This article is a corrected, and slightly revised, version (2011) of a paper that originally was published in Philosophy Forum, (1975), Vol. 14, pp. 241-267.

Emergence and materialist theories of sentience

Simon Fraser University


CONTEMPORARY MATERIALIST theories of mind, viz. Causal Correspondence and Identity, are usually contrasted with several alleged historical competitors: Parallelism; Epiphenomenalism; Dual-aspect; and Emergence. What I shall here attempt to argue is that this last-mentioned theory, Emergence, is no competitor at all, but rather is a natural supplement to a materialist theory. I shall try to argue that there is a good case for saying that if, in particular, sensation-states are caused by or are identical to brain-states, then they are caused by or are identical to emergent brain-states.

Materialist theories of mind have had a significant internal conceptual chasm from the outset: neither the state of a single neuron, nor the state of a small cluster of neurons, could reasonably be associated[Note 1] with, for example, the state of 'seeing green', yet 'brain-states' are somehow to be so associated.

There is an implicit assumption within Materialist Theories that if sensation-states ever should be correlated with brain-states, then the items on the physical pole of the correlation will be fairly complex descriptions of the brain (or more accurately, the central nervous system and its several sensory receptors). No one supposes that 'seeing green', for example will be correlated with the discharge of a single neuron. And on the whole we must judge this assumption a reasonable one. The only alternative to it within the context of a Materialist Theory, an alternative to be resisted as far as possible, is to associate some subliminal degree of sentience with the discharge of a single neuron. So doing would require that we conceive even of threshold perception, which we generally believe involves a vast array of neural circuitry, to be built up out of minute quanta of subliminal sensation-states — a conclusion as unattractive as the suggestion that even a minimal life form such as a virus is constructed of molecules each of which possesses a minute quantum of vitality. The Discontinuity Hypothesis is a far more attractive solution.

Even so, the Discontinuity Hypothesis, the hypothesis that sensation-states are associated only with complex brain-states and not with the states of one or few parts (i.e. neurons), is in need of examination. Most authors, by their neglect of the matter, would seem to imply that it is something not in need of explanation. But of course it is. Unless the existence of this discontinuity can be subsumed under a viable conceptual framework, it ought to be viewed as something deeply mysterious. We should want to inquire how it is possible that connecting up more and more neurons eventually yields a new item, sentience, in our ontology.

The kind of discontinuity which exists within contemporary Materialist Theories traditionally has typified a rather different kind of theory, to wit, Emergence. In Emergence Theories the phenomenon of discontinuity plays a central and essential role.

My task in the following will be twofold: it will be constructive and it will be speculative. These aspects are not entirely separable. I shall attempt to extend materialism along a new dimension. In effect I shall try to borrow just those features from Emergence Theory which make it an attractive solution and yet try at the same time to preserve a Materialist Hypothesis.

The constructive task is hampered by the fact that there is at present no fully satisfactory theory of Emergence. Emergence was a popular thesis at the outset of the second quarter of this century. {Ref. 149} But subsequent criticism {Ref. 257} struck it a severe blow and it temporarily withdrew from widespread favor. Recently, however, some philosophers {Ref. 36} have returned to the concept of Emergence and have tried to repair and rescue it from its detractors. What we have in the end inherited is a set of partial contributions. Specific objections to Emergence have been met and corrected, but the corrections are piecemeal. We must synthesize a new theory out of them.

I am not confident that what is about to follow is the only, or even the best way that Materialist Theories can henceforth develop. It is to be emphasized that the following scheme is a postulated instance of theoretical micro-reduction. But micro-reduction is not the only type of reduction. George Schlesinger {Ref. 8} exhorts us not to overlook the possibility for a macro-reduction. Whether a macro-reduction could capture the Discontinuity Hypothesis, I must admit I simply have no idea; but tolerance dictates that I do not dismiss the possibility. I leave it to others to work out a macro-reductive account. Once such a scheme is in hand, we can examine it to see whether it can accommodate Discontinuity. In the meantime I shall proceed along a direction whose outlines I can discern.


Let us begin, then, to try to make sense of the concept of emergence. The only condition of adequacy that we lay down at the outset for our analysis is that we should be concerned with emergence as a logical, epistemological, or ontological explicandum; but not as an historical or psychological explicandum.

We recognize that the universe has undergone an evolution with new properties appearing from time to time on the scene. Psychologically it is entirely possible that we should be quite unprepared for the appearance of new features and we might find ourselves duly surprised. But such facts as these assume little significance within a philosophic analysis of emergence.

We are not interested in the question, for example, whether historically the mental evolved out of the physical; rather we will pursue the question whether the mental may emerge out of the physical as an on-going phenomenon – whether each mental state in the universe is an emergent of some concurrent or immediately preceding physical state. In particular, we would raise the question whether each person's sensation-states are emergents of his/her own neural states.

The distinction between these two senses of "emergence" can be illustrated by considering the ambiguous phrase, "the emergence of life". In one sense, "the emergence of life" marks an historical moment or period – it constitutes the demarcation between the epoch when there was no life and the latter epoch when there was. In the second sense, "the emergence of life" connotes an ongoing process or relation – it is that peculiar relation which obtains between the presence of life (at any time, in any place) and states of co-present non-living things. It is solely this second sense of "emergence" which concerns us here.


C.D. Broad is generally acknowledged as the principal historical figure among the Emergentists. Broad illustrated and developed his thesis on the basis of a variety of examples.

