This rough idea sufficed so long as we concentrated on the status of the physical universe as a whole. We could ignore problems about what sort of relation is supposed to obtain between the physical entities, as defined by PE in §3.1.1, and organisms, sentience, intentions, values and the rest. But physicalism claims to be a kind of unified theory or synthesis of all the diverse sciences, and indeed of all the domains of truth in or out of the sciences. Physicalism thus claims to provide the new, unified picture of existence that should replace the largely medieval one shattered piecemeal by successive discoveries in the sciences. So we must inquire into the techniques of this alleged unification.

Until recently physicalists and others generally assumed that the key relation, if physicalism were to succeed, must be one of reduction. Physical reduction, in the sense relevant here, occurs when terms from another domain are defined solely by terms from physics. Different views as to the variety of definition admissible for this purpose give rise to different varieties of reduction. The strongest variety requires that the two terms -- one nonphysical, the other from physics -- be fully synonymous, or at least "translatable" one into the other without significant loss of meaning. The weakest requires only that they be coextensive. Somewhere between is a coextensiveness that is not accidental but entailed by the laws of science, hence a lawlike coextensiveness. And there are still other varieties of reduction weaker than synonymy but stronger than accidental coextensiveness.

In some cases a variety of reduction does succeed. Thus the absolute temperature of a gas is identical with the mean kinetic energy of its molecules; the two terms are lawlike coextensive, thanks to the kinetic theory of gases. And thanks to ongoing discoveries about DNA and RNA, a few terms from Mendelian genetics (some structural terms, like `heterozygous') are coextensive with certain terms from molecular biology, though perhaps not (yet) lawlike coextensive. A few more terms from Mendelian genetics might be reduced to those of molecular biology, if Mendelian genetics were to be suitably modified. Indeed it often happens that a theory must be modified if reduction of its terms is to succeed; what is loosely called reduction of that theory's terms to those of another is really reduction of the modified theory's terms.

In many cases, notoriously, reduction either has been shown to fail or has not been shown to succeed to the satisfaction even of many physicalists. Talk about persons, intentions, consciousness and the functional states of organisms, for example, seems especially resistant to reduction even of the weakest kind, whereby the terms need only be accidentally coextensive with certain terms from neurophysiology and eventually from physics.

There is no need to review here the obstacles encountered by the reductionist enterprise. They are numerous, severe and vigorously expressed by many authors, including a growing number of physicalists.

Perhaps the most insurmountable obstacle is that certain functional states and intentional states seem not to be identifiable with any particular physical states, and not even with finite sets of alternative physical states. One and the same functional or intentional state can be realized or embodied in an indefinite variety of distinct physical systems, and perhaps even in an indefinite variety of distinct physically specifiable states of the same physical system. Functional and intentional states are defined without regard to their physical or other realizations.

The idea that physicalism does not after all entail reductionism is not especially new, and by now may even be widely accepted. But the claim merely that physicalism need not be reductive is not very illuminating. Like a number of recent sketches of nonreductive physicalism, it is mute on the following urgent questions. If no variety of reduction need obtain, what then is the relation between the physical phenomena and the nonphysical? How are the terms and truths in other domains related to the terms and truths in physics, if not at least by accidental coextensiveness? How can physicalists bring off their attempt to unify all the domains, in or out of the sciences? In what sense are the truths in the higher domains -- biology, psychology, history and so on -- determined by or manifestations of truths at the level of physics, if not via some sort of reduction? How can it be that nothing occurs at these higher levels without some occurrence at the level of physics, so that there is "no difference without a physical difference"?

Answers to these challenges appear below, in the sections on the physicalist's minimal theses -- the weakest one could accept and remain a physicalist. In slogan form, the minimal principles are (i) `Everything is physical' (§4.1), (ii) `No difference without a physical difference' (§4.2), (iii) `All truth is determined by physical truth' (§4.3), and, if not already implicit in these three, a realism of the sort explained in §1.1. The realism would be implied if, for example, the kind of systematic unity (i)-(iii) presuppose requires our physical theories to be true, not merely empirically adequate, as seems likely. The challenges are met in the sense of explaining what the minimal principles are by which physicalists believe they can relate the other domains to mathematical physics, and thereby achieve their kind of unification.

