THREE DEFINITIONS OF ‘EMERGENT’

I.

“If P is a property of w, then P is emergent iff (1) P supervenes with nomological necessity, but not with logical necessity, on properties the parts of w have taken separately or in other combinations; and (2) some of the supervenience principles linking properties of the parts of w the w’s having P are fundamental laws.” (McLaughlin, p. 93)

“A-properties supervene on B-properties = df. Necessarily, for any object x and A-property a, if x has a, then there is a B-Property b such that (i) x has b, and (ii) necessarily, if anything has b, it also has a.” (McLaughlin, p. 91, quoting from van Cleve)

“A law L is a fundamental law iff it is not metaphysically necessitated [and therefore not nomologically necessitated – my addition] by any other laws, even together with initial conditions.” (McLaughlin, p. 93).

[Mclaughlin on this definition of emergent property: It captures the spirit of the British Emergentist concept. It is coherent. That chemical and biological properties are emergent has since been empirically refuted by Quantum Mechanics. It remains an open question whether or not conscious properties are emergent in this sense, but his bet is that they are not.]

II.

“The occurrence of a characteristic W in an object w is emergent relative to a theory T, a part relation Pt, and a class G of attributes if that occurrence cannot be deduced by means of T from a characterization of the Pt-parts of w with respect to all the attributes in G….A characteristic W is emergent relatively to T, Pt, and G if its occurrence in any object is emergent in the sense just indicated.” (Hempel, pp. 64-5).

[Note: Although Hempel refers to this as a definition or ‘redefinition’, it is formulated merely as a sufficient condition. E.G., let T be physics, and contain only homophonic laws; Let G encompass certain physical attributes had by the physical parts, Pt, considered apart from their role in w; then if the occurrence of W in w cannot be deduced from T, it is emergent]

III.

Let S be a system made up of constitutive elements a, b. c,… If the occurrence of a ‘system feature’, F,.of S must be explained in terms of causal interactions among S’s constitutive elements, then F is an ‘emergent1’ feature of S. If F in addition has, or grounds, causal powers that cannot be explained by the causal interactions of S’s constitution features, then F is ‘emergent2’.

[Searle then claims that consciousness is an emergent1 feature of certain systems of neurons in the same way that solidity and liquidity are emergent1 features of systems of molecules. (cf., Searle, pp.; 69-70)]

PEPPER ON EMERGENCE

A Taxonomy of Change:

1. chance occurrences (do not fall under a law)

2. ‘shifts’ (one characteristic replaces another in a lawlike way,

describable as functional relation)

3. ‘emergence’ (certain characteristics supervene on others,

where the occurrence of these others is explainable in a lawlike

way on their own)

Emergence:

1. There are levels of existence defined in terms of degrees of

Integration.

2. There are marks which distinguish these levels from one

another over and above the degrees of integration.

3. It is impossible to deduce the marks of a higher level from

those of a lower level.

‘epiphenomenal occurrences’ (standard definition): occurrences that are caused, but that are not themselves causally efficacious. ‘Epiphenomenalism’ wrt to occurrences of a certain kind of property: the view that all such occurrences are epiphenomenal.

Pepper’s 1^st thesis: All natural regularities are shifts and cannot be otherwise described, on pain of epiphenomenalism.

Argument: Suppose that there is a shift, a lawlike relation at level B, between the values of variables q,r,s, and t, correctly expressed as the function f1(q,r,s,t). Suppose further that at level C, supervening on level B, there are occurrences of new variables a and b, which are claimed to be emergent, and which satisfy the function f2(r,s,a,b). “But these new variables either have some functional relationship with the rest of the lower level variables or they haven’t. If they haven’t they are sheer epiphenomena…. If they have, they have to be included among the total set of variables described by the lower level functional relation; they have to drop down and take their place among the lower level variables as elements in a lower level shift.”

Pepper’s 2^nd thesis: Either emergent laws are ineffectual and epiphenomenal, or they are effectual. But they are only effectual (useable to make reliable predictions) if they are consistent with, don’t conflict with, the lower level shifts that they are taken to supervene on. And the only way to secure that is if they are deducible from those lower level shifts, i.e., if they are reducible to those lower levels laws, and thus in effect amount to a lower level shift after all.

In an (so far as I know) unpublished ms, Richard Boyd argues against emergence in a way reminiscent of Pepper, invoking the following principle about causation:

“Suppose that under certain circumstances causal factors f1…fn are sufficient to change the state of a system S from its initial state S1 to some subsequent state S2 over a time interval T. Suppose, now, that under otherwise the same circumstances the causal factors f1…fn act on a system that is initially in state S, and it is also true that a causal factor, call it g, acts on the same system. At the end of the time interval T the state of the system in question will be different from S2, unless either g is one of the factors f1…fn, or g is a constituent of one of those factors; or g is made up of , or constituted from, aspects of some or all of the factors f1…fn or their constituents….Some such principle as this is, I think, central to our conception of causation, and to the way in which we individuate causal factors.”

Suppose then that the causal factors f1…fn are all at the lower level, and the factor ‘g’ is being put forward as an ‘emergent’ factor. According to this principle g must either be one of the f1…fn, or a ‘constituent’ of one of these, or ‘made up of or constituted from aspects of some or all’ of these. It is as though g must be on the same level as the f1…fn after all; and g will be apparently predictable from f1…fn together with certain facts of constitution.

But is emergence ruled out? It seems to depend on how we construe ‘constituted from aspects of’. E.g., if we allow that factors on one explanatory level can be constituted, in this way, of factors at lower levels, then the principle seems perfectly compatible with emergent properties and powers, notwithstanding Boyd’s insinuations to the contrary.

MEEHL AND SELLARS ON PEPPER.

“What the emergentist says is that there is a region within the fourspace qrst within which f1(q.r.s.t) =0 holds. This region is the “lower level of integration” – e.g., physicochemical 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, f1=/=f2. ….But while the notion of different regions in the fourspace qrst exhibiting different functional relationships is mathematically unexceptional, is it emergence?...no emergent variables have been introduced…and it has not been claimed that there are ‘piggy-back’ regularities…thus to the extent that ‘emergence’ connotes a simultaneous presence in a single situation of two or more levels, the notion we have been analyzing is not, as such, a matter of emergence.”

Two senses of emergence.

“But if we add to this the notion that protoplasm exhibits a constellation of physiochemical variables which belongs in a region of the n-space defined by those variables that conform to a different function than do the regions to which belong constellations exhibited by less complex physiochemical situations, then the use of the term “emergence” seems not inappropriate. And, indeed many philosophers [and scientists] who have made use of the concept of levels of integration or levels of causality seem to have had something like the above in mind. But it is reasonably clear that most emergentist philosophers have had something more in mind. They have spoken of the emergence of properties….[including allegedly basic, simple, non-dispositional properties such as qualia; and have wanted to claim that occurrences of these emergent properties, while dependent on the particularities of subvenient properties, are not reducible to them]”.

[Sidebar: ‘methodist’ vs. ‘particularist’ approaches to sorting this out.]

Pepper’s Worry

Suppose the emergent properties to be a and b.

Suppose also that the occurrence of a and b depends in a certain functional way on the values of q,r,s, and t:

a = g(q,r)

b = h(s,t)

Then the function which adequately describes the interrelationships of the inclusive set of variables qrstab, call it E(q,r,s,t,a,b), can be written without a and b thus: E[q,r,s,t,g(qr),h(s,t,)] or f3(q,r,s,t).

1. Unless f3(q,r,s,t) is equivalent to f1(q,r,s,t), they cannot both hold. (True, but only if they are each intended to cover the entire fourspace of these variables.)

2.But for f3 to be equivalent to f1 is for a and b to be epiphenomenal (i.e., in Pepper’s sense of ‘making no difference’)

3. If f3 holds and a and b are not epiphenomenal, then f1 cannot hold.

4. So E(q,r,s,t,a,b) must adequately describe both the before and after integration of the phenomenon in question.

5. So the supposed emergents a and b have to be included among the total set of lower level variables after all. Q.E.D.

Does this give Pepper the last word?

Meehl and Sellars on the emergence of ‘raw feels’

Suppose that the a and b in the above function E are the raw feels that some philosophers have wanted to claim are emergent. “That is, raw feels depend upon the variables q,r,s,t which also characterize pre-emergent situations. But raw feels do not occur in the presence of matter generally; only matter as it is in the living brain. The function f1(q,r,s,t) which fits the behavior of matter everywhere else, breaks down when applied to brains.”

But must the scientist introduce the variables a and b? Cannot he either just differentiate two different regions of qsrt space, governed by two different functions; or, failing that, introduce a single complex function E involving the constitutive functions g and h but not a and b? (Call that the behaviorist’ or maybe ‘eliminativist’ gambit.)

On the other hand, what prevents the scientist from affirming his experience of raw feels, introducing variables a and b for them, and insisting that the functions g and h do not constitute reductive analyses of a and b? (Call that the ‘emergent realist’ gambit.)

THEMES IN WIMSATT

1. We need to acknowledge an important sense of ‘emergence’ on which emergence is compatible with reduction, where “…a reductive explanation is one showing it to be mechanistically explicable in terms of the properties of and interactions among the parts of the system”, and where an emergent property is, roughly “…a system property which is dependent upon the mode of organization of the system’s parts”(pp. 99-100).

2. Wimsatt alludes to a list of “well-understood” reductive examples of emergence in this sense (p. 101).

[Sidebar: particularism!]

3. The sorts of property occurrences typically characterized as emergent tend to be “non-aggregative” wrt the properties occurring on subvenient structural levels.

4. To get a fix on what that comes to, we can focus on what it takes for a property occurrence to be “aggregative” wrt structurally underlying property occurrences. Wimsatt’s account of this suggests that non-aggregativity can then come in degrees, and is ubiquitous.

FODOR ON THE SPECIAL SCIENCES AND REDUCTION

The generality of physics: all events which fall under the laws of any science are physical events and hence fall under the laws of physics (p. 395). To that extent, physics is the most basic science. Compare:

Token Physicalism: the view that all the events that the sciences talk about are physical events (p. 397). versus

Reductivism: the view that all of the special sciences reduce to physics, in the sense that the laws of any special science at the ideal limit of its development will be derivable from the laws of physics at ideal limit of its development, via bridge laws establishing a correspondence between each ‘natural kind’ predicate distinctive of the special science laws and a respective natural kind predicate of physics (p. 396). Compare:

Type Physicalism: the view that every property mentioned in the laws of any science is a physical property (p. 397.

Fodor takes Reductivism (hence Type Physicalism) to be too strong a constraint on the special sciences (while acknowledging that this is ultimately an empirical question). But he holds that there is a weaker notion of reduction, that preserves token physicalism, the generality of physics and the ‘basic’ position of physics. Instead of bridge laws linking a natural kind term occurring in a special science law to a physical natural kind term, there can be bridge laws linking a natural kind term of a special science law to a disjunction of heterogenous physical natural terms (i.e., not itself constituting a physical kind term.)

