Len Yabloko's List: Philosophy of Science

Posted by Dave Snowden on February 16, 2011

The workshop title is Influencing the Causality of Change in Complex Socio-technical Systems, which is a real mixture of words, concepts and intellectual traditions. It also became clear that that is no clear agreement on what a system is. I define it as any network with coherence, others see it as something with boundaries. The system of systems ideas came up as predicted, with one protagonist arguing that there was no distinction between complex and complicated systems, seeing them ends of a spectrum The clear implication being that complex systems are simply ones that we have not yet managed to model properly which is disturbing.

In my works of 2002-2006 cited above, I made it clear that at the level of the human agent, there are no magical "cultural" or "economic" forces controlling individuals, other than those affecting the dispositions, thoughts and actions of individual human actors. People do not develop new preferences, wants or purposes because mysterious "social forces" control them. What have to be examined, I argued, are the social and psychological mechanisms and constraints leading to such changes of preference, disposition or mentality.

Can there be higher level laws of nature even though everything is reducible to the fundamental laws of physics? The computer science notion of level of abstraction explains how there can be.

The Game of Life is a 2-dimensional cellular automaton in which cells are either alive (on) or dead (off). Cells turn on or off synchronously in discrete time steps according to the following rules.
· Any cell with exactly three live neighbors will stay alive or become alive.
· Any live cell with exactly two live neighbors will stay alive.
· All other cells die.
In a Game of Life universe the preceding rules are analogous to the fundamental laws of physics. They determine everything that happens on a Game of Life grid.

Certain on-off cell configurations create patterns-or really sequences of patterns. The glider is the best known. Since nothing actually moves in the Game of Life-the concept of motion doesn't even exist- how should we understand this?

Gliders exist on a different level of abstraction from that of the Game of Life. But at the glider level not only do gliders move, one can even write equations for the number of time steps it will take a glider to move from one location to another and when a glider will "turn on" a particular cell. What is the status of such equations? Just as gliders are subject to the laws of glider equations, Turing machines too are subject to their own laws-in particular, computability theory. While not eluding the Game of Life rules, in both cases autonomous new laws apply to phenomena that (a) appear on a Game of Life grid but (b) are defined on a different and independent level of abstraction.

When autonomous higher level laws apparently effect lower level phenomena the result has been called [3] downward causation. But downward causation doesn't make scientific sense. It is always the lower level phenomena that determine the higher level: the Game of Life rules are the only things that determine whether cells go on or off. So how can computability theory and glider equations let us draw conclusions about whether cells will go on or off? In [1] I call this downward entailment.

Physics recognizes four fundamental forces. Evolution is not one of them. Similarly there is no "computational functionality" in a Game of Life universe. Neither evolution nor computation have any causal power; they are both epiphenomenal. Do we need them? In some sense we don't. Game of Life Turing machines don't do anything. It is only the Game of Life rules that make cells go on and off. Reductionism has not been overthrown. One can always reduce away macro-level terminology and phenomena and replace them with the underlying micro-level terminology and phenomena. It is still the elementary mechanisms-and nothing but those mechanisms-that turn the causal crank. So why not reduce away epiphenomenal levels of abstraction?

Reducing away a level of abstraction produces a reductionist blind spot. Computations performed by Game of Life Turing machines cannot be described as computations when one is limited to the vocabulary available at the Game of Life level of abstraction. Nor can one explain why the Game of Life halting problem is unsolvable. These concepts exist only at the Turing machine level of abstraction. Similarly, biological evolution cannot be explicated at the physics and chemistry level of abstraction. The evolutionary process exists only at the evolution level of abstraction. Furthermore, reducing away a level of abstraction throws away elements of nature that have objective existence. At each level of abstraction there are entities, such as Turing machines and biological organisms, that instantiate types at that level. These entities are simultaneously causally reducible and ontologically real-a phrase coined by Searle [8] in another context.

Weinberg argues that higher level entities like cold fronts and thunderstorms are just conceptual conveniences. Are they? Robert Laughlin [7] argues that higher level entities are objectively real. He talks about what he calls "protectorates," including both the solid state of matter and Newtonian physics. Like computation and evolution, protectorates exhibit properties that simply don't have a meaning at lower levels.

Higher level entities are objectively real in two additional ways. They have reduced entropy, and they have either more mass or less mass than their components considered separately. Biological and social entities are examples. (Hurricanes are the only naturally occurring non-biological and non-social dynamic entity of which I am aware.) Because dynamic entities have energy flowing through them, they have more mass than the aggregation of their components considered separately.

This can be summarized as the principle of ontological emergence: extant levels of abstraction are those whose implementations have materialized and whose environments enable—or at least do not prevent—their persistence.

We use papers written by Steven Weinberg, a reductionist physicist, and Jerrold (Jerry) Fodor, afunctionalist philosopher, as our points of departure.... Where Weinberg and Fodor disagree is not about supervenience but about whether the principles of the special sciences can be derived from the principles of physics.

If one dismisses the possibility of strong emergence and agrees that the only forces of nature are the fundamental forces as determined by physics, then Fodor must also agree (no doubt he would) that any force-like construct postulated by any of the special sciences must be strictly reducible to the fundamental forces of physics. Note that this is a truly stark choice: strict reductionism with respect to forces or strong emergence. There is no third way.

This leads to an important conclusion. Any cause-like effect that results from a force-like phenomenon in the domain of any of the special (i.e., higher level) sciences must be epiphenomenal. Compare this with the conclusion Hume reached in his considerations of causality-that when one looks carefully at any allegedly direct causal connection, one will find intermediary links. Since Hume did not presume what we now consider to be a bottom level of fundamental physical forces, he dismissed the notion of causality entirely.

The fact that all special (i.e., higher level) science interactions are epiphenomenal is not a problem for functionalism. Rather, the functionalist claim is that the regularities (be they epiphenomenal or not) that appear at the level of any special science are of significance on their own. And of course, the very name of the school of thought, functionalism, underlines its concern with how things function. Functionality is by definition a relationship between something and its environment-even if we limit the notion of an environment to the "inputs" and "outputs" of the element under consideration.

