruction of it. This also speaks in favor of his endorsing P 2.

8 266 N. J. Goldberg Quine might object that even if naturalism does make him accept historicism, it does not make him draw lessons from historical accidents. And in our example, Quine might claim, (a) s and (c) s both being revolutionary in Newton s day was accidental because history might have played out differently. Newton might never have even been born. Hence while Quine could grant that historicism plays a role elsewhere, he might insist that treating entrenchment as historically relative relies on this and similar historical accidents. Entrenchment itself should therefore not be treated as historically relative. Though (a) and (c) both could have been revolutionary, Quine could still conclude that only the former was entrenched. He would then reject P 2. This objection, however, conflates the claim that Newton rather than someone else had to introduce (a) to formulate and test (c), which Friedman is not making, with the claim that when Newton (or any one so historically situated) introduced (c) he also had to introduce (a), which Friedman is making. Further, while the first claim is false, the second is true. As we see in 4, Friedman is right that Newton could not have tested, let alone formulated, (c) without having assumed the truth of (b). And Friedman is also right that the very intelligibility of (b) depends on making use of the resources encapsulated in (a). Newton s law of universal gravitation would have been impossible to confirm, let alone evaluate, without appealing to both the laws of motion and the calculus. This (as we also see in 4) is a historical fact, so it was no accident that when Newton introduced (c) he also had to introduce (a). That (a) and (c) were both revolutionary was no accident in that sense. While it might have been accidental that Newton introduced the law of universal gravitational, it was not accidental that to do so he also had to introduce the calculus. The objection therefore fails. In the case under consideration there is no historical accident on which this conclusion depends, and we have no reason to think that similar cases depend on historical accidents either. Quine should still accept P Of course Quine might remain unpersuaded. He might reject P 2 because he rejects historicism tout court. Like Rudolf Carnap and the logical positivists generally, Quine tends to treat science ahistorically. Like them, he tends to prefer rational reconstruction to historical fact. And, like them, he (1975/1968, pp ) tends to be critical of Kuhn. No naturalist, however, should prefer Carnapian rational reconstruction to Kuhnian historicism. Whatever reticence Quine might have toward accepting P 2 would indicate deeper tension in his view. In fact if Quine opts for rational reconstruction and so against P 2, then we have reason to doubt the coherence of Quine s project overall. For rational reconstruction is at odds with that project. Hence either Quine must concede the truth of P 2 to Friedman or we have reason to discount what Quine says generally. 12 The second reason that I can offer in support of P 2 generalizes the first. Regardless of what Quine would do, we should treat the philosophy of science in a historically sensitive manner, and that includes treating those properties invoked to explain science in a historically sensitive manner as well. Even were Quine to insist on denying P 2, neither he nor anyone else should in fact do so. Rational reconstruction is make-believe. Quine is right to say so emphatically, even if he might not himself follow through on its consequences. Nor is Quine, or for that matter Kuhn or Friedman, the only theorist providing insights into the 11 Friedman later (2008a) urges that there is an additional sense in which episodes like the historical introduction of Newtonian physics are not accidental: they are driven by the inner logic of the nexus of the various scientific, philosophical, and at times theological and other views of their proponents. 12 In fact Fogelin (1997, 2004) suggests that Quine is not a thoroughgoing naturalist, while Putnam (1990) calls Quine the greatest logical positivist. If aspects of Quine s view are so at odds with themselves, then he has graver troubles than any that Friedman or I observe.

