Quine’s Structural Holism and the Constitutive A Priori

8 Robert Sinclair 8.1 Introduction Recent work on the general structure of scientific theories has placed a renewed emphasis on the significance of a priori principles for the formulation of scientific theories and empirical laws. From this perspective, scientific theories are depicted as having an asymmetrical structure with mathematical and logical principles being presupposed through the very formulation of empirical laws. The supporters of this general position are also united in thinking that Quine’s famous holistic depiction of human knowledge, as one interconnected ’web of belief ’, cannot capture this asymmetrical structure nor the central constitutive role played by a priori framework principles in enabling the formulation and eventual testing of empirical statements and laws. In Michael Friedman’s Dynamics of Reason, we find the most developed presentation of this general viewpoint (2001). Here, Quine’s holism is depicted as unable to make sense of historical revolutions in science precisely because of its failure to account for the constitutive nature of the a priori frameworks that make possible the formulation of empirical laws. Friedman notes how Quine’s view can only explain differences in a given theory by degrees of entrenchment, with, for example, our reluctance to revise logical laws stemming from their deep entrenchment within our current theories. Such entrenchment is blind to the asymmetries between logical, mathematical, and empirical principles within the overall structure of science and which Friedman takes as necessary for the formulation and testing of scientific theories and laws. The main aim of this chapter is to clarify what is at stake in this apparent disagreement between Friedman and Quine over the structure of scientific theories. Using key insights from recent work on Quine’s epistemology of logic it argues that his ‘web of belief ’ account also contains asymmetric structure with logic and mathematics serving as basic elements that are presupposed in the formulation of empirical scientific theories. This further suggests that what I will call Quine’s Robert Sinclair, Quine’s Structural Holism and the Constitutive A Priori In: Quine, Structure, and Ontology. Edited by: Frederique Janssen-Lauret, Oxford University Press (2020). © Robert Sinclair. DOI: 10.1093/oso/9780198864288.003.0008 Downloaded from https://academic.oup.com/book/33532/chapter/287885625 by Temple University user on 15 May 2024 Quine’s Structural Holism and the Constitutive A Priori 148 robert sinclair ‘structural holism’ can indeed capture some of the central aspects of the constitutive a priori that Friedman deems central to understanding the structure of scientific theories. Friedman and Quine then agree on these three basic points concerning the overall structure of scientific knowledge: However, Friedman explains that the true significance of the constitutive a priori is further clarified by noting its fundamental role in coordinating the abstract mathematical component of scientific theories with concrete sensible experience. Nothing in Quine’s structural holism directly addresses this ‘coordination’ problem and this, I will argue, captures the central difference between their respective viewpoints, involving a divergence over how the formal is related to the empirical in order to enable empirical testability. I then conclude by briefly explaining how this difference is located in their different perspectives on scientific theories, with Quine treating them as fixed structures worthy of logical analysis and Friedman viewing them from the historical standpoint of revolutionary scientific change. This indicates, I suggest, that their views be seen as complementary rather than opposed, and further highlights the rather complex ways in which they both accept a key Kantian insight: empirical theories require formal constraints for their very formulation as empirical theories. 8.2 Friedman’s Dynamics of Reason and the Constitutive A Priori Friedman’s attempt to articulate a dynamical conception of constitutive a priori principles emerges out of his examination of philosophy’s deep historical connection with science.1 This connection can be illustrated with a familiar example. The natural science of the seventeenth century did not become a new scientific paradigm simply because of its mathematical and empirical successes. Friedman emphasizes that at this stage it was simply too programmatic, it aimed at a precise mathematical depiction of nature by means of the corpuscular theory of matter, a goal only fully realized much later with the use of entirely different and unforeseen mathematical and physical concepts (2001: 22–3). What further motivated and sustained this new mechanical paradigm was the philosophical vision of Descartes and Galileo who developed this 1 His most developed treatment of this theme is found in his (2001) with a more critical discussion of Quine’s view in his (1997). Recent extensions of his account can be found in (2010, 2011, and 2012). Downloaded from https://academic.oup.com/book/33532/chapter/287885625 by Temple University user on 15 May 2024 (1) The centrality and generality of logic and mathematics within that systematic structure. (2) The in principle revisibility of all scientific beliefs (even ‘constitutive a priori’ principles). (3) Its asymmetric nature and the need for formal presuppositions in empirical science. quine’s structural holism and the constitutive a priori 149 2 Friedman stresses that this interplay between philosophy and science can also be seen in more recent times. For example, the development of Einstein’s theory of relativity resulted in modifications to Kant’s original conception of the synthetic a priori by logical empiricism (see 2001: 12–18, 30–3, 61–8). 3 See De Pierris (1993) for more historical background on the general idea of the constitutive a priori in Kant’s philosophy. Downloaded from https://academic.oup.com/book/33532/chapter/287885625 by Temple University user on 15 May 2024 new understanding of nature against the background of medieval Scholasticism. This required purging Aristotle’s natural philosophy of its hierarchical and teleological elements in favour of the mathematical and geometrical viewpoint that characterizes modern natural science. Galileo’s aim was then to emphasize Euclidean geometry, itself already part of Aristotelian natural philosophy and, as Friedman explains, viewed as an exemplar of rational inquiry, while eliminating its association with the hylomorphic and teleological elements of Aristotelian philosophy (2001: 67). This effort was further supported through Descartes’ philosophical reorganization of the central concepts of Aristotelian metaphysics within the new scientific advances of Copernican astronomy, geometrical optics, and Descartes’ own analytic geometry. In describing this move from the Aristotelian view to classical physics, Friedman explains that: ‘we retain Euclidean geometry intact, discard the hierarchically and teleologically organized spherical universe, and modify the Aristotelian conception of natural motion—in such a way that we retain the idea, in particular, that there is a fundamental state of natural motion following privileged paths of the underlying geometry’ (2001: 63).2 Friedman takes this and more recent historical episodes to illustrate an important truth about the structure of natural science, first made explicit with the transcendental conception of philosophy introduced by Immanuel Kant. The facts of revolutionary scientific change reveal that the mathematical and formal elements of scientific theories do not face the ‘tribunal of experience’ in the same way as empirical laws do, rather, as he further explains, ‘What characterizes the distinguished elements of our theories is rather their special constitutive function: the function of making the precise mathematical formulation and empirical application of the theories in question first possible’ (2001: 40).3 However, unlike Kant’s formulation of this idea, Friedman emphasizes that we should not view this constitutive notion of the a priori as providing an unrevisable set of