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1. The Traditional Mind-Body Problem

        The traditional mind-body problem is ontological. It addresses the fundamental nature of the conscious and cognitive mind and the relationship between mental and physical events. Arguably, it is this ontological focus that has kept the problem open even after more than one century of groundbreaking work in the behavioral and brain sciences. These sciences have already discovered physical events correlated empirically with specific mental events. But the further claim that all mental events are numerically identical to physical events remains controversial. Doubters can still insist that this increase in empirical knowledge has not produced any philosophical advance over historical materialisms (ones formulated prior to this increase in empirical knowledge).
        Consider one example. Neuropsychologists have discovered that the capacity of primates (humans included) to recall and act upon explicit memories of previous episodes depends upon activity in subcortical structures in the brain’s medial temporal region (especially the hippocampus and hippocampal formation). Empirical evidence includes both clinical and experimental documentation that bilateral damage to these structures severely impairs performance on tasks requiring subjects to use this type of memory (Kandel and Squire, 1999). (In humans, bilateral damage to these structures produces a pathological syndrome called global amnesia. See Kolb and Whishaw, 1996.) But one can still insist that it remains as mysterious as ever to identify the experienced episodic memory with electrochemical activity in these neural regions, or even to claim that this activity is a component or part of the mental event. What does knowledge about the location of correlated neural activity, or even details about the underlying cellular and molecular events, contribute toward reducing the perennial mystery? (This intuition, expressed using different arguments and focusing on different features of conscious mental events, motivates the much-discussed recent criticisms of physicalism by Thomas Nagel 1974, 1989, Jackson 1983, and Chalmers 1996.) Philosophy of mind remains to this day the battleground over which two ontological intuitions clash, seemingly without hope of rational resolution:

  1. That the nature and core properties of mental phenomena as ordinarily conceived and experienced assures that they cannot be identical to physical (i.e., neural) events;
  2. That the domain of the mental should ultimately be brought under the scope of our otherwise comprehensive and wholly physical scientific world-view.

2. A Contemporary Perspective

        As a way to break this deadlock, it has been fashionable for nearly four decades to construe intuition 1 as resting on allegiance to a primitive theory—"folk" or "common sense" psychology—deeply ingrained in existing human cultures. The central posits of this theory, beliefs and desires, are said to be theoretical expressions, constructed to explain and predict behavior. The "ontological facts about the mental," paraded as "conceptually autonomous" by defenders of intuition 1, depend upon constitutive principles and generalizations of this theory. Some find this construal exciting because it can ground an eliminativist account of the mind. Future scientific research and theory might reveal the scientific impropriety of folk-psychological principles and generalizations, as past science did with folk theories of witchcraft and proto-scientific theories about caloric fluid. If this happens, eliminativists conclude that the mind as ordinarily conceived and experienced does not exist, in the same way that witches and caloric fluid doesn’t exist (Feyerabend 1963; Rorty 1970, Paul Churchland 1981, 1989; Patricia Churchland 1986). But one need not be an eliminativist to find value in this "folk theory" construal of intuition 1. This construal also allows us to reformulate the traditional mind-body problem as first and foremost a question about intertheoretic relationships, and only secondarily as an ontological question. Our justified ontological conclusions about the fundamental nature of the mind (as ordinarily conceived and experienced) will depend upon whether the appropriate intertheoretic relationship(s) obtain between folk psychology and its scientific successors (scientific psychology, neuroscience). Historically in science, intertheoretic reduction has been a relation thought to yield cross-theoretic ontological conclusions about the entities and properties of the reduced theory. For obvious reasons, I’ll call the resulting approach the Intertheoretic Relation (IR) Reformulation of the mind-body problem. Its guiding hope is that by reorienting the traditional issue away from its ontological focus, and making the ontological conclusion justified by—secondary to and dependent upon—the methodologically prior intertheoretic reduction issue, the deadlock that surrounds the traditional problem might be overcome: in a way that brings to bear some of the rich and rigorous resources of 20th century philosophy of science and contemporary cognitive and brain science upon this perennial philosophical issue.

3. The IR Reformulation is Born Following Ernest Nagel’s (1961) Theory of Intertheoretic Reduction

        The early identity theories of U.T. Place (1956) and J.J.C. Smart (1959) did not utilize any account of intertheoretic reduction. But after Ernest Nagel’s (1961) work filtered beyond the philosophy of science, his account—especially his "temperature-to-mean molecular kinetic energy" example—became a common physicalist resource. It became so common that Fodor (1974) took himself to be attacking the entire reductionist program in philosophy of mind by pointing out difficulties that the "special sciences" pose for Nagel’s account. In footnote 2 Fodor asserted (without argument) that "many of the liberalized versions of reductionism suffer from the same base defect as what I shall take to be the classic form of the doctrine." (The "classic" form was built on Nagel’s account, published thirteen years prior to Fodor’s essay. Some works become classics very quickly!)
        In the spirit of logical empiricism, Nagel held that the reduction of one theory to another consists of a logical derivation of the laws or principles of the former (the reduced theory TR) from the laws or principles of the latter (the reducing or basic theory TB). In interesting cases, where TB’s descriptive vocabulary lacks terms from that of TR ("heterogeneous" cases, as Nagel 1961 called them), various "correspondence rules" or "bridge principles" must be introduced to effect the derivation. Eschewing niceties and many details, we can represent Nagel’s account as follows:

TB & BP (as necessary)

logically entails


BP stands for whatever bridge principles are necessary to connect up disparate elements of TR’s with TB’s vocabulary. Also in the spirit of logical empiricism, Nagel characterized TR, TB, and BP syntactically, as sets of statements or propositions.
        The traditional mind-body problem focuses on the ontological status of mental properties, states, and events as ordinarily conceived and experienced. Reformulated in light of the "theory" status of folk psychology (as the theory with which our common sense mentalistic ontology is affiliated) and Nagel’s theory of intertheoretic reduction, the issue becomes: Will future cognitive and brain science develop theories (TB’s) from which, with appropriate BPs, the generalizations of folk psychology (TR) are derivable? If physicalism about the (common sense) mental is to be defended in light of this reformulation, some theory from the physical sciences must occur at the end of a chain of reductions: from folk psychology to . . . to, e.g., neuroscience. And each link in this chain must meet the demands that Nagel’s account places on the intertheoretic reduction relation.
        What does the IR reformulation accomplish? What do we achieve by reformulating the traditional issue in this fashion? First, it replaces the murky notion of "ontological reduction" with a well-studied, (circa early-1960 philosophy of science), scientifically-grounded notion: intertheoretic reduction. It allows proponents to appeal to cases from the history of science to defend future psychology-to-physical science reductions. Taking intertheoretic reduction as the central issue provides clear and defensible verdicts about the variety of philosophical arguments brought to bear on the traditional mind-body problem. Evidence and arguments relevant to deciding for or against predicted future psychology-to-physical science theory reductions are legitimate; evidence and arguments irrelevant to this issue are not. One interesting consequence of this methodological prescription is that the familiar philosophical tactic of "conceptual separability" thought experiments often used to "prove" non-identity—our capacity to imagine the one property or event occurring in the absence of the other—is irrelevant. There are plenty of properties and events affiliated via the bridge principles in intertheoretic reductions that can be "conceptually separated": lightning and large-scale atmospheric electron discharge, for example. Nevertheless the identities in these cases have been established on clear scientific grounds. Yet consider the number of recent anti-physicalist arguments that rest upon the "logical possibility" of e.g., conscious minds in physical vacuums or unconscious zombies with functioning human nervous systems. If the IR reformulation captures the traditional mind-body problem, this popular tactic is irrelevant. The underlying arguments are invalid: conceptual separability does not imply theoretic irreducibility, from which cross-theoretic identities can follow. The methodological upshot is significant: we can finally address questions about the ontology of mind from the perspective of a rigorous philosophy of science.

4. The Revolt Against Nagel

        As philosophers of mind began applying Nagel’s account to the mind-body problem, the account itself came under decisive attack within the philosophy of science. Constructed within the logical empiricist program, Nagel’s account incorporated that program’s strengths and weaknesses qua theory of science. One weakness, stressed increasingly throughout the 1960s, was its assumption about the continuity of scientific progress. Reduction as deduction of TR from TB reflects this assumption. Modus tollens and logical consistency both require that if some principles of TR are false, then something in the reducing complex must be, also. But this consequent contradicts the assumed truth of TB and the BPs. Careful historical analysis revealed that principles of the TR in some "textbook" scientific reductions are false. Falling bodies near the surface of the earth do not really exhibit uniform vertical acceleration over any finite interval. Yet this assumed uniformity is central to Galilean physics. Galilean physics is empirically false. It does not describe correctly the behavior of falling objects in any portion of the actual world. Yet the reduction of Galilean physics to Newtonian mechanics is a "textbook" historical case of the relation.
        For many historical examples (including the one just discussed), Nagel’s account can handle falsity in the principles of TR with a simple addition to the premises of the derivation. These must include not only the principles of TB and the appropriate BPs, but also various and often counterfactual boundary conditions or limiting assumptions (BC/LA) on the applicability of TB. In the Galilean physics-to-Newtonian mechanics case, we can conjoin with the Newtonian principles either a counterfactual assumption describing conditions near the surface of the earth that permit uniform vertical accelerations over a finite interval, or a counterfactual assumption that limits the applicability of Newton’s laws to moving bodies that fall distances only negligibly greater than zero. From this reducing complex the principles of Galilean physics (TR) can be derived, and their falsity is explained by and hence confined to the counterfactual BC/LA component.
        Yet this strategy cannot handle every historically-acknowledged reduction of a false TR. Sometimes a TR turns out to be so "radically" false that central elements of its ontology must be rejected as illusory or completely uninstantiated. This creates a problem for the status of the BPs. Referents of the descriptive terms of TB cannot be identical to nor nomologically connected with the "referents" of descriptive terms of TR if the latter are non-existent or nowhere instantiated. And some central posits of "textbook" TRs appear to meet this condition. Relativistic mass is a two-place relation between an object and countless reference frames. Classical mass is a one-place property of objects. A two-place relation can never be identical to a one-place property, Relativistic mass is never even co-extensive with classical mass at any actual velocity. Strictly speaking, classical mass is nowhere instantiated in physical reality: no physical object actually has that property. So what is the logical status of a BP that "bridges" these elements of the disparate theoretical vocabularies: especially if we construe BPs as laws? Neither synonymy nor material identity between the terms’ extensions are plausible interpretations. And no BC/LA appears to alleviate this "radical" falsity within the TR.
        Close historical investigations into actual scientific practice and results revealed a number of intertheoretic reductions that implied significant corrections to the TR. Even the case that Nagel (1961) used to illustrate his approach turned out to involve a significantly false TR: classical equilibrium thermodynamics-to-statistical mechanics and microphysics. This case is a limit reduction, and the limits in which the laws of equilibrium thermodynamics can be derived from statistical mechanics are never actually realized (e.g., an infinite number of gas particles whose diameter divided by the average distance between particles is only negligibly greater than zero). At best, equilibrium thermodynamical explanations approximate the actual microphysical events and their statistical distributions. Second, many key thermodynamical concepts fragment into distinct statistical mechanical/microphysical concepts, with each of the latter being the appropriate candidate for "identification" within the appropriate limit. (Clifford Hooker 1981 demonstrates this point for "entropy.") Third, a diachronic view of this case reveals mutual developmental feedback between the TR and TB. Problems confronting classical thermodynamics (TR) spurred the application and development of statistical approaches. And the injection of statistical results and developments (TB) back into classical thermodynamics yielded corrections to the latter resulting in more accurate predictions. (Hooker 1981 provides a nice introduction to these details. Bickle 1998, chapters 2 and 3, shows how to capture some of these details within a quasi-formal account of the intertheoretic reduction relation, discussed further in section 7 below.)
        What consequences do these features have for the ontology of classical thermodynamics? Hooker (
1981) is explicit on this point: "In a fairly strong sense thermodynamics is simply conceptually and empirically wrong and must be replaced" (p. 49). This quote reflects one important criticism against Nagel’s account. Intertheoretic reductions in actual science typically imply significant corrections to the TRs. Beyond a point, these corrections make logical empiricist proposals for handling falsity within the TRs increasingly untenable.
        Criticisms like this one spurred a variety of alternative approaches to reduction. Patrick Suppes (1956, 1965) proposed characterizing scientific theories semantically, in terms of a set of models sharing some set-theoretic structure. He in turn characterized intertheoretic reduction as set-theoretic isomorphism (the formal analog of "sameness of structure"). He applied his account explicitly to psycho-physiological reduction: "The thesis that psychology may be reduced to physiology would be for many people appropriately established if one could show that for any model of a psychological theory it was possible to construct an isomorphic model within physiological theory" (1965, p. 59). His account turned out to be too weak, however. Kenneth Schaffner (1967) pointed out that "different and nonreducible (at least to one another) physical theories can have the same formal structure—e.g., the theories of heat and hydrodynamics—and yet we would not want to claim that any reduction could be constructed here" (p. 145). In other words, Suppes’ account implied that obvious cases of non-reducibility meet the conditions on an intertheoretic reduction. So set-theoretic isomorphism is too weak: its obtainment is not sufficient for intertheoretic reduction.
        Another alternative that received more attention is often attributed independently to Karl Popper (1962), Paul Feyerabend (1962), and Thomas Kuhn (1962). This approach focused on the difficulties that obtain in trying to characterize a "close fit" between a TR and "special cases" of the TB (i.e., those cases already cordoned off from TB proper by application of counterfactual BC/LAs). Its central contention held that in addition to explaining why the TR works in situations where it does, the TB must also explain why the TR fails in other expected applications. In this sense, successful reductions correct the TRs. Feyerabend (1962) famously expressed this contention by denying that reductions involve deductions at all. Instead, he insisted that "ontological replacement" was the key to understanding the relationship between a TR and its "incommensurable" TB. He went so far as to call for philosophers of science to abandon the search for any formal or "objective" account of intertheoretic reduction or scientific progress.
        Like Suppes, Feyerabend also applied his approach explicitly to the "mind-body problem":