A term commonly used in Functionalism is multiple realizability, which refers to the notion that many regularities (many functions) can be realized in multiple ways. Although use of the term epiphenomena in this context sounds strange, a requirements document or a system specification is intended to describe epiphenomena of systems that satisfy those requirements or that meet that specification. From our perspective epiphenomena exist only when there is an implementation. Epiphenomena are, first of all, phenomena. A specification for a system that did not exist would not describe epiphenomena.

Janna Levin is a Professor of Physics and Astronomy at Barnard College of Columbia University. Her scientific research concerns the Early Universe, Chaos, and Black Holes. Her second book - a novel, "A Madman Dreams of Turing Machines" - won the PEN/Bingham Fellowship for Writers that "honors an exceptionally talented fiction writer whose debut work...represents distinguished literary achievement..."

Stanford University Email: feferman@stanford.edu

But it is hubris to think that by mathematics alone we can determine what the mathematician can or cannot do in general. The claims by Gödel, Lucas and Penrose to do just that from the incompleteness theorems depend on making highly idealized assumptions both about the nature of mind and the nature of machines. A very useful critical examination of these claims and the underlying assumptions has been made by Shapiro in his article, 'Incompleteness, mechanism and optimism' (1998), among which are the following.

Gödel first laid out his thoughts in this direction in what is usually referred to as his 1951 Gibbs lecture, 'Some basic theorems on the foundations of mathematics and their implications' (Gödel 1951). There are essentially two parts to the Gibbs lecture, both drawing conclusions from the incompleteness theorems. The first part concerns the potentialities of mind vs. machines for the discovery of mathematical truths. The second part is an argument aimed to "disprove the view that mathematics is only our own creation", and thus to support some version of platonic realism in mathematics...

So why didn't Gödel state that outright in the Gibbs lecture instead of the more cautious disjunction in the dichotomy? The reason was simply that he did not have an unassailable proof of the falsity of the mechanist position. Indeed, despite his views concerning the "impossibility of physico-chemical explanations of …human reason" he raised some caveats in a series of three footnotes to the Gibbs lecture, the second of which is as follows:
It is conceivable ... that brain physiology would advance so far that it would be known with empirical certainty
1. that the brain suffices for the explanation of all mental phenomena and is a machine in the sense of Turing;
2. that such and such is the precise anatomical structure and physiological functioning of the part of the brain which performs mathematical thinking.

Some twenty years later, Georg Kreisel made a similar point in terms of formal systems rather than Turing machines:
It has been clear since Gödel's discovery of the incompleteness of formal systems that we could not have mathematical evidence for the adequacy of any formal system; but this does not refute the possibility that some quite specific system … encompasses all possibilities of (correct) mathematical reasoning …

I shall call the genuine possibility entertained by Gödel and Kreisel, the mechanist's empirical defense (or escape hatch) against claims to have proved that mind exceeds mechanism on the basis of the incompleteness theorems. The first outright such claim was made by the Oxford philosopher J. R. Lucas in his article, 'Minds, machines and Gödel' (Lucas 1961). Paul Benacerraf and Hilary Putnam soon objected to Lucas' argument on the grounds that he was assuming it is known that one's mind is consistent, since Gödel's theorem only applies to consistent formal systems. But Lucas had already addressed this as follows:
"… a mind, if it were really a machine, could not reach the conclusion that it was a consistent one."

Roger Penrose is another well-known defender of the Gödelian basis for anti-mechanism, most notably in his two books, The Emperor's New Mind (1989), and Shadows of the Mind (1994). Sensitive to the objections to Lucas, he claimed in the latter only to have proved something more modest (and in accord with experience) from the incompleteness theorems: "Human mathematicians are not using a knowably sound algorithm in order to ascertain mathematical truth." And more recently, Stewart Shapiro (2003) and Per Lindström (2001, 2006) have carefully analyzed and critiqued his "new argument." But Penrose has continued to defend it, as he did in his public lecture for the Gödel Centenary Conference held in Vienna in April 2006.

As I see it, a principal reason for the implausibility of this modified version of the mechanist's thesis lies in the concept of a formal system S that is currently taken for granted in logical work. An essential part of that concept is that the language L of S is fixed once and for all. In recent years I have undertaken the development of a modified conception of formal system that does justice to the openness of practice and yet gives it an underlying rule governed logical-axiomatic structure; it thus suggests a way, admittedly rather speculative, of straddling the Gödelian dichotomy. This is in terms of a notion of openended schematic axiomatic system, i.e. one whose schemata are finitely specified by means of propositional and predicate variables (thus putting the 'form' back into 'formal systems') while the language of such a system is considered to be open-ended, in the sense that its basic vocabulary may be expanded to any wider conceptual context in which its notions and axioms may be appropriately applied.

Insofar as human mathematical thought is concerned, mind is mechanical in that it is completely constrained by some open-ended schematic formal system. If the concepts of mathematics turned out to be limited to those that can be expressed in one basic formal language L, the two theses would be equivalent. So the point of this second thesis is that the conceptual vocabulary of mathematics is not necessarily limited in that way, but that mathematics is otherwise constrained once and for all by the claimed finite number of open-ended schematic principles and rules. The idea is spelled out in the final section of (Feferman 2009), to which the reader is referred given the limitations of space here.

Finally, there is a theoretical argument for openness, even if one accepts the language L of set theory as a determinately meaningful one. Namely, by Tarski's theorem, the notion of truth TL for L is not definable in L; and then the notion of truth for the language obtained by adjoining TL to L is not definable in that language, and so on (even into the transfinite).

PLATO'S GHOST: The Modernist Transformation of Mathematics. Jeremy Gray. x + 515 pp. Princeton University Press, 2008. $45.

Gray has worked since 1975 as a member of the Centre for the History of the Mathematical Sciences at the Open University in the United Kingdom and has made extensive contributions to the history of modern mathematics, especially concerning geometry and parts of analysis. In Plato's Ghost he has moved beyond that to present us with an ambitious and in many respects remarkable synthesis of the modern transformation of mathematics via structural and set-theoretic notions, together not only with its logic and philosophy but also with related developments in artificial languages and psychology.

This article is a companion to another one (2008), in which my main concern is to examine Cantor's Continuum Hypothesis (CH) from the point of view of conceptual structuralism. I argue there, contrary to Gödel and his successors, that CH is not a definite mathematical problem since the concepts of set and function used in its formulation are inherently vague; that is, no sharpening of these concepts is possible that does not violate what they are supposed to be about.