universal conditions that make empirical science possible. Here he appeals to central features of the logical empiricist attempt to reorient the function of the a priori elements of scientific knowledge. Central for this perspective is Reichenbach’s attempt to articulate a view of a priori principles which distinguishes two senses of the Kantian a priori: necessary and unrevisable on the one hand, and constitutive of the concept of the object of scientific knowledge on the other. In light of turn-of-thecentury developments in physics, Reichenbach argued that the first sense should be dropped but the second retained. Friedman describes the results in these terms: 150 robert sinclair What we end with, in this tradition, is thus a relativized and dynamical conception of the a priori mathematical-physical principles, which change and develop along with the development of the mathematical and physical sciences themselves, but which nevertheless retain the characteristically Kantian constitutive function of making the empirical natural knowledge thereby structured and framed by such principles first possible. (2001: 31) 4 For more details on Carnap’s program see Friedman (1999), Richardson (1998), and Ebbs (2014). Downloaded from https://academic.oup.com/book/33532/chapter/287885625 by Temple University user on 15 May 2024 This view of the constitutive a priori and its role in empirical knowledge reaches its highpoint with Carnap’s philosophy of linguistic frameworks (1937, 1950). According to Carnap, standards of ‘correctness’, ‘validity,’ and ‘truth’ are relative to the logical principles that define a linguistic framework. These rules are then constitutive of the concepts ‘validity’ and ‘correctness’ within a specific linguistic framework and are viewed as a priori rather than empirical. This further leads to the well-known distinction between the formal or analytic sentences of the framework and the empirical or synthetic sentences, which allows Carnap to mark the difference between logical rules of the framework (analytic sentences), and the physical rules of the framework (empirical sentences). Linguistic frameworks contain analytic sentences that constitute the framework in which one can formulate meaningful empirical laws. The formal, analytic sentences are constitutive a priori relative to a specific linguistic framework, and this provides the context within which the formulation of empirical laws becomes possible. 4 It is here that Friedman suggests an affinity between Carnap’s idea of constitutive linguistic frameworks and Kuhn’s emphasis on the importance of scientific paradigms (Kuhn 1970). Kuhn’s account of normal science, where a scientific paradigm offers agreed upon rules that are constitutive of what counts as correct solution to a puzzle is similar to Carnap’s claim that logical rules of a specific linguistic framework are constitutive of the concept of ‘validity’ with regard to that framework. In addition, Kuhn’s analysis of revolutionary science, where the change of a paradigm is not based on a set of agreed upon rules, resembles Carnap’s insistence that the choice of adopting a linguistic framework is not made on the basis of logical rules but must be decided on pragmatic grounds. While not endorsing Carnap’s specific attempt to give a precise logical explication of the analytic–synthetic distinction, Friedman takes these similarities between Carnap and Kuhn to provide further support for the presence of a fundamental difference between a priori constitutive principles and the empirical laws formulated against the background of such formal principles (Friedman 2001: 41). Friedman’s overall conception of the constitutive a priori and its role in scientific change yields what he describes as a ‘dynamical yet nonetheless stratified or differentiated system of knowledge’ (2001: 45). At one level, we find the concepts and principles of empirical natural science and the empirical laws of nature that are subject to a rigorous empirical testing, such as the law of universal gravitation quine’s structural holism and the constitutive a priori 151 5 Friedman also emphasizes an additional level containing philosophical meta-frameworks that offer concrete proposals and suggestions in helping mediate the transition to a new scientific period of normal science (2001: 23–4, 46, 105–15). 6 Carlson notes that centrality does not simply involve resistant to revision, since observation sentences are also unlikely to be revised (2015: 2). As we will see, the centrality of logic is further tied to its functional role in lending unity and system to scientific knowledge 7 This view of scientific knowledge as one large ‘web of belief ’ is first presented in Quine’s ‘Two Dogmas of Empiricism’ (1953: 42) and is developed in many of his later writings including (1960: 9–13), (1986a: 5–7), and (1992: 13–16). Downloaded from https://academic.oup.com/book/33532/chapter/287885625 by Temple University user on 15 May 2024 and Einstein’s gravitational field equations. At a further level are the constitutive a priori principles that define the basic spatio-temporal framework within which the testing of the empirical principles is possible, these include basic principles of geometry and mechanics. Friedman takes these relativized a priori principles to be Kuhnian paradigms, stable rules of the scientific game, which make possible the activities witnessed in periods of normal science. During periods of deep conceptual change these a priori principles are subject to change, under pressure from new empirical findings and various anomalies. We will later see that while such principles remain ‘sensitive’ to empirical findings they are not empirically tested in the process of formulating empirical laws, but are what make possible empirical testing itself. Friedman further explains that neither of these levels remain fixed for all time, but change as empirical discoveries suggest the need for a new set of constitutive principles that give rise to a new period of normal science.5 Friedman’s stratified system of knowledge view is further developed in explicit opposition to Quine’s epistemological holism, which presents the structure of knowledge as a ‘web of belief ’ that confronts experience only at its edges (2001: 33–5). In place of any stratified divide between the a priori and the empirical, Quine presents our system of knowledge as consisting of a large and thoroughly empirically interconnected set of beliefs with experience or sensory input having direct contact only along the edges of this web. In the face of recalcitrant experience that conflicts with our system of beliefs, we have a choice concerning where we might revise the system. Such revisions may be made close to the perimeter of our system of beliefs, where such a change would involve a peripheral element of natural science, or in situations where the conflict is particularly persistent we may decide to revise the more abstract parts of science, including the truths of logic and mathematics, which occupy a more central place in this web of belief.6 Quine stresses that such mathematical and logical truths are more deeply entrenched within this system, causing us to be quite reluctant to revise them. Nevertheless, once such a view of our system of knowledge is adopted, we are confronted with the characteristic Quinean claim that no belief is immune to the possibility of revision in light of new conflicts with experience.7 Friedman places special emphasis on the additional well-known point that empirical support is taken to spread across the entire web of theoretical interconnections, so that all elements of this structure equally confront experience. It is in this precise sense, 152 robert sinclair 8 For a detailed look at the Carnap–Quine debate, see Richardson (1997). Friedman (2006) links the differences between Carnap and Quine to their respective sources in Kant and Hume. This essay questions such an easy assimilation. For useful discussion from Quine’s perspective on this debate see Hylton (2002, 2007). The Lewis–Quine connection is explored in my (2012 and 2016). 