9 Historicism, Entrenchment, and Conventionalism 267 value of historicism. Others including Paul Feyerabend and Norwood Russell Hanson have shown that historical details illuminate how scientific theories develop and how parts of theories relate. More generally the philosophy of science today is a thoroughly historicized discipline. There is no turning back on the historicist turn, not if a naturalistic analysis of science is sought. This is as true for Quine as it is for the rest of us. I conclude that we have reason to think that Friedman s objection succeeds and that Quine should agree. Recall, however, that Friedman offers two historicist objections to Quine s method of accounting for the necessity of mathematical claims relative to those in physics and the second sciences. The second objection is that Friedman s alternative method better accounts for the historical development of science. Next we start by considering Friedman s method of accounting for the relative necessity of mathematical claims. Then we see how it functions in his second objection to Quine. 4 Friedman on Historicism and Conventionalism Like Quine, Friedman wants to account for the necessity of mathematical claims relative to those in physics and the special sciences. 13 Unlike Quine, Friedman thinks that mathematical claims are constitutive of those in physics and the special sciences. They serve as principles constitutive of agreed-upon languages or frameworks within which empirical claims in physics and the special sciences can be formulated and empirically tested. 14 And chief among these constitutive principles are various mathematical claims. Now, according to Friedman, constitutive principles are not themselves tested against experience along with claims in physics and the special sciences; he rejects Quine s holism. Rather they are postulated to provide the framework within which empirical claims can be formulated and tested. Friedman therefore understands constitutive principles as conventional or, as he prefers, relativized a priori. They are a priori because, like Kant s own synthetic a priori judgments, they are meant to be constitutive of what can be said about experience without their truth depending on experience. 15 Friedman s constitutive principles are relativized because, unlike Kant, Friedman recognizes that different frameworks can allow different things to be said about experience; the apriority of constitutive principles is relativized to particular frameworks. Now Friedman had earlier (1999) argued that a central achievement of logical positivism culminating in Carnap s notion of the analytic is just this relativization of Kant s synthetic a priori. 16 Regardless of whether Carnap s notion should be so construed, Friedman maintains that his constitutive principles, like Carnap s analytic statements, are meant to be constitutive of languages or frameworks within which claims about the world Friedman s empirical claims and Carnap s synthetic statements can be formulated and tested against experience. Friedman maintains that his constitutive principles, like Carnap s analytic statements, are themselves not empirical but conventional. And Friedman maintains that his notion of a constitutive principle, like Carnap s notion of the 13 See note See Goldberg (2004b) for Davidson s (2001, essay 13) argument against the intelligibility of such frameworks. 15 See Goldberg (2004a) for discussion of Kant s account of the acquisition of a posteriori concepts. 16 Friedman (1999, 2001) focuses on Carnap (1988/1950), though Carnap s distinction is prefigured in Carnap (2003/1934). Creath (2008) calls Carnap s analytic and synthetic statements constitutive and substantive ; cf. Friedman s (2001) constitutive and empirical. (See Coffa 2008/1991 for similar treatment of Carnap.)

10 268 N. J. Goldberg analytic, traces to Hans Reichenbach (1965/1920), who distinguishes two meanings in Kant s notion of the synthetic a priori: (i) necessary in the sense of being unrevisable and holding with apodictic certainty; and (ii) constitutive of, and therefore necessary for, empirical knowledge. According to Friedman, his constitutive principles, like Carnap s analytic statements, are necessary in the sense of (ii). For Friedman, therefore, insofar as it makes sense to speak of mathematical claims as necessary at all, their necessity is linguistic and relative. It is linguistic because mathematical claims, which are conventional, are constitutive of languages or frameworks within which claims in physics and the special sciences can be formulated and tested. It is relative because mathematical claims are necessary for the formulation and testing of these others, and so their linguistic necessity is relative to particular frameworks in which scientific theories are formulated. Nonetheless, unlike the relative necessity of mathematical claims for Quine, which results from scientists being less willing to revise them than they are claims in physics and the special sciences, the relative necessity of mathematical claims for Friedman results from scientists being unable to revise them without making claims in physics and the special sciences unintelligible. Before exploring in detail why this is so, we should note two differences between Friedman s constitutive-empirical and Carnap s analytic-synthetic distinctions. Both trace to Friedman s endorsement of Kuhn s (1996/1970, 2002) historicist picture. First, though Friedman s and Carnap s distinctions attribute the same logical structure to theories, only Friedman s is introduced as a way of accounting for the historical development of science. Friedman explains: [C]areful attention to the actual historical development of science, and in particular, to the profound conceptual revolutions that have in fact led to our current philosophical predicament, shows that relativized a priori principles of just the kind Carnap was aiming at are central to our scientific theories (2001, p. 41). This is ironic because though, according to Friedman, the history of science reveals the existence of relativized a priori principles of just the sort that Carnap and Friedman both think exist, historical circumstances of theory development are inessential to Carnap s view, and actual practices of scientists are less important for him than rational reconstructions thereof are. Friedman later explains: [M]y implementation of this idea of relativized constitutively a priori principles essentially depends on an historical argument (2008a, p. 96); Carnap s implementation of his own idea of analytic truths does not. (I return to this difference below when considering Friedman s second historicist objection to Quine.) Second, while Carnap s distinction is meant to be drawn formally within a logically regimented language, Friedman seems content to draw his informally within natural language. Here Friedman takes himself to be following Kuhn s own informal narrative approach to the history of science. All this becomes clearer when we consider in more detail Friedman s analysis of Newtonian physics, introduced in 2. Recall that, according to Friedman, Newtonian physics divided into three components: (a) a form of mathematics, the calculus; (b) conceptions of force and mass embodied in his three laws of motion; and, (c) a universal law of nature, the law of universal gravitation. As I mentioned in 2, Friedman maintains that as a matter of historical fact Newton s formulation of (b) required access to the mathematical resources encoded within (a). We can consider here more carefully why this is so. Essential to Newton s second law of

11 Historicism, Entrenchment, and Conventionalism 269 motion specifically was the notion of acceleration construed as velocity s instantaneous rate of change. Yet acceleration as velocity s instantaneous rate of change was unintelligible without the notion of an instantaneous rate of change, and that notion was supplied by the calculus. Without the calculus, therefore, Newton s second law could not have been formulated. Indeed, according to Friedman, had Newton not devised (a), then any statement of (b) would have had no meaning or truth-value at all (2001, p. 36). The notions to which (b) appealed were meaningful only against the background language provided by the calculus. As Friedman explains, the inferential connections established by (a) created a logical space of possibilities (p. 85) within which (b) made sense. Varying the metaphor, we might say that (a) provided the rules for a specific game in physics rules constitutive of which moves were legitimate and which were not. These rules concerned mathematical functions and relations embodied by the calculus itself. By introducing the mathematical rules for this game, Newton made possible the playing of that game and various moves within it, moves that would otherwise not have been possible. Newton therefore devised (a) so that he could formulate (b). Friedman likewise maintains that as a matter of historical fact formulating (c) required the conceptual resources encoded within (b). For what Friedman takes to be Newton s empirical law of universal gravitation could not have been hypothesized without the concept of an inertial frame of reference. But such a reference frame just is one in which objects obey Newton s three laws of motion. Thus, without (b), (c) would likewise have had no meaning or truth-value. This time the notions to which (c) appealed were meaningful only against the background language provided by the calculus and supplemented by the laws of motion. Newton s notion of force as used in the law of universal gravitation would have been ill-defined had his laws of motion not also been promulgated. The inferential connections now established by (a) and (b) together created what we might call an empirical space of possibilities. Put differently, (b) provided further rules for the game that (a) began. It further defined which moves were legitimate, and now those moves were empirical. They concerned claims whose truth-value depended on experience, and (c) counted as just such a claim. Hence Newton devised (a) and (b) so that he could have the linguistic resources with which to formulate (c). Further, Friedman contends that as a matter of historical fact Newton had to assume (a) and (b) not merely to formulate (c) but also to make (c) amenable to empirical testing. While (a) established the mathematical framework in which empirical claims were to be analyzed, (b) served as coordinating principles (2001, p. 74) or general rules coordinating the application of the mathematical framework to the physical phenomena described by the empirical claims. Coordinating principles are thus meant to provide the linguistic means necessary for the description of concrete observations by abstract mathematical representations. 