My purpose here is to provide still another philosophical perspective that I call conceptual structuralism for which the above conceptions of the continuum from geometry, analysis and set theory are essentially different. Comparisons will also be made with some other conceptions of the continuum, including phenomenological, non-standard, predicativist, intuitionist, and physical interpretations, all of which fail to satisfy as basic structural conceptions.(Searle prefers the term 'collective intentionality' to 'intersubjectivity', which has a phenomenological history. Since my emphasis is on firmly shared conceptions, understanding and knowledge, I prefer 'intersubjective objectivity' at the risk of that association.)

The indispensability of mathematics to the practice of natural science is indisputable, but the reasons for that have been the subject of endless philosophical and semi-philosophical discussion. One view, as encapsulated in the famous quotes of Galileo, "Nature's great book is written in the language of mathematics," and Jeans, "God is a mathematician," is that mathematics is integrally involved in nature itself. Whichever view of the relation of mathematics to nature one takes, there is no independent physical conception of the continuum on offer in all this, since all the mathematics is filtered through the real number system (or Hilbertian geometry as a surrogate). Moreover, I don't see that any argument can be made from the enormously successful applications of mathematics in natural science to the conclusion that one or another of the mathematical conceptions of the continuum surveyed above is uniquely singled out as the "real one". Finally, such questions as Cantor's continuum hypothesis should not take the core role of R in pure and applied mathematics for support as a definite mathematical problem, but have to be considered on their own merits and in my view only make sense within the foundational framework of set-theoretical platonism.

Entropy, February 2010

Abstract: In the biosemiotic literature there is a tension between the naturalistic reference to biological processes and the category of 'meaning' which is central in the concept of semiosis. A crucial term bridging the two dimensions is 'information'. I argue that the tension can be resolved if we reconsider the relation between information and entropy and downgrade the conceptual centrality of Shannon information in the standard approach to entropy and information.... I show how we can conceive of the semiosphere as a fundamental physical phenomenon. Following an early contribution by Hayek, in conclusion I argue that the category of 'meaning' supervenes on nested functions in semiosis, and has a function itself, namely to enable functional self-reference, which otherwise mainfests functional break-down because of standard set-theoretic paradoxes.... I equate the Peircian interpretant with an evolved function, and the relation between sign vehicle and object as Peircian abduction, now formally specified as Jaynes' inference, thus naturalizing semiosis.... Following a proposal by Hayek, I argue that qualia are a function that enables self-referential physical systems with functions to solve the paradoxes of self-referentiality, which is favoured by natural selection.

In the Shannon sense, the information stored in the genome is just that: the relation between the realized sequences of nucleic acid bases and the state space of possible sequences. Evidently, this is not the same as storing an image of the phenotype or even a blueprint or something else. There is no 'information' about the phenotype in the genotype at all. The reason lies in the confusion between the causal process and the information flow. Once the causal sequences in ontogeny had been discovered, and so the causal priority of the processes related to the chromosomes had been realized, it was a quick step to infer the informational sequence from the causal sequence. Ontogeny as a causal process seemed to suggest that the flow of information goes into the same direction, again, in the Shannon sense, hence equating the causality with a flow of messages.

Two systems a and b are causally coupled in a way so that, if system a is in state F, system b is in state G, which implies that state G carries information about state F. This notion of information is independent from the existence of a sender and a receiver, yet, the actualization of the information depends on a third system that is coupled with those two systems, and which infers F from G, which is a movement in the reverse direction than the causality. Normally, this is where the observer comes into play again, who interprets the causal coupling in terms of an inference. So we can reach the important conclusion that the most general notion of information already points towards the more complete picture of semiosis.

If we start out from the genotype, and try to reconstruct the information that is supposed to flow to the phenotype, we face the problem of the arbitrary assignment between source and channel in information theory, i.e., the so-called 'parity thesis': Thus, we can see the environment as a channel through which the (hypothesized) information of the genotype as a source flows, or we can see the genotype as the channel through which the (hypothesized) information carried by the environment flows. This reflects the fact that information only resides in the entire causal chain, and that only the phenotype can be regarded as a sign that points towards that information. This is where inference comes into play.

Following Gibbs, Jaynes had shown that entropy always refers to a state of ignorance about a physical system. However, his approach is entirely different from the Shannon approach, which only superficially corresponds to the Boltzmann notion. Jaynes argued that entropy is a measure of the degree of uncertainty related to the number of possible microstates that corresponds to an observable macrostate. This uncertainty can be interpreted in two senses. One is the sense that an observer is ignorant about the realized microstate, given the knowledge about the macrostate. The other is the degree of control that an experimenter has about the microstate if he is only able to manipulate the macrostate. That is, the Gibbs/Jaynes version puts the relation between micro- and macrostate into the center, whereas the Boltzmann/Shannon version only concentrates on the microstates, relegating the macrostates to the purely epiphenomenal realm.

The information that G carries about F depends on the specific causality that underlies that relation, and this in turn varies with the state space of G, not F. This corresponds to Jaynes' notion of entropy: The less certain the information G carries about F, the higher the degree of entropy in the corresponding micro-system. To be exact, Jaynes argues that for this reason the entropy of the system a is not a physical given, but obtains different magnitudes relative to the specific process of inference. But we can also say that this endogeneity, i.e., observer relativity of the entropy of system a means that the coupled systems can have different entropies, depending on the nature of the underlying causal process of coupling (Jaynes gives the example of a crystal, which can be put into different experimental settings, one with choosing temperature, pressure and volume as macrostates, another with temperature, strain and electric polarization etc.).

A function is a special kind of causal process that can be described as having the following general structure. The function of X is Z means:
(a) X is there because it does Z, and
(b) Z is a consequence (or result) of X's being there.
If we integrate the technological function and the design function qua mental function into one higher-level system, we could argue, for instance, that the technological function is a part of a mental function....

This discussion directly applies for the Jaynes notion of entropy: Its assignment depends on whether we include the observer system O into the analysis or not....There are two different notions of entropy. Observer relative EntropyOR is ontologically subjective and can only be determined with reference to a function. Observer independent EntropyOI relates to coupled physical systems of functions and object systems. If two physical systems are causally connected in a way that the proper functioning of system O is the result, we have a substantial modification of the standard conception of causality. This is because the effect of system A on O is mediated by all other factors that determine the proper functioning of O.