9 For the consensus see Goldberg (2009), Klein (2008), Richardson (2002), Stump (2003), and Tsou (2010). Downloaded from https://academic.oup.com/book/33532/chapter/287885625 by Temple University user on 15 May 2024 that all beliefs, even those found in mathematics and logic, are ‘equally empirical’ (2001: 35). Friedman further explains how the widespread influence of Quine’s view is connected to the famous mid-twentieth century debates over the philosophical viability of the analytic–synthetic distinction. Quine’s holism is predicated on a rejection of the analytic–synthetic distinction as formulated in the work of Rudolf Carnap and C. I. Lewis.8 Importantly, Friedman accepts Quine’s main criticism of this distinction while denying that his undifferentiated holism is our sole remaining option. More specifically, he argues that while Quine is right that both formal logic and empirical psychology are insufficient to characterize the relativized constitutive a priori principles that Carnap was attempting to clarify, it does follow that the ‘phenomenon he was attempting to characterize does not exist’ (2001: 41, emphasis in the original). The historical accounts of scientific change briefly discussed above indicate to him that the presence of such constitutive a priori frameworks remain essential for understanding the rationality of scientific revolutions. This portrayal of the disagreement between Quine and Friedman amounts to a difference over how to view the structure of our system of knowledge. Friedman emphasizes the asymmetric structure between formal principles and empirical laws in order to argue that such a priori principles constitute the framework for the very formulation of empirical claims. In Quine’s case, such formal principles can only be understood as one part of our empirical web of belief, simply farther removed from its periphery. Mathematical statements appear to have a different epistemic status than empirical claims because of their deep entrenchment within this web and our subsequent reluctance to change it. Friedman takes this view to be a complete misrepresentation of the way a formal mathematical framework makes possible the formulation and testing of physical laws, and which further yields our empirical systematic knowledge of the natural world. Summing up his general diagnosis of the failures of Quine’s empiricist position, he explains that it remains ‘…simply blind to the essential constitutive role of modern mathematics in making modern empirical physical science possible in the first place’ (2006: 51). The rest of chapter will then focus on exactly this structuring role played by the introduction of the constitutive a priori, since there has been almost unanimous agreement with Friedman that this role is not only absent from Quine’s all-encompassing web of belief, but can in no way be made to fit such a holistic view.9 Exclusive focus on the standard entrenchment interpretation of Quine’s holism misses the way his more abstract understanding of the ‘logic of science’ retains the kind of asymmetric quine’s structural holism and the constitutive a priori 153 structure witnessed in Friedman’s own view. More specifically, we will see that Quine retains a role for the formal, including both logical and mathematical principles, as necessary presuppositions for the formulation of empirical theories.10 8.3 Quine’s Structural Holism The kinship I speak for is rather a kinship with the most general and systematic aspects of natural science, farthest from observation. Mathematics and logic are supported by observation only in the indirect way those aspects of natural science are supported by science; namely, as participating in an organized whole which, way up at its empirical edges, squares with observation. I am concerned to urge the empirical character of logic and mathematics no more than the unempirical character of theoretical physics; it is rather their kinship that I am urging, and a doctrine of gradualism. (Quine 1986a: 100, my emphasis) Quine here describes an affinity between logic, mathematics, and theoretical physics where they represent the most general parts of scientific theory furthest away from 10 The entrenchment view is Quine’s better known psychological attempt to clarify his web of belief metaphor. For valuable discussion of the connections between the logical and psychological aspects of Quine’s epistemology, see Carlson (2015), Ebbs (2014) and Johnsen (2014). Downloaded from https://academic.oup.com/book/33532/chapter/287885625 by Temple University user on 15 May 2024 Let us then return to Quine’s famous ‘web of belief ’ metaphor, which describes the structure of scientific knowledge as one large overarching web of belief that confronts experience only at its edges. The result is confirmational holism: the view that our theories as a whole are supported through their contact with sensory experience. When experience runs counter to our expected predictions, we must modify this theory, where we change only what is needed to restore the balance between our previous theoretical commitments and their current conflict with experience. While Quine famously claims that even logic is in principle revisable, due to its central place within our theories and our preference to conserve as much of our existing theory as possible, we usually shield it from revision in such cases. It is this tendency that gives logic its ‘air of necessity’ for Quine (1986: 100). Recent work on Quine’s epistemology of logic seeks to further explain this centrality that Quine assigns to logic within this holistic view of theory revision (Carlson 2015). More specifically, the key question concerns why such revisions to the central logical core of our theory would greatly disturb the rest of our theory (they would reverberate intolerably, in Quine’s phrase). In answering this question, Carlson argues that contrary to the standard entrenchment interpretation, Quine’s web of belief requires, as he puts it, ‘ramified, asymmetrical internal structure’ (2015: 1). He further argues that this reveals Quine’s view as capable of accommodating the idea that logic and mathematics are presupposed by physical parts of our theory, and the functional role Friedman assigns to constitutive a priori formal principles. To see this, we should begin by noting the kinship Quine recognizes between mathematics, logic and theoretical physics: 154 robert sinclair 11 So, for example, he states: ‘Logical laws are the most central and crucial statements of our conceptual scheme’ (1982: 3). 12 Quine makes a similar distinction between narrow and broad uses of logic in his Mathematical Logic, Revised Edition (1983: 3). 13 For example, one could reject the law of excluded middle but still accept the sentence ‘John is tall or John is not tall’ as an empirical truth about John. See Carlson for a more extended treatment explaining why the rejection of a logical law does not lead to intolerable results (2015: 2–5). Of course, the need for such rejections can be evaluated case by case with some being more drastic than others. Downloaded from https://academic.oup.com/book/33532/chapter/287885625 by Temple University user on 15 May 2024 observation. When taken together, this generality and empirical distance make logic, mathematics, and theoretical physics the most central aspects of that scientific theory. Quine makes the additional claim that logic be seen as the most central and general portion of scientific theories (1986a: 98–100).11 In clarifying the nature of this generality, Carlson notes that Quine assigns two kinds of generality to logic involving the difference between logical truths and logical laws.12 A logical truth is defined as a true sentence such that any consistent replacement of its non-logical vocabulary would result in another true sentence, with a simple example being ‘Socrates is mortal or Socrates is not mortal’ (Quine 1986a: 55; 1983: 2). Logical laws are further defined as generalizations over the forms of such logical truths, which then identify the valid forms of sentences, where all instances of such forms are then true (Ricketts 2004: 24). For example, the law of excluded middle is a generalization of the above logical truth and then counts as a logical law (Quine 1983: 51). Logical truths are general because every