What physical explanation one gives of the occurrence of a special science kind will therefore depend on how it happens to be physically realized, and that can vary with the context. There will, by the same token, be different physical explanations of the applicability of a special science law, S1x à S2x, varying with how the natural kind terms S1 and S2 happen to be physically realized (p. 404). So this weaker notion of reduction makes the special sciences more autonomous than Reductivism does, and to that extent makes science less unified. The second full paragraph on p. 408 gives a nice summaric formulation of this thought. And here is a feisty Fodor again in 1997 (from “Special Sciences: Still Autonomous After All These Years”, Philosophical Perspectives, 11, pp. 149-63, see esp. pp. 160-161):

The very existence of the special sciences testifies to reliable macrolevel regularities that are realized by mechanisms whose physical substance is quite typically heterogeneous […] Damn near everything we know about the world suggests that unimaginably complicated to-ings and fro-ings of bits and pieces at the extreme microlevel manage somehow to converge on stable macrolevel properties.

On the other hand, the ‘somehow’ really is entirely mysterious, and my guess is that that is what is bugging Kim […] [Kim] doesn’t see why there should be (how there could be) [macro level regularities] unless, at a minimum, macrolevel kinds are homogeneous in respect of their microlevel constitution. Which, however, functionalists in psychology, biology, geology, and elsewhere, keep claiming that they typically aren’t.

MICHAEL POLANYI, “LIFE’S IRREDUCIBLE STRUCTURE” (1968)

“…the organism is shown to be, like a machine, a system which works according to two different principles: its structure serves as a boundary condition harnessing the physical-chemical processes by which its organs perform their functions. Thus, the system may be called a system under dual control. Morphogenesis, the process by which the structure of the living beings develops, can then be likened to the shaping of a machine which will act as a boundary for the laws of inanimate nature.”

‘A boundary condition is always extraneous to the process which it delimits. In Galileo’s experiments on balls rolling down a slope, the angle of the slope was not derived from the laws of mechanics, but was chosen by Galileo. And as this choice of slopes was extraneous to the laws of mechanics, so is the shape and manufacture of test tubes extraneous to the laws of chemistry. The same thing holds for machine-like boundaries; their structure cannot be defined in terms of the laws which they harness…. Therefore if the structure of living things is a set of boundary conditions, this structure is extraneous to the laws of physics and chemistry which the organism is harnessing. Thus the morphology of living things transcends the laws of physics and chemistry.”

DNA acts as a blueprint. It functions as a code of instructions. “As the arrangement of a printed page is extraneous to the chemistry of the printed page, so is the base sequence in a DNA molecule extraneous to the chemical forces at work in the DAN molecule.”

“…the existence of dual control in machines and living mechanisms represents a discontinuity between machines and living things on the one hand and inanimate nature on the other hand, so that both machines and living mechanism are irreducible to the laws of physics and chemistry.”

“…the control of a system by irreducible boundary conditions does not interfere with the laws of physics and chemistry. A system under dual control relies, in fact , for the operations of its higher principle, on the working of principles of the lower level, such as the laws of physics and chemistry.”

Biological Hierarchies Consist of a Series of Boundary Conditions.

Living beings comprise a whole sequence of levels forming such a hierarchy.

“Each level relies for its operations on all the levels below it. Each reduces the scope of the one immediately below it by imposing on it a boundary that harnesses it to the service of the next-higher level, and this control is transmitted state by stage, down to the basic inanimate level.”

P.W. ANDERSON; “MORE IS DIFFERENT: BROKEN SYMMETRY AND THE NATURE OF THE HIERARCHICAL STRUCTURE OF SCIENCE” (appeared in Science, 1972, based on a talk given in 1967)

The “reductionist hypothesis” widely accepted by scientists.

But “[t]he ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe. In fact, the more the elementary particle physicists tells us about the nature of the fundamental laws, the less relevance they seem to have to the very real problems of the rest of science, much less to those of society. The constructionist hypothesis breaks down when confronted with the twin difficulties of scale and complexity.”

While symmetry is of great importance in physics, where symmetry is the existence of different viewpoints from which the system appears the same,…the internal structure of a piece of matter need not be symmetrical even if the total state is,…and the state of a really big system does not at all have to have the symmetry of the laws which govern it; in fact it usually has less symmetry.”

Important examples of “broken symmetries” include crystalline structures, superconductivity, antiferromagnets, ferroelectrics, liquid crystals. “…matter will undergo mathematically sharp, singular “phase transitions” to states in which the microscopic symmetries, and even the microscopic equations of motion are in a sense violated.”

“In some sense, structure – functional structure in a teleological sense, as opposed to mere crystalline shape – must be considered a state, possibly intermediate between crystallinity and information strings, in the hierarchy of broken symmetries. To pile speculation on speculation, I would say that the next stage could be hierarchy or specialization of function, or both. At some point we have to stop talking about decreasing symmetry and start calling it increasing complication.”

BACKGROUND TO KAUFFMAN:

Self-organisation: the tendency of complex systems to become organized – to exhibit particular systemic structural properties or behavioral patterns – where the explanation of this is in important respects not attributable to factors external to the system.

Emergent self-organisation: the self-organisational properties are not mere aggregations of properties of the elements of the self-organising system, but distinct system properties occasioned by non-linear lawfully constrained interactions among the elements.

Order for free: order explainable without appeal to any new fundamental forces or new basic laws of nature.

Kauffman’s View of life as emergent self-organisation, and as order for free: roughly, life as the mathematically expected outcome inherent in the physico-chemical conditions of the right chemical ‘soup’, specifically (1) the relative spatio-temporal placement of the self-organising elements of the system (i.e.its molecules), (2) salient intrinsic chemical properties of these elements, and (3) various lawlike constraints on the local causal interactions of elements having these properties. The math used to model this: ‘autonomous random Boolean NK networks’, where N=the number of elements of the network, K=the number of input links per element, ‘autonomous’ because none of the inputs comes from outside the network’ ‘Boolean’ because a Boolean function is assigned to process each input link, ‘random’ because assigned randomly. (S. Kauffman, “Antichaos and Adaption” Scientific American (August 1991)p. 80)

P.W. Anderson, D.L. Stein: “Broken Symmetry, Emergent Properties, Dissipative Structure, Life; Are They Related? (1987)”

1. Can properties emerge from a more complex system if they are not present in the simpler substrate from which the complex system is formed?

Yes. “In ‘equilibrium’ systems containing large numbers of atoms, new properties such as rigidity or superconductivity, and new stable entities or structures such as quantized vortex lines can emerge that are not just nonexistent but even meaningless at the atomic level.” (p. 446)

2. Are there emergent properties in dissipative systems driven far from equilibrium?

Yes. e.g., dynamic instabilities, like turbulence or convection, which exhibit ‘broken symmetry effects’ (e.g. bifurcations) sometimes (i.e., by Prigogine) called “dissipative structures”

3. Is there a theory of dissipative structures comparable to that of equilibrium structures, explaining the existence of new stable properties and entities in such systems?

No.

Are living structures “stable”?

Life is more stable than vortexes. “…one has an intuitive feeling that living systems have an extraordinary great ability to ignore perturbations and changes in boundary conditions, i.e., to be autonomous and rigid in some sense.”(p. 447) It is relative to time scales, of course.

4. Can we see our way clear to a physical theory of the origin of life that follows these general lines?

Not yet.

“…there is no analogy between the stability, rigidity, and other emergent properties of equilibrium broken symmetry systems and the properties of dissipative systems driven far from equilibrium. The latter types of systems have never been observed to exhibit the rigidity, stability and permanence that characterize the thermodynamically stable broken symmetry systems, nor has any mathematical reason been found why they should….[Yet] it is indeed an obvious fact…that life succeeds in maintaining its stability and integrity, and the identity of its genetic material, at the cost of increasing the rate of entropy production of the world as a whole. It is at least in that sense a stable ‘dissipative structure’” (p. 454)

More recently, cf. “Random Boolean network models and the yeast transcriptional network”, by Stuart Kauffman, Carsten Peterson, Bjorn Samuelsson, and Carl Troein”, “communicated by Philip Anderson” (Note!) in Proceedings of the National Academy of Science, Dec. 9, 2003 vol. 100 no. 25, pp. 14796-14799.

Abstract: “The recently measured yeast transcriptional network is analysed in terms of simplified Boolean network models, with the aim of determining feasible rule structures, given the requirement of stable solutions of the generated Boolean networks. We find that, for ensembles of generated models, those with canalysing Boolean rules are remarkably stable, whereas those with random Boolean rules are only marginally stable. Furthermore, substantial parts of the generated networks are frozen, in the sense that they reach the same state, regardless of initial state. Thus, our ensemble approach suggests that the yeast network shows highly ordered dynamics.

PAUL HUMPHRIES: “HOW PROPERTIES EMERGE”

The exclusion argument:

1. If an event x is causally sufficient for an event y, then no event x* distinct from x is causally relevant to y (exclusion).

2 For every physical event y, some physical event x is causally sufficient for y (physical determinism).

3. For every physical event x and mental event x*, x is distinct from x* (dualism)

4. So: for every physical event y, no mental event x* is causally relevant to y (epiphenomenalism). (Yablo, 1992)

The downwards causation argument:

1.But if emergentism (or non-reductive physicalism) is committed to causation from the mental to the physical (‘downwards causation’), then the exclusion argument rules it out.

2. Emergentism is committed to downwards causation, because:

3. Emergent mental properties must have novel causal powers .

4. These powers must manifest themselves either by causing

physical properties or other mental properties.

5. If the former, there is downward causation.

6. If the latter, then call ‘M*’ the emergent mental property

caused by emergent mental property M.

7. But all emergent mental properties strongly supervene on

physical properties. (supervenience)

Let M supervene on physical property P and M* on P*.

8. How can M* supervene on P* yet have been caused by M?

9. the only way is by M causing M* by causing its supervenience

base P*.

10. So the causal exclusion argument rules out emergence. (Kim, 1992)

Generalizing the above, assume a hierarchy of levels: L0, L1,…,Ln.

The generalized exclusion argument:

Df. An event z is causally connected to a second event x iff x causes z or z causes x. z is causally disconnected from x iff z is not causally connected to x.

1’. If an event x is causally sufficient for an event y, then no event x* distinct from x and causally disconnected from x is causally relevant to y. (exclusion)

Assumption: events are dated particulars; so the exact time of occurrence and manner of occurrence are crucial to an event having the identity that it does.

2’. For every 0-level event y, some 0-level event x is causally sufficient for y (0-level determinism)

3’. For every 0-level; event x and every i-level event x*i (i > 0) x is distinct from x*i (pluralism)

4’. Therefore for every 0-level event y, no i-level event x*i (i > 0) that is causally disconnected from every 0-level event antecedent to y is causally relevant to y.

Note: this argument, claims Humphries, allows higher level events to causally affect 0-level events if the former are part of causal chains that begin and end at the 0-level.

How might this go? Very roughly, let us suppose that occurrences of emergent properties happen as a result of the fusion of occurrences of lower level properties, where fusion is a physical operation, an example of which could be causal interaction. Think of causal interactions as taking place over time, so that the onset of the causal fusion operation at the lower level i will be t1 and the resulting property occurrence at level i+1 will be at t2 > t1. We are to think of fusion as involving the ‘submergence’ (to coin my own phrase ;-) of the lower level properties. They no longer exist at the same time as the supervenient property occurrence. But supervenience is a synchronic relation between property occurrences. So at t1 we do not yet have supervenience, and at t2 we have a violation of supervenience. At no point do we have supervenience! Similarily, think of the“defusion” of a property occurring at level i+1 as a causal process whereby it comes not to exist, and the erstwhile submerged lower level property occurrences whose fusion originally led to its existence now themselves reappear at level i.