Jaynes original setting is seen as an evolving system O which produces inferences about the behavior of system A, which translate into further causal interactions between system A and O, that in turn impact on the reproducibility of system O. This process takes place against the background of a population of observer systems O1,…,n, the reproduction of which is maintained by energy throughputs which are constrained so that selection among observer systems takes place, depending on the degree how far the observations approximate the true physical functioning of system A. In other words, I assume that observations have a fitness value.

Following Dewar, we can apply this on the relation between physical theories and the MaxEnt principle. The physical theory posits a set of macroscopic constraints of an object system, and the MaxEnt principle serves to generate predictions about the macro-behavior of the system, such that a failure of those predictions implies the need to change the physical theory. From the viewpont of evolutionary epistemology, and therefore equating the physical theory as a function in the sense of a physical state of the observer system, we can therefore also argue, that in a process of natural selection, the MaxEnt principle will also underlie the convergence of functional macrostates with macrostates of object systems. Proper functioning requires that all other possible causal interactions between the object system and the function are irrelevant to the fulfilment to the function, such that any information about a deviation from equal probability of all states is also irrelevant.

From this follows, that the entropy measure implied by the Gibbs/Jaynes approach is not arbitrary if the two systems interact with a function involved. The function implies a certain set of constraints on the macrostates of system A, and it is the possible tension between functional relevance and irrelevance that determines the evolution of constraints, in a similar way as the experimenter produces physical models in order to explain her observations, and continuously improves the estimates.... For this conceptual transfer of the of the MaxEnt principle from theory evolution to physical evolution it is sufficient to refer to a general principle of computational efficiency, in the sense that the MaxEnt principle allows for a minimization of effort (time, energy, resources) invested into the processing of epistemically or functionally relevant information.

I summarize: The Jaynes approach to entropy as an inference procedure corresponds to an evolutionary sequence of adaptations of macro level constraints in the observing system O to the macro level constraints in the observed system A, such that all micro states of the observed system are assigned to the maximum entropyOR state. This process is driven by natural selection, such that deviations from the state of equiprobability trigger further adaptations of the observer system, if they prove to be causally relevant for its proper functioning. Hence, evolutionary change follows the MaxEnt principle.

This argument links the reproducibility of the function with the reproducibility of the macrostates of system A, in the sense of that predictions which correspond to the MaxEnt principle will be confirmed in the course of time....By this argument we have stated that evolving functions as observations will maximize entropyOR in the process of adapting their structure according to the macrostates of the system A with which they causally interact.

Clearly, this assertion is actually a statement of the relation between entropyOR and entropyOI, as maximum entropy production is a process that is observer independent. Yet, at the same time the determination of this entropy can only happen in a relation between observer and observed system. So, the evolutionary correspondence between the MaxEnt principle and the Maximum Entropy Production provides the foundation for the assumption that the two entropies converge. This second step in the evolutionary interpretation of Jaynes' notion of entropy results into the hypothesis:
In physical systems with evolving functions, the structural features of the functions which establish an observational relation between them and object systems will result into a causal interaction between functions and systems in which those structures correspond to a set of constraints on the macro-level of the object systems which maximize entropyOI in the object system. This entails a correspondence between the MaxEnt principle and MaxEnt production.

Now, we can further develop on this insight by modifying the assumption about system A: We consider the case that system A is a function, too. In other words, we deal with the case of mutual observation. In this case, the structural features of function O become the constraints that are the object of the observation by system A'....In the naturalistic interpretation of the observation relation, we can say that this is a structural equilibrium that, according to the MaxEnt process, results into maximum entropy production of both systems, hence also of the coupled system. So we can posit another hypothesis:
In physical systems with coupled evolving functions, the functions will mutually adapt their structures such that the implied constraints of the respective object system maximize entropyOI production; from this follows, that the integrated system also maximizes entropyOI production. Maximum entropy production defines the point of optimal mutual adaptation, hence an equilibrium. In this state, entropyOR and entropyOI converge because the mutual adaptation of constraints removes the contingency involved in observer relative entropy.

This hypothesis is very significant, as it shows that the Schrödinger approach needs to be corrected and amended, for very fundamental ontological reasons. Systems with functions evolve structural constraints precisely by means of maximizing entropy production. For this, we do not need the more special approach of dissipative systems, because the ontological argument counts for both equilibrium and non-equilibrium states....From the viewpoint of the previously presented argument, the increasing selectivity of the evolving networks of chemical reactions corresponds to the Second Law, but simultanously reduces the contingency of entropyOR on the level of the single functions, in the sense of the contingency of the constraints operating in the MaxEnt process. This reduction of contingency is what we perceive as increasing "order," but it does not imply that the Second Law does not hold.

...it is wrong to state that a function carries information with reference to the state space that reflects its specific constraints. It can only carry information relative to other functions that are coupled with it. The best illustration for this distinction is the fact that genomes carry a lot of 'junk' DNA. Interestingly, there is even no relation between genome size and complexity and the level of complexity of the phenotype. This observation clearly shows that there is no direct correspondence between the role of the genome in causing development and its role of carrying information. The information resides in the system into which the genome as a set of functions is embedded. For this system, only parts of the genome carry information, here understood as having a higher level function. From this follows, that the increasing divergence between the functional and the non-functional DNA in genomes just reflects the MaxEnt process over time: All functions evolve into a state in which there is a maximum amount of diversity which is non-functional. In plain, this is why simple organisms can have larger genomes than humans: All depends on whether the system can make use of the genome, which otherwise just accumulates diversity.

Firstly, the triadic structure reflects the different structure of causality in relating a cause=object to an effect=sign via a function=interpretant. Secondly, we can use the same triadic structure to analyze the function: The object corresponds to the object system A, the sign corresponds to the effect Z in the function, and the interpretant is the embedding function with Z'. The X is the pivot in the sense of being the physical link between the two causalities, one the direct physical impact from A to X, and the other the functional causality involving X and Z.... The sign obtains a central position in the entire structure because objects can never be observables directly, but only via certain aspects. These aspects are the signs. The central point is that semiosis can be seen as a function in the sense that the fundamental causal relation between an object system A and X in the function is insignificant, unless it is coupled with the Z that results from proper functioning with relation to Z'

In the Peircian triangle it is also evident that the sign does not carry information but that the information is created by the relation with the interpretant. This is the part of the argument which allows to draw the separating line to Shannon information. It is impossible to relate the use of the sign as such to a space of states of signs, similar to a message in a space of possible messages. This is because the process of semiosis, seen in physical terms, involves the MaxEnt process in the evolution of the functions, i.e., the interpretants, which is a process that leads to more and more complex internal contexts of the primordial object-sign relation. This results into a sequence of entropiesOR.