area of science contains at least some truths that are logical truths. On Quine’s characterization, logical vocabulary consists of grammatical particles such as ‘and’ or ‘not’ that are lexically neutral and so they can be applied across scientific disciplines (Quine 1986a: 102). The generality of logical laws (generalizations over logical truths) is captured in a further special way. Using the distinction between object and metalanguage, we can express their general nature using a metalanguage equipped with a truth predicate famously defined by Tarski, for all of the sentences of the object language. So, for example, we can then say: ‘Every sentence of the form ‘p or not p’ is true’ (Quine 1986a: 12). Logic’s generality can now be further clarified in terms of why it is deemed central to scientific theories. Firstly, logic has universal application in every branch of science, such that whenever we are concerned with truth, logical vocabulary is used (Hylton 2007: 77). However, as Carlson emphasizes, it is not logical truths that exhibit this generality, but logical laws, since they are universally applicable in all branches of science by having substitution instances, that is, particular logical truths, in all areas of scientific theory (2015: 3). However, this type of generality is itself insufficient as an explanation for why the rejection of a logical law would lead to intolerable changes to the rest of our scientific theory. Carlson points out that a logical law could be rejected while most of its substitution instances retained within a scientific field (2015: 4).13 Explaining why such a rejection remains a serious difficulty requires a deeper recognition of the specific type of epistemic commitment that accompanies quine’s structural holism and the constitutive a priori 155 It is only by way of the relations of one statement to another that the statements in the interior of the system can figure at all in the prediction of experience, and can be found deserving of revision when prediction fails. Now of these relations of statements to statements, one of conspicuous importance is the relation of logical implication: the relation of any statement to any that follows logically from it…[B]ut for implication, our system of statements would for the most part be meaningless; nothing but the periphery would make sense. (Quine 1982)14 Here, Quine explains that the type of presupposition made through logical implication indicates a significant epistemic commitment. This is because the acceptance of the laws of any particular science reveals a further implicit acceptance of the logical laws that connect these scientific laws to experience. Without this connection, scientific statements would be severed from any link to empirical information or content (Carlson 2015: 5–6). Through accepting scientific laws we presuppose logic by ensuring that the scientific theory in question has empirical content at all.15 The crucial importance of this epistemic presupposition is further developed by Carlson when he argues for an important connection between it and Quine’s further insistence on system as vital for scientific knowledge. Beginning with the idea that scientific knowledge does simply consist of the indiscriminate collection of truths, but the construction of a unified system, Quine is further presented as committed to what 14 Also consider this statement: ‘Given the second dogma, analyticity is needed to account for the meaningfulness of logical and mathematical truths, which are clearly devoid of empirical content. But when we drop the second dogma and see logic and mathematics rather as meshing with physics and other sciences for the joint implication of empirical consequences, the question of limiting empirical content to some sentences at the expense of others no longer arises (Quine 1986c: 207, my emphasis). Related remarks can be found at the start of his Pursuit of Truth (1992). 15 As we will see, this idea is also emphasized by Friedman and it indicates Quine’s acceptance of the general Kantian idea where empirical claims presuppose formal principles (Friedman 2001: 83–7). Downloaded from https://academic.oup.com/book/33532/chapter/287885625 by Temple University user on 15 May 2024 our use of logical laws. Once this commitment is clarified, Carlson suggests we recognize Quine’s holistic web of belief as requiring additional asymmetrical structure of the sort advocated by Friedman. The epistemic commitment tied to our use of logic comes in two forms. The first emphasizes the familiar point that in making inferences we depend on logical laws. In accepting their consequences of logical inferences, we appeal to the use of logical laws, which enable that inference from other claims that we hold true. We must then accept (perhaps only tacitly) the logical laws that we use in making inferences, since to reject them would make our theory unstable by giving up the very logical law that enables us to make the inference in the first place. A further type of epistemic commitment points to the way our theories presuppose logic in much broader terms. Here, it is through logic, or more specifically the relation of logical implication, that large portions internal to our system are connected with its periphery, thereby supplying it with empirical content. Quine often emphasizes that it is through such logical links that our overall theory admits of empirical confirmation whatsoever. For example, he explains: 156 robert sinclair At the end of Philosophy of Logic I contrasted mathematics and logic with the rest of science on the score of their versatility: their vocabulary pervades all branches of science, and consequently their truths and techniques are consequential in all branches of science. This is what has led people to emphasize the boundary that marks pure logic and mathematics off from the rest of science. This is also why we are disinclined to tamper with logic and mathematics when a failure of prediction shows that there is something wrong with our system of the world. We prefer to seek an adequate revision of some more secluded corner of science, where the change would not reverberate so widely through the system. This is how I explain what Parsons points to as the inaccessibility of mathematical truth to experiment, and it is how I explain its aura of a priori necessity. (Quine 1986b: 399–400) Downloaded from https://academic.oup.com/book/33532/chapter/287885625 by Temple University user on 15 May 2024 is called the ‘classical model’ of systematic science (de Jong and Betti 2010; Tsou 2010). There are two central features of this model. First, science is viewed as containing basic elements within its systematic structure, elements that are presupposed in all other scientific disciplines. Second, the various scientific subdisciplines that make up the system of science are characterized by having different degrees of generality, with the basic elements of the system consisting of its most general elements. Quine’s remarks quoted above concerning the close affinity between logic, mathematics, and the systematic aspects of natural science strongly suggest his commitment to this view of systematic science. Given that view, what remains most central to the web of belief model and least likely to be revised are the most general and systematically basic scientific laws. The obvious candidate for this role are logical laws, which we have seen are presupposed through our inferences and which establish links between our theories and experience. Without presupposing these logical laws, the interior parts of our theory would lack any link to experience and be meaningless. As we have seen, the system would be severed from the empirical links needed for its status as empirical knowledge. Moreover, these logical laws enable the inferences needed in establishing systematic connection between what we know. Accepting logical laws as systematically basic in terms of both logical inference and empirical content then reveals the significance of this epistemic commitment. Rejecting these logical laws would cause major disruptions to our theory, since these basic logical laws serve to unify our theory and make it an organized system