Of course merely explaining what the minimal principles are is not directly to argue for their truth. It is simply to give some clear idea of what they are and how they function, and thereby to answer the complaint that "In the literature it is possible to find at least a half dozen accounts of what [physicalism] is, no pair of which is equivalent and all of which are desperately obscure." The principles to be explained are modifications of those due originally to Hellman and Thompson, but they prove equivalent, nearly enough, to some of the notions of "supervenience" subsequently developed by others. Eventually someone might develop minimal physicalist principles that are preferable. If so, suitable revisions in this chapter and some to follow would be required. But the improved principles would so closely resemble those discussed in §§4.1-4.3 that no very fundamental changes would be necessary.

The minimal version of physicalism is distinguished from other versions by a number of things it is not. The following list of nots will serve also to preclude stereotyping this version as just more of the same dreary old materialist dogma.

To begin with, the minimal version does not exclude emergent entities and properties (such as, presumably, organisms, persons, works of art, languages and so on, plus certain of their properties). An entity or property is emergent or "novel" with respect to a domain (such as physics), roughly, if our term for it cannot be defined by any terms from the domain (hence not "predicted" by any truths from the domain). The kinds of definition relevant here are those mentioned above, which range from full synonymy to accidental coextensiveness. Thus an entity or property is emergent with respect to a domain if the term (or terms) for that entity or property cannot be reduced to any term from that domain, in any of the above senses of reduction. Since nonreductive physicalism requires none of these varieties of reduction, clearly it is compatible with the existence of emergent entities and properties.

Nor is the minimal version eliminative, as we see in §§4.5-4.6. It does not entail, for example, that there are no persons, minds, feelings, sensations, thoughts, freedoms or whatever. Nor does it entail that all talk about such things is either false or meaningless or otherwise defective, or that it ought to be replaced, or even someday might be replaced by talk about purely physical things.

Also, it is not an identity theory, typically so-called (according to which all properties and states of things are really physical properties and states). True, like all versions of physicalism the theory must require that any entity mentioned outside physics -- a person, say -- is identical with something in the physicalist's inventory of what there is. In this trivial, limiting sense the minimal theory is an identity theory, meaning, in the jargon of the trade, a token-token identity theory (meaning in turn that each particular entity or event of some general type N is identical -- token-identical -- with a particular mathematical-physical entity or event, even if the type N is not itself identical -- type-identical -- with any physical type). But of course any metaphysics is an identity theory (that is, a token-token identity theory), insofar as it must claim that everything at bottom is somehow token-identical with or constituted from certain basic entities or processes, whether physical, mental, spiritual or whatever. When a theory does not entail that everything is at least token-identical with something or other in some ontology O, then either the theory is not a metaphysics in the first place, or it is one whose inventory exceeds O.

Note also that an entity or state x could be token-identical with something in the physicalist's inventory without being token-identical with something in the inventory that satisfies a term (or a complex of terms) from physics or even the neurosciences (where a [complex of] P-term(s) is understood to be a first-order open sentence whose only nonlogical words are the P-terms). The vocabulary of physics and neuroscience, in this sort of case, would be incapable, by itself, of picking out or individuating x; for x would not be denoted by any term from (or definable by) such vocabulary (where a term is said to be definable by a given P-vocabulary only if the term is [necessarily] coextensive with some first-order open sentence whose only nonlogical words are from the P-vocabulary). We could not say that x is nothing but a physical entity, meaning that all of x's (characteristic) traits are physical traits. Moreover, certain states and (other) abstract entities (if abstracta exist) can be token-identical with something or other in the physicalist's inventory, as we see in §4.1, without being token-identical with some spatiotemporal whole composed of parts that are basic physical entities. We could not say of such an x that it is nothing but some whole composed of such parts.

Thus nonreductive physicalism, unlike identity theories typically so-called, does not require x to be individuatable by any clearly physical or other scientific term, does not require x to be some ST-whole composed of basic physical entities, and perhaps above all does not require nonphysical states and properties to be type-identical with physical states or properties. Nor does the minimal version entail any particular theory of mind, whether an identity theory (again typically so-called), eliminitivism, functionalism or whatever, though of course these theories are all motivated by some sort of materialism (and functionalism by a nonreductive sort).

Nor is the minimal version an "embodiment" theory, according to which a person, say, is a particular embodied in a certain physical entity, where the embodiment relation is sui generis -- a relation neither of instantiation, nor set-membership, nor composition of parts into a whole. Instead, embodiment is said to be a relation such that if x and y are both particulars, then x is embodied in y iff: (i) x is not identical with y; (ii) the existence of x presupposes the existence of y; (iii) x instantiates some properties that y does and some properties that y does not; (iv) the individuation of x presupposes the existence of some embodying particular; and (v) y is not a part of x.