17 What resulted were predictions that could be used to determine the empirical adequacy of (c). Stipulating (a) and (b) thereby permitted empirical data to count as evidence for or against (c). Stipulating them therefore permitted (c) not merely to be empirically possible but also to be tested to see whether it was empirically adequate Friedman (1999, chap. 3; 2001, part 1, chap. 2; 2002a, pp ; 2002b, pp ) traces the notion of coordinating principles to Reichenbach (1965/1920). Because my focus is on mathematical claims like (a), I do not discuss coordinating principles further. 18 Admittedly Friedman s historical analysis of Newtonian physics itself has elements of rational reconstruction. While Friedman writes as if at Newton s hand the calculus achieved the status of conventional truth, Newton regarded the calculus as true in virtue of the structure of absolute space and time. Nonetheless there are two ways to reconcile this with Friedman s otherwise historicist account. First, we might recognize that Friedman s analysis occurs at two levels: properly historical and ahistorically

12 270 N. J. Goldberg Now, for Friedman, our understanding of the epistemic relations among claims like (a), (b), and (c), as they hold not merely historically but also generally, is itself illuminated by these historical considerations. According to Friedman, were scientists today to test what he takes to be Newton s empirical claim, the law of universal gravitation, then they would first have to stipulate those claims, the calculus and laws of motion, which he takes to be constitutive of it. That is the only way in which they could coordinate empirical phenomena with the mathematical structure that the law of universal gravitation presupposed. Of course were scientists today to test some reformulated version of the law of universal gravitation, then this historical point would not carry. But Newton s law itself, Friedman maintains, does require for its testing assumptions embodied in the calculus and laws of motion. Then and now (a) and (b) serve as principles constitutive of the language within which (c) could be formulated and empirically tested. This is the sense in which the history of science, for Friedman, illuminates the nature of science. Finally, Friedman urges that regarding mathematical claims in particular as principles constitutive of frameworks within which empirical claims can be formulated and tested not only accounts for the necessity of the former relative to the latter historically and generally. It also, as we have just seen in Friedman s paradigm case, better accounts for the historical development of science than Quine s regarding mathematical claims as entrenched does. This, recall, is Friedman s second historicist objection to Quine. Friedman is correct. The calculus simply was not entrenched in Newton s day. Newton did in fact stipulate it to be able to formulate and test the law of universal gravitation instead. That is where the necessity of the calculus relative to the law of universal gravitation derives, and Friedman s explanation is consistent with history while Quine s is not. Nor should this be surprising. Recall that Friedman s constitutive-empirical distinction differs from Carnap s analytic-synthetic distinction partly by being introduced as a way of accounting for the historical development of science. Carnap s distinction, like Quine s holism-cumentrenchment, was introduced with no such aim. Neither Carnap nor Quine took the historicist turn. As we saw at length in 3, however, Quine should have taken that turn. Because Friedman s constitutive-empirical distinction matches historical fact, while Quine s holism-cum-entrenchment matches merely its rational reconstruction, we have Quinean and general grounds to think that Friedman s second historicist objection to Quine succeeds too. Now because Friedman s constitutive-empirical distinction still does share much with Carnap s analytic-synthetic distinction, Friedman recognizes the worry that Quine s arguments against Carnap apply to him. Specifically Friedman recognizes that his distinction, like Carnap s, might for Quinean reasons be seen as untenable. To appease this worry Friedman reminds us of the second difference between his distinction and Carnap s: his trades Carnap s formal approach to the philosophy of science for Kuhn s informal one. And doing so, Friedman contends, inoculates his distinction against W. V. Quine s wellknown and widely accepted attack on the Carnapian conception of analytic truth (2001, p. xii). Nonetheless Friedman never demonstrates how informalism inoculates his view. Next I consider arguments that Quine would presumably have made against Friedman s Footnote 18 continued reflective. Besides what the historical Newton thought that he was doing, Friedman can ahistorically reflect on what he was doing by attributing to Newton a kind of conventionalism. Second, we might recognize that from both the properly historical and ahistorically reflective levels, Friedman can maintain that Newton treated the calculus as a priori: Newton historically treated the calculus as a priori in a metaphysical sense, while Friedman ahistorically treats it as a priori in a conventional sense. By employing a priori rather than conventional, Friedman s description can therefore be historically and ahistorically accurate.