      In the course of the progress of knowledge, we may have to abandon a certain point of view and the meanings connected with it—for example, if we are prepared to admit that the mental connotations of mental terms may be spurious and in need of replacement by a physical connotation according to which mental events, such as pain, states of awareness, and thoughts, are complex physical states of either the brain or the central nervous system, or perhaps the whole organism. (1962, pg. 30)

He advocated this view (albeit cautiously at first) for "all so-called mental states." Using the resources of his approach to reduction, the philosopher of mind’s agenda is to "develop a materialistic theory of human beings." Such a result would "force us to abandon the mental connotations of the mental terms, and we shall have to replace them with physical connotations" (1962, p. 90). Within a reformulation of the traditional mind-body problem built on Feyerabend’s approach to reduction, eliminative materialism received it first serious expression and defense.
        Eliminative materialism remains deeply controversial. Its current status makes it enlightening to look back at the writings of some famous "identity theorists" throughout the mid-1960s, as their views came under attack. Feyerabend’s eliminativism and his "radical empiricist" philosophy of science that undergirded it began to look increasingly attractive. Just four years after his influential (1959) paper, for example, J.J.C. Smart claimed to be

      attracted to P.K. Feyerabend’s contention that in defending materialism we do not need to show its consistency with ordinary language, any more than in defending the general theory of relativity we need to show its consistency with Newtonian theory. . . . Feyerabend is perhaps therefore right in arguing that the scientific concept of pain does not need to be (and indeed should not be) even extensionally equivalent with ordinary language. (1963, p. 660)

Four more years later, Smart clarified his (cautious) change in view. He admitted to being even closer to Feyerabend, both in philosophical methodology and eliminativist conclusion, in an attempt to stave off an "ordinary language" criticism of his earlier "topic-neutral translation" approach to mental terms:

      I am even doubtful now whether it is necessary to give a physicalist analysis of sensation reports. Paul Feyerabend may be right in his contention that common sense is inevitably dualistic, and that common sense introspective reports are couched in a framework of a dualistic conceptual scheme. . . . In view of Bradley’s criticisms of my translational form of the identity thesis, I suspect that I shall have to go over to a more Feyerabendian position. (1967, p. 91)

Nor was Smart the only famous identity theorist attracted to Feyerabend’s resources and results. In his (1967) postscript, Herbert Feigl also moved explicitly toward Feyerabend’s views: "I now agree with Smart (and perhaps with Feyerabend) that within the conceptual frame of theoretical natural science genuinely phenomenal (raw feel) terms have no place" (p. 141). He cited a scientific analogy that later became prevalent in eliminativist writings: the properties of common sense physical objects vis-à-vis their "successor concepts" from physical science. He concluded that "the phenomenal predicates used in the description of after-images, sensations, feelings, emotions, moods, etc., are to be replaced by the (as yet only sketchily known) neurophysiological and ultimately microphysical characterizations" (1967, pp. 141-142). (However, Feigl 1967 shied away from some of the radical consequences of these views that Feyerabend embraced, appealing to some of Wilfrid Sellars’ ideas in an attempt to soften them.)
        In light of the themes I am developing here, these shifts toward Feyerabend’s philosophy of science and eliminativist conclusions by early identity theorists are important for at least two reasons. First, they demonstrate how intractably dualistic is our common sense ("folk") conception of the mental. It is not just extremely difficult to find some kind of physical "translation" for mental terms (even via a "topic neutral" intermediary): it is probably impossible. Second, these capitulations to Feyerabend show how attractive philosophers of mind found resources from the philosophy of science. Every account of intertheoretic reduction that was taken seriously by philosophers of science was adopted quickly and explicitly by philosophers of mind in an attempt to reformulate the traditional mind-body problem.
        And so the IR reformulation developed on the back of accounts of intertheoretic reduction. "Ontological reduction" and "linguistic analysis" gave way to potentially clearer (and increasingly clarified) notions of intertheoretic reduction. For many, philosophy of mind became a specialized part of applied philosophy of science—the philosophy of the cognitive and brain sciences and their cross-theoretic relations—albeit a part with special intrigue, since we are its subject matter.