The problem with embodiment versions of physicalism is not that the embodiment relation is unclear (though some philosophers might argue it is fatally unclear). Rather, the relation is all too clear in precluding x, which is not a universal but an embodied particular, from being identical with (cf. clause (i)) or composed of (clause (v)) any embodying entity y, whether or not y is denoted by some physical term. But if x is not identical with something or other in the physicalist's inventory, then x exceeds the physicalist's ontology. Embodiment versions, evidently, are not really versions of physicalism. They posit an extra sort of entity. By contrast, the minimal version avoids the embodiment relation, relying instead on relations of instantiation or realization (§4.5) to characterize the relations between bodies and properties or states of persons, in such a way that persons do not exceed the physicalist's inventory of what there is, and yet are not nothing but physical things.

Nor does the minimal version violate the methodological autonomy of the various domains. Each domain continues to enjoy its own methods of investigation and understanding, its own vocabulary for describing and explaining matters within its scope. Each can proceed without waiting to see how its terms, its descriptions or its explanations would connect with those of some domain closer to physics. None need fear that physical terms or methods are necessarily superior to its own with respect to matters within its scope. Indeed physical terms and methods will often be inferior with respect to such matters (§§4.5, 4.6, 5.1). This is so despite the unity of method we saw in §1.5, which is simply the trial by prerequisites. Such unity is quite compatible with diversity of vocabulary and of modes of description and understanding. The trial by prerequisites is realized in each domain by means appropriate to that domain.

Nor does the minimal version of physicalism preclude the existence of abstract entities like sets or numbers. Whether such things exist is left entirely open. When we speak of sets and numbers, or of (other) universals, what we say may be regarded either platonistically, as referring to such entities, or nominalistically, as a mere manner of speaking (§4.1).

Nor is this version dogmatic about what the basic physical entities are, or vague about them. It is not dogmatic, as we saw in §3.1, because it realizes that our concept of the physical changes as physics itself changes in the ongoing trial by prerequisites. It is not vague, because it provides a specific definition PE (§3.1.1) of a physical existent in terms of a definite list of positive predicates from physics at any given stage.

Nor is it committed to some mirror theory of truth, though of course it is committed to a realism of the sort elaborated in §1.1. Nor is it committed to some causal relation between words and the world in virtue of which there is some objective fact of the matter as regards the reference of our terms (§1.1). It does not even require the terms to have any precise reference, determinate or otherwise (§4.4). The physicalist can heartily agree that vagueness and tortured but novel usage often are indispensable, in everything from poetry to physics, for creating momentous new ways of seeing ourselves and our worlds. Metaphors especially are essential in this regard, though exploration of a physicalist accommodation of metaphor must await §§5.2-5.3.

Perhaps above all this version is not monopolistic, in at least three fundamental senses. It is not monopolistic in the sense that (i) all domains of discourse beyond physics either are reducible to physics or else are somehow defective. Reducibility, once again, is irrelevant; so too is extensional isomorphism, a relation we encounter in §4.6, which is even weaker than merely accidental coextensiveness.

Nor is it monopolistic in the sense that (ii) physics enjoys unconditional pre-eminence or priority over all other domains of truth. Naturally only if physics enjoys some kind of priority will it seem significant that all other truths are somehow determined by physical truths. But the priority physics enjoys is highly conditional. If we are interested in the kind of objectivity, comprehensiveness and explanatory power physics pursues, then the truths of physics take on a corresponding priority, in light of which it seems significant that all other truths are determined by them. In many other contexts, we remain free and often even obligated to be interested in other sorts of truth, and to value them more highly. Indeed there are senses in which physical truth is dependent on certain other truths -- evidentially dependent, for example, and semantically dependent. The point will be elaborated in §§5.0 and 5.3, and throughout Chapters 7-8. Here we need only emphasize that the principles to be explained in §§4.1-4.3 do not entail unconditional priority or pre-eminence for physical truth. Indeed no principles should, since there is no unconditional priority to be enjoyed by any domain, if we may believe §§7.2-7.3.

Nor are the minimal physicalist principles monopolistic in the sense of entailing that (iii) physics in particular or science in general describes the ultimate nature of existence, or the way the world is. There is no such thing, no such thing as the face of existence (§§7.2-7.4). There are as many faces as there are aspects or attributes of the whole of existence (§§1.2, 4.6, 5.3), some of which are expressed by today's vocabularies and some of which are not (§5.4). Even though they are all attributes of one and the same thing, it does not follow that this one thing of which they are all attributes is or represents the way the world is, as we see in §4.6, or that "the physical world [is] the world."