"… most of the chemical and physical properties of water have no known connexion, either quantitative or qualitative, with those of Oxygen and Hydrogen. Here we have a clear instance of a case where, so far as we can tell, the properties of a whole composed of two constituents could not have been predicted from a knowledge of the properties of these constituents taken separately, or from this combined with a knowledge of the properties of other wholes which contain these constituents.
"… It is clear that in no case could the behaviour of a whole composed of certain constituents be predicted merely from a knowledge of the properties of these constituents, taken separately, and of their proportions and arrangements in the particular complex under consideration." {Ref. 1, p. 63.}

And a few pages later he added,

"… Take any ordinary statement, such as we find in chemistry books; e.g. 'Nitrogen and Hydrogen combine when an electric charge is passed through a mixture of the two. The resulting compound contains three atoms of Hydrogen to one of Nitrogen; it is a gas readily soluble in water, and possessed of a pungent and characteristic smell.' If the mechanistic theory be true … [a mathematical] archangel could deduce from his knowledge of the microscopic structure of atoms all these facts but the last. He would know exactly what the microscopic structure of ammonia must be; but he would be totally unable to predict that a substance with this structure must smell as ammonia does when it gets into the human nose. The utmost that he could predict on this subject would be that certain changes would take place in the mucous membrane, the olfactory nerves and so on. But he could not possibly know that these changes would be accompanied by the appearance of a smell in general or of the peculiar smell of ammonia in particular, unless someone told him so or he had smelled it for himself." {Ref. 1, p. 71.}

Broad's thesis is neither wholly right nor wholly wrong. There is in one part of it a valuable insight and in another a logical howler. Our task is (1) to see whether in the part that is right there is anything upon which we can capitalize in constructing an emergence theory suitable for supplementing a Materialist Theory of Sentience, and (2) to avoid scrupulously the pitfall that Broad fell into when he went astray.

Curiously, as it turns out, what Broad says which is right will be less helpful to us than our repair of what he says that is wrong.


Arthur Pap {Ref. 6}, like many other contemporary writers (one of whom we shall examine in the next Section), takes Broad to task for the logical lapses in his thesis. But unlike these others, Pap purports to detect one genuine insight in Broad's doctrine. Pap argues that on the basis of Broad's insight a viable sense can be given to the doctrine of emergence: in particular a determinate sense can be given to the concept of absolute emergence. Pap identifies absolute emergent properties[Note 2] with those that are definable only by ostension (e.g. Broad's case of the peculiar smell of ammonia). His reasoning is that a property which can be 'given' only ostensively can never be predicted (deduced from a theory) unless the existence of that property is already explicitly contained in the premises of the deduction; that is, the predicate naming the property must appear in the premises[Note 3]. Even if the presence of such a property should be physically dependent upon precisely describable and inducible states of the physical organism, the 'felt aspect', the phenomenology, of such a property could not be deduced from the theory. Even if a person was directly acquainted (by cerebroscopy of another person) with the precise neural state that gave rise to 'seeing green', he himself would not know what green 'looked like' unless he, too, had experienced a green sensation.

Thus, while Pap's argument allows that there is in principle no barrier to the subsuming of mentalistic and phenomenological phenomena within physics, it goes on to point out that such an encompassing can be accommodated only by incorporating phenomenological predicates within physics. There is a fundamental difference, for example, between "density" and "looks green"; for while there is an analysans by description for the former, i.e., "M(ass)/V(olume)", there could be none for the latter.

Admittedly Pap's discussion is quite ingenious and certainly gives the emergentist his due. Yet, in spite of its merit, this particular characterization of emergence will not do for our stated purposes. Absolute emergence is a category which admits of too many members. Apparently Pap did not recognize the potential vastness of this class.

The difficulty probably arises from the fact that Pap concentrated on only a few examples and built his case primarily on the problem of color and sound perception. He argued that color properties are absolutely emergent because they cannot be 'defined-away'. But this justification, this characteristic of not being able to be defined-away, is hardly unique to properties which are definable solely by ostension.

The classes determined by "only ostensively definable" and "non-eliminable in favor of other predicates" are not extensionally identical. The former is a proper subset of the latter. Insofar as the members of the former are identified as emergents just because they are included in the latter, then all of the latter must be similarly identified as emergents.

Electric charge, for example, is surely not given ostensively – one does not know of its existence by Russellian 'acquaintance' – but neither is it definable in the 'strong' sense which Pap's analysis requires. That is, it cannot be eliminated, it cannot be defined-away, by replacement with other predicates in any known theory. 'Electric charge', like 'seeing green', must be considered to be emergent, for, as in the case of the latter color property, the only way to predict the presence of an electric charge would be to include the incompletely-defined predicate, "electric charge", in the premises of the deduction.

The class of properties which are not analyzable without residue, includes not only those properties which can be given only ostensively, but in addition all the so-called hypothetical constructs of science. (It should be noted in passing that these two concepts are not necessarily exclusive. Indeed on occasion we can point to an overlap. Once we have introduced the term "anomie" into our science as a hypothetical construct, we may begin to see instances of anomie. Nevertheless the term "anomie" still remains undefinable linguistically. [Similar remarks hold for "gene", "hysteria", "regression", etc.])

On the basis of Pap's argument it becomes clear that we must enlarge the class of emergents to include all properties which are definable solely by ostension, as well as all the hypothetical constructs of science. Non-emergent properties will encompass the complement-class.

This extension of Pap's attempted salvage of Broad's theory does succeed in providing a determinate sense for the concept of (absolute) emergence. But it does so at a price higher than we are willing to pay. The trouble with extending Pap's analysis in the way we have done, is that now we have succeeded in labelling just about every important scientific variable or parameter as emergent. Force, extension, and direction, would presumably now have to be deemed emergents, and curiously enough, emergents with respect to (among other things) the very theory (i.e. mechanics) in which they play a role. In general, in any theory, every non-redundant term would be an emergent.

We have given a sense to "emergence" only to have lost the usefulness of the concept. Absolute emergence is too broad for our expressed purposes. We want to explain sensation-states as emergents of (i.e. relative to) brain-states. We do not want an analysis that makes them emergents of everything else; rather we want an analysis of emergence that can accommodate its limited relational character.


Ernest Nagel {Ref. 5} has argued that the doctrine of emergence can be summarily dismissed because it rests on a logical absurdity. As seen by him, Broad's doctrine of emergence states, roughly, that there are certain properties in some systems whose existence is not implied by other properties of the system; that is, these properties are said to be emergent and although discoverable, the existence of these properties could not have been predicted.