5. Nagel’s Insights Revived and Modified: Schaffner and Hooker

        Attractive as some early identity theorists found Feyerabend’s approach, most Anglo-American philosophers of science were less enamored by it. Consensus held that his views were too radical, too dismissive of precise, formal resources to illuminate scientific concepts and historical episodes. (As radical a critic of orthodox logical empiricism as Thomas Kuhn 1962 maintained that the majority of scientists spent the majority of their careers doing "normal science," i.e., puzzle-solving within an accepted paradigm). Even cases of wholesale theory change—physical optics-to-electromagnetism, classical thermodynamics-to-statistical mechanics and microphysics, Newtonian mechanics-to-special relativity theory—seem to approximate the formal relations proposed by Nagel and other logical empiricists. Feyerabend dismissed the possibility of accounting for this sense of "approximation," but many philosophers of science proceeded on the assumption that something like it could be clarified. What resulted were accounts of intertheoretic reduction that incorporated weakened Nagelian conditions, in an attempt to capture features of scientific history and practice emphasized by Feyerabend and other radical empiricists.
        Kenneth Schaffner’s (1967) General Reduction Paradigm, later developed more fully and renamed the General Reduction-Replacement (GRR) model (Schaffner 1992), was the first important attempt explicitly to conciliate Nagelian conditions with radical empiricist historical insights. Schaffner’s model included conditions of connectability and derivability that yielded Nagel’s exact conditions as special cases. But it included "corrected" reducing and reduced theories (TB* and TR*, respectively) that weakened these general conditions. Connectability and derivability between TB* and TR* permitted these relations to hold in cases where (actual) TB corrects (actual) TR by making more accurate predictions in TR’s domain of application (at least potentially). (See Schaffner 1992, p. 321, for the detailed conditions.) Furthermore, TB (or TB*) explains TR in that TR and TR* stand in a relation of "strong analogy." Hence since TR* is derivable from TB (or TB*), this being Schaffner’s weakened condition of derivability, the latter indicates why TR "worked as well as it did historically" or explains TR’s domain "even when TR is replaced" (Schaffner 1992, p. 321). These weakened notions "allow the "continuum" ranging from reduction as subsumption to reduction as explanation of the experimental domain of the replaced theory" (Schaffner 1992, p. 320). Cases that closely approximate Nagel’s conditions coalease around the first pole; cases with features emphasized by the radical empiricists coalease around the second. Both orthodox logical and radical empiricist intuitions were thereby accommodated within Schaffner’s GRR model. (Although it must be noted explicitly that Schaffner has yet to explicate the relation of "strong analogy" between corrected TR* and actual TR.)
        Schaffner offers a further reason in support of his GRR model: the same one we saw emphasized in the previous section. He writes: "The flexibility of the GRR model is particularly useful in connection with discussions concerning current theories that may explain "mental" phenomena" (1992, p. 320). The IR reformulation lives on! Schaffner showed in detail how his model applies to a case of (potential) reduction in psychology and neurobiology: the neural mechanisms of short-term and long-term learning as revealed by cellular studies in the sea slug, Aplysia californica (1992, p. 323-329; Bickle 1998, chapter 5, discusses related features of this same example). Although the cellular and molecular explanations Schaffner discusses are now somewhat dated (see, e.g., Kandel and Squire 1999 for a good introduction to the current account), the lessons he stressed from this extended discussion remain topical. According to Schaffner (1992)

  • This case does not involve laws akin to those in "textbook" cases of reduction from physics (p. 329).
  • The reducing complex is an intricate system of causal generalizations with a variety of scopes of applicability (from nervous systems in general to specific types of neural processes). These generalizations are not framed within the vocabulary of a specific science (e.g., biochemistry), but rather are characteristically interlevel (e.g., containing terms from biochemistry, molecular biology, cellular neurophysiology, neuroanatomy, and behavioral psychology) (p. 330).
  • When a phenomenon described at one level (e.g., the behavioral, as "sensitization") gets explained in lower-level terms (e.g., molecular mechanisms), the former description is mapped into the lower-level vocabulary (pp. 330-331).

It is by virtue of this last feature that Schaffner’s GRR generalization of Nagel’s conditions of connectability and (in light of expected developments in biochemistry, i.e., the development of some "corrected" TB*) derivability obtain. The point relevant to my concerns is that Schaffner’s GRR model appears supple enough to handle the special complexities and details that psychology-to-neurobiology reductions generate, yet it retains Nagelian-inspired conditions of connectability and derivability. And it achieves this concilience using a case that emphasizes actual scientific details, far beyond the extent that is typical in philosophy of science or mind.
        Clifford Hooker (1981) provides another approach that amounts (in part) to a weakened set of Nagel-inspired conditions. Hooker agrees that intertheoretic reduction involves deduction, with TB and possibly counterfactual BC/LAs serving as premises. But unlike Nagel, the conclusion of the derivation is not TR; and unlike Schaffner, it is not a corrected TR* of TR. Instead, what gets deduced is an equipotent isomorphic image IB of TR, specified within the conceptual framework and vocabulary of TB. The generalizations comprising IB match the syntactic structure of those comprising TR and provide explanations (using the resources of TB) of TR’s domain of application. Simplifying, and ignoring some complexities, we can express Hooker’s account as follows:

TB & BC/LA (as needed)

logically entails

IB (a set of theorems of [restricted] TB)

e.g., (x)(Ax Bx), (x)((Bx & Cx) Dx)

which is relevantly isomorphic to ("analogous to")


e.g., (x)(Jx Kx), (x)((Kx & Lx) Mx)

(I adopt this schema from Paul Churchland 1985. The example is meant only to be illustrative of the "analog relation" between IB and TR. It is not intended to ground an analysis of the relation (which, incidentally, neither Hooker nor Churchland ever provides).) It is important not to confuse Hookewr’s deduced structure IB with Schaffner’s TR*. Hooker’s IB is characterized completely within the framework and vocabulary of TB; Schaffner’s TR* is a corrected version of TR. This difference yields the very different ways that Hooker and Schaffner attempt to capture radical empiricist insights within a modified Nagelian account, and every topic discussed in the remainder of this section hinges on this difference. (For this reason, I’ve changed the symbol Hooker 1981 uses to denote the "analog structure.")
        Hooker acknowledged explicitly the radical empiricist insights about scientific history and progress built into his approach. But his guiding intuition is Nagelian:

      While the construction of IB within TB might be a complicated affair—[BC/LA] might be fearfully complex (cf. biological reductions), counterfactual (e.g., assume continuity), necessarily counterfactual qua realization (e.g., "force free"), and so on—the ultimate relation between TB and IB remains straightforward deduction. (1981, p. 49)

Even his justification of this feature is Nagelian: "TB continues to directly explain IB and this is the basis for TB’s indirect explanation of TR’s erstwhile scientific role" (1981, p. 49). Hooker’s guiding idea is that deduction is necessary for explanatory unity, which remains one goal of his approach to reduction: a goal he shares with logical empiricists.
Notice that the premises of the deductive component of a Hooker reduction do not contain bridge principles (BP), unlike either Nagel’s or Schaffner’s approach. None are needed to effect the derivation. IB is already specified within (a restricted portion of) TB. There are no disparate vocabularies to bridge across premises and conclusion. Structures analogous in some ways to BPs appear in the second stage of the reduction, involving IB and TR. But these components are only ordered pairs of terms that indicate the substitutions in IB that yield the actual generalizations of TR. By themselves, these ordered pairs imply neither synonymy, material identity, nor coextension. Thus one central difficulty with Nagel’s approach vanishes: that of specifying the logical status of BPs in reductions implying significant falsification to the TRs.
Earlier in this section we saw that Schaffner’s (1992) generalizations of Nagel’s conditions of connectability and derivability yielded a spectrum of reductions, ranging from ones in which Nagel’s actual conditions are closely approximated to others displaying features emphasized by radical empiricists. Hooker’s approach yields a similar spectrum, ranging from "relatively smooth" to "extremely bumpy" intertheoretic reductions. A case’s location depends upon the "amount of correction" implied to the TR, the "closeness of fit" obtaining between the IB and TR. Cases approximating Nagel’s relation fall near the "smooth" endpoint. The derived IB is equipotent and strongly analogous in structure to the TR, and few counterfactual BC/LAs are needed to derive it from the TB. (Historically, the physical optics-to-electromagnetism reduction seems to reflect these conditions.) Cases involving features emphasized by radical empiricists fall toward the bumpy endpoint. Only an IB weakly analogous to TR can be derived from TB, and this only with the help of numerous and wildly counterfactual BC/LAs. (Historically, the phlogiston theory-to-oxidative chemistry case seems to reflect these conditions.) "Mixed" cases sharing some features of both extremes fall on the spectrum separating these two endpoints, depending on the "amount of correction" implied to the TR (captured in these two conditions, the strength of analogy between IB and TR and the number and counterfactual nature of the BC/LAs necessary to derive such an IB). (Problematic historical cases for logical empiricism, like the classical thermodynamics-to-statistical mechanics and microphysics reduction, seem to reflect these conditions.) However, it is crucial to realize that according to Hooker’s account, the TR itself is never deduced, not even in the "smoothest" cases. Rather, it is always the target of a kind of complex mimicry.
If Hooker’s account of reduction nowhere employs BPs, how does it justify the cross-theoretic ontological consequences typically thought to follow from an intertheoretic reduction? Such consequences are justified by a higher-order relational feature of the intertheoretic reduction. Not only do historical intertheoretic reductions line up on a spectrum (just described): the cross-theoretic ontological consequences drawn in specific cases do, also. The latter range from entity and property/event identities (visible light is electromagnetic radiation with wavelength between 350-750h m) to significant conceptual revision (pressure p and temperature T of a gas are only identical to statistical mechanical/microphysical constructs in an empirically unrealizable mathematical limit) to outright elimination (there is no such thing as phlogiston). When we lay out the location of historical reductions on these two spectra—the intertheoretic reduction "amount of correction" spectrum and the ontological consequences spectrum—we discover a rough isomorphism. A case’s location on the intertheoretic reduction spectrum correlates closely with its location on the ontological consequences spectrum (see the diagram in Bickle 1998, p. 30). This observation suggests a strategy for predicting the ontological consequences of a developing or potential intertheoretic reduction. First discover where on the intertheoretic reduction spectrum the case appears to be headed (in terms of "amount of correction" to TR). How equipotent and structurally analogous is an image IB of TR derivable within TB? How numerous and wildly counterfactual are the BC/LAs needed to effect the derivation? Which historical reduction does the case seem most closely to resemble in these respects? Answers will locate the developing or potential case on Hooker’s intertheoretic reduction spectrum. The predicted ontological consequences will then be those obtaining at the roughly isomorphic location on the other spectrum. The isomorphism across the two spectra that permits this approach are, as emphasized above, inspired by cases from the history of science.
We can now see how Hooker’s theory of reduction leads further support to the IR reformulation of the traditional mind-body problem. It generates another argument in favor of this approach: the "everything in its place" argument (Bickle 1998, chapter 2). All the influential "solutions" to the traditional problem emerge as specific predictions about the future intertheoretic reducibility (or lack thereof) of folk psychology to proposed scientific successors. As we saw above, the traditional mind-body problem is about the ontological status of mental states and events as ordinarily conceived and experienced. This ontology is commonly assumed to be the one affiliated with folk psychology qua explanatory theory of cognition and behavior. Substance dualism thus becomes the prediction that folk psychology will not reduce completely to any physical science (although it might reduce completely to some future science of nonphysical substances and their properties). We remain committed to the entities and properties postulated by our best explanatory theories. Property/event dualism becomes the prediction that the ultimate reducing theory for folk psychology will still postulate special nonphysical (emergent?) properties (essential subjectivity, intrinsic intentionality, qualia): perhaps ones that obtain only in complex collections of physical entities. Behaviorism becomes the (unlikely) prediction that the best future scientific psychology will be some autonomous behaviorist account, to which folk psychology will smoothly reduce. This result will yield identities between specific mental states and specific behavioral dispositions. Functionalism (aka cognitivism, classical computationalism) becomes the prediction that the best future science of mind will be some cognitivist/computationalist theory, autonomous from the physical sciences, to which folk psychology will smoothly reduce. This result will yield identities between specific mental states and specific nodes in a processing network mediating between perceptual inputs, other "internal" processing states, and behavioral outputs. The mind-brain identity theory becomes the prediction that folk psychology will smoothly reduce to some future neuroscience (perhaps by way of reducing first to some scientific psychology that in turn reduces to the neuroscience). This result will yield identities between specific mental states and specific brain states, events, and processes. Finally, eliminativism becomes the prediction that folk psychology will only reduce in bumpy fashion to whatever future scientific theory best explains human cognition and behavior; eliminative materialism in particular predicts that neuroscience will provide the best theory and an ultimately bumpy reducer for folk psychology. The result will be an elimination of mental states and events as ordinarily conceived an experienced from our best scientific ontology.
Two additional observations dovetail with this argument. First, this "everything in its place" argument answers the question as to why so few influential solutions to the traditional mind-body problem have emerged (Searle 1985). The above solutions, reformulated as predictions about possible future intertheoretic reductions, by and large exhaust the sciences that have been investigated seriously to develop a comprehensive explanation of human cognition and behavior. Second, the spaces between the "smooth" and "bumpy" endpoints on the intertheoretic reduction spectrum and the "retention" and "replacement" endpoints on the ontological consequences spectrum provide for the possibility of a "revisionary" outcome for folk psychology (Bickle 1998, chapter 6). There are a variety of historical cases useful as models for a revisionary psychophysical reduction, e.g., classical thermodynamics-to-statistical mechanics and microphysics and classical mechanics-to-general relativity theory. Ontologically speaking, revisionary physicalism predicts enough conceptual change to rule out cross-theoretic identities between folk psychology’s propositional attitudes, developing neurophysiological posits, and their theoretically central properties. It differs in this fashion from reformulated identity theory. However, it also denies that folk psychological kinds will undergo the radical elimination that befell, e.g., phlogiston and caloric fluid. One kind of cognitive representation concept, the sententially-structured folk psychological one, will be replaced by a different cognitive representation concept emerging from developing neuroscience. This is exactly the result that obtained in historical revisionary reductions. Relativity theory still posits a length concept, a mass concept, and a velocity concept: just not the specific ones from classical mechanics. If a revisionary intertheoretic reduction obtains between folk psychology and some neuroscientific successor, it will yield significant conceptual change that will rule out strict cross-theoretic identities. But it will not yield wholesale elimination of the caloric fluid/phlogiston variety.
An IR reformulation grounded on Hooker’s theory of reduction suggests a promising approach for addressing the traditional mind-body problem. Perhaps it afford resources that can break the impasse stressed in section 1 above. But at least two big problems remain. First, we’ve seen nothing in the IR reformulation presented so far that addresses the most influential criticism in the philosophical (and cognitive-psychological) literature against the possibility of psychophysical reduction: the "multiple realizability" argument . Second, Hooker’s theory of reduction is subject to serious criticism from within the philosophy of science. It is handwaving about detailed applications to historical cases (and silent regarding detailed applications to current psychophysical cases), leaving the key notion of an analog structure IB without a clear illustration. And as Hooker (1981) himself admits, his concept of the analog relation between IB and TR lacks precise formulation. Without some answer to these shortcomings a Hooker-inspired IR reformulation remains problematic. What can be said in its defense?