13 Historicism, Entrenchment, and Conventionalism 271 constitutive-empirical distinction. In so doing I demonstrate that Friedman s informalism is inessential; his historicism by itself inoculates his view against Quine. That is ultimately why his distinction fares better than Carnap s. 5 Quine s Objections to Friedman and Reason to Think They Fail Though Quine did not himself object to Friedman, he would presumably have applied his arguments against Carnap s analytic-synthetic distinction to Friedman s constitutiveempirical distinction. Now, on my reading, Quine lodges six arguments against the analytic-synthetic distinction, which divide into three groups. Here I try each group against the constitutive-empirical distinction. Because Quine s arguments are familiar and my use for them is limited, I summarize them as succinctly as possible. 19 The first group of Quine s arguments has two members. (i) Quine (2004c/1936) argues that if claims in logic and mathematics, which are supposedly analytic, can be regarded as conventional, then so can anything. But then convention is too weak to distinguish analytic from synthetic. And (ii) he (2006b/1951, 6) argues that because any statement can be held true come what may given adjustments elsewhere, the alleged class of analytic statements lacks identity conditions. Since (for Quine) there is no entity without identity, there is no such class. 20 Taking a step back from the particulars we see that Quine s point in both arguments is not that scientists ever did or would regard claims in lunar geology rather than those in linear algebra as conventional, or hold beliefs belonging to molecular biology true come what may if that required holding those belonging to arithmetic false. His point instead is that reconstructing relations among statements by bracketing how they were, are, or probably ever would be related in reality and so by appealing to a purely rational reconstruction of theories proves that scientists could take them to be so related. Quine concludes that the analytic-synthetic distinction is unsustainable. Whether or not Quine is entitled to appeal to rational reconstruction in formulating his positive view (in 3 4 I claimed that he is not), he is entitled to do so when objecting to Carnap. Carnap himself employs rational reconstruction when discussing science. So we might understand these Quinean arguments as reductiones ad absurdum: Carnap assumes the legitimacy of rational reconstruction to draw the analytic-synthetic distinction, and Quine assumes the same to show that the analytic-synthetic distinction cannot be drawn. Quine cannot, however, appeal to rational reconstruction when objecting to Friedman. Unlike Carnap s analytic-synthetic distinction, Friedman s constitutive-empirical distinction is to be illuminated historically. For Friedman, it does not matter that the historical case of Newtonian physics could be rationally reconstructed so that (c) the law of universal gravitation would be conventional and (a) the calculus would be empirical, or that (a) or (c) could with enough ingenuity be held true come what may. That is not how history played out. Regardless of whether (i) and (ii) succeed against Carnap, they are inapplicable 19 There is much debate concerning how to read Quine s arguments against the analytic-synthetic distinction. See Creath (2008, p. 327) for a survey. See Friedman (1999, chaps. 7, 9) for his take on the Carnap- Quine debate. See Soames (2003, chap. 16) for discussion more sympathetic to Quine, and Russell (2007) for current research on the analytic-synthetic distinction that includes an alternative summation of Quine s arguments. I take my own summation to be plausible rather than necessarily definitive; along the way I reference others who agree with aspects of it. 20 In interpreting (i) and (ii) I follow Gibson (1982, pp ) and Rey (1994, pp ) in taking Quine to argue from holism to no analytic-synthetic distinction. See Dummett (1993) and Sher (1999), who take Quine to argue the converse.