of scientific knowledge. The overall coherence of the theory would be threatened because ‘systematically fundamental elements play a crucial role in unifying our overall theory . . . To give up such systematically fundamental parts of our overall theory as logical laws, say, is just to give up our theory-an organized, unified, systematic whole-altogether’ (Carlson 2015: 6). Without logical laws to provide this unified structure, we lack the system required for any organized attempt at knowledge. Revising logical laws would require widespread revision to our theory, threatening the very structure needed for knowledge. In most cases we adopt a more conservative strategy and make the needed changes elsewhere. And it is this that explains Quine’s claim that the rejection of these basic logical laws would result in an intolerable disturbance to our theory (Carlson 2015: 7): quine’s structural holism and the constitutive a priori 157 Quine’s structural holism presents science as a system of knowledge that contains asymmetric structure, with logical laws viewed as systematically basic in being presupposed by the rest of our scientific theory. This further highlights the central epistemic commitment behind our use of logical laws, where they serve as formal presuppositions of scientific theory that enable it to have the empirical links required for it to count as empirical science. Once we then apply Quine’s epistemology of logic to his holistic view of human knowledge, we can recognize that it retains the resources to account for structural differences between aspects of scientific theories, where it further exhibits the asymmetric structure seen in the classical model of systematic science. It is not the generality usually associated with logical laws that explains their central place in our system of knowledge and the further intolerable consequences of revising them. Nor is their centrality simply a matter of entrenchment. Rather, Carlson convincingly shows that logic’s centrality is due to its being systematically basic such that it guarantees that our knowledge can count as a unified scientific system. Friedman’s critical focus on the entrenchment reading of the web of belief fails to recognize that Quine’s structural holism contains asymmetric structure with logical laws presupposed in the formulation of other empirical scientific laws. Distinguishing Quine’s psychological entrenchment view from his more abstract logical analysis of the structure of scientific theories reveals that both he and Friedman accept that scientific knowledge has an asymmetric systematic structure that requires formal presuppositions for empirical science. Consider another example offered by Friedman to illustrate his view (2001: 35–6). In order to create his revolutionary conception of mathematical physics, Newton needed and created three conceptual advances: 1. The mathematics of the calculus. 2. The three laws of motion and the new conceptions of force and matter that accompany them. 3. The law of universal gravitation. These advances are functionally asymmetric in Newton’s physics. Take Newton’s second law of motion, which states that force equals mass times acceleration. Acceleration is here understood as instantaneous rate of change of velocity, and Newton’s calculus is needed to describe this concept in mathematical terms. The laws of motion then presuppose the mathematical principles of the calculus, which further enable the formulation of these laws. It is precisely these functional asymmetries between the mathematical component and physical components of a scientific theory that suggest to Friedman that the formal component functions as a set of constitutive a priori principles that make empirical laws both stateable and testable. Downloaded from https://academic.oup.com/book/33532/chapter/287885625 by Temple University user on 15 May 2024 8.4 The Constitutive A Priori and the Coordination Problem 158 robert sinclair Downloaded from https://academic.oup.com/book/33532/chapter/287885625 by Temple University user on 15 May 2024 As we have seen, when Quine examines the logical connections between theory and observation and further emphasizes the systematic aspirations of scientific knowledge, he too stresses the importance of functional asymmetries between parts of this overarching theoretical structure. Here scientific theory is presented as a systematic structure that takes the general principles found in logic, mathematics, and theoretical physics as fundamental for all other scientific areas. More specifically, Quine thinks that the laws of more specific sciences, such as the physical sciences discussed by Friedman, presuppose logic and mathematics in terms of their formulation and application to empirical events. In addition, we saw that logical laws establish the necessary links between the peripheral and core areas of scientific theory, which thereby enable scientific laws and theories to have empirical content at all. Like Friedman’s view, logical laws are necessary presuppositions for the formulation and empirical application of physical law. Quine takes such basic systematic principles to have a special status within our theories, where they represent significant epistemic commitments that enable the formulation of such theories and which further secure their empirical credentials. His holism contains structural theoretical principles that count as presuppositions for empirical laws, which then mirror the kind of structural requirements found with Friedman’s introduction and use of constitutive a priori principles. The further issue concerns whether Quine’s view captures the ‘constitutive’ function that Friedman assigns to the a priori principles needed for the formulation of empirical laws. Even with the introduction of asymmetric structure within Quine’s account, we still have what may appear to be two contrasting pictures of the system of scientific knowledge. Friedman offers us several distinct levels of dynamical principles that interact to produce his ‘stratified system of knowledge’. On this view, the constitutive a priori principles of logic and mathematics provide the framework within which empirical laws can be formulated but still retain a distinct level removed from empirical testing and confirmation. While Quine’s holistic view of knowledge maintains a centrality and generality for logic and mathematics, he famously rejects any sharp theory-wide divide between a priori and empirical elements of that system. He accepts that system and structure is required for scientific knowledge, but without the need for a sharp distinction between a priori framework principles and empirical principles that can be confirmed through experience. That distinction is, for Quine, insignificant for epistemological purposes, since the specific appeal to analyticity to mark out such a divide fails to offer an empiricist explanation for a priori knowledge. By assigning an a priori status to formal principles Friedman suggests a stratification of levels that appears to conflict with Quine’s rejection of any epistemically significant analytic–synthetic distinction. That Friedman’s view may suggest such a division between logic, mathematics, and science appears when he maintains that constitutive principles are revised ‘in response to empirical findings’ but are not rejected on the basis of empirical testing (2001: 71). In order to see if this is a significance difference between them, we need quine’s structural holism and the constitutive a priori 159 16 Here I disagree with Carlson who claims that the functional asymmetries he finds in Quine’s holism are able to show in a way similar to Friedman’s views that “logical laws are required in order to coordinate empirical phenomena with the rest of our overall theory” (2015: 17, my emphasis). 