That is, we do not need to refer to the category of meaning in order to show that there is an observer relative role of information. Meaning is dissolved into the hierarchy of functionings. In other words, if we ask for a meaning, we just ask for a higher-level function. So, on the one hand we are able to interpret a particular entropyOR in the sequence of functions in the Shannon sense, and we would even be able to think of the sequence of entropiesOR as sequences of Shannon information. But this would only be a static snapshot of the essential dynamic process, and would fail to grasp the increase of complexity that inheres the evolution of functions Z', Z'',….It is then straightforward to see that the embeddedness of functions is equivalent to changing role of signs and interpretants through evolution, that is, an interpretant becomes a sign in the higher level function, which in turn corresponds to a further step in the growing complexity of the dynamical object.

... the semiosphere is just identical with the biosphere in the sense of another Russian scholar, Vernadsky... Adopting this perspective, the semiosphere and the biosphere are just two sides of one coin, which is a common physical reality. This implies that our previous analysis of the role of energy flows in functions also applies for the semiosphere. This is the final step in naturalizing Peircian semiosis.

This is the so-called 'handicap principle' which obtains a central position also in a naturalized semiotics. If we consider coupled systems in an evolutionary context, there is no prima facie reason why the information processed in the systems should be truthful. the costly signal is an evolutionarily optimal solution to the problem of coordination between prey and predator. As I have already stated previously, the theory of signal selection implies that in the semiosis of living systems, there is an inherent tendency to increase energy throughputs, as a most universal indicator of costs, and this is because the information processed is approximating the true states in coupled functions. This argument is a substantial modification to Corning's notion of control information, which just focuses on the energetic efficiency. In the theory of signal selection, energy throughput becomes a sign itself...

Evolution with signal selection implies that there will be mutual leveraging of information transmitting signals, such that relative advantages tend to converge (Red Queen principle), with increasing levels of energy thoughput. (Lotka's principle). There is one possibility to directly relate Lotka's principle with the energetics of signs. This is Chaisson's measure of free energy rate intensity Φm (measured in erg s-1g-1), whch is an intensive measure of complexity which includes the efficiency of a system in processing energy flows. Empirically, Chaisson hypothesizes about a general regularity of increasing Φm during the evolution of the world, which also applies to systems and subsystems. For example, protocells have a lower Φm than plants, or the human brain has a much higher energy rate intensity than the human body etc. Also, the miniaturization of technological functions involves an increasing free energy rate intensity.

One view states that this naturalization finally has to fail because it cannot deal with the notion of 'consciousness', with which the notions of 'intentionality' and 'meaning' are essentially related... This is a very difficult issue, and I only want to present a largely forgotten argument that has been developed by Hayek more than fifty years ago This argument states, in my parlance, that systems with nested and networked functions will always develop "meaning" as a category of functioning to refer to themselves, because self-reference entails fundamental logical paradoxes. Hayek applied this argument on the brain as a neuronal system; it can be translated on other systems in a homologous way

What is distinctive with Hayek's view is that he presents a fully-fledged physicalist view of the human brain and relates this with a perspective on logical paradoxes which comes close to the Gödel theorems (which Hayek himself only has realized much later), thus adopting a view which today is maintained, for example, in the universal theory of cellular automata and computation). Hayek argues that the brain can be seen as a purely physical network of neurons and their interactions. Such kind of a network, according to Hayek, can never give a full acount of its own operations in physical terms, because that would require to build a copy of itself with larger complexity than its own, which is a contradiction in terms. Hayek states that the notion of 'mind' just refers to the total ensemble of the neuronal network, which, so to speak, cannot be viewed upon from the outside. This notion is a functional substitute for the impossible construction of a workable internal copy of itself.

There are two core ideas which clear the ground for this exercise. One is to regard functions as a special kind of physical causation, which connects with the general evolutionary paradigm, which is also central in Peirce's thinking. The other idea is to establish a conceptual link between Jaynes' notion of entropy and functions in terms of observations. There is an important bridge between the two concepts, which is the notion of observer relativity. This notion plays the role of a conceptual catharsis with reference to any possible tendency to anthropomorphism. This is not only useful to clarify semiosis, but also some aspects of the concept of entropy.

One main result of this conceptual blending is that I can present a naturalistic interpretation of Jaynes inferential concept of entropy. If I substitute the 'anthropomorphic' observer by a sequence of evolving functions, basically following generalizations of evolutionary epistemology, I can draw the conclusion that functional evolution will end in a relation between function and object system in which the function reflects the constraints of the object system on the macrolevel, corresponding to a state of maximum entropy on the microlevel. Further, in the naturalistic framework, this interpretation of Jaynes inference implies that the object system also manifests maximum entropy production. From this follows, that the evolution of functions obeys to the Second Law.

Australian Centre for Astrobiology, Macquarie University
New South Wales, Australia 2109

By tradition, physics is a strongly reductionist science. Treating physical systems as made up of components, and studying those components in detail, had produced huge strides in understanding. A minority of physicists challenges this account of nature. Whilst conceding the power of reduction as a methodology, they nevertheless refute that the putative final theory would yield a complete explanation of the world. The anti-reductionist denies that, for example, a living cell is nothing but a collection of atoms, or a human being is nothing but a collection of cells. This, they say, is to commit the fallacy of 'nothing-buttery.'

All physicists concede that at each level of complexity new physical qualities, and laws that govern them, emerge. These qualities and laws are either absent at the level below, or are simply meaningless at that level. Thus the concept of wetness makes sense for a droplet of water, but not for a single molecule of H2O. The entrainment of a collection of harmonic oscillators such as in an electrical network makes no sense for a single oscillator. The Pauli exclusion principle severely restricts the behaviour of a collection of electrons, but not of a single electron. Ohm's law finds no application to just one atom. Such examples are legion. The question we much confront, however, is so what? What, exactly, is it that the anti-reductionist is claiming emerges at each level of complexity?