Nagel says that the doctrine of emergence stated in this fashion is untenable. For, he says, it is only propositions, not properties, which can stand in the relation of implication. A property is not the right type of thing to imply another property, be it emergent or any other kind. At root the doctrine of emergence rests on a category mistake – attributing to properties of things or systems characteristics which are appropriate only to propositions.

His argument for dismissal continues by saying that a property is emergent or not relative to a body of scientific propositions and hence is relative to our formulatable scientific knowledge. The only sense in which a property can justifiably be said to be emergent is within an historical setting – at some point in the development of scientific knowledge no proposition containing an occurrence of the predicate (naming the property in question) could be deduced from available theory; subsequently with the growth of scientific theory such a proposition may become deducible. In a word, unconditional emergence is nonsense; there is only 'theory-relative' emergence.

Nagel tries to strengthen this point with an observation about the nature of the deductive enterprise itself.

… all descriptive expressions occurring in a statement that is allegedly deducible from … a … theory must also occur among the expressions used to formulate the theory or the assumptions adjoined to the theory when it is applied to specialized circumstances. Thus a statement like 'Water is translucent' cannot indeed be deduced from any set of statements … which did not contain the expressions 'water' and 'translucent'; but this impossibility derives entirely from purely formal considerations and is relative to the special set of statements adopted as premises in the case under consideration." {Ref. 5, p. 369.}

The illustration which Nagel provides is quite correct. "Water is translucent" cannot be deduced from a (consistent) set of premises unless those premises contain both the terms "water" and "translucent". But this simple case does not establish the general claim which it is supposed to instance. The first sentence in the above quotation is false; consider: any theory, θ, which entails "water is translucent" will also entail "water is translucent or liquid". This latter conclusion follows from the premises of θ even if those premises do not contain the descriptive expression, "liquid". It is simply not true that every descriptive term in the conclusion of a deductively valid argument must occur in the premises.

Can Nagel's criticism be re-formulated to circumvent this difficulty? It can.

Any descriptive term occurring in the conclusion of a deductively valid argument which was not in the premises occurs vacuously, in a dummy capacity, or in a non-essential role; that is, it could be replaced in the conclusion by any other descriptive term and the argument would remain valid. Nagel's point can be re-formulated in the following analytic claim:

Any descriptive expression occurring essentially in the conclusion of a deductively valid argument must also occur among the premises of that argument.

The test whether a given predicate, s, is emergent relative to some specified theory, T, depends not only upon its non-deducibility from T (or more precisely, the non-deducibility of a proposition containing an essential occurrence of s), but in addition the eventual deducibility of s from an improved subsequent version of T. Without this last obvious qualification, the class of emergents relative to a theory T would include all possible predicates, except the very few which constituted the primitive and defined descriptive terms in T. We must, of course, restrict the class of emergents relative to T to at most the class of predicates which potentially could fall under the purview of that theory.

With the imposing of this latter restriction, it becomes clear that the decision whether a given term, s, is emergent relative to a given theory, can be made only after we have seen how T develops. What this means is that we can never say of any current theory what its emergents are; we can make only calculated guesses as to what they might prove to be. (And obviously, when we proceed later to argue that sensation-states may be associated with emergent brain-states, we shall have to understand that the implicit rider, "relative to current neurological theory", qualifies that claim.)

Left at this stage, Nagel's repair and qualification of Broad's theory is still insufficiently restricted. The objection we lodge against Nagel's argument is that it is altogether too facile and too thorough in its discounting of emergence. It refuses to consider seriously that the emergentists may have some valuable insight however poorly they may thus far have managed to express themselves.

In explicating "emergence" in terms of "non-deducibility from available theory", Nagel has placed the concept on a sound logical footing. Nevertheless his explicans seems to bear insufficient resemblance to the pre-analytic concept which must to a large extent arbitrate the acceptability of the analysis.

It seems entirely proper and in keeping with many of the examples in the earlier literature that we impose as a necessary condition for a term to be an emergent relative to a theory, T, that that term should not be deducible within T. And in light of Nagel's reconstruction, we add the further condition that it should be deducible from an improved subsequent version of T.

But are these stipulated necessary conditions also sufficient? Is the emergence of a term relative to a theory just simply its eventual inclusion within that theory? Something more seems to be needed.

Just how the term in question comes to be included in the theory apparently constitutes the crucial additional information needed to demarcate the 'emergents' from the merely 'subsequently included'. In the extreme, two theories dealing with distinct subject matters could be logically conjoined, and the terms of either original theory would then come to be included within the expanded version of the other. Clearly this must not count as a case of emergence: its artificiality is blatant. We must restrict our considerations to cases where the theory in question undergoes modification but is recognizably a latter stage of one theory; we do not consider cases where a theory is either totally replaced or simply conjoined to another. The distinction perhaps can be made between the growth of a theory in contrast to a radical departure from it.

The determination that a theory has persisted although it has undergone some modification cannot be made on formal grounds. All sorts of enormously vague and varied criteria enter into any such decision. It is pointless for the purposes of our discussion to try to specify them in general. Rather, I shall be concerned solely with one very special kind of growth that a theory may experience, and I shall develop a concept of emergence adaptable to this one highly specific context.

I shall be concerned to explicate a concept of emergence within the context of the micro-reduction of one explanatory level to a lower one. The point in choosing this particular area in which to pursue our studies is that it is here that we can (1) preserve Nagel's logical strictures; (2) often achieve a consensus that a given micro-theory under scrutiny has persisted through the reduction; and (3) impose certain distinctions, one of which can profitably be manipulated to yield our hitherto elusive class of emergents.