17 For example, Russell’s famous example ‘The present King of France is bald’ presupposes that there is one and only one present King of France (Friedman 2001: 74). Downloaded from https://academic.oup.com/book/33532/chapter/287885625 by Temple University user on 15 May 2024 to further clarify the a priori status of the constitutive principles that Friedman deems fundamental to both the structure of scientific knowledge and which explains revolutionary change in science. We will see that because such principles are not used to explain a priori knowledge or justification but only to highlight a key functional and structural element in science (an ‘a priori element’ we may say), their a priori status does not result in the type of analytic–synthetic distinction that would worry Quine. However, this will further reveal that the importance of constitutive a priori principles stems from the key problem of coordinating mathematical principles with concrete physical phenomena, which Friedman takes as central for understanding scientific change and the formulation of scientific knowledge (2001: 33–42, 71–82). Quine’s view does not attempt to address this ‘coordination problem’ and it is here, then, that we can locate the central difference between his and Friedman’s respective views.16 We have seen the way Friedman emphasizes that his a priori framework principles are revisable in response to empirical findings, but that they still retain Kant’s constitutive function of providing the necessary conditions for empirical science. He expands on this idea in the following way: ‘Since they formulate the necessary conditions or rules for establishing empirical knowledge, a priori principles cannot themselves be similarly established; and it is in precisely this sense that they are prior to or independent of experience’ (2001: 73). But what does it mean here to stress that they serve as necessary conditions? Friedman responds to such concerns by noting that necessary conditions cannot simply mean where A is a necessary condition for B then B implies A. To claim that A is a constitutive condition of B is to claim that A is a necessary condition not simply for the truth of B but of B itself possessing a truth value or being meaningful. For example, Newton’s law of universal gravitation uses the concept ‘absolute acceleration’ which has no empirical application or meaning unless his three laws of motion hold. In other words, empirical sense can be made of the law of universal gravitation by presupposing that the laws of motion are themselves true. If this is not the case then it is not possible to even raise the issue of the empirical truth or falsity of the law of universal gravitation (2001: 74). However, this characterization is not strong enough to capture Friedman’s neoKantian version of the constitutive a priori, since it may appear to apply to any empirical statement.17 Instead he argues that constitutive a priori principles, as presuppositions of the meaningfulness of empirical scientific claims, be reserved for those logical and mathematical principles which are taken to be basic presuppositions of all empirical truth. Friedman notes that the special status given to these presuppositions is due, in large part, to their generality with regard to empirical, natural facts, a point 160 robert sinclair The Newtonian laws of motion are thus presuppositions of the properly empirical laws of Newtonian physics (such as the law of gravitation) in the sense considered earlier, but they are presuppositions of a very special sort. Their peculiar function is precisely to mediate between abstract mathematical representations and the concrete empirical phenomena these abstract mathematical representations are intended to describe. As such, they do in fact fulfill the characteristically constitutive function first delimited by Kant, and accordingly, they have a genuine claim to be thereby considered constitutive a priori. (Friedman 2001: 77) We are then presented with the following view of physical theory as containing three central asymmetrical functioning elements: 1. A mathematical part (mathematic and geometric principles) that contains the basic mathematical theories that are used to describe the space-time framework. (In the case of Newton, Euclidean geometry) 2. A mechanical part (coordinating principles) that function to provide a correspondence between the mathematical element and the empirical component. (Newtonian laws of motion) 3. An empirical part (physical principles) that uses the concepts of the mathematical part to formulate empirical laws that describe concrete empirical phenomena. (Newton’s law of universal gravitation) (Friedman 2001: 79–82; Tsou 2010: 437) Here, the principle of coordination found in the mechanical part (in this case, the Newtonian laws of motion), are used to establish a correspondence between the mathematics in question (Newton’s calculus) and concrete empirical phenomena so that precise laws of nature (law of universal gravitation) can be formulated and which further will then possess empirical meaning. Given this threefold division, the laws of nature found in the physical part of our theory can be empirically tested (Friedman 2001: 80). It would be wrong, however, to view the other parts of the theory as empirically tested in the same way, something that Friedman thinks is a consequence Downloaded from https://academic.oup.com/book/33532/chapter/287885625 by Temple University user on 15 May 2024 that we saw Quine also emphasize. But their special status goes further with a problem that develops in the context of modern mathematical physics. As the mathematical tools of modern physics have become increasingly abstract in relation to concrete sensory experience there emerged a problem of coordinating these new mathematical representations with that experience. Friedman explains that Newton’s laws of motion serve as constitutive principles that establish a coordination between the abstract mathematics that is fundamental to Newtonian physics and the empirical phenomena to which such abstract conceptual tools are intended to apply. Importantly, without these general coordination rules we have no way to understand what it would mean for empirical events to be described in terms of this mathematical framework (Friedman 2001: 76–7). In other words, without these coordination principles we have no way to understand what it would mean to describe empirical phenomena using these abstract mathematical concepts. Friedman expands on this point in the following way: quine’s structural holism and the constitutive a priori 161 18 Friedman notes the way Carnap’s attempted formulations of the analytic-synthetic distinction obscured the crucial importance of the coordination problem. This then encouraged many to see Quine’s holism as the sole remaining option (Friedman 2001: 82). Downloaded from https://academic.oup.com/book/33532/chapter/287885625 by Temple University user on 15 May 2024 of Quine’s holism. The mathematical part considered independently of empirical application is not tested, but it is the specific coordination where mathematical structures are used to formulate empirical laws that is subject to this testing. Moreover, the coordinating principles contained in the mechanical part are not empirically tested either since the required testing procedure cannot be set up without such principles in place first. Once his account is further clarified along these lines, we see, once again, the way Friedman’s use of the constitutive a priori highlights the structural role played by mathematics and logic as a needed presupposition for empirical science. However, this does not simply point to a structural asymmetry between a priori and empirical principles. This asymmetry is used to note the different functions played by various parts of our theory, where this is especially seen with the distinctly modern problem of knowledge involving the coordination of abstract mathematics with empirical, natural phenomena. The constitutive a priori is then introduced to address this problem, when it was recognized that we require a prior set of mathematical principles for the formulation of empirical laws that are themselves not established empirically. Friedman is not then introducing an a priori–a posteriori divide in order to provide a satisfactory empiricist account of a priori knowledge or justification. Moreover, we saw that he agrees with Quine’s argument against Carnap’s attempts to clarify the analytic–synthetic distinction (2001: 33). We can now see that the importance of stressing the a priori, formal