“MAKING SENSE OF EMERGENCE,” JAEGWON KIM (1999)

Part I (pp. 127-139): re. Explanation, Prediction, and Reduction

p. 128; “…the fortunes of reductionism correlate inversely with those of emergentism (modulo the rejection of substantival dualism).”

Can we make the idea of emergence at least intelligible?

Two groups of ideas usually associated with emergence:

Group 1: emergents are ‘novel’ and ‘upredictable’ from knowledge of their lower-level bases, and are not ‘explainable’ or ‘mechanistically reducible’ in terms of their underlying properties.

Group 2: emergent properties bring into the world new causal powers of their own, and have powers to influence and control the direction of lower level processes from which they emerge.

Kim takes the Group 1 ideas as ‘constitutive ‘ of the idea of an emergent property, and proposes to make this idea coherent in terms of a certain model of reduction. Then in Part II (pp. 139-150) he will argue against the ideas of Group 2.

p. 130; ‘Mereological Supervenience’: systems with an identical total microstructural property have all other properties in common; i.e., all properties of a physical system supervene on, or are determined by, its total microstructural property. Among those properties supervenient on a system’s total microstructural property, some may be emergent, while others are (merely) resultant.

Re. Unprediictability. The emergent properties are novel and unpredictable from the base properties, while the merely resultant properties are familiar and readily predictable.

pp. 130-1; “…an emergent property is new in an epistemological sense because it is unpredictable, and it is new in a metaphysical sense because the emergent property has new causal powers.”

The predictability that is denied by emergentists is theoretical unpredictability, not inductive unpredictability. We can know all there is to be known theoretically about the basal conditions M of emergent property E, but this alone will not suffice to predict E.

Re. Reductive unexplainability.

What would constitute such reductive explainability of an emergent property E?

The functional conception of reduction. For emergent property E to be reducible to the reduction base B,

(1) it first must be ‘functionalized’, i.e., construed or reconstrued as a property defined by its causal/nomic relations to other properties, specifically those in the B, where this definition would take roughly the following form: Having E =def Having some property P in B such that (i) C1,…,Cn cause P to be instantiated, and (ii) P causes F1,…,Fm to be instantiated; (Discussion)

(2) then realizers of E in B must be empirically detected; and finally

(3) how those realizers of E in B perform the causal tasks constitutive of E must be theoretically explained. (cf. pp. 132-3)

How this type of reduction differs from classical theoretical reduction: it involves no bridge laws or derivation of laws. Yet it can be held to meet the explanatory and predictive requirements of reduction.

The explanatory question: Why do systems exhibit E whenever they instantiate Q?

Ans: because E is a functional property defined by causal role C, and Q is a realizer of E for these systems, and there is a theory that explains how Q realizes E in these systems.

The predictive question: Will this system exhibit E at time t?

Ans. We can so predict on the basis of having identified a realizer of E for the system solely on the basis of knowledge of the causal/nomic relations obtaining in the base domain. What enables the prediction of a higher order property is the conceptual connections generated by the functionalization of the higher properties , not bridge laws taken as auxiliary premises.

The ontological question: In what sense does the functional model of explanation provide a model of reduction? That is, if system S having E has been explained in terms of the functional definition of E together with the detection of a realizer Q, of E in S and an account of how Q realizes E, has the occurrence of E in S been reduced to the occurrence of Q, and can E’s occurrence be said to be nothing over and above Q’s occurrence? (Discussion.)

Ans. We must carefully distinguish here between the case of tokens of the property E and the property type E per se.

A. Tokens (instances) of the type E obey

‘The causal inheritance principle’: if a functional property E is instantiated on a given occasion in virtue of one of its realizers, Q, being instantiated, then the causal powers of this instance of E are identical with the causal powers of this instance of Q.

But if the causal powers of these tokens of E and Q are identical, what empirical reason could we have for deny that the tokens per se are identical? (p. 137). (Discussion)

B. Turning now to consider the issue of reduction as it applies to types, the property type E may have multiple realizers, with different tokens realized by tokens of disparate realizers. So under what conditions may we regard E as having been reduced?

(1) Should we (could we) identify the property type E with a disjunction of the types of all of its actual and potential realizers? (Discussion.)

(2) Should we deny E as a genuine property, as opposed to a concept? (Discussion.)

(3) Or should we embrace the emergence of E and therefore its irreducibility? (But then, e.g., where does this leave the proposed account, in A above, of the reduction of each of its tokens? Discussion.)

If acceptable, (1) would count as a ’conservative’ reduction, while (2) would be an ‘eliminative’ reduction.

(3), says Kim, is the view favored by many philosophers, but it is, he claims, problematic when Group 2 ideas about emergence are added. (See Part II)

Kim also suggests that if anything is going to turn out be emergent, it will be the phenomenal properties of consciousness. They are the most likely to resist functionalization entirely. (So presumably he think that this would apply to both types and tokens of these properties.)

As for what properties may turn out to be emergent, then, Kim is comparable to McLaughlin in leaving just the emergence of consciousness as an open question, but unlike McLaughlin, expressing a bias in favor of it. Where does this bias come from? McLaughlin took the issue to be an empirical one, to be settled by science. Kim appears to be appealing a prioiri to his intuition or sense that the phenomenal properties of consciousness experience are intrinsic and non-relational, and therefore not subject to functionalization.

Would it follow, then, that if Kim’s bias were borne out, then, given his line of argument, in Part II (still to come) against emergent properties having causal powers, Kim would be willing to bite the bullet and regard the phenomenal properties of consciousness as epiphenomenal?

Kim also briefly expresses doubts, citing Chalmers, about self-organizational phenomena being emergent in his sense. (Discussion.)

PART II: Downward Causation, The Very Idea.

Why posit emergent properties if they are not going to have causal powers? But one may distinguish between “horizontal” causal powers, i.e., those that are exercised and have their effects at the level of structure at which the emergent property occurs, and “vertical” causal powers, i.e., those exercised by the emergent property and having their effects at higher or lower levels of structure. The latter direction would be so-called “downward causation”(p. 139).

Early emergentists were interested in the history or evolution of order in the world – how molecules arose from atoms, how life arose from chemistry, and in general how higher levels of structure arose from lower levels. But contemporary emergentists accept the layered model of the world, and are interested in the synchronic structure of the world, or its structure over small (not historical ) time intervals, how it all hangs together (p. 140). (Discussion)

Central doctrines of emergentism:

1. the emergence of complex higher-level entities, entities that are new structural configurations of lower level entities

2. the emergence of higher level properties, that are not merely ‘resultants’ of the properties of lower constituents of the emergent entity (or system), but new properties not occurring at the lower level of structure, and where the relation between the occurrence of the lower and higher level properties is understood in terms of causation or in terms of supervenience.

3. Emergent properties are not predicable from exhaustive information about their “basal conditions”

4. Emergent properties are neither explainable nor reducible solely in terms of their basal conditions.

5. Emergent properties have novel and irreducible causal powers of their own (pp. 140-141)

But the causal power of emergent properties can only be understood in terms of downward causation. I.e., either upwards or same level causation presupposes downwards causation. First, upwards causation presupposes same level causation; e.g., the beauty of the sculpture , assuming it to be an emergent property of the sculpture, was brought bout by the physical work of the sculptor on the block of marble, and this latter is an instance of same level causation. Second, same level causation presupposes downwards causation, except in the limiting case of the very bottom level of structure (if there is one), according to the following ‘principle of downward causation’:

To cause any property (except those at the very bottom level) to be instantiated, you must cause the basal conditions from which it arises (either as an emergent or as a resultant). (p. 143)

So downward causation must be coherent if emergent properties are to have causal powers.

Now there is nothing incoherent in general about the idea of downward causation, cf. Kim’s smashing vase example, p. 144.

The problem arises in cases of “reflexive downwards causation”, cf the discussion of Roger Sperry’s wheel example, and eddies, p. 145. Can one hold both upwards determination of the emergent property and its downward reflexive causal influence? (p. 146)

Case 1: At a certain time t, a whole, W, has emergent property M, where M emerges from the following configuration of conditions: W has a complete decomposition into parts a1,…,an, each ai has property Pi, and relation R holds for the sequence a1,…,an. For some ai W’s having M at t causes aj to have Pj at t.

This case is incoherent, claims Kim, because it violates ‘the causal power actuality principle’:

For an object x to exercise at time t the causal/determinative powers it has in virtue of having property P, x must already possess P at t. When x is caused to acquire P at t, it does not already possess P at t and is not capable of exercising the causal/determinative powers inherent in P. (Discussion: Kim’s rejection of a mutual causal interdependence interpretation of this)

Case 2: As before, W has an emergent property M at t, and aj has Pj. We now consider the causal effect of W’s having M at t on aj at a later time t+ Delta t. Note that this is a case of Diachronic reflexive downwards causation.

This latter type of downwards causation escapes the problems noted in Case 1. Which brings Kim to his ‘critical question’ on p. 149: If an emergent, M, emerges from basal condition, P, why can’t P displace M as a cause of any putative effect of M, e.g., P*? Why cannot P do all the work in explaining why an alleged effect of M occurred? He then argues thus:

“…if causation is understood as nomological (law based) sufficiency, P, as M’s emergence base, is nomologically sufficient for it, and M, as P*’s cause is nomologically sufficient for P*. Hence (by transitivity) P is nomologically sufficient for P*, and hence qualifies as its cause.” (p. 149).

But, then why couldn’t this be viewed as a causal chain with emergent M as an intermediate link? And now here is the revealing clinker. Kim does not suppose that causation can be understood simply as nomological sufficiency, as per the antecedent in the quotation. He does not think that the emergence of M from P can be regarded as a causal relation. P* has P as its sufficient cause (by invoking physical causal closure). M is “otiose and dispensible” as a cause of P*. M can serve as a cause of anything only if it isn’t emergent but reducible to lower level properties (p. 150).

DOWNWARD CAUSATION AND AUTONOMY IN WEAK EMERGENCE

Mark A. Bedau

The problem of emergence.

· Complexity Science as the science of ‘weak’ emergence.

· Two ‘hallmarks’ of emergence explain why emergence is controversial: (1) emergent phenomena are dependent on underlying processes; (2) emergent phenomena are autonomous from underlying processes.

· Explaining the way in which both (1) and (2), may require some ‘revisionary metaphysics’ (p. 157).

Three kinds of emergence.

· ‘nominal emergence’: when a macro-property is the kind of property that cannot be a micro-property. [dependency: nominally emergent properties are properties of macro wholes that are dependent on their micro constituents; autonomy: nominally emergent properties do not apply to the underlying entities.]

· ‘strong emergence’: when a nominally emergent macro property also supervenes on properties at the micro level, and grounds irreducible causal powers. [dependency: strongly emergent properties supervene on the properties of their underlying base; autonomy: strongly emergent properties ground irreducible causal powers.]

