Questioning Nineteenth-Century Assumptions about Knowledge, II

Reductionism

Richard E. Lee

• Publisher: SUNY Press
• Year: 2010
• Print ISBN: 9781438434407, 9781438434414
• eBook ISBN: 9781438434421
• Topic: Social Sciences
• Subtopic: Philosophical Criticism
• Index: Social Sciences

During the last few decades, the fundamental premises of the modern view of knowledge have been increasingly called into question. Questioning Nineteenth-Century Assumptions about Knowledge II: Reductionism provides an in-depth look at the debates surrounding the status of "reductionism" in the sciences, social sciences, and the humanities in detailed and wide-ranging discussions among experts from across the disciplines. Whether or not there is or should be a basic epistemological stance that is different in the sciences and humanities, and whether or not such a stance as exemplified by the approach to reductionism is changing, has enormous consequences for all aspects of knowledge production. Featured are an overview and subsequent discussion of this pervasive concept in the social sciences that parses reductionism into the categories of strong social constructionism and anti-essentialism, social ontology and the apathetic actor, dualisms, and individualism. Also of interest in chapters and follow up discussions are the relations between essentialism and emergentism in complex systems theory.

SESSION III

REDUCTION AND EMERGENCE IN COMPLEX SYSTEMS

Jean Petitot

I
INTRODUCTION

Classically, a reductionist thesis posits that complex high level phenomena, structures, and processes can be reduced, as far as their scientific explanation is concerned, to underlying lower level phenomena, structures, and processes. The most paradigmatic and best-investigated example is the reduction of macroscopic thermodynamics to microscopic molecular and atomic movements (temperature = mean kinetic energy per degree of freedom, etc.). Let us begin with some conceptual precisions.

1. Reductionism can be a particular scientific thesis concerning a specific scientific theory: it is precisely the case with the reduction of macro thermodynamics to micro statistical mechanics. But it can be also a general metaphysical claim on the ultimate nature of reality, as is the case with different forms of monism. Idealist monism posits the universal reducibility of reality to mind while materialist monism posits the universal causal reducibility of reality to matter and energy. In this paper we will consider only scientific reductionism.
2. Reductionism can concern theories dealing with empirical data and in that case focuses on the problem of causality. But it can also concern purely linguistic and formal theories. For instance, lexical definitions or logical axioms consist in trying to reduce complex contents to a small list of primitive contents. In mathematics, many theories deal with the possibility of eliminating higher order concepts, objects, or axioms in proofs and deflate rich theories to more restrained ones (theorems of elimination): for instance one can prove that quantifiers can be eliminated in algebraic geometry (Tarsky-Seidenberg theorem) or that a proof using the axiom of choice can be transformed into a proof without the axiom of choice, etc. In this paper, we will be concerned only with theories having an empirical content.
3. Scientific object-oriented reductionism can be ontological or methodological. It is ontological when it concerns explanations in terms of primitive objects (atoms, neurons, etc.) and methodological when it concerns deflationist nominalist explanations (Occam's razor). There are well-known examples of eliminative methodological reductionism that have eliminated pre-scientific speculative concepts and entities such as “vital,” etc. Today, a very important debate in cognitive science has to do with the eliminability of “mental” or “conscious” concepts and their reduction to neural concepts (see e.g., the Dennett/Chalmers controversy). In this paper we will be concerned with “ontological” reductionism. However, as we endorse a transcendentalist perspective, we prefer the expression “objective reductionism.” Indeed, transcendental conceptions introduce a strong opposition between the concepts of ontology and objectivity. They posit that scientific theories cannot concern any independent transcendent reality, but only an objective reality mathematically reconstructed from phenomena. For them, any theory necessarily includes epistemic background structures (called priors).
4. In our narrow, scientific, empirical, and objective sense, reductionism concerns mainly complex systems that possess at least two levels of reality: a micro underlying level where a great number of elementary units are in interaction and a macro-emergent one where macro self-organized structures emerge (Thom 1972). In such a perspective, reductionism is inseparable from converse concepts such as emergence, supervenience, or functionalism. Functionalism means that macrostructures that have a functional role can exist only if they are materially implemented in an underlying material substrate, but are at the same time, as functionally meaningful structures, largely independent of the fine-grained physical properties of the substrate they are implemented in. The paradigmatic example is the opposition software–hardware in computer sciences (see philosophers like Putnam, Fodor, Pylyshyn, etc.), but functionalism also applies in natural sciences, where it is an aspect of emergence.
5. There is general agreement on the fact that in complex systems that have different levels of reality at different scales, there exist collective behaviors ruled by laws that are not the laws of the micro underlying level. It is the case for critical phenomena, percolation, self-organized criticality, reaction-diffusion equations, dissipative structures, turbulence, cellular automata, neural networks, ant colonies, swarms, stock markets, etc. According to one's conception of laws, one can develop different conceptions of this empirical fact.
   1. Eliminativism and epiphenomenalism: laws being only empirical regularities lacking any objective (and a fortiori ontological) content (Hume's empiricist thesis), emerging structures are purely epiphenomenal and can be scientifically eliminated salva veritate.
   2. Holistic realism (the converse of the previous position): laws being real in the ontological sense, the emerging level possesses an ontological reality and cannot therefore be reduced.
   3. Causal reductionism and objective emergentism: laws being objective, that is, at the same time empirically grounded and mathematically formalized, the emerging level has no ontological content but is nevertheless much more than a simple empirical regularity. It is causally reducible to complex interactions at the micro underlying level but it shares nevertheless some empirical and theoretical autonomy.
   We will be concerned here with this third type of reductionism.
6. The main difficulty