The problem of downward causation from the physicist's point of view is: How can wholes act causatively on parts if all interactions are local? Indeed, from the viewpoint of a local theory, what is a 'whole' anyway other than the sum of the parts? The first is whole-part causation, in which the behaviour of a part can be understood only by reference to the whole. The second I call level-entanglement (no connection intended with quantum entanglement, a very different phenomenon), and has to do with higher conceptual levels having causal efficacy over lower conceptual levels.

There are a few examples of clear-cut attempts at explicit whole-part causation theories in physics. One of these is Mach's principle, according to which the force of inertia, experienced locally by a particle, derives from the particle's gravitational interaction with all the matter in the universe. There is currently no very satisfactory formulation of Mach's principle within accepted physical theory, although the attempt to construct one is by no means considered worthless, and once occupied the attention of Einstein himself.

Recent work by Max Bennett in Australia has determined that neurones continually put out little tendrils that can link up with others and effectively rewire the brain on a time scale of 20 minutes! This seems to serve the function of adapting the neuro-circuitry to operate more effectively in the light of various mental experiences (e.g. learning to play a video game). To the physicist this looks deeply puzzling. How can a higher-level phenomenon like 'experience,' which is also a global concept, have causal control over microscopic regions at the sub-neuronal level?

Consider a computer that controls a microprocessor connected to a robot arm. The arm is free to move in any direction according to the program in the computer. Now imagine a program that instructs the arm to reach inside the computer's own circuitry and rearrange it, e.g. by throwing a switch or removing a circuit board. This is software-hardware feedback, where software brings about a change in the very hardware that supports it.

The much-vaunted wave-particle duality of quantum mechanics conceals a subtlety concerning the meaning of the terms. Particle talk refers to hardware: physical stuff such as electrons. By contrast, the wave function that attaches to an electron encodes what we know about the system. The wave is not a wave of 'stuff,' it is an information wave. Since information and 'stuff' refer to two different conceptual levels, quantum mechanics seems to imply a duality of levels akin to mind-brain duality.

As I have already stressed, top-down talk refers not to vitalistic augmentation of known forces, but rather to the system harnessing existing forces for its own ends. The problem is to understand how this harnessing happens, not at the level of individual intermolecular interactions, but overall - as a coherent project. It appears that once a system is sufficiently complex, then new top-down rules of causation emerge.

There is no logical impediment to constructing a whole-part dynamics in which local forces are subject to global rules. For example, it is straightforward to design a cellular automaton in which the evolution rules for a given pixel are determined by a global variable, such as some measure of the complexity of the entire pixel array.

Since complexity is another higher-level concept and another global variable, this would introduce explicit downward causation into physics. To use the now-discredited terminology of the quantum measurement problem, one might posit that the wave function 'collapses' when the system of interest (e.g. the electron) couples to an environment that is sufficiently complex....but as far as I know there is no mathematical model of system complexity entering the dynamics of a complex system to bring about this step.

As the universe ages, so the particle horizon expands, and more and more particles come into causal contact. So the universe begins with very limited information-processing power, but its capability grows with time. Seth Lloyd (2002) has estimated the maximum amount of information that the universe has been able to process since the big bang. The answer comes out to be about 10120 bits. Now this number 10120 is very familiar.

A possible solution of the cosmological constant problem comes from top-down causation. Suppose this quantity, normally denoted Λ, is not a constant at all, but a function of the total amount of information that the universe has processed since the beginning. Lloyd points out that the processed information increases like the square of the age of the universe, t2. Then I hypothesise

Λ(t) = ΛPlanck (tPlanck/t)2

where 'Planck' refers to the Planck time, 10-43 s, at which the universe contains just one bit of information.

Richard J. Campbell and Mark H. Bickhard

Richard.Campbell@anu.edu.au
The Australian National University
Canberra, ACT 0200
Australia

mark.bickhard@lehigh.edu
Lehigh University
Bethlehem, PA 18015
USA

Kim has (apparently) evaded causal drain, but there are serious problems. First, why should we accept his definition of supervenience, complete with his exclusion (by omission) of relations? It blocks causal drain, but only via definitional stipulation, and stipulation that violates the basic sense of supervenience: no higher level differences without accompanying differences at the lower level, including relational differences... he argued explicitly that higher-level configurations of micro-particles could generate novel causal regularities in virtue of those relations, but that such regularities would themselves be no more than the working out of the causal interactions of the basic particles involved in those configurations. Such configurations, therefore, would not generate any novel, emergent, causal powers.

Nothing in this book resurrects organization as a legitimate potential locus of causal power against Kim's own original arguments. What he has now done is to insert relations - organization - as a locus of emergent causal power, but he never addresses his own previous arguments that would debar that move. He introduces relations by definition and by example, not by argument.

The crucial point remains that, assuming causal closure of a particle world, higher level organization is causally superfluous relative to the working out of the causal powers of the most basic constituent particles - unless organization, configurations, or relations can themselves be legitimate loci of genuine causal power. If they can, then new organization can yield emergent causal power, but, in that case, not all causal power is resident in particles, or in whatever micro-particulars a physicalist prefers. Kim has given no reason why organization can be a locus of causal power, given the particle metaphysics that he assumes. He has given no reason why any causal regularities at a higher level of organization are not merely 'causally epiphenomenal'.

Clearly, if we are to find a way forward, we need an alternative and scientifically justifiable concept of emergence. Simply to put 'configurations' into the specification of 'base' properties, and leave the rest of the physicalists' ontological ingredients untouched, is too arbitrary and ad hoc to provide a credible concept of emergence. Clearly, not all properties that derive from higher levels of organization of processes warrant being called emergent. Nor is novelty sufficient: every new organization is an instance of the higher level property of having that particular organization. In our view, causality is what is crucial, and provides the criterion of nontrivial emergence, namely, the emergence of novel causal properties.

One much-discussed example, because it seems to involve reflexivity, is a wheel. The trajectory of some molecule in an iron wheel cannot be explained other than by taking account of its location in that wheel. The motion of the wheel as a whole, as it rolls along, is clearly what determines the curving trajectory of that single iron molecule. Yet, the wheel is made up of molecules like this one. It seems as if the properties of the whole depend upon the properties of its parts, yet the movement of each part depends upon the movement of the whole. Kim has cogently argued that there is nothing in this that is puzzling or metaphysically challenging, provided we understand this reflexive 'downward causation' diachronically. That is, any appearance of incoherence is avoided if there is a time lag - even if only tiny - between the whole's acquiring some property and its causing some change in its parts. So, while linear processes do yield examples of downward causation, the kind of emergence they support is not sufficient to trouble physicalism.