There are two principal accounts in the philosophic literature which try to come to grips with the problem of trans-level emergence. The earlier, that of Stephen Pepper, endeavored to show that a trans-level account must either entail epiphenomenalism or reduce simply to an extension (augmentation) of the lower level. In other words, Pepper found himself unable to accommodate emergence within the context of theoretical reduction whose formal properties he examined.

The more recent discussion, that of Meehl and Sellars, attempts to rebut Pepper's contention. It purports to find in Pepper's argument a non-sequitur which renders the argument totally ineffectual. The core of Pepper's argument is as follows:

What I wish to show is that all natural regularities are shifts[Note 4] and can not be otherwise described. Let us suppose a shift at level B is described as a function four variables q, r, s, and t. Let us then suppose that r and s constitute an integration giving rise to Level C at which level a new cosmic regularity emerges that can be described as a function of four variables r, s, a, and b. r and s must necessarily be variables in this emergent law even though they are variables of level B, because they constitute part of the conditions under which the emergent law is possible. Theoretically, to be sure, the emergent law may be thought of either as a function of new variables or as a new function of C-level variables. But actually only the former is possible. For if the new law were not f1(q, r, s, t), but were f2(q, r, s, t), then, of course, it would never be f1(q, r, s, t), unless the event were a chance occurrence in which case no regularity could be described anyway. The point is, either f1 adequately describes the interrelationships of (q, r, s, t) or f2 does; or if neither adequately describes the interrelationships there is some f3 that does, but there can not be two adequate descriptions of the same interrelationships among the same variables." {Ref. 7, p. 242.}

Pepper's argument, as it stands, contains a straightforward mathematical error. Fortunately this first error is readily repaired and when corrected will not change the thrust of his remarks. Let us reproduce schematically the situation Pepper describes.

Level B:  f1(q, r, s, t)
The 'integration' of variables r and s gives rise to level C.
Level C:  f(r, s, a[ = g(r, s)], b[ = h(r, s)]) = f2(r, s)

f2 is, we note, a function of only two B-level variables, not four as Pepper mistakenly contends. Thus f1 and f2 do not even purport to describe the same thing. For Pepper's argument even to get started, all four original B-level variables must appear in f2 but as he has described the situation, q and t drop out completely.

Meehl and Sellars do not call attention to this error, but tacitly correct it when they come to reconstruct the former's argument. (They define a = g(q, r) and b = h(s, t); not as Pepper had done, a = g(r, s) and b = h(r, s).)

In order for Pepper's argument to become intelligible we must understand that 'integrations' giving rise to a and b must exhaust the B-level variables. Meehl and Sellars gave one possibility, but many others would be equally sound.

a = g(q, r, s)


a = g(q)

b = h(s, t) b = h(r, s, t)

The only point is that each B-level variable must appear at least once and non-vacuously in the functions defining a and b.

Having corrected this error, we can now pass on to the more serious objection of Meehl and Sellars. {Ref. 3}

Meehl and Sellars object to the argument (which as mentioned they tacitly understand in its corrected form) on the grounds that various, differing functions may apply to the set of variables over different regions of their possible ranges.

"But surely this [Pepper's conclusion] is too strong – a veritable ignoratio elenchi. What the emergentist says is that there is a region in the fourspace qrst within which f1(q, r, s, t) = 0 holds. This region is the 'lower level of integration'—e.g., physiochemical processes which are not occurring in protoplasm. On the other hand, there is another region—the 'emergent' region—in which f2(q, r, s, t) = 0 holds,  f1f2. And a claim of this kind is mathematically unexceptionable, since it amounts to no more than the claim that a function may graduate the empirical data in restricted regions but break down when extrapolated. Such a 'break-down' does not mean, however, that the fit attained in either the subregion fitted by f1 or that fitted by f2 is a 'chance occurrence'. The fit may be excellent, and the demarcation of the regions precise (or, if gradual, thoroughly lawful) so that the 'chance occurrence' interpretation is as definitely excludable as it ever can be by inductive methods." {Ref. 3, p. 246.}

The matter cannot rest here. We must appraise the cogency of Meehl and Sellars' counter argument, and in so doing we must be careful to recognize that an argument which shows that another argument does not successfully disprove the existence of emergents, does not itself show that they exist. This latter point requires further independent support.


Our immediate task is to seek an example to which we can apply Meehl and Sellars' conclusions.

It is no criticism of our procedure to point out that a specific theory we choose to illustrate our example has been superseded or is (of course) capable of being superseded. We are not trying to explicate a timeless, theory-independent, absolute sense of "emergence". We shall content ourselves with a defensible sense of "emergence" which can be predicated of a property (or a state, or process) only relative to some specified theory at some particular stage in its historical development. My intention is to argue that a profitable theory can be constructed upon the hypothesis that sensation-states are emergent relative to brain-states as these latter are described within contemporary theories (or in theories whose terms for the most part are taken from the currently accepted terms in chemistry, physics, and neurophysiology). In making this claim, however, I do want to insist that something more is being asserted than just the bare verity that the occurrence of sensation-states cannot be inferred from the kinds of descriptions of brain-states which are allowable in contemporary theories. Among other things, one thing that is intended in describing sensation-states as "emergents" is that laws stating the relationships between brain-states and sensation-states must embody kinds of discontinuities already familiar in theories elsewhere in the scientific corpus.

There are various examples we could choose to illustrate the discontinuities which Meehl and Sellars require for the predication of "emergence". The case we single out is the 'triple point' in classical thermodynamics.

It is of course well known that many substances can exist in three phases[Note 5]: solid, liquid, and gas. For water, the solid and gaseous phases are given special names: "ice" and "steam" respectively. Substances can be changed from one phase to another by appropriate changes in pressure, volume, and/or temperature. A three-dimensional surface obviously is required to plot the interfaces of these transition points. If we were, however, to take the projection of such a surface onto the P-T (pressure-temperature) plane, as is common practice in texts in thermodynamics, we would produce Figure 1.