· ‘weak emergence’: when emergent causal powers can be explained from full knowledge of the micro facts, but only in a certain ‘complex’ way [dependency: weakly emergent phenomena are ontologically dependent on and reducible to their underlying phenomena; “their existence is nothing more than the coordinated existence of certain microphenomena”; autonomy: weakly emergent phenomena have explanatory autonomy and irreducibility given the complex way that they are generated.] (p. 160)

Weak emergence as underivability except by simulation.

“Assume that P is a nominally emergent property possessed by some locally [ontologically] reducible system S. Then P is weakly emergent iff (Df.) P is derivable from all of S’s micro facts but only by simulation” (p. 162). Compare this with the following sufficient condition: “P is weakly emergent if in principle underivable except by finite feasible simulation”. That might seem too epistemic. The definition is meant to express a formal limitation, not an epistemic one: a Laplacian supercalculator could not derive weakly emergent properties except by simulation. (p. 163).

“A derivation by simulation involves the temporal iteration of the spatial aggregation of local causal interactions among micro elements….Derivation by simulation is the process by which causal influence typically propogates in nature….Natural systems compute their future behavior by aggregating the relevant local causal interactions and iterating these effects in real time. They “simulate” themselves in a trivial sense…The behavior of weakly emergent systems cannot be determined by any computation that is essentially simpler than the intrinsic natural computational processes by which the system’s behavior is generated.” (p. 164. For more on this notion of simulation and of ‘natural computation,’ see the short paper by Stephen Wolfram, “Undecidability and Intractability in Theoretical Physics” pp. 387-393 of your text.)

Downward causation of weak emergence.

1. Ordinary downward causation is unproblematic (cf. examples p. 177)

2. Weak downward causation is simply a species of ordinary causation: macro causal powers are constituted by the causal powers of their micro constituents, and these are typically so complicated that the only way to derive their effects is by iterating their aggregative, context-dependent effects – i.e., by simulation.

· Since a weak macro cause is identical with the aggregation and iteration of micro causes, weak macro causation cannot violate micro causal laws.

· Since a weak macro cause is nothing more than the aggregation of micro causes, macro and micro causes are not two things that can compete with each other for causal influence.

· Weak downwards causation is diachronic; it cannot alter the conditions from which it arose. (cf. pp. 177-8)

The autonomy of weak emergence.

But then, how could the explanations of weak emergence be sufficiently autonomous? If the underlying explanation of the macro phenomena is merely the aggregation of micro-phenomena, how could there be macro level explanatory autonomy?

Is ‘the autonomy’ merely epistemic? (p. 179)

Sometimes, but not always. Sometimes, in addition to the aggregative micro causal history, there is an overarching, generalizing macro explanation that captures counterfactual patterns not derivable from the micro-history, such that if that if various details of that micro-history had been different, if the micro explanation had varied in an indefinite variety of different ways, the macro explanation would still have been true. The macro-explanation is to that extent autonomous from the micro-explanation, and contributes something to our understanding of the weakly emergent phenomenon: why it was to be expected independently of many of the underlying micro details, why it is a ‘universality’. (cf. transit strike example, pp. 181-182).

[Compare, e.g., Fodor, and other defenders of special science autonomy.]

“EMERGENCE AND EXPLANATION,” CH. 6 OF BEING THERE (1998)

Andy Clark

“What kinds of tools are required to make sense of real-time, embodied, embedded cognition?” (p. 103)

3 Styles of Cognitive-Scientific Explanation:

1. Componential explanation; explaining the functioning of the whole by detailing the individual roles and overall organization of its parts. This is a kind of ‘reduction’, but contrasts with traditional ‘theoretical reduction’, in that it does not involve explaining by derivation of higher level laws from lower level laws plus bridge principles, but involves explaining via the development of a ‘partial model’. Note: the ‘whole’ can either be, e.g., a brain, or a brain together with the the body that it is in and the surrounding environment in which the body is embedded (‘extended mind’). Typical examples of such explanation may involve the positing of representational functions to various parts of the whole, where what is being represented is elements in the environment and is determined by suitable interactions with those elements.

2. ‘Catch and Toss’ explanation; like componential explanation, but the brain is flagged as central to explanatory understanding. There is a primacy to ‘inner processing’. The world tosses inputs to the brain, which catches them, and then processes them, leading to action in the world, while a firm boundary is maintained between the brain and the rest of the world.

3. Emergent explanation; consider, e.g., convection rolls, a ‘self-organizing’ property of a contained collection of liquid molecules. Once heat is applied and the rolling begins, the convection feeds and maintains itself. There is a sense in which the actions of the parts cause the overall behavior, and simultaneously, the over-all behavior guides the actions of the parts (‘circular causation’, p. 107). Convection rolls are an instance of ‘direct emergence’: the emergent phenomena can be tweaked by tweaking one of the system’s external ‘control parameters’, in this case temperature. But the convection behavior is not centrally or internally controlled. So, there is emergence in this sense whenever interesting non-centrally-controlled behavior ensues as a result of the interactions of multiple simple, homogeneous components within a system. (p. 109)

One models convection cells by introducing ‘collective variables’ (cf. p. 108), that fix on and track ‘higher level’ features such as the behavior of the convection cell, and do not track properties of the component molecules in the container. By plotting the values of such collective variables as a system unfolds over time, we may come to understand important facts about the actual and potential behavior of the larger system. And by plotting the relation between the values of the collective variable and the system’s control parameters, we may come to understand important facts about the circumstances in which the higher–level patterns will emerge, when one will give way to another, (e.g., bifurcations, chaos) etc..

Sometimes functionally valuable side-effects are brought about by the interactions of heterogeneous components, which ‘foregrounds’ the action between behavior systems and local environmental structure (p. 109). The example is given of a robot programmed in such a way that it will back into its recharging station, between two poles. The charging station is indicated by a light. The robot is programmed with a phototaxis system that yields a zig-zag approach towards any light source, and an obstacle avoidance system that causes the robot to turn away when it hits something. That is all the programming required. Clark calls this ‘indirect emergence’ (because there is something fortuitous or undirected about it?).

Sometimes the emergent phenomena comes about as a result of ‘uncontrolled variables’, where these are variables which track behavior or properties that arise from the interaction of multiple parameters and hence tend to resist direct and simple manipulation.

So Clark arrives at the following general understanding of ‘emergent phenomena’: a phenomena is emergent if best understood by attention to the changing values of a collective variable of a system, where all uncontrolled variables are collective, and where sometimes we must think of the system as (at times) extended to include aspects of its environment (p.112)

There will be degrees of emergence, a la Wimsatt, correlated with degrees of complexity of the interactions involved. Wimsatt’s “aggregate systems” are limiting cases, for which componential explanation alone is perhaps best suited, or sufficient. The more complex and interesting systems are ones evidencing nonlinear relations among the explanatorily salient variables, where a nonlinear relation between variables is one in which the two quantities do not alter in smooth mutual lockstep. Instead, the value of one quantity may (e.g.) increase for some time without affecting the other at all, and then suddenly, when some hidden threshold is reached, cause the other to make a sudden leap or change.” (n. 8, p. 236)

It is Dynamic Systems Theory which provides the explanatory framework for emergent explanations as sketched above. Dynamic Systems Theoretic explanations owe their explanatory status to their ability to help us find and learn to detect dynamic patterns (cf. p. 125) of behavior and illuminate counterfactual aspects of the occurrence of those patterns wrt the behavior of structural elements of the system. But they do this without showing us how to build such a system from simple well-understood phenomena. Rather, DST explanations abstract from the micro-details of the physical structure of the system to the topological structure of the system’s dynamics. (pp.117 ff.)

But it is not a choice, insists Clark, between emergent explanation and, say, componential explanation or the computational modelling of catch and toss explanation. We need all three. The system parameters tracked in DST explanations of an agent’s behavior can be arbitrarily far removed from facts about their real internal structure and processing (p. 118). To really understand a complex phenomenon, an uncontrolled collective variable, it is at least necessary that we understand “at least something” of how it’s behavior is rooted in the more basic properties of the system’s biological or physical proper parts. What is really needed for full understanding of the system is a kind of ‘explanatory interlock’ between all three modes of explanation, where each mode of explanation constrains the others (pp. 125, 126).

“REAL PATTERNS”: Daniel Dennett

A question raised by Clark’s account of emergent explanation is the extent to which it nudges us towards a kind of epistemological emergence; not Hempel’s kind, of course, at least not to the extent of embracing Hempel’s Deductive-Nomological conception of explanation, and his conception of theoretical reduction to physics as our ontological scientific goal, with talk of epistemological emergence as a hopefully a mere temporary expedient; but rather explanation as abstract model construction, whose explanatory force lies centrally in the accuracy of its counterfactual predictions about the behavior of the system modelled, and not necessarily in giving us, or contributing to our having, an accurate representation of the ontological nature of the system’s constitutive parts or even of its system features.

Enter Daniel Dennett, who published an influential paper which brought useful focus to the discussion of this very issue. When we seem to discern patterns or regularities in the behavior of a system, patterns which seem to help us understand something about its nature, which can sometimes lead to the discovery of ways to predict and control its behavior, what is the status of these patterns? Dennett identifies a number of dimensions of this issue. Are patterns real? In what sense do they exist? Where are they located? If you cannot discern the pattern might it still be there --are there indiscernible patterns?

One contrast offered is between the idea of pattern and the idea of “utter randomness”. Dennett here invokes Gregory Chaitin’s definition of mathematical randomness of a series of entities (dots, numbers, functions, whatever): it is random iff the information required to describe (transmit) the series accurately is incompressible in the sense that nothing short of the full bit map will preserve the series. The series is not random – has a pattern – iff there is some more efficient way to describe it (p. 193). ‘Detecting the pattern is just finding one of these more efficient ways of describing it.

[As somewhat of an aside, a question: Is there an interesting connection between this notion of incompressibility and Bedau’s notion of derivability of the occurrence of an emergent phenomenon from the underlying base, but only by simulation?]

But what if the series is taken to be compressible in a certain way only under the assumption that certain observed deviancies from this would-be compression are the result of “noise”? So in adopting the compressed, more efficient, description – in attributing the pattern – we seem then to be idealizing away from our actual observations, our data, in order to embrace it. This kind of idealization could sometimes be thought of as a mere ‘rounding out’ idealization, if, as per Dennett’s barcode example D, there are just a few stray pixels one has to ignore in order to see it as a nice neat row of 5 black squares. In D there is just 1% variance from the proposed compression. But what if it were 25% variance like in his barcodes A and C? What if it is 33% or even 50%, as with his barcodes E and F respectively? Is the pattern really there in F? We cannot eyeball it. Our only reason for thinking it is there is that we have been told about the settings on the algorithm that generated it. Is that enough?

Independent of this, a limitation of Dennett’s barcode example for our context is that the kind of patterns that are central to dynamic system theoretic explanations are diachronic patterns of behavior, where the values of different system variables salient to the pattern are tracked over time. The relevant pattern, if there is one, is a pattern in the relations between the values of the system’s parameters. So it isn’t something that you can just eyeball in the system, like you can eyeball a barcode. Maybe it is something you can in effect detect by eyeballing a piece of paper on which the changing values of these parameters over time have been recorded.

Dennett’s gives a definition of pattern formulated so as to accommodate the above:

A pattern exists in some date – is real – if there is a description of the data that is more efficient than the bit map, whether or not anyone can concoct it. (p. 194)

[Questions:

(1) How (if at all) might this idea of pattern be seen as accommodating or helping with the idea of emergent phenomena?