6. Handling Multiple Realizability

        Just as intertheoretic reduction was being brought to bear on the issue, Hilary Putnam and Jerry Fodor (among others) were emphasizing the problem that multiple realizability raises for psychoneural reduction. (Putnam published a number of papers throughout the 1960s that developed this theme; key ones are reprinted in his 1975 collection. Fodor extended these arguments in his 1974 essay and the first chapter in his 1975 book. Bickle 1999 reviews key themes in the literature, but see Bickle 1998, chapter 4, for a more detailed, technical discussion.) The contention is that a given mental type (property, state, event) is realized by a variety of distinct physical kinds sharing nothing of significance at that level of description. Putnam’s now-familiar example was pain (see especially his 1967 essay): the same pain state seems ascribable to creatures with very different nervous systems (humans, rats, octopi, and so on), and perhaps even to beings lacking terrestrial nervous systems (silicon-based space aliens, appropriately programmed digital computers). But then any postulated type-identity or "reduction" of pain to any one of its multiple physical realizers is false.
Not only was multiple realizability the central premise in influential arguments against early mind-brain identity theories; it also served indirectly in arguments for functionalist theories of mind. (Fodor 1981, "Introduction," describes this connection nicely.) And although functionalism has by now been by and large replaced by nonreductive physicalism as the dominant theory of mind in Anglo-American philosophy, proponents of the new orthodoxy adopt uncritically the functionalist multiple realizability criticism of psychophysical reductionism (see, e.g., Horgan 1993). So the question that any proposed IR reformulation of the mind-body problem must answer is: Do any recent accounts of intertheoretic reduction skirt the multiple realizability challenge?
First, notice that if multiple realizability is a premise in a sound argument for functionalism, the IR reformulation proposed above finds a place for that theory of mind. Functionalism emerges as the prediction that folk psychology will reduce rather smoothly to a functionally-specified cognitive/computational psychology, with the latter remaining autonomous from lower-level physical sciences (perhaps due to multiple realizability). Fodor (1981) seems to have exactly this picture in mind when he lists some "common sense psychological etiologies" and urges their lesson:

      Seeing that a is F is a normal cause of believing that a is F; the intention that it should be the case that so and so is a normal cause of actions whose goal is to bring it about that so and so; statements that P are normally caused by beliefs that P . . . The point of such examples is not, of course, that any of them are likely to figure in serious cognitive psychology. It is rather that our attempts at a serious cognitive psychology are founded in the hopes that this kind of generalization can be systematized and made rigorous. (pp. 25-26)