Graph showing triple point

Figure 1 – An idealized substance
which contracts on freezing

Suppose that all our experimental observations have been along the line AB, and that we have empirically fitted a function (within some acceptable error margin) to this line.

If we now imagine that all these observations were made in a world (which although different from ours is still logically possible), where the temperature and pressure are sufficiently low, we shall not yet have observed our theoretical substance in its liquid phase. Indeed we shall have no reason to suspect that such a property as liquidity even exists. (And lest this contention prove too preposterous, let us recall that no one expected the existence of the 'Curie-point' in metals, a low temperature point at which the electrical resistance suddenly falls to zero. This phenomenon of super-conductivity was stumbled upon accidentally and was totally unaccounted for by the then-current theories).

We can begin to see the cogency of Meehl and Sellars' argument. A function which may adequately describe a set of variables over one portion of their range may give way to another outside that range.

There is a counter-objection that could be levelled at this point. One could try to defend Pepper's thesis by focusing on the notion of 'an adequate description'. It could be objected that, precisely because there is a liquid phase and F1 cannot be extrapolated beyond PB and TB, F1 never was an 'adequate description' of the situation. But clearly a counter-move such as this is to be avoided, for it saves the theory at the expense of introducing an unrealistic methodology:

No function can be an adequate description of a phenomenon unless its scope is the entire range of the possible values of the constituent variables.

But the criteria for the adequacy or inadequacy of description are by no means exhausted by considerations of scope. Very often there are overriding considerations such as simplicity, closeness of fit, compatibility with (and preferably, derivability from) theory. Especially when there are sharp changes or discontinuities in the behavior, we prefer to partition the range into several functions. Of course we still acknowledge that there may be some one (more complicated) function which applies to the entire range, but it is just arbitrary and question-begging to insist that it alone is "adequate". There is no one criterion of adequacy; we must weigh several different dimensions. It is just as likely as not that several 'simple' functions of limited but consecutive application would be 'more adequate' than an unwieldy one of more extensive application.

With this minor misgiving put at ease, we can turn to a more pressing issue.

Having come this far and having countered Pepper's 'proof' of the impossibility of Emergence, it is tempting, as Meehl and Sellars have done, to be content and to identify Emergence with (the possibility of) an F2-type function. In the example under scrutiny here, a new property (viz. liquidity) has appeared in the region of this new second function. The appearance is a genuine theoretical novelty on the basis of the F1 function. Thus, if we were to consider it an emergent, we would satisfy our first criterion of adequacy.

Nonetheless, haste ought not to make us careless. The trouble with labelling 'liquidity' an emergent is that pre-analytically we do not see precisely how, if at all, the concept of 'levels' is involved. We do note that our intuitions would probably want to assign liquidity, gas, and solid all to the same level, and we do not yet see whether so doing would count for, or against, liquidity being an emergent.


The contrast that is essential to our purposes is not that between gaseousness, liquidity, and solidity, but rather between all of these and such properties of molecules as vibrational energy, velocity, axes of rotation, etc. We seem in this case to be able to construct laws describing the behavior of parts (i.e. molecules) in such a way that the relevant variables are all property-variables of the part itself, or of sub-parts, but not of the whole. Other laws, often containing new variables, must be constructed in order to describe the behavior of the whole. No individual molecule has a temperature, although the gas (or liquid, or solid) does; and the molecules have a characteristic binding energy while the gas (or liquid, or solid) does not.

Let us simply call the properties which are those of the parts the "part-properties", and those of the resultant ensemble, the "whole-properties".

Whole-properties can be divided into two kinds: (1) those which are in principle impossible to bring into a lawful micro-explanatory relationship with the part-properties (either because no lawful relationship exists or because a macro-explanatory one does), and (2) those which are in, or can be brought into, a lawful micro-explanatory relationship with the part-properties. Our concern is solely with the latter kind of whole-property.

Let us, in addition to the relatively non-technical concepts of part- and whole-property, also introduce the somewhat technical concept of a "global-property". Rather than immediately defining "global-property", let me offer two examples of what I shall take to be instances of this kind of property.

Consider first, for example, the property, mass, which attaches to an ordinary-sized macroscopic object. The presence of this whole-property, mwhole (abbreviated, "mw"), is accounted for by the part-property, mpart (abbreviated, "mp"). To be explicit, the relationship (to first approximation[Note 7]) is:

mw Global property

I call the property,

Global property

, a "global-property" of the part-property mp.

Or consider the example of the theoretical identification of thermodynamical temperature with the average kinetic energy of the molecules of the gas:

Tw =  Global property

The property, 

Global property 

, is a "global property" of the part-properties, mp and vp.

It is all too common a practice in science textbooks and in science courses to explicate scientific formulae in logically offensive ways. It is the rare textbook which does not say about the formula, "F = ma", for example, that this is to be understood as meaning: "Force equals mass times acceleration." Taken literally (a course which far too many students adopt), the suggested translation is utter nonsense. The property, mass, surely cannot be multiplied by the property, acceleration. To suggest so, is to commit an egregious category error. Multiplication has been defined for numbers and numbers alone; mass and acceleration are simply not the right sorts of things to be multiplied one by the other. The correct understanding of formulae in scientific contexts is that the various terms therein stand not for properties themselves, but for the magnitudes of properties. And what the formula defines or reports is that the magnitude (numerical value) of the property referred to on the left of the equals sign is a mathematical function of the magnitudes (numerical values) of the properties referred to on the right-hand side. The relationship is mathematical not ontological. For our purposes, in the context of micro-reduction we must understand that whole-properties are not literally constellations of part-properties. They are, rather, ontologically distinct properties, whose magnitudes stand in certain lawful or functional relationships to the part-properties. This relationship is conveniently portrayed as an equality between whole-properties and global-ones. But no logical confusion ought to ensue if we keep our wits about us. Returning for a moment to our ultimate quarry, we can say that whole-properties are properties of brain-states just as much as are part-properties; the only point is that they stand in certain determinate lawful relationships to the part-properties. But for all that, they are still logically and ontologically distinct from any of the part-properties.