elements in scientific knowledge stems from their central epistemological function in enabling the coordination of the abstract and the empirical required for scientific knowledge.18 Quine’s structural holism has much in common with this view. Like Friedman’s view it recognizes the centrality and generality of logic and mathematics for scientific theories, while also highlighting the asymmetric nature of such principles as formal, structural presuppositions needed systematic scientific knowledge. While Quine then rejects the idea of a priori justification, he still recognizes the epistemological significance of formal, mathematical principles in virtue of their role in structuring empirical scientific knowledge. Moreover, although Quine affirms only one general standard for empirical justification for all statements, this does not, for him, mean that mathematics and logic are empirical in the same way as every other science, something that we saw suggested by some of Friedman’s remarks (2001: 35). Recall the kinship he finds between mathematics, logic, and theoretical physics. They equally participate in the most general and systematic aspects of natural science, furthest from observation and they receive support from observation only indirectly through the way they contribute (that is, structure) an organized system that fits with observation (Quine 1986a: 100; Hylton 2002). Friedman emphasizes stratified levels of principles to distinguish his view from what he sees as Quine’s undifferentiated holism, but 162 robert sinclair 8.5 A Shared Kantian Viewpoint To see the compatibility between their respective positions we need to recognize how their differences are located in the divergent ways in which they examine scientific theories. Quine examines the structure of scientific theory and its relationship to observation from the standpoint of a logician, one with his own distinctive conception of the nature of logic. By contrast, Friedman looks at scientific theories from the standpoint of historical change and examines how the interlocking roles played by mathematics, mechanics, and empirical laws help explain the rationality of historical scientific change. The Kantian idea that emphasizes the asymmetry between the logical and the empirical is then applied from two different perspectives on scientific theories. For Quine this asymmetry is a feature of scientific theories when they are treated as relatively fixed logical structures. Friedman on the other hand, notes the way asymmetry is a feature of the logical structure of a scientific theory as it Downloaded from https://academic.oup.com/book/33532/chapter/287885625 by Temple University user on 15 May 2024 his view also shows a general acceptance of the idea that abstract mathematics and formal logic are only indirectly supported through their structural contributions to systematic theory. As a result, once we see Quine’s commitment to this asymmetric structure between formal and empirical principles, and his further emphasis on the kinship between formal principles and theoretical physics, his view looks very similar to Friedman’s. However, Friedman’s discussion of the way the constitutive a priori highlights the need for a coordination between abstract mathematics and empirical phenomena points to a real difference with Quine’s holism, involving a divergence over how the formal is related to the empirical in order to enable empirical testability. While Quine notes structural asymmetries between logic, mathematics, and the rest of science he does not note the way such functional differences between mathematical and empirical principles indicate the distinctly modern problem of the ‘coordination’ between the abstract formal frameworks and empirical events. On Quine’s account the functional asymmetries between logic and empirical science yields his holism of theory testing, which explains prediction and modification to theory by means of hypothetico-deductive method. Friedman’s emphasis on the further need for a priori coordination principles suggests a more fundamental way in which formal presuppositions enable empirical testability since it addresses how this contributes to revolutionary scientific change. This may give the impression that Quine’s view fails to fully account for the role of constitutive a priori principles in establishing systematic scientific knowledge. But given that their views of scientific structure both share the key Kantian idea of the need for formal presuppositions in science suggests that their perspectives be seen as complementary rather than opposed. In section 8.5 I will briefly argue that they are indeed compatible and that this allows us to see them as more alike than standard accounts suggest. quine’s structural holism and the constitutive a priori 163 Philosophy is in large part concerned with the theoretical, non-genetic underpinnings of scientific theory; with what science could get along with, could be reconstructed by means of, as distinct from what science has historically made use of. If certain problems of ontology, say, or modality, or causality, or contrary-to-fact conditionals, which arise in ordinary language, turn out to not rise in science as reconstituted with the help of formal logic, then those philosophical problems have in an important sense been solved: they have been shown not to be implicated in any necessary foundation of science. (1976: 151; also see Ricketts 2004) Here, Quine offers logic as an adequate framework for science because it permits the clear formulation of the logical connection or ‘bridges’ that link scientific theory to what he would later call ‘observation categoricals’ that enable empirical testability.19 Quine sketches this approach where he speaks of his interest in the ‘logical structure of empirical evidence’ and his further insistence that this can be done by explaining how scientific theory is tested through prediction using little more than logical analysis (1992: 1–2, 18). In doing so, he argues that we can examine more closely the relation of evidential support where theory is tested by prediction (1992: 1–2). Beginning with his acceptance of hypothetico-deductive method as central to science, he further emphasizes how our background theory logically implies the truth of a certain claim and if this turns out to be the case we then continue to accept our theory as vindicated for the moment (1992: 9). If the claim is false then modifications to the theory are needed that preserve as much of it as possible while also preventing the false 19 Observation categoricals are generalizations built out of observation sentences, where the fulfilment of one is invariably followed by the fulfillment of the other. Examples would include: ‘Whenever it rains, it pours’, ‘Wherever there’s smoke, there’s flame’. Quine further takes these generalizations as capturing what happens in experimental situations when a hypothesis is being tested. For further details see his (1992 and 1995). Downloaded from https://academic.oup.com/book/33532/chapter/287885625 by Temple University user on 15 May 2024 historically changes. Explaining revolutionary change in science may very well need the additional epistemic role Friedman assigns to the constitutive a priori for addressing the coordination problem, but Quine’s more historically ‘static’ holistic view is still capable of highlighting the important way formal and mathematical laws are presupposed by the empirical explanations offered by scientific theory. My suggestion is that Quine’s view is best seen as capturing the logical structure of science, including its relation to observation, when considered as a relatively stable activity, where scientists proceed with the kind of piecemeal modifications to theory carried out within normal science through the standard process of hypothetico-deductive method. Friedman’s view looks at the kind of modifications characteristic of revolutionary scientific change and is thus central for understanding how formal principles can be coordinated with the empirical events within the context of such revolutionary conceptual changes in modern science. Since they discuss these different phases of scientific theorizing, I