A smooth intertheoretic reduction of folk psychology (qua collection of "common sense psychological etiologies") to a "serious cognitive psychology" would be one clear way to "systematize and make rigorous" this kind of generalization. So even if multiple realizability establishes the autonomy of psychology (folk or scientific) from physical sciences, this fact alone would not nix an IR reformulation of the traditional mind-body problem. Indeed, this fact can be accommodated within it.
Still, the IR reformulation has obvious roots in physicalist reduction projects. We saw in sections 1 and 2 above that the approach is motivated by the attempt to bring the mind within the scope of physical science. Can psychophysicalism be salvaged from the multiple realizability challenge by adopting some alternative approach to intertheoretic reduction?
Some early replies to Putnam and Fodor utilized resources from theories of reduction. Robert Richardson (1979) pointed out that Nagel (1961) himself countenanced conditional bridge principles in intertheoretic reductions. Although Nagel’s examples employed biconditional bridge principles, all the "connectability" that his condition of derivability required was one-way conditionals: For all x, if Bx [predicate of reducing TB], then Rx [predicate of reduced TR]. And conditional bridge principles are consistent with the multiple realizability of TR types: as B’ in TB, B’’ in TB’’, and so on.
Another popular reductionist reply rested upon an insight first noted by David Lewis (1969). Intertheoretic reductions are typically domain-specific. Berent Enç (1983) and Patricia Churchland (1986), among others, have pointed out that domain specificity obtains in the "textbook" reduction of classical thermodynamics-to-statistical mechanics and microphysics. Temperature in a gas is mean molecular kinetic energy. Temperature in a solid is a different statistical mechanics/microphysical property, mean maximal molecular kinetic energy, because the molecules in a solid are bound up in lattice structures and are restricted to a variety of vibratory motions. Temperature is multiple realized in distinct statistical mechanical/microphysical states, and yet it is a central reduced kind in the paradigm case from the history of science. Clearly, multiple realizability alone is not enough to block an intertheoretic reduction. Jaegwon Kim (1993) builds domain specificity directly into his very concept of reductive bridge principles. In "local reductions" cross-theoretic bridge principles have the form, "For all x, if Sx, then Bx if and only if Rx," where S is a predicate denoting a type of structure in the appropriate branch of science. Different Bs (typically) occur in the embedded biconditional for different structure types, accommodating multiple realizability. According to Kim, local reductions "are the rule rather than the exception in all of science, not just in psychology" and are "reductions enough . . . by any reasonable scientific standard and in their philosophical implications" (1993, p. 257).
However, this strategy does not handle all types of multiple realizability. Since Fodor (1974), psychophysical anti-reductionists have emphasized a more radical sense of the relation. Call the sense introduced by Putnam " multiple realizability across physical structure types": distinct types of physical structures realize a given mental kind differently. The domain specificity reply undercuts an anti-reductionist argument built on this sense. But now consider "multiple realizability within a token system across times": a single instance of a cognitive system might realize a given mental type in different types of physical states at different times. (The terms for these two senses are from Bickle 1998, chapter 4.) The plasticity of mammalian brains—in responding to trauma, changing task demands, developmental processes, and the neural mechanisms of learning—suggests that this more radical sense of multiple realizability is genuine. Ned Block (1978) once suggested that narrowing the scope of psychological generalizations to handle Putnam’s sense of multiple realizability (by way of the domain specificity approach just discussed) would render legitimate comparative psychology across species problematic (not to mention routine methodologies in experimental psychology using animal models!). But a psychology narrowed enough in domain specificity (scope of applicability) to handle this more radical sense of multiple realizability—generalizations applicable only to individuals at times—would surely render it insufficient to accommodate even the most minimal assumed generality of science.
Appeals to scientific practice and history can give the physicalist some ammunition against arguments built on this more radical sense of multiple realizabiltiy. Pertaining specifically to psychoneural reduction, Kim (1993, chapter 16) and Bickle (1998, chapter 4) point out that a guiding methodology in contemporary neuroscience assumes continuity of underlying physical mechanisms both within and across individuals and species. This assumed continuity is more than a mere analogy, especially at the level of cellular and molecular neuroscience, and informs most experimental techniques, research paradigms, and theoretical conclusions. (Special techniques also exist to control for idiosyncratic activity on individual trials: e.g., subtraction techniques in PET (Positron Emission Tomography) imaging. See Posner and Raichle 1994.) If the radical sense of multiple realizability really obtained to the degree stressed by anti-reductionists, the experimental techniques of contemporary neuroscience would have borne little fruit. But clearly these techniques are effective and not hopelessly naïve, and this is evidence that the kinds postulated by psychological theories might not be as radically multiply realized as anti-reductionists imagine. Why has a detailed study of the macaque’s visual system been so instructive for learning about the human’s? Why has PET and functional magnetic resonance imaging (fMRI) revealed common areas of high metabolic activity across and within individual humans, down to a resolution of less than 1 mm (and promising to go lower as techniques and analytical tools improve)? (See Posner and Raichles 1994.) Even neural plasticity is a systematic process. It follows a regular progression both during development and following damage to a principal structure. There are underlying neural mechanisms that subserve it in all its forms, and the cellular and molecular mechanisms are shared across a wide variety of creatures (Kandel and Squire 1999). In addition, function is often compromised following serious neural damge. Persons can still, e.g., talk, manipulate spatial representations, or move their limbs, but their performance is typically degraded. This fact gives rise to tricky questions about individuation of mental types. Do these distinct pre- and post-plasticity neural events realize the same mental kind?
Appealing to science generally, Enç (1983) and Bickle (1998) suggest that this radical sense of multiple realizability is also present in historical cases of intertheoretic reduction, including the paradigm classical thermodynamics-to-statistical mechanics and microphysics case. For any token aggregate of gas molecules there is an indefinite number of microphysical realizations of a given temperature: a given mean molecular kinetic energy. So even this radical sense by itself appears not to block an intertheoretic reduction. (Bickle 1998, chapter 4, also argues that exactly this sense of multiple realizability is emerging between propositional attitude and cognitive neuroscientific/"connectionist" theories of representational content.)
So proponents of the IR reformulation can adopt the following attitude toward the multiple realizability challenge, expressed eloquently by Hooker:

      It is often argued that, e.g., cognitive psychology cannot be reduced to neurophysiology because the former cross-classifies the latter: any number of different systems (from brains to machines to leprechauns passing notes) could realize the same functional or computational theory. It helps to remove the intellectual dazzle of this fact to realize that this is true of any functionally characterized system. The same cross-classifications turn up within such prosaic fields as electrical engineering (cf. "is an amplifier of gain A" vis-à-vis particular circuit diagrams) and physics (cf. "is a high energy electron source" vis-à-vis quantum specification). (1981, p. 505)