Non-linearity is crucial to causal emergence. By definition, every instance of nonlinearity is an instance of something whose causal properties cannot be derived aggregatively from lower level consequences. In that sense, every instance of nonlinearity is an instance of emergence.

Combinations of such stable 'energy well' processes exist at the macroscopic level, and some of the properties that such combinations manifest are the resultant of aggregating the properties of more microscopic processes that are their constituents. (Energy well stable process organizations can themselves also manifest emergent properties: e.g., van der Waals forces among molecules, or differing molecular properties that manifest quantum interactions within the molecules.) Note that aggregation is itself a form of spatio-temporal organization, and that more is involved in being a causally effective aggregate than simply the logical sum (a bare conjunction) of its constituents. The components have to stick together.

More remarkable is the second kind of stable organization. Far-from-equilibrium stability occurs in an organized process when it is not in thermodynamic equilibrium, and yet it persists for some significant period without moving to equilibrium. The most primitive kind of stable system in which far-from-equilibrium processes persist without collapsing is one that is kept going artificially, entirely by external means.

A further level of complexity is exhibited by systems that can maintain stability not only in certain ranges of conditions, but also within certain ranges of changes of conditions. That is, they can switch to deploying different processes depending on conditions they detect in the environment. A relatively simple example is a bacterium that can swim up a sugar gradient, but tumble if it finds itself to be swimming down a sugar gradient. These two kinds of activity - swimming and tumbling - are different ways for the bacterium to act appropriately to its environmental conditions.

The bacterium's ability to detect sugar-gradients, and to respond by switching between its two modes of action, means that it exhibits a kind of maintenance of its own ability to be self-maintenant; it is able to switch between its self-maintenant processes as the environment changes. That is, it exhibits recursive self-maintenance. Note that even in these relatively primitive examples, the description of these systems of organized process has to use self-reflexive locutions and to speak of its abilities and actions.

These considerations entail a radically different ontology. Biological systems - including humans - are not substantial entities ('things' in the thick sense) whose constituents are cells (smaller things), which in turn (after a few more reductions) are constituted out of elementary particles. They are open, organized action systems, in essential interactions with their environments, such that we cannot say what they are without taking those interactive processes into account.

So, we have to dismiss the argument that if there were emergent entities and properties, they could have no causal powers of themselves. It ignores the crucial role of organization in the emergence of properties and powers from systems of lower-level processes. It also ignores the essential role of external relations in the self-maintenance of stable far-fromequilibrium process systems, from flames to human beings. Yet stable far-fromequilibrium process systems are the ones that have given rise to the most interesting and intriguing of emergent causal powers: life, consciousness, and self-consciousness.

Larry Shapiro and Elliott Sober University of Wisconsin, Madison

Abstract: When philosophers defend epiphenomenalist doctrines, they often do so by way of a priori arguments. Here we suggest an empirical approach that is modeled on August Weismann's experimental arguments against the inheritance of acquired characters. This conception of how epiphenomenalism ought to be developed helps clarify some mistakes in two recent epiphenomenalist positions - Jaegwon Kim's (1993) arguments against mental causation, and the arguments developed by Walsh (2000), Walsh, Lewens, and Ariew (2002), and Matthen and Ariew (2002) that natural selection and drift are not causes of evolution. A manipulationist account of causation (Woodward 2003) leads naturally to an account of how macro- and micro-causation are related and to an understanding of how epiphenomenalism at different levels of organization should be understood.

Weismann was not arguing that parental phenotypes are causally inert; he wasn't claiming that they have no effects of any kind. Rather, he was advancing the more modest thesis that they have no effect on offspring genotypes. Parental phenotypes are epiphenomenal with respect to the process of genetic inheritance.

The basic idea behind Weismann's experiment was this: to find out whether X causally contributes to Y, you manipulate the state of X while holding fixed the state of any common cause C that affects both X and Y; you then see whether a change in the state of Y occurs. We find it useful to think of this procedure probabilistically. The question is whether the following inequality is true:

For any genotype Gp that a parental pair might have,
Pr(offspring has a tail│ parents have Gp & parents have tails) >
Pr(offspring has a tail │parents have Gp & parents' tails were cut off
when they were born).

Weismann's experiments indicated that this inequality is false; the two conditional probabilities are equal.

We have gone into some detail about the logic of Weismann's experiment because we think it is important for philosophers to see clearly what Weismann did not do. As we have explained, Weismann manipulated the parental phenotype while holding fixed the parental genotype. He did not manipulate the parental phenotype while holding fixed the micro-supervenience base of that phenotype. What's the difference between these two procedures? We assume that cause precedes effect; causation is a diachronic relation. In contrast, the (mereological) supervenience relationship is synchronic; it relates the macro-state of the organism at time t to its micro-state at time t. The idea is that the micro-state at t determines the macro-state at t; however, the converse is not true, owing to the fact that macro-properties are multiply realizable at the micro-level.

The most important lesson we draw from Weismann is that investigating whether X causes Y involves figuring out whether wiggling X while holding fixed whatever common causes there may be of X and Y will be associated with a change in Y. It is not relevant, or even coherent, to ask what will happen if one wiggles X while holding fixed the micro-supervenience base of X.

We conjecture that the mistake we just described underlies the main intuition that makes epiphenomenalist doctrines attractive. Consider the question of mental causation. How could believing or wanting or feeling cause behavior? Given that any instance of a mental property X has a physical micro-supervenience base MSB(X), it would appear that X has no causal powers in addition to those that MSB(X) already possesses. The absence of these additional causal powers is then taken to show that the mental property X is causally inert.

The crucial mistake in this line of reasoning is that it requires one to consider a counterfactual situation that is in fact impossible and is in any case irrelevant to the question of whether the mental property X, or any other supervening property, is epiphenomenal with respect to an effect term Y. To see if X has an effect on Y that is additional to whatever effect MSB(X) has on Y, one would have to compare what would happen to Y if both MSB(X) and X were present with what would happen to Y if MSB(X) were present and X were absent...To assess whether X causes Y, the common causes of X and Y must be held fixed, but not the micro-supervenience base of X.