see their perspectives as largely compatible. Quine’s logical, ahistorical perspective on scientific theories is clearly evident from the following passage: 164 robert sinclair The mathematical representations employed in modern physics have become increasingly abstract in relation to concrete sensory experience. Infinite Newtonian space is not sensibly given like finite Aristotelian space - nor is natural inertial motion given like natural Aristotelian motion, uniform Newtonian time like uniform Aristotelian time. For precisely this reason, however, there is a new problem of somehow coordinating our new mathematical representations with concrete sensible experience before we are even in position to be fully explicit about our new physical theory actually says. (Friedman 2001: 76, emphasis in the original) With the advent of this problem, we need further resources to help explain revolutionary historical change in science. It is here that Friedman’s account of the constitutive Downloaded from https://academic.oup.com/book/33532/chapter/287885625 by Temple University user on 15 May 2024 implication (1992: 13–15). This viewpoint is clearly connected to the systematic view of science that we attributed to Quine in earlier sections, and the key idea concerning the way formal, logical considerations are central epistemic presuppositions or commitments needed for scientific theories to have empirical content. All of these ideas (logic as a tool for clarifying the way theory is connected to evidence, the asymmetric character of the formal and empirical, logic itself as a prior epistemic commitment of our theorizing) are best understood as facets of the application of formal logic to theories treated as fixed logical structures, where Quine provides a logical schematization of the everyday work of normal science, highlighting the way hypothetico-deductive method is used to modify scientific theories. Importantly, even if Quine sometimes uses historical examples to motivate this view, his account is not designed to explain historical revolutionary scientific change. Friedman’s viewpoint is, of course, predicated on his explicit interest in understanding the revolutionary historical development of scientific theories, more specifically mathematical physics, and he rightly perceives the deficiencies of Quine’s holism in accounting for these changes. Quine’s use of hypothetico-deductive method to explain the way theories as whole require modification in the face of failed prediction is seen by Friedman as clearly insufficient: ‘But can this beguiling form of epistemological holism really do justice to the revolutionary developments within both mathematics and natural science that have led up to it?’ (2001: 29–35). From this perspective seen here, Friedman is clearly right that this view lacks sufficient resources to explain such historical developments, however, as we have seen above, it was never intended as providing a historical account of scientific change. Rather, Quine treats theories as stable logical structures and then proceeds to use formal analysis to clarify various philosophical problems concerning empirical testability and ontological commitment. The acceptance by both Friedman and Quine that the special status of mathematics and logic is partially explained by their generality and centrality for empirical scientific knowledge does not explain historical scientific change. Friedman then seeks to address this problem by emphasizing the important role played by the constitutive a priori in solving what I have called ‘the coordination problem’. He describes the nature of the historical situation in these terms: quine’s structural holism and the constitutive a priori 165 8.6 Conclusion Friedman and Quine share the central Kantian insight concerning the asymmetry between ‘the formal’ and the empirical, where the former must be presupposed in the formulation of scientific laws and theories. However, the coordination problem highlights the central difference between their respective views. I have claimed that Friedman is right in thinking that we need a different perspective to account for this problem within the context of revolutionary scientific change. Quine treats theories as static logic structures, and can only depict the sorts of predictive failure and modification to theory that occurs during normal science, but not explain how new mathematical, mechanical tools yield the conceptual scientific advances needed to make sense of revolutionary scientific change. Quine’s claim that no statement is immune from revision merely highlights the possibility of such revolutionary change, since the rejection of mathematics and logic would result in widespread revisions to our theory. But this does not offer an explanation of how such changes might work to account for scientific change.21 Friedman’s account of the constitutive a priori then stands as an explicit attempt to address a historical problem central for understanding scientific change: namely the coordination problem. However, this should further help us see that Quine and Friedman treat theories from different philosophical perspectives that examine distinct facets of scientific activity. This coupled with their general acceptance of the Kantian asymmetry between the formal and empirical, should lead us to conclude that their different perspectives on science serve to complement each other. Lastly, we can recognize, rather surprisingly, the 20 Friedman provides more detailed historical examples illustrating the need for constitutive a priori principles for addressing this problem in (2001: 71–92). 21 Quine’s remarks about radical revisions to mathematics and logic within his holistic view of theory testing suggest to Friedman a historical motive for this view (2001: 29). However, this simply shows that such revisions are consistent with possible revolutionary changes in science but does not explain them. The limits of Quine’s position then highlight the need for the complementary historical account of the very sort offered by Friedman and his use of the constitutive a priori. Downloaded from https://academic.oup.com/book/33532/chapter/287885625 by Temple University user on 15 May 2024 a priori becomes significant, since it is this conceptual innovation that is responsible for addressing the coordination problem of modern scientific knowledge and for this explaining how science changed in order to solve it. As we have seen earlier, in this particular case, the Newtonian laws of motion serve as principles of coordination in order to establish a correspondence between the mathematics of Newton’s calculus and concrete empirical phenomena so that his law of universal gravitation can be formulated so to apply to concrete experience.20 Friedman’s account is then vital for helping explain how conceptual innovation and historical change in science while departing further from concrete experience was nonetheless still able to maintain this connection through the use of constitutive a priori frameworks as coordinating principles. 166 robert sinclair complex ways in which they both accept a key Kantian insight about science: empirical theories require formal constraints for their very formulation as empirical theories.22 References 22 I would like to thank Frederique Janssen-Lauret for her editorial work on this volume. Comments from two anonymous referees helped to improve an earlier draft. 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(2004) ‘Frege, Carnap, and Quine: Continuities and Discontinuities’ in S. Awodey and C. Klein (eds) Carnap Brought Home: The View from Jena. Chicago, IL: Open Court, 181–202. Sinclair, R. (2012) ‘Quine and Conceptual Pragmatism’, Transactions of the C. S. Peirce Society 48: 335–55. Sinclair, R. (2016) ‘On Quine’s Debt to Pragmatism: C. I. Lewis and the Pragmatic A Priori’ in F. Janssen-Lauret and G. Kemp (eds) Quine and his Place in History. Basingstoke: Palgrave Macmillan 76–99. Stump, D. (2003) ‘Defending Conventions as Functionally A Priori Knowledge’, Philosophy of Science, 70: 1149–60. Tsou, J. (2010) ‘Putnam’s Account of Apriority and Scientific Change: Its Historical and Contemporary Significance’, Synthese, 176: 429–45.