With these distinctions and caveats in hand we can proceed to garner two important features from the various examples we have given of cases of micro-reduction. It is upon these features in particular that we shall want to capitalize in order to conjoin an emergence theory with a materialist theory of sentience.

First we note an important difference between the case of 'mass-reduction' and the case of 'temperature-reduction'. In the first example, both the whole and its parts possessed some degree of mass; in the second example only the whole possessed a temperature, the parts did not. Temperature is strictly a whole-property and not a part-property. Simply put, an ensemble of parts may exemplify properties which the parts do not.

Second, laws associating properties of the whole with global-properties of the parts may, and often do, break down as the values of the variables for the parts are extrapolated. Gaseousness 'gives way' to liquidity, and liquidity to solidity, as the number of molecules per unit volume increases. The whole-property, liquidity, occurs (shortly we shall say, "emerges,") as the gas laws in our slightly artificial model (viz. in the low temperature world described in the previous Section) break down under increased extrapolation; that is, a property unpredicted on the basis of the confirmed laws in the theory appears as these laws fail to continue to hold in new regions. Reductive laws may have limited scope; but we may not know of such limitation, and might hypothesize a scope too great for a given law.

Micro-reductive laws associating whole-properties with global-properties of the parts can and sometimes do break down under extrapolation, and often when they do break down, whole-properties unpredicted by the failing law may occur. Under such a circumstance we can point to the occurrence of this new property as a genuine theoretical novelty (psychological surprise need play no role in our account). Such an unexpected property can profitably be said to be emergent relative to the failing law (or failing theory in which the law in question occurs).

The species of emergence being proposed here is rather different from the confused sort of thing that Broad earlier described and which Nagel so incisively demolished. Broad overlooked the essential need for laws which link the behavior of a whole with the behavior of its parts. Without these laws there is an absolute logical hiatus which makes all talk of the relationship between the properties of wholes and the properties of their parts totally unsound.

But our account also differs in a significant way from Nagel's. He had argued that an emergent is any property in a system whose presence cannot be deduced essentially from the theory treating that system. Our claim is a bit stronger. In our reconstruction, an emergent is a whole-property which is not inferable essentially from a theory where that theory would, by extrapolation, have led us to predict falsely the occurrence of some other whole-property. In other words, an emergent-property occurs when a given law associating some whole-property with some global-property fails for some region of the n-space of the part-variables, and must be superseded for that n-space region by a new law introducing to the theory a new whole-property (and/or a new global-property).

Actually the definition just given, although a natural outgrowth of our examples, is slightly too specialized for our purposes. The law introducing a new whole-property for a distant n-space region of the part-variables need not replace another law. We shall also consider a property an emergent if it is a whole-property occurring only for distant n-space regions of the part-variables. It, too, would be unpredicted on the basis of laws which had been confirmed for only a familiar sub-region of the n-space of the part-variables. This is to say that a whole-property may come into existence without replacing any other whole-property (unless one wants to call its absence a property) as some variables characteristic of the parts increase (or decrease). I doubt that there are any tunes, for example, which consist of only one, or two, or even three single notes. (What I am working toward, of course, is the claim that while the state of a small collection of brain cells could not be said to be 'seeing green', the state of a large collection might be. Let us turn to this question directly.)


The speculative thesis now to be advanced is that sensation-states are either emergent whole-properties of the central nervous system, or are caused by emergent whole-properties of the system.

We cannot prove, indeed we are not even attempting to prove, this speculative thesis. As we said at the outset of this study an attempt will be made to reconcile some persistent conceptual difficulties. How, it is often questioned, are mental predicates to be subsumed, linked, implied (or whatever,) to a physical description of brain-states, a description which in many materialist accounts is 'complete' or at least 'self-contained'? In Feigl's picturesque phrase, how do we conjoin physicalistic descriptions with mentalistic ones, without the latter being 'nomological danglers', or from a formal point of view, mere idle wheels? Is the joining of the two to be of such a kind that the mentalistic terms are strictly intervening variables with no other raison d'être than that they are formal shorthand for certain complex physical expressions?

My suggestion is that 'completeness' or 'self-containedness' in description is a peculiar technical notion which does not imply exhaustiveness in description. Again we call upon our example from statistical mechanics to make this clear. There is a quite straightforward sense in which the description of the molecules in terms of it their individual positions and momenta (at a particular instant) is 'complete'. That is, from this description (and certain suitable laws) we can infer both the earlier and the latter positions of these same molecules. In relation to these laws, the set of part-properties (i.e. position, momentum]), is closed (or 'complete' or 'self-contained') under retrodiction and prediction.

Yet the whole-property, temperature (or liquidity, or tensile strength, or viscosity, or pressure, or superconductivity) can be accommodated into this scheme of things. The trick is to equate it with a global-property of the ensemble. The original set of part-properties (i.e. [position, momentum]), remains self-contained; still we are able to accommodate other properties in a way which does not destroy this self-containedness.

Materialist theories are sometimes rejected because it is argued that on the assumption that the human neural system is entirely a physical system it could in principle be duplicated by an elaborate electro-mechanical system, but it would be absurd to suppose that any such artificially constructed contrivance could, for example, have a 'raw feel'. Therefore no neural state could be associated with the having of a raw feel either.

Now while I concur that it is rather difficult to admit either of a few neurons discharging, or of a few transistors firing, that such episodes could constitute or cause the having of a green square sense datum, I think that the objection levelled is far from compelling.

A circuit, whether it is composed of neurons or of transistors, which in isolation falls under one micro-reductive law, may fall under quite a different law when it is imbedded in a massive network. (The simple modules which make up the vastly more complex addition register of a computer are not adding when they are tripped through a step or two in their shakedown testing before installation. Adding is a large-scale phenomenon and it transcends the mere 'firing-level'.) The problem in attributing consciousness or sentience to a physical circuit lies, I submit, in thinking that states of consciousness can be located as residing in isolated sub-structures. I do not want to be understood, however, as suggesting that some state of the entire brain or central nervous system constitutes or causes the feeling of pain. Rather the stress is on the earlier word, "isolated". Perhaps the having of a raw feel can be identified as occurring or residing in some sub-structure of the brain, but the important thing to note is that this sub-structure does reside within the brain. If this sub-structure were to be excised from the living brain and preserved in its electrical state by a suitable connection to external electrical cells, it would be absurd to say 'it' was feeling pain. In being removed from the environment of the rest of the network, it would revert to the non-emergent n-space region of the part-variables.

No circuits we now build do 'see green'. But perhaps if we were to put enough of them together, they could. The trick (if the extended. Materialist Theory being suggested here is true) is not to add a new kind of thing (soul, mind, etc.) to a circuit, but simply to add enough other circuitry.

Woodger, several years ago, called attention to the fact that a part may function atypically when removed from one 'environment' and placed in another.

"… it must be remembered that when a part is isolated it no longer has its typical relations, in other words its environment is different, and the concept of environment applies as much to parts as to wholes, with the important difference that the environment of a part is the whole organism and not an inorganic environment. Hence when a part is isolated one of three possibilities will be realized. (1) If it is put into an inorganic environment it may behave as a new whole (e.g. an isolated piece of a planarian). (2) It may perish, i.e. cease to persist as a living thing as when a man's leg is cut off. (3) It may be furnished with an artificial organic environment, as in many physiological experiments, tissue-culture, etc. This process of isolation is absolutely indispensable in many cases in physiological research and the results obtained are of the highest interest—an enormous part of our knowledge is dependent upon them. But from the point of view of interpretation of those results it is extremely important to bear in mind one obvious methodological point: it is never safe to assume uncritically or assert dogmatically that an isolated relatum say A taken from … a … level … exhibits the same properties in isolation as it does in its place in the level—even when it is furnished with an artificial environment which is as 'normal' as possible." {Ref. 10, p. 313.}

Woodger has directed his attention to the biological cases. But it is clear that his remarks instance a more general claim. Nothing he has said regarding this phenomenon is singularly appropriate to the biological context; rather the logic of the claim is every bit as valid for any chemical or electro-mechanical system as well.

The methodological presupposition, which we may aptly call The Presupposition of the Invariance of Scale (or the Validity of Extrapolation) is easily, and often has been, abandoned.

How various parts will interact is always a contingent matter and cannot be known a priori. There can be no sound argument to the effect that the laws which hold for the interaction of a few parts must also hold for the interaction of a large number.[Note 8] Extrapolation is always a risky business. And even if it be granted that the firing of this or that neuron does not constitute 'seeing green', it does not follow that 'seeing green' is not a neural discharge. The firing of several neurons within a large network could be associated with 'seeing green'. Indeed it has been the purpose of this paper just to show that the logic of such a claim is coherent and that a carefully constructed Theory of Emergence is a worthy supplement to a Materialist Theory of the relationship between sensation-states and brain-states.


I have sought principally to examine one question in this paper.

Materialists tend to view the central nervous system as an electro-chemical network subject to the same physical laws as commonplace radios and computers. But no one is inclined to attribute sentience, or more specifically the having of pains or the seeing of colored patches, to these artefacts. Moreover, the laws describing the behavior of these devices are singularly devoid of all phenomenological predicates. Put in its most personal and untechnical form, the question becomes: how is it that I, whose human brain is just simply an electro-chemical network, am able to see a green patch?

The speculative answer which I have offered to this query consists in denying that our brains are just simple electro-chemical networks, and to argue instead that they are very vast electro-chemical networks. And further I suggest that it at least makes sense to propose that the occurrence of phenomenological states depends upon the vast scale of our brains and upon nothing else.

What I have tried to show is that phenomenological states can be accommodated in the scheme of things without either (1) having to abandon the well-confirmed laws governing the behavior of computers and the like, or (2) having to abandon a thoroughgoing materialism.

I think that the materialist has no choice in this matter. Phenomenological states must be accounted for. And since they are absent in ordinary electrical circuits and by hypothesis are present in or caused by the central nervous system of human beings, either we have to account for this difference in terms of a physical difference between these two systems, or we must abandon Materialism. But there is at least one very great physical difference between these two systems: it is that of scale or complexity. Just what other physical differences there may also be are much less apparent. At any rate, I have tried to argue that this one difference, that of scale, is sufficient for us at least to postulate that it alone accounts for the absence of sensation-states in our electronic artefacts and their presence in our own nervous systems.

There seems little doubt that this proposal has about it initially an air of the fantastic. My hope has been, however, that this air can be somewhat diluted by the arguments and examples presented in this paper.

The technical details of our argument can be briefly recapitulated. But it should be emphasized that I am not at all claiming that our actual world is in fact like the world I have described. All I have proposed is that it may be—that it makes sense to say that phenomenological states arise out of the sheer size of the brain.

Earlier accounts of Emergence were infested with confusions and logical improprieties. These we have exposed and hopefully avoided repeating.

I have chosen to highlight some peculiarities which might arise in cases of micro-reduction. These peculiarities conceivably provide the means to solve our problem.

In reducing one set of phenomena (or the laws thereof) to another (or, again, to the laws thereof), we often end by associating members of the former class with complex ensembles of the latter. (In the formal aspects of the reduction this association is effected by making the individual variables of the former class determinate functions of one or more variables of the latter.) As the values of these independent variables are extrapolated, it is possible, and indeed we have seen instances where it is the case, that the functions co-coordinating the dependent (or 'macro' or 'whole') variables with the independent (or 'micro' or 'part') variables may fail, and hence necessitate being replaced, for that n-space region of the range of the independent variable, by another function.

Even while these reductive laws co-coordinating whole-properties to complexes of lesser properties may be undergoing breakdown, other laws, confined just to the interrelationships between these lesser properties over the same n-space region may persist undisturbed. Here we have the means to preserve our current well-confirmed laws of electro-chemical behavior. These laws do not coordinate any phenomenological states to any electro-chemical state whatever. Nevertheless we could add reductive laws incorporating such a coordination onto these known laws without altering these known laws in any way. My speculation is, however, that if any such reductive laws are going to be added to the known laws of electro-chemistry, they will be for values of the relevant variables far beyond the typically small n-space region we have hitherto examined in our laboratories. (Obviously we have not yet even approached constructing a circuit of anywhere near the complexity of the brain.)

In sum I have argued that if we are willing to entertain seriously the hypothesis that sensation-states are materially dependent upon brain-states, then we would do well to consider the proposal that sensation-states are to be associated with emergent global brain-states.

A property (or state) can be global without being emergent. In adding the further qualification, "emergent", we signal our belief that laws coordinating sensation-states with global brain-states will be restricted to distant regions of the brain-state-variable n-space. Whatever global properties might be introduced for small electro-chemical systems, we predict that none will be associated with sensation-states; only global properties of very large electro-chemical systems will be so associated.

It would be easy to argue that in order for a Materialist Theory to come to fruition, contemporary physical theory would have to undergo certain changes, the details of which we are not in a position to discern. Apparently a tacit fear shared by many philosophers of materialistic persuasion has been that current concepts falling under the extension of "physical" are inadequate to explain the occurrence of phenomenological states; that only a modified and expanded concept of "physical" will allow for the eventual establishment of a Materialist Theory.

Now while I think it a virtual certainty that our concept of 'physical' will continue to evolve, I do not share the belief that it is impossible at this time, given contemporary physical theory, to see any way in which phenomenological states might be accommodated in our materialist theories. One possible way would be to associate phenomenological states with emergent global brain-states. There is nothing mysterious or metaphysical about emergence. All we are trying to do by invoking this concept is to draw attention to the possibility that new properties in a system may arise simply as a function of the sheer size of that system.

My proposal is speculative. But it does have the virtue of being coherent and possibly being true. I hope time will decide the latter point.


  1. I am using the term, "associate" (and its cognates), in a sense explicitly intended to be neutral between the two materialist theories, Causal Correspondence and Contingent Identity. [ Resume ]
  2. For the remainder of this Section, I speak of "properties which are definable by …". While I freely admit to the strict logical impropriety of this manner of expression, I prefer it to the more correct, but clumsy, expression: "properties for which the designating predicate is definable by …". I trust no confusion will follow upon my abbreviation. [ Resume ]
  3. This point has been stated loosely and intuitively. It will be stated rigorously in the next Section. [ Resume ]
  4. Pepper coins the term, "shift", at the outset of his article {Ref. 7, p. 241.} and defines it in this fashion: "… there is what we may call a 'shift', a change in which one characteristic replaces another, the sort of change traditionally described as invariable succession and when more refined described as a functional relation." [ Resume ]
  5. Some substances apparently exhibit fewer than three phases. Helium, for example, is believed not to have a solid phase. But many substances are known to exhibit several 'forms' within a phase. There are two forms of liquid helium, and no fewer than seven forms of ice. [ Resume ]
  6. "As the critical temperature is approached, the properties of the gas and liquid phases approach one another, resulting in only one phase at the critical point: a homogeneous supercritical fluid. … beyond this critical point, … there is no distinction between the two phases. Above the critical temperature a liquid cannot be formed by an increase in pressure, but with enough pressure a solid may be formed." ]
  7. It is well to bear in mind that the relation between the magnitude of a property of a part, and the magnitude of that property for the whole, is always a contingent one. Even for as 'familiar' a property as mass, we learn that our predilection to assume simple scalar addition for chemical or nuclear combination is false. There is in every case of such combinations a portion of the total mass which is converted into binding energy, the so-called 'mass-defect' in the assembling of a nucleus. [ Resume ]
  8. Prior to the creation of Quantum Theory, no one would have imagined that merely adding more 'stuff' to a sample of that 'stuff' could result in anything different from simply more of that stuff. But this, inductively-warranted, supposition was to be dramatically overturned when physicists joined two sub-critical masses of fissile material together producing in the first experiments a chain-reaction – emitting lethal radiation – and nuclear explosions in later instances. See., e.g., Louis Slotin. [ Resume ]


  1. C.D Broad, The Mind and Its Place in Nature (London, 1925, reprinted Paterson, N.J., 1960), Chapter II. [ Resume ]
  2. C.G. Hempel and P. Oppenheim, "On the Idea of Emergence", Part II of the Paper, "The Logic of Explanation," Philosophy of Science 15 (1948), reprinted in Readings in the Philosophy of Science, ed. Feigl and Brodbeck (New York, 1953). [ Resume ]
  3. P. Meehl and W. Sellars, "The Concept of Emergence", Minnesota Studies in the Philosophy of Science 1 (Minneapolis, 1956), 239-252. [ Resume ]
  4. C. L. Morgan, Emergent Evolution (London, 1923), esp. Chapter I. [ Resume ]
  5. E. Nagel, "The Doctrine of Emergence", The Structure of Science (New York, 1961), Chapter 11, 366-397. [ Resume ]
  6. A. Pap, "Emergent Laws and Emergent Qualities", An Introduction to the Philosophy of Science (New York, 1962), Chapter 19, 359-373. [ Resume ]
  7. S. Pepper, "Emergence", Journal of Philosophy 23 (1926), 241-245. [ Resume ]
  8. G. Schlesinger, "The Principle of Micro-Reduction", Method in the Physical Sciences (London, 1963), Chapter II, 45-72. [ Resume ]
  9. J.C. Smuts, Holism and Evolution (1926, reprinted New York, 1961). [ Resume ]
  10. J.H. Woodger, Biological Principles (1929, revised edition, New York, 1967). (References above are to the later edition.) [ Resume ]

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Footnote #6