Suppose that smart Martians wouldn't need to attribute beliefs and desires to us to predict our behavior. Like Laplace's demon, they could simply survey the state of the atoms that make up our bodies, subject that information to a very complex calculation, and thereby predict what we'll do next. It therefore appears that the only reason we have for attributing beliefs and desires to each other is that we can't do what smart Martians can do.

Ockham's razor is relevant only to the choice between competing hypotheses. However, there is no conflict between saying that we have beliefs and desires and saying that we occupy neurophysiological states. And there is no conflict between saying that a behavior has physical causes and saying that it has mental causes.

Just as philosophers of mind sometimes contend that mental properties are epiphenomenal, so philosophers of biology sometimes contend that natural selection is epiphenomenal.

August 9, 2011 · 3:06 pm

What does itmean to say that epiphenomenal gliders and other epiphenomenal patterns can implement a Turing Machine? How can it mean anything? Neither the patterns nor the Turing Machine are real; they are all epiphenomenal. Furthermore, the interactions between patterns aren't real either. They're also epiphenomenal; the only real action is at the level of the Game of Life rules. The use of emergent patterns and their epiphenomenal interactions to implement a Turing Machine-which can then be used to do real computations-illustrates the use of epiphenomena to do real work.

Recall Weinberg's statement: there are no autonomous laws of weather that are logically independent of the principles of physics. Clearly there are lots of autonomous "laws" of Turing Machines (namely computability theory), and they are all logically independent of the rules of the Game of Life. An implementation of a Turing Machine on a Game of Life platform is an example of what might be called a nonreductive regularity. The Turing Machine and its implementation is certainlya kind of regularity, but it is a regularity that is not a logical consequence of-is not reducible to and cannot be derived from-the Game of Life rules.

Because higher level abstractions are physically identifiable from both an entropy and mass perspective, we feel justified in asserting that they are objectively real. The dilemma is resolved when one realizes that (a) the subject matter of the higher level sciences are abstractions; (b) those abstractions are instantiated as physically real when implemented by lower level phenomena; yet (c) interaction among those abstractions is epiphenomenal and may always be reduced to the fundamental forces of physics. Abstractions at all levels are central to how we look at the world, but one must always be aware of the feasibility ranges within which an abstraction is implemented. A tragic example is the case of the O-rings on Challenger. They failed when they were used outside the temperature feasible range for which they functioned as sealants.

In this paper, it is the computer science notion of an abstract software specification that is most significant. Software abstractions are both conceptual and real. An implemented software specification combines the formality and abstraction of mathematics with the reality of nature. Computers are reification devices, capable of making the abstract concrete. Nature's abstractions differ from software abstractions in that they are not conceptual; they are always implemented by something. The combination of higher level abstractions along with the epiphenomenal and range-limited nature of higher level causality makes multiscale systems unavoidable-a problem which typically doesn't plague abstractions implemented in software.

Russ Abbott Department of Computer Science, California State University, Los Angeles, Ca, USA Russ.Abbott@GMail.com

In "Gulliver's Travels," Swift satirizes the machine without naming Lull. In the story, a professor shows Gulliver a huge contraption that generates random sequences of words. Whenever any three or four adjacent words made sense together, they were written down. The professor told Gulliver the machine would let the most ignorant person effortlessly write books in philosophy, poetry, law, mathematics, and theology.

Traditionally, one thinks of a computation as a contingent process-one defined in a programming language. Like a Turing Machine, it runs for free. Real world computations result from non-contingent processes, have energy requirements, and operate in contingent environments. ... Computing involves configuring environmental contingencies, i.e., setting up an environment within which a process (or multiple processes) will play itself (or themselves) out. We refer to this as non-algorithmic computing. The focus is on how an environment will shape a process, not on the algorithm the shaped process will perform. A Game of Life glider has no algorithm.

Why can't we look to Turing Machines (and their equivalents) for a definition of computation that does not rely on the notion of thought externalization? Turing Machines, recursive functions, and equivalent models rely on the notions of symbols and symbol manipulation, which are fundamentally mental constructs. They identify symbol manipulation to be what we intuitively think of as computational activity. The Turing Machine model is our way of externalizing an entire class of mental activities, the class that we intuitively identify as symbolic.

The various models of computational activities are all defined constructively, i.e., in terms of the operations one may perform when constructing a computational procedure. Furthermore, the equivalence proofs among the standard models are also constructive. We can constructively transform any Turing Machine into a recursive function and vice versa. The equivalence of these models shows that Turing Machines, recursive functions, etc. are equivalent as programming languages.

What's important about the Church-Turing thesis is not the class of functions that can be computed but the possible programs one can write. Our revised version of the Church-Turing thesis is that to be considered rigorous a thought process must, at least in principle, be expressible as a software.... one need not think of the program that a Turing Machine embodies in functional terms, i.e., as closed with respect to information flow. One can also think of a Turing Machine as open with respect to information flow. This parallels the distinction in physics between systems that are closed and open with respect to energy flows.

What might one gain from being open to information flows? An illustrative example is Prisoner's Dilemma (PD). If one were to develop an optimized PD player for a one-shot PD exchange-since it's one shot, the system is closed-it will Defect. Playing against itself, it will gain 1 point on each side-using the usual scoring rules. If one were to develop an optimized PD player to engage in an iterative PD sequence-the system is open-it will Cooperate indefinitely (presumably by playing a variant of Tit-for-Tat), gaining 3 points on each side at each time. Thus the same problem (PD) yields a different solution depending on whether one's system is presumed to be open or closed with respect to information flows.

Our revised version of the Church-Turing thesis gives us confidence that our current understanding of agents as entities that embody programs is reasonably close to how we think about thinking. We are still quite far from the goal of formalizing appropriate environments within which to situate such agents. ... An environmentally sophisticated agent-based paradigm involves agents, each of which has the computing capability of a Turing machine, situated in an environment that reveals itself reluctantly. Such an agent in a real-world environment is like an Oracle machine, with nature as the oracle. Combining agents with dynamic entities yields real-world agents, which (a) must extract energy from their environment to persist and (b) embody software capable of processing information flows from the environment. The agent-based thesis is that this paradigm represents how, at the start of the 21st century, we have externalized our thoughts about our place with the world.