(2) Does it provide a compelling model for the existence of emergent phenomenon, or just for the objectivity of explaining something by alluding to a pattern or an emergent phenomenon?]

Now if there are a few apparent counterexamples to the proposed compression in the data, it could be explained away in various ways, such as limitations in the ways in which we are measuring the values of these parameters. We could suppose that the projected pattern really is there in the behavior of the system, and that this would be increasingly confirmed with the improvement of our measuring methods. So, ‘in principle’ we could verify its presence. One might think that the presence of idealization in our dynamic models of the behavior of complex systems will always be like that: in principle eliminable by the improvement of our empirical methods of observation and measurement. Once eliminated, if our hypothesized model has been sustained, we can now be assured that it represents a feature of the system. But is all such idealization in our explanatory models eliminable in principle like that?

[Batterman, in one of your readings, argues that there are idealizations that appear to make essential contributions to our explanatory understanding of certain physical phenomena, that are not eliminable in principle in this way.]

A NEW PROBLEM FOR ONTOLOGICAL EMERGENCE

Daniel Heard

I. Intro.

‘Emergent predicates’ are predicable only of whole systems, and allow predictions that would be difficult or impossible to derive from the dynamical laws plus boundary conditions alone; e.g., ‘is convection rolling’. (p. 56)

Ontological emergence says that distinctly emergent predicates can be explained through reference to distinct kinds of property – emergent properties. [What is ‘distinct in kind’ about properties that are said to be emergent?]

Epistemological emergence denies that there is a distinct class of emergent properties. Rather, the distinction between emergent and non-emergent predicates is rather to be explained through reference to facts about our epistemic status. (p. 56) [Such as our inability to derive the emergent ones from the underlying dynamics and boundary conditions?]

II. The Old Problem.

Ontological emergentism is incompatible with ‘ontological minimalism’: the latter is committed to ‘mereological supervenience’ of all system properties, whereas emergentism is committed to the denial of this. [Really??] This is ‘the old problem’ of ontological emergence. [It is?]

Mereological supervenience is the view that the properties of the system as a whole are fixed by the properties, including relational properties, of its constituent parts. (p. 57) [Would reference to such fixedness amount to an explanation of the system properties?]

But this incompatibility seems to amount, au fond, to just a question-begging in both directions ‘clash of intuitions’ about the role of ontological parsimony in theory construction, which leaves things in a stalemate. (p. 58)

III. The New Problem

An emergent predicate like ‘is convection rolling’

(1) applies only to a whole system, like a flask of oil, not to its individual lipid molecules of oil. The latter would make no sense (p. 59).

(2) The usefulness of predicating an emergent predicate of a system is that it can enable us to make inferences about the behavior of the system without invoking underlying dynamical laws; e.g., in this case one can predict the motion of a ‘marker’ dropped into the oil: that it will follow a toroidal path, rising up the center of the flask and sinking down again at its edges. (p. 56).

And it is for these reasons that the ontological emergentist wants to reify emergent properties as the referents of emergent predicates. But the problem with this, ‘the new problem’ of ontological emergence, is that both of these sorts of reasons are also satisfied by abstract mathematical predicates such as ‘satisfies the central limit theorem’. (The central limit theorem states that a large number of uncorrelated deviations from a mean yield a normal distribution about that mean.) Such a predicate applies only to systems and not to their individual constituents (i.e., satisfies (1)), and allows us to make predictions about the system without deriving those predictions from underlying dynamical laws. (i.e., satisfies (2)). (p. 60) So if the ontological emergentist is going to reify the property of being a convection rolling, she must by the same token reify the property of satisfying the central limit theorem. “But this will yield what is to many a very implausible ontology indeed”. (p. 60)

IV. Difficulties For Ontological Responses to The New Problem.

Ontological emergentists cannot simply bite this bullet. The reason is that they are committed to the failure of mereological supervenience. [No they are not] “…they think that the emergent properties cannot be explicated [note the leap from mereological supervenience to explication] purely in terms of the properties of the constituents of an emergent system….Yet this is clearly false…” for mathematical predications like ‘satisfies the central limit theorem’, which are defined as a mathematical operation on properties of the constituents (in this case on uncorrelated deviations from a mean). (p. 61)[This all seems very confused.]

If this bullet cannot be bitten, then the only other option is to distinguish between causally efficacious [concrete]emergent properties and the others [abstract], and to only reify the former. Then the property of being a convection roll will be reified, but not the property of satisfying the central limit theorem. But this begs the question against the opponent of ontological emergence, who will argue that all causation is takes place at a more fundamental level. (p. 61) [Sigh.]

But, concludes Heard, surely the explanatory work done by real emergent properties could be done without the need to postulate them, as in various accounts of epistemological emergence, such as those elaborated by Bedau, Clark, and Batterman. So ontological emergence should be abandoned (p. 61-62).

[But are Bedau, Clark, and Batterman plausibly construed as ‘epistemologicall emergentists’ as characterized by Heard? (Cf. n.2 p. 56)

Recall that Bedau defines weakly emergent properties as derivable from all of the system’s micro facts, but only by simulation, where this is meant as a formal limitation: a Laplacian supercalculator could not derive weakly emergent properties except by simulation. That doesn’t

sound like epistemological emergence in Heard’s sense.

Clark takes emergent phenomena to be those “…best understood by attention to the changing values of a collective variable of a system, where all uncontrolled variables are collective,….” The patterns of dynamic behavior that we detect using Dynamic systems Theory are there to be detected in the system, and the topological structure of the dynamics within which they are embedded gives us counterfactual understanding of the behavior of the system. That doesn’t sound like the emergent phenomena are being explained “through reference to facts about our epistemic status”.

Batterman, as we shall see (but in a more recent paper than the work cited by Heard), in discussing the role of mathematical idealizations in the explanation of empirical phenomena, distinguishes between “Galilean” and “non-Galilean” idealizations. The Galilean ones are explanatory stand-ins that we regard as potentially removable through further work. So the view that all explanatory idealizations are Galilean is naturally viewable is epistemically motivated. But Batterman makes clear that he is committed to the existence of ineliminable non-Galilean mathematical idealizations in theoretical explanations of empirical macro-level phenomena. So here is one place, at least, where he seems to eschew a merely epistemic perspective. But does that make him an ontological emergentist? It is not clear. His paper is noted for its studied avoidance of the issue of the existence of mathematical structures, for instance, and instead focuses on the mathematical processes of asymptotic reasoning , and of mathematical ‘limit operations’. But does that make him an epistemic emergentist after all? Well maybe in some sense, but not in Heard’s sense. Batterman is not referring the distinction between emergent and non-emergent predicates to just facts about our epistemic status. He seems to be referring it to facts about the nature of ineliminable logical or inferential relations between our ground level theories and our explanations of ‘emergent’ phenomena. The properties of the singularities we reach asymptotically are, for Batterman, objectively explanatorily revealing.

At the very least this suggests that in order to correctly classify Batterman’s views on emergence we would need a richer taxonomy of options than presented by Heard.

“STRONG AND WEAK EMERGENCE,” DAVID CHALMERS

I. Two Concepts of Emergence (1^st approximations)

A high level phenomenon is strongly emergent wrt a low-level domain when the high level phenomenon arises from the low- level domain, but truths concerning that phenomenon are not deducible even in principle from truths in the low level domain (or: high level truths are not conceptually or metaphysically necessitated by low level truths – see n. 1). Note the this is meant to be incompatible with physicalism. New fundamental laws are required in addition to the fundamental laws of physics

A high level phenomenon is weakly emergent wrt a low level domain when it arises from the low level domain, but truths concerning that phenomenon are unexpected given the principles governing the low-level domain; e.g., the emergence of high level patterns in cellular automata. Note that this is compatible with physicalism.

“If one wants to use emergence to draw conclusions about the structure of nature at the most fundamental level, it is only strong emergence that is relevant.” Weak emergence, on the other hand, can be used to support the physicalist picture of the world.

II. Strong Emergence

Are there strongly emergent phenomena? Yes: consciousness. Facts about consciousness – about what something feels like from the system’s own perspective -- are not deducible from physical facts. Although in our world facts of human consciousness are strongly correlated with physical facts about human brains, it is logically coherent to suppose a world physically identical to this one in every respect yet lacking consciousness.

We must distinguish between deducibility from low level laws and deducibility from low level facts.

“Medium Emergence” (‘intermediate but still radical’): high level facts and laws not deducible from low level laws plus initial conditions. Note that this implies the “incompleteness” of physical laws, and with it the failure to deduce some of the low level facts from low level laws plus initial conditions. Why? Because if all the low level facts were deducible, then presumably a Laplacian demon would be able to deduce the high level facts from there. [Would the Laplacian demon also be able to deduce the high level laws?]

Two concepts of downward causation:

With strong downward causation, the causal impact of a high level phenomenon on low level processes is not deducible even in principle from initial conditions and low-level laws.

With weak downward causation, the causal impact of the high-level phenomenon is deducible but is nevertheless unexpected.

These are both coherent ideas, and stand independently of the notions of strong and weak emergence. One can conceive of strong downward causation without emergence. An example from quantum mechanics may be the so called “collapse of the wave packet due to measurement.

The idea in “medium emergence” about the incompleteness of physical laws can be understood interms of downwards causation. “Such causation requires the formulation of basic principles which state that when certain high level configurations occur, certain consequences will follow….These consequences will themselves either be cast in low level terms, or will be cast in high level terms that put strong constraints on low-level facts. Either way, it follows that low level laws will be incomplete as a guide to both the low level and the high level evolution of processes in the world.”

III. Weak Emergence

Examples: The game of life; connectionist networks; the overloading threshold of an operating system; the evolution of intelligence (p. 9)

Re. Clark’s ‘nominal emergence’: too ubiquitous to be interesting.

Re. ‘deducibility without reducibility’: this would encompass lots of functional properties that do not seem unexpected or interesting enough to be weakly ‘emergent’.

Some elaborations of weak emergence, arriving finally at:

A weakly emergent property of a system is an interesting property that is unexpected, given the underlying principles governing the system. E.g., maybe raw consciousnss was not selected for, but it somehow emerges as an unexpected by-product (or ‘spandrel’) of selection for adaptive processes such as intelligence.

Apart from the interesting example, this seems very close to his initial characterization, except for the additional qualifier “interesting”.

TERRENCE W. DEACON ON EMERGENCE

[‘ECE’: “Eliminativism, Complexity, and Emergence” (with Tyrone Cashman), (2007). ‘HWH’: “Emergence: the Hole at the Wheel’s Hub” (2006). ‘HLE’: “The Hierarchic Logic of Emergence: Untangling the Interdependence of Evolution and Self-Organization” (2003).]

Ontological emergence.

What emerges? “The answer is not some ‘thing’, but rather something like a form, or pattern, or function. The concept of emergence seems to apply to phenomenon in which relational properties tend to dominate over constituent properties in determining aggregate features….it is with respect to the configurations and topologies, not the specific properties of constituents that we trace processes of emergence” (HLE, 276).