(Notice that at least the latter case clearly admits of indefinite realizations in the same token high energy electron source over time: the more radical sense of multiple realizability). The key is a better understanding of intertheoretic reduction across all of science. Hooker continues: "In these cases, the issue is not whether reduction is possible, but how it goes. The same applies, I hold, between theoretical domains as well" (1981, p. 505). According to Hooker, any theory of reduction must handle multiple realizability of reduced on reducing kinds. Any theory that does not is insufficient for science generally, not just for the cognitive and brain branches.
This section is not intended to be a comprehensive review of the multiple realizability literature and its implications for philosophy of mind. All that I have attempted to do here is to indicate ways that alternative approaches to reduction in the philosophy of science and their application to philosophy of mind can address some of the issues. Establishing that multiple realizability does not spell immediate doom for IR- reformulated psychophysical reductionism is enough for my present purposes. But this brings us now to the crucial step: is there an account of intertheoretic reduction that is sufficient for science generally and capable of handling the special complexities raised by potential psychology-to-neuroscience reductions? Or is the IR reformulation ultimately a hopeless approach for addressing the traditional mind-body problem?

7. New Wave Reduction

        Up to this point I’ve stressed the advantages of Clifford Hooker’s account of intertheoretic reduction as the basis for an IR reformulation of the traditional mind-body problem. Now it is time to address the shortcomings. Although Hooker (1981) mentions numerous historical cases of scientific reduction in presenting his theory, he never applies it to the quantitative details of any particular example. Nor does he analyze the concept of the "analog structure" IB much beyond the simple schema presented in section 5 above. This lack leaves this central notion in his account mysterious. Second, as he himself reluctantly admits, he is unable to give a precise formulartion to his equally central concept of the "analog relation" between IB and TR. This latter concept grounds Hooker’s idea about the "amount of correction" implied to TR via its reduction, and in turn the entire intertheoretic reduction spectrum between "smooth" and "bumpy" cases. He writes: "Unhappily, I can think of no neat formal conditions which would intuitively separate the two" (1981, p. 223). He hints that "category-theoretic methods" might ultimately give some quantitative account of "comparative preservation indices" for a theory’s "theoretically relevant properties," and subsequently for its posited entities and events (1981, p. 224). But he admits that "all of this is very programmatic and as yet lacking in deep yet simple insight" (1981, p. 224). To date, Hooker has not returned in print to this lacuna.
Bickle (1998, chapter 2) takes on this first shortcoming by reformulating in Hooker-reduction terms the mathematical derivation of the classical ideal gas law (pV = nrT) from Avogadro’s hypothesis, the universal gas constant, kinetic-theoretic assumptions about the nature of microparticles, and principles of Newtonian mechanics. A step of mathematical rearranging to standard treatment of this derivation yields an equation containing only quantitative expressions from statistical mechanics and microphysics that mimics exactly the ideal gas law (Bickle 1998, pp. 34-39). Although the mathematical details are beyond the scope of this essay, this result gives a clear example of the structure of an IB in an actual scientific case. Happily, it also illustrates a case that lies midway between the "smooth" and "bumpy" endpoints on the intertheoretic reduction spectrum.
However, the second shortcoming is less tractable using the resources Hooker himself develops. To address it, Bickle (1998, chapter 3) proposes adopting a fundamentally different account of theory structure. He draws on work from the "structuralist" program in philosophy of science, initiated by Joseph Sneed (1971) and Wolfgang Stegmüller (1976) and developed most completely and rigorously in Balzer et al. (1987). This program builds upon earlier developments of the semantic view of theories (Suppes 1956, 1965), which characterized theory structure not as a set of sentences or propositions but rather as a set of models meeting specific set-theoretic conditions. (See the brief discussion in section 4 above.) The structuralist literature on intertheoretic reduction contains two principal accounts, one constructed self-consciously to capture Nagelian intuitions (Balzer et al. 1987, chapter 5), the other constructed to capture Thomas Kuhn’s alternative (Mayr 1976). Bickle’s goal was to build Hooker’s concept of the analog structure IB, once illuminated by the detailed quantitative application to the classical thermodynamics-to-statistical mechanics and microphysics case mentioned in the previous paragraph, into the basic structuralist account. His proposed result is a precise, semi-formal account of "location on the intertheoretic reduction spectrum." The structuralist concept of a "blur," extended by Bickle to apply to intertheoretic relations, even provides a rough cardinal estimate of the "amount of correction" implied to TR in specific cases. Application of another structuralist resource, "ontological reduction links" (Moulines 1984), even provides the account with an answer to an objection that Schaffner (1967) leveled against related set-theoretic accounts of reduction. In a later chapter, Bickle seeks to reconstruct semi-formally parts of the reduction of a schematic propositional attitude psychological theory to a connectionist-inspired counterpart (1998, chapter 5).
The technical (set-theoretical) details of Bickle’s account are complex and beyond the scope of this essay, but the basic intuition behind the details is straightforward. Instead of characterizing intertheoretic reduction in terms of syntactic derivations, the "new wave" approach construes the relation as the potential constructability of an image of (the set-theoretic structure of) TR within TB. New wave psychoneural reductionism is the prediction that as psychology and neuroscience develop matured theories, this "constructable image" condition will obtain. Evidence for this prediction is the fact that this relationship is obtaining already, in recent (and still sketchy) cognitive psychological and neuroscientific theories. (Bickle 1998, chapter 5, cites some details of the "learning-long-term potentiation" link as an actual case in point. In Bickle forthcoming he extends this treatment to more recent discoveries from cellular and molecular neuroscience.) The upshot is that the challenge Hooker (1981) was unable to meet can be addressed when his insights about reduction are reconstructed and extended within an alternative model of scientific theory structure.
"New wave" reductionism and its IR reformulation of the traditional mind-body problem is a viable approach—and at present, the most fully developed one—for defending psychophysical reduction. It is the current heir to the tradition running from U.T. Place and J.J.C. Smart through Ernest Nagel and Paul Feyerabend to Kenneth Schaffner, Clifford Hooker, and Paul and Patricia Churchland (to name just a few). In the best tradition of scientifically-informed philosophy, it seeks to weave together both philosophy of science and the best current science itself, and to apply the resulting mosaic to more traditional questions of perennial philosophy: specifically, the mind-body problem.

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