“Emergence is about the topology of causality.” (HLE, 281)

“In functionalist accounts, only certain substrate details are essential; others may vary without functional consequence. But function is defined extrinsically, at least in computer science and cognitive theories, because function is a semiotic distinction, not a physical one. What is the physical analogue? It is…something like topology: the form, configuration, or distribution of component features.” (HLE, 282)

“…topology is not just a descriptive feature of a physical system, it is a constitutive fact about the spatio-temporal relationships among component elements and interactions with intrinsic causal consequences.” (HLE, 282)

“What needs to be explained…is not a new form of causality, but how some systems come to be dominated by their higher order topological properties so that these appear to “drag along” component constituent dynamics, even though, at the same time, these higher order regularities are also constituted by lower-order interactions. In other words, an explanation of how topologies come to make a difference is required. I believe that the secret to explaining this lies in what can be called amplification processes. I believe that we can understand emergent phenomena as all being variant forms of what might be called topological reinforcement or amplification in pattern formation….I will argue that a kind of compound interest of topologies is the basis for all forms of emergence. We are justified in calling something “emergent,” I will suggest, if it is the result of a recurrent amplification of configuration or topology. This recurrent architecture is itself a topological concept, so in some sense emergence is a special case of topological transformation of topologies. Wherever it occurs, amplification is accomplished by a kind of repeated superimposition of similar forms….In all cases, it is a form that is amplified; repetition either multiplies the number of its appearances in some physical medium, or else gets it embodies in a progressively larger fraction of the physical medium (as in sound amplification). Thus amplification is a kind of compound interest of physical form….amplification occurs because of iterated superimposition of events sharing the same form occurring across levels of scale”. (HLE, 283-4)

Other causal topologies contributing to such amplification: ‘circular causation’ in positive and negative feedback systems. (cf. HLE 284-5)

“By ‘amplified’ I mean something like “come to be more coherently expressed over ever more extensive scales of both space and time.” (HLE, 286)

“The critical role played by ascent in scale in physical emergence is that it creates the context for causal circularity and amplification. It affords the substrate for structural influences to recirculate, so to speak.” (HLE, 287)

“The causal architectonic feature I will use as my central diagnostic feature might be described as trans-scale causal recursion, that is, circles of deviation amplifying causality that develop up levels of scale. (HLE, 287)

COMPARE:

“…the key to understanding emergent phenomena is to understand organization in terms of what is not included, not realized, not present…a “constitutive absence,” created by a “…constraint: that which reduces the possible degrees of freedom of a process…. E.g., self-organisation is merely an intrinsically arising asymmetric change from more to fewer dynamical tendencies, which results when a system is continually perturbed, or pushed away from thermodynamic equilibrium.” (ECE, 200)

“The principal hypothesis of this essay is that emergent phenomena grow out of an amplification dynamic that can spontaneously develop in very large ensembles of interacting elements by virtue of the continuing circulation of interaction constraints and biases, which become expressed as system-wide characteristics. In other words, these emergent forms of causality are due to a curious type of circular connectivity of causal dynamics, not a special form of causality. This circularity enables certain distributional and configurational regularities of constituents to reinforce one another iteratively throughout an entire system.” (HWH: 124)

‘1^st order emergence’: simple higher order properties of an aggregate, such as the statistically or stochastically determined phase states of matter, e.g., liquidity, whose occurrence can, without distortion, be regarded as synchronically related to the underlying properties of the liquid molecules. (HLE, 288)

‘2^nd order emergence’: “Whereas micro-configuration can be ignored in 1^st order emergent systems, with minimal loss of descriptive adequacy, this is not the case for systems exhibiting 2^nd order emergence, such as chaotic and self-organised phenomena”. Also ‘autopoietic’ systems. See discussion of snow crystal formation, and Kauffman’s ‘autocatalytic’ sets. (HLE, 294-6) What these systems of 2^nd order emergence have in common is “…a kind of tangled hierarchy of causality where micro-configurational particularities can be amplified to determine macro-configurational regularities, and where these in turn further constrain and/or amplify subsequent micro-configurational regularities.” (HLE, 296)

3^rd order emergence’: adds some form of information or memory to 2^nd order emergence, and a developmental or evolutionary (thus temporal, diachronic) character, adding an “…additional loop of recursive causality, enclosing the 2^nd order recursive causality of self-organised systems. E.g. life even in its simplest forms. (Re. consciousness, see last 2 sentences, HLE, 306)

SELF, SENTIENCE, AND CONSCIOUSNESS,

from the final three chs. of

INCOMPLETE NATURE: HOW MIND EMERGED FROM MATTER, by TERRENCE W. DEACON,

W.W. Norton & Co., (N.Y., 2012, pp. 463 ff.)

Definitions from the Glossary (pp. 547-53):

Emergence: A term used to designate an apparently discontinuous transition from one mode of causal properties to another of a higher rank, typically associated with an increase in scale in which lower–order component interactions contribute global properties that appear irreducible to the lower order interactions. The term has a long and diverse history, but throughout this history it has been used to describe the way that living and mental processes depend upon chemical and physical processes, yet exhibit collective properties not exhibited by non-living and non-mental processes, and in many cases appear to violate the ubiquitous tendencies exhibited by these component interactions.

Strong Emergentism: The argument that emergent transitions involve a fundamental discontinuity of physical laws.

Weak Emergentism: The argument that although in emergent transitions there may be a superficially radical reorganization, the properties of the higher and lower levels form a continuum, with no new laws of causality emerging. Often associated with epistemological emergentism because it is attributed to incomplete knowledge of the critical causality.

Emergent dynamics: A theory developed in this book which explains how homeodynamic (e.g., thermodynamic) processes can give rise to morphodynamic (e.g., self-organising) processes, which can give rise to teleodynamic (e.g., living and mental) processes. Intended to legitimize scientific uses of ententional (intentional, purposeful, normative) concepts by demonstrating the way that processes at a higher level in this hierarchy emerge from, and are grounded in, simpler physical processes, but exhibit reversals of the otherwise ubiquitous tendencies of these lower-level processes.

Constraint: The state of being restricted or confined within prescribed bounds. Constraints are what is not there but could have been. The concept of constraint is, in effect, a complementary concept to order, habit, and organization because something that is ordered or organized is restricted in its range and/or dimensions of variation, and consequently tends to exhibit redundant features or regularities. A dynamical system is constrained to the extent that it is restricted in degrees of freedom to change and exhibit attractor tendencies. Constraints can originate intrinsic or extrinsic to the system that is thereby constrained.

Attractor: An attractor is a “region” within the range of possible states that a dynamical system is most likely to be found within. The behavior of a dynamical system is commonly modeled as a complex “trajectory of states leading to states” within a phase space (typically depicted as a complex curve in a multidimensional graph). The term is used here to describe one or more of the quasi-stable regions of dynamics that a dynamical system will asymmetrically tend toward. Dynamical attractors include the state of equilibrium of a thermodynamic system, the self-organized global regularity converged upon by a morphodynamic process, or the metabolic maintenance and developmental trajectory of an organism (a teleodynamic system). An attractor does not “attract” in the sense of a field of force; rather it is the expression of an asymmetric statistical tendency.

Absential: The paradoxical intrinsic property of existing with respect to something missing, separate, and possibly nonexistent. Although this property is irrelevant when it comes to inanimate things, it is a defining property of life and mind. Elsewhere described as a constitutive absence.

Constitutive absence: A particular and precise missing something that is a critical defining attribute of “ententional” phenomena, such as functions, thoughts, adaptations, purposes, and subjective experiences.

Homeodynamics: Any dynamic process that spontaneously reduces a system’s constraints to their minimum and thus more evenly distributes system properties across space and time. The second law of thermodynamics describes the paradigm case. [previously ‘1^st order emergence’?]

Morphodynamics: Dynamical organization exhibiting the tendency to become spontaneously more organized and orderly over time due to constant perturbation, but without the extrinsic imposition of influences that specifically impose that regularity. [‘2^nd order emergence’]

Teleodynamics: A form of dynamical organization exhibiting end-directedness and consequence-organized features that is constituted by the co-creation, complementary constraint, and reciprocal synergy of two or more strongly coupled morphodynamic processes. [‘3^rd order emergence’]

SELF.

How did we come to be creatures with selves?

In trying to answer this, don’t start with the problem of human subjective experience. Start small. What is the most minimal case where we can feel justified in identifying something vaguely like self? Build up from there an account of the dynamical architecture of subjective self.

Proposal: start with a simple living organism (sans brain). All aspects of their constitution are organized around the maintenance and perpetuation of this form of organization. “It is the circularity of this consequential architecture – teleodynamics – that both delineates and creates the individuality that is ‘organism self’….Understood in this more general sense, self is not a property limited to organisms with brains like humans.” (pp. 465-6). So subjectivity is not a critical defining feature of self. “In an organism…each functional feature embodies a trace of the whole individuated organism, reflecting the coherent influence of the whole and contributing to its future coherence. This is the essence of reflexive individuation: a compositional synergy, functioning to determine its constituents in a way that both embodies and reinforces their synergistic relationship. The whole/part hierarchy thus becomes inextricably tangled.” (p. 469))

The ‘mental self’ is subordinated to and nested within the more general form of self that is characteristic of all living things. The ‘subjective self’ is to be identified with a locus of the mental self’s neurological teleodynamics . The ‘self-as-agent’: the generation of interactive constraints which do work to perpetuate the reciprocal maintenance of the constraints that maintain organism self.

The Extentionless Cogito:

“There is no ghost in the organic machine and no intender serving as a witness to a Cartesian theater. The locus of self-perspective is a circular dynamic, where ends and means, observing and observed, are incessantly transformed from one to the other.” (p. 483-4)

“Thus autonomy and agency, and their implicit teleology, and even the locus of subjectivity, can be given a concrete account. Paradoxically, however, by filling in the physical dynamics of this account, we end up with a non-material conception of organism and neurological self, and by extension, of subjective self as well: a self that is embodied by dynamical constraints. But constraints are the present signature of what is absent. So, surprisingly, this view of self shows it to be as non-material as Descartes might have imagined, and yet as physical, extended, and relevant to the causal scheme of things as the hole at the hub of a wheel.” (p. 484)

SENTIENCE.

Like selves, there are also grades of sentience.

“Reframing the concept of sentience in emergent dynamical terms will allow us to address questions that are not often considered to be subject to empirical neuroscientific analysis. Contrary to many of my neuroscience colleagues, I believe that these phenomena are entirely available to scientific investigation once we discover how they emerge from lower-level teleodynamic, morphodynamic, and thermodynamic processes. Even the so-called hard problem of consciousness will turn out to be reconceptualized in these terms. This is because what appeared to make it hard was our predisposition to frame it in mechanistic and computational terms, presuming that its intentional content must be embodied in some material or energetic substrate.” (p. 489).

“The central claim of this analysis is that sentience is a typical emergent attribute of any teleodynamic system. The distinct emergent higher-order form of sentience that is found in animals with brains is a form of sentience built upon sentience” (p. 508)

“…sentience is constituted by the dynamical organization, not the stuff (signals, chemistry) or even the neuronly cellular-level sentience that constitutes the substrate of that dynamics” (p. 510)

CONSCIOUSNESS

“…we have broken the spell of dualism by focusing attention on the contributions of both what is present and what is absent. Surprisingly, this even points the way to a non-mystical account of the non-materiality of consciousness. The apparent riddle of its non-materiality turns out not to be a riddle after all, but an accurate reflection of the fact the locus of subjective sentience is not in fact a material substrate. The riddle was not the result of any problem with the concept of consciousness, but of our failure to understand the causal relevance of constraint. With the realization that specific absent tendencies – dynamical constraints – are critically relevant to the causal fabric of the world, and are the crucial mediators of non-spontaneous change, we are able to stop the search for consciousness “in” the brain or “made of” neural signals….We are what we are not [so, not what we eat!]: continually, intrinsically, necessarily incomplete in our very nature. Our sense of self, our experience of being the originative locus of agency, our interior subjective isolation, and the sense of emerging out of nothing and being our own prime mover – all these core characteristics of conscious experience – are accurate reflections of the fact that self is literally sui generis, emerging each moment from what is not there. There can be no simple and direct neural embodiment of subjective experience in this sense. This is not because subjectivity is somehow other-worldly or non-physical, but rather because neural activity patterns convey both the interpretation and the contents of experiences in the negative, so to speak; a bit like the way that the space in a mold represents a potential statue. The subjectivity is not located in what is there, but emerges quite precisely from what is not there….I believe that despite its counterintuitive negative framing, this figure/background reversal of the way we conceive of living and mental causality promises to reinstate subjective experience as a legitimate participant in the web of physical causes and effects, and ultimately reintroduce intentional phenomena back into the natural sciences. It also suggests that the subtitle of this book is slightly misleading. Mind didn’t exactly emerge from matter, but from constraints on matter.” (pp. 534-8)

“A ROLE FOR MATHEMATICS IN THE PHYSICAL SCIENCES”

By Christopher Pincock (Nous, 2007)

I. Mathematics can seem theoretically indispensable for physical science, and yet metaphysically dispensable, contra the Quine/Putnam argument. Even if mathematics is theoretically indispensable, it seems to play a different role in physical theories than the positing of theoretical entities.

Field: argues for the metaphysical dispensability of math via arguing for its theoretical dispensability after all, via a nominalization of physical theory.

Balaguer, Azzouni and Yablo, argue for metaphysical dispensability directly in various ways, without insisting on a nominalization of the science.

“Impatient Naturalism”: the view that one can accept both theoretical indispensability and metaphysical dispensability by simply appealing to standards of scientific practice (Burgess and Rosen), without having to come up with an explanation.

“Patient Naturalism”: the view that one should consider various proposed explanations and wait for one that works.

Proposed role of mathematics in physical science: it allows us to make claims about higher-order or large-scale features of physical systems, while remaining neutral about the basic or micro-scale features of such systems. But this only works on the supposition that the pure math in question has a large measure of (mathematical) confirmation prior to its application.

II. III. Can we defend theoretical indispensability by rejecting metaphysical dispensability, say on the grounds of math’s causal irrelevance, because it only has a representational, mapping, or indexing function?

This would seem to fall prey to Field’s nominalistic strategy.

But what about ‘abstract’ explanations in physical theory that do not seem to pivot on a mapping role, or on a coordinate system for units of measurement, but instead on appealing to formal relational features of the system being explained? Cf. the bridges of Konigsberg example; also Batterman’s asymptotic explanations which simplify a fundamental mathematical law by taking one or more of the quantities that it relates to a limit, such as 0 or infinity. Apparently on a Field program these will require their own separate representation theorems (involving a mapping, plus axioms characterizing salient physical properties of the system).

A defender of theoretical indispensability but who accepts such mappings can, contra Balaguer, block the proof of a representation theorem by finding reasons to doubt or withhold assent from some of the axioms (say because of their current lack of empirical support).

Yet even in the face of this, scientists can and do offer abstract mathematical descriptions of physical systems and have these descriptions confirmed to a reasonable degree, even when in ignorance of those many physical features of the system. This amounts to an indispensable epistemic role for mathematics that is consistent with its metaphysical dispensability, and at the same time undermines the role of indispensability arguments for platonism.

IV. Can we accept the indispensability of mathematics to empirical explanation without adjusting our ontological commitments in any way, a la Balaguer, Azzouni and Yablo? Surely we at least have to offer an account of the subject matter of pure mathematics, assigning truth values to its statements that accord with mathematical practice – whether these be Platonist or nominalist.

Balaguer’s nominalistic principles:

(NC) Empirical science has a purely nominalistic content that captures its “complete picture” of the world

(COH) It is coherent and sensible to maintain that the nominalistic content of empirical science is true and the platonistic content of empirical science is fictional.

(TA) Empirical theories use mathematical-object talk only in order to construct theoretical apparatuses (or descriptive frameworks) in which to make assertions about the physical world.

TA is supported by NC and COH, which are in turn supported by a Principle of Causal Isolation for mathematical objects. ‘Mixed facts’ supervene on bottom level physical facts and possibly on purely mathematical facts. But those latter are not needed except to underpin our claims that statements of pure math that we accept are in fact true.

But what if we do not have a good understanding of the physical facts responsible for the physical phenomenon we are investigating? Given such ignorance, NC and COH are surely in doubt for the nominalist. In science, at least, it is surely not rational to fix one’s commitments using an indeterminate collection of claims! Note that the nominalistic content of the bridges of Konigsberg is left completely unspecified, so how will the nominalist deal with this example?

How about replacing COH with COH*?

(COH*) it is coherent and sensible to maintain that the actual bottom-level physical facts render the nominalistic content of empirical science true and the platonistic content of empirical science fictional.

But what is the empirical evidence for that claim? This would require rejecting Quine’s confirmational holistic criterion for existence, via the existential quantifier.

V. Yablo’s “figuralism”; Azzouni’s distinction between ‘quantificational commitment’ and genuine ontological commitment. (The latter would raise the question why scientists are committed to mathematical entities, via quantificational statements, yet not thereby be ontologically committed.)

VI. Objection: Don’t these worries simply apply to those cases of mathematical application that involve idealization? Reply: But those cases are central to the use of math in scientific theories.

Another objection: Can’t these concerns be limited to just the portion of math that we actually do need and use in physical theory (so not requiring a full representation theorem).?...Reply: it remains to be seen.

Wants to conclude from all of this: that we cannot, at present, make our commitments in our mathematical scientific theories determinate without taking the mathematics we use seriously. All of this may be consistent with the eventual removal of mathematics from our scientific theories. But for now, by including it, scientists can formulate definite claims that zero in on those aspects of the physical situation that they wish to take a stand on, while remaining neutral about the aspects they have yet to understand and that are not relevant to the phenomena that they do understand.

“ON THE EXPLANATORY ROLE OF MATHEMATICS IN EMPIRICAL SCIENCE”

Robert W. Batterman

Are there genuine mathematical explanations of physical phenomena? Assuming so, how do they work? (p. 1)

If mathematical objects are abstract and acausal, and if the natural sciences are fundamentally causal, then it would seem that mathematical objects cannot play a fundamental explanatory role. (p.2)

But, as Pincock has argued, there are acausal ‘abstract’ explanations of empirical phenomena, such as the explanation of the bridges of Konigsberg, abstracting away from the physical details to their exhibiting the structure of a non-Eularian graph. (p. 3)

Pincock classifies ‘asymptotic’ explanations with his “abstracting” explanations, but this is wrong, to the extant that the former do not proceed by focusing on abstract structure realized by the physical system. (p. 3)

For instance, to explain why distinct fluids behave the same way at their respective critical temperatures (i.e., at phase transition) one introduces a ‘limiting idealization’ known to be false. And that limiting idealization is explanatorily essential. (pp. 6-7)

“…one can explain the fact that the spacings and intensities of the bows of rainbows are the same, despite the fact that the (causal) details of how each rainbow gets formed will be completely distinct -- for instance the sizes and shapes of the rain drops will vary from rain shower to rain shower. The explanation in this case also involves the taking of a limit: In order to explain the universal pattern we witness in rainbows, we need to examine the wave theory of light in the limit as the wavelength goes to zero. When the wavelength equals zero, we are in the domain of ray theory or geometrical optics, and it turns out that stability properties of ray-theoretic structures explain the universal rainbow pattern that we witness.” (p. 8).

Mapping/structuralist accounts of the role of mathematics in explanations of physical phenomena posit a mapping between some mathematical structure and a physical structure. (p. 8)

That works for the abstract explanation of the bridges of Konigsberg, but not for asymptotic explanations, whose idealizations are false but ineliminable. (p. 8)

…various attempts by mapping account theorists to accommodate the explanatory role of mathematical idealization: matching models, partial mappings…

These attempts seem to presuppose that idealizations are perfectly respectable in science, provided they are “Galilean”, i.e., provided one can provide, in principle, a story about how they might be removed through further work. (p. 16)

But the interesting cases of idealization are those for which no de-idealizing story is possible, even in principle, including the universalities at singularities/phase transitions. Call these “non-Galilean”.(p. 17)

There are no possible physical structures analogous to such mathematical structures s that might be pointed to by the limiting mathematical operations in asymptotic explanations. (p. 19).

Question: Does the physical world dictate in any way the kind of mathematics that must be used?

Answer: yes.

In order to explain the robustness (the repeatability) of the patterns we see, our mathematical representations have to be stable under changes of detail. One way achieve such stability is through the taking of a variable to its limit. …this can lead us to focus on mathematical singularities that can emerge in those limits. (p. 20)

“…if one’s interest is in understanding the robustness of the patterns of behavior that we see, a focus on regularities and lawlike equations very often turns out to be the wrong place to look! We need to understand why we have these regularities and invariances. We need, that is, to ask for an explanation of those very regularities and invariances. This is the fundamental explanatory question…. To explain and understand the robustness of patterns and regularities, one sometimes needs to focus on places where those very regularities break down.…this is one way to begin to understand the effectiveness of mathematics in applied situations. Furthermore, it is an approach that is completely orthogonal to structuralist/mapping accounts that take explanations necessarily to involve static representational maps.” (p. 21)

These non-Galilean idealizations “…play essential explanatory roles involving operations or mathematical processes without representing the system(s) in question”. (p. 23)

We must look to the world as the ‘driving influence’ for how mathematics gets applied, rather than to fortuitous analogies between mathematical structures and physical structures. …the world itself tells us that a certain kind of mathematical language is required for genuine understanding” (p. 24).

Discussion question: How does that world tell us this? How does the world constrain our non-Galilean mathematical modeling? And what if anything does this tell us bout the world? Is it that these false idealizations “point” to something about the world, about the system in the world being explained? Not the something that is literally expressed by the idealization, by its ‘literal truth conditions’ as it were, since it is non-Galilean.

“EMERGENT PHYSICS AND MICRO-ONTOLOGY”

Margaret Morrison

(Highlights):

Main examples considered: macro-physical universalities of symmetry breaking at critical points/phase transitions: e.g. , superconductivity, ferro-magnetism.

Macro-physical universalities are higher-order organizing principles that cannot be deduced from their underlying microphysics (cites Laughlin and Pines; cf. p. 149). Quite the opposite: certain aspects of whatever micro-physics happens to underlie the emergent phenomenon of a system will be deducible from it. As an explanatory strategy, then, emergence is the converse of micro-physical reduction, a kind of macro-physical reduction, if you will.

The macro-physical universalities of critical point emergence do not supervene on the underlying microphysics. This is not because of ‘fusion’, a la Humphreys, but because once the system reaches the critical point, the universal behavior (the would-be supervenient properties) are dominant and information about the micro-level structure (the subvenient properties) is simply lost.

So with emergence there is no form of reduction comparable to cases of ‘multiple realizability,’ and, in particular, no identification of the causal powers of the macro-phenomena to the causal powers of their micro-realizers. Emergent phenomena have their own causal powers.

What is missing from Batterman’s account of physical emergence is an appeal to symmetry breaking as a high level independent physical organizational constraint. It is such an appeal that is needed to ground an ontological account of emergence.

Appealing to the mathematics of ‘renormalization’ fails to provide such an account, contra Batterman. The renormalization mathematics does contribute important details to our explanatory understanding of emergent phenomena. But the mere fact that we need not appeal to micro-phenomena to explain emergent macro-phenomena, as RG explanations demonstrate, at most shows the epistemic independence of emergent phenomena from microstructural details, it does not show their ontological independence. But emergence is about ontological independence, and to demonstrate this we must appeal to higher order physical principles of symmetry and to the universality of the orderly pattern by means of which such symmetry may be broken.

Morrison plays down the ‘idealizing’ aspects of the renormalization, characterizing it instead as a kind of simplification: neutralizing one of the variables in order to make clear the behavioral pattern of the system at the critical point.

So, it turns out that there is a debate in physics and philosophy of physics about the nature of emergent phenomena, paralleling the debate in philosophy about the emergence of consciousness. Exponents of robust physical emergence include Laughlin and Pines, Anderson, Bangu, and Morrison. Detractors include Batterman, Callendar, and Earman.

FUNCTIONALISM, PLASTICITY, AND PSYCHOLOGICAL EXPLANATION

In an early article, “The Mind-Body Problem,” Scientific American (Jan., 1981) pp. 114-123, Jerry Fodor characterizes functionalism as involving the following two theses:

The Causal Role Thesis: “…what determines the psychological type to which a mental particular belongs is the causal role of the particular in the mental life of the organism”

The Structural Thesis: “…the psychology of a system depends not on the stuff it is made of (living cells, metal, or spiritual energy) but on how the stuff is put together” (op. cit., pp. 114, 118)

Fodor also makes the following claim about functionalism:

The Neutrality Thesis: Functionalism is “….a philosophy of mind…” that “…is neither dualist nor materialist” (op. cit., p. 114)

The Causal Role Thesis is supposed to imply The Structural Thesis, and that The Structural Thesis is true of functionalism is supposed to imply The Neutrality Thesis.

But, looking ahead, both the Structural and Causal Role theses admit of different interpretations, and for varying reasons both theses are unacceptable in interpretations that imply The Neutrality Thesis.

The Structural Thesis invokes a distinction between composition and structure, and suggests that mental phenomena are ‘merely structural,’ or ‘relational,’ in a way that is independent of the composition of the relata. But how should we interpret ‘independent’ here? Independent in what sense? How can the explanatory power of mental particulars depend on the special causal explanatory features that they have, and yet not depend on the sort of stuff involved? For one thing it seems to presuppose that how stuff is or can be put together is independent of what sort of stuff it is, and in general this seems to be false. In the case of psychological systems, it is surely not enough to show that there are several distinct empirically possible realizations of some psychology, because that is still compatible with other envisaged realizations being empirically ruled out on grounds having to do with the sort of stuff envisioned to have been involved. One would have thought, therefore that the question of how much the explanatory power of mental particulars depends on the sort of stuff involved, ought therefore to be treated as an empirical question.

Plasticity.

By the ‘plasticity’ of a type of event, state, process (or power), let us mean its capacity to be realized in more than one way. Following Richard Boyd, in “Materialism Without Reduction: What Physicalism Does Not Entail,” in Block, N. (ed.), Readings in Philosophy of Psychology, Vol. I, Harvard U. Press (Cambridge, Mass, 1980) pp. 67-106, we distinguish two ‘dimensions’ of plasticity: compositional and configurational.

If a type of state or process has a high degree of compositional plasticity,that means that there can be a high degree of variability in the sorts of substances or causal factors that may constitute realizations of the state or process.

If a type of state or process has a high degree of configurational plasticity,that means that there can be a high degree of variability in the structural arrangements of constituent parts constituting a realization of the state of process (cf. pp. 87-90).

[Compare, e.g., the state of being an inscription of a certain English sentence vs the process of smelting iron.]

One way of interpreting The Causal Role Thesis is as the claim that the only essential characteristic of a mental particular is its causal role in the mental life of the entity that has it. Boyd says that mental particulars “…are like computational states in being entirely configurational, that is, in possessing maximal compositional plasticity;” “…in any particular world, only the causal laws governing that world limit the possible composition of realizations of such computational states; such states have no essential properties that constrain the sorts of substances or causal factors that can be constituents of their realizations” (op. cit. p. 88). This in turn suggests a corresponding interpretation of the Structural Thesis, according to which mental particulars are maximally compositionally plastic.

Boyd’s 3 accounts of maximal compositional plasticity (‘mcp’) of the mental (put forward as equivalent):

1. Mental phenomena are mcp in being ‘entirely configurational’.

[But relations differ widely on how constraining they are, so being mcp on this account would be compatible with greater or lesser degrees of realizability both within and across worlds. Compare, e.g., being a computation of e to the power x for x=9; being to the left of x, being x’s brother, being the cause of x’s felt sensation of warmth…]

2. Mental phenomenon are mcp in that, in any particular possible world, only the causal laws governing that world limit the possible composition of realization of such phenomena.

[But this seems false, since it is surely also going to depend on the constitution of the world: i.e., what sorts of stuff, and in what distributions, it contains. But taking that into account, why isn’t every property mcp?]

3. Mental phenomena are mcp in the sense that they have no essential properties that constrain the sorts of substances or causal factors that may be constituents of their realizations.

[But surely this suggests that mental phenomena could not essentially be causal roles, for being a causal role might well constrain the sorts of substance or causal factor that could be constituents of their realization. At least, it seems question begging to suppose otherwise. For one thing only concrete entities can realize causal roles. For another, the ability to realize a causal role must surely be grounded in the nature of what realizes it. If there are causal roles that place no constraints on the nature of what may realize them, then we require a separate argument for this. And then we require an additional argument for the thesis that mental phenomena are among such realizations.

Consider also the evolution of ‘higher functions’. One can think of an evolved system as consisting of a number of distinct hierarchical levels of organization, each of whose spatial boundaries coincides at the system’s interface with its environment – e.g., its skin. Now to say that mental phenomena are mcp seems to imply that being a mental phenomenon of a certain sort is independent of the sort of underlying constituents, at hierarchically lower levels of organization, that may happen to realize that mental phenomenon in a given instance. Whereas some evolutionary theorists have suggested that part of what explains the relative ‘stability’ of hierarchically complex evolved systems is that a kind of ‘causal integration’ or ‘coadaptation of the various organizational levels has occurred over time, and under maximizing conditions of natural selection, such that, e.g., mental phenomena qua mental phenomena are subject to physical, chemical and biological constraints at a number of levels, “…and never completely lose the marks of the levels of organization they have evolved from, even down to the level of basic chemical elements or which they are composed” (cf. Bill Wimsatt, “Complexity and Organization” in Cohen, R.S. and Schaffner, K.Y., (eds.) Boston Studies in the Philosophy of Science, Vol. XX, D.Reidel Pub. Co., (Dordrecht-Holland, 1974) pp. 76-78). But if so, then it would seem that mental phenomena, as we know them, are not maximally compositionally plastic. They are not just a ‘structural overlay’ of what realizes them.]

What seems at this point to be the case is that mental phenomena are mcp if and only if they are (type) abstract. For then, qua being mental, they are neither material nor immaterial, and they do indeed have no essential properties that constrain the sorts of substance or causal factor that can be constituents of their realization.

But of course, abstract entities are not part of the causal nexus; that is part of what we mean by ‘abstract’. So, supposing that mental phenomena are mcp raises problems for Fodor’s Causal Role and Structural theses.

Another interpretive issue for The Causal Role Thesis is what is meant by “determines”.

Three Grades of Functionalism (in order of strength):

First grade: determination of psychological type by analyticity (e.g., D. Lewis) [What definitions?]

Second grade: determination of psychological type by a posteriori identity (e.g., early Putnam, late Dennett)

Third grade: determination by material equivalence

The third grade might make the Causal Role Thesis true, but not in a sense that implies the Structural Thesis. A mere extensional equivalence of mental state types and causal role types does not imply that mental states are ‘merely structural’, or even that they essentially involve relational properties, let alone that they are highly,let alone maximally, compositionally plastic. If so, then the Causal Role Thesis manages to imply the Structural Thesis only by being at least as strong as on the second grade, by being a ‘Strong (Functional Identity) Theory”. According to The Strong Theory, there is a level of structure of any system having a psychology, such that the functioning ‘parts’ of the system at that level are causally related to each other, and to inputs and outputs, such that each distinct mental particular attributed to the system is, qua being a mental particular of some given type, nothing but the correspondingly distinct causal contribution made to the over-all functioning of the system by one of these parts. Their causal roles are exhaustively constitutive of their mentality.

If so, then mental state types are to be abstract states of a complex relational sort, concretely realizable, of course, in various ways. But for any given realization, what is mental about it is abstract, and therefore cannot contribute to the state’s particular causal efficacy. So, while epiphenomenalism acknowledges the special mental nature of the mental but deprives it of causal potency, the Strong Theory sustains the causal potency of the mental, but only by depriving the mental qua mental of any special nature contributing to its potency.

Concluding remarks. Explanations do not have to be causal; e.g., Pincock’s ‘abstract’ explanations are not causal. Functional explanations of state types are causal, and, to be causal, must be ‘concrete’. But if the above line of argument holds, it follows that such ‘structuralist’ explanations must rest on a notion of structure that is thicker than that of maximal configurational plasticity. There is something concrete, in the world, that grounds or constrains the specific (less than maximal) degree of configurational plasticity of that particular functional type.

Compare Morrison on physical emergence. She wants macro-physical phenomena to have their own causal powers; so when she invokes the higher level symmetry principles of physics, and the emergence of the universal pattern of symmetry breaking captured by Renormalization Group mathematics, she must be understanding these as not merely abstract.

Compare Deacon on the role of constraints, and of particular absences they may enforce, in shaping the causal topology of a complex living system. The absences -- the hole at the wheels hub -- cannot contribute causally if they are taken to be merely abstract. So by that token causal topology must not be seen as merely mathematical.

As Batterman shows us, sometimes our mathematical models of emergent behavior of complex systems can only work when embodying in principle ineliminable false idealizations. To that extent, such mathematical models behave like an abstract explanation. They can help us understand important aspects of the emergent behavior, but cannot by themselves help us understand any causal role that we may want or need to attribute to it. The choice we are then left with is either to rest content with epistemic emergence, or to embrace salient aspects of higher level structure as fundamental.

Resting content with epistemic emergence leaves one with pretty much everything that, e.g., Clark invoked in his elaboration and defense of emergent explanation. At worst it would have to be supplemented with the prefatory qualifier “It is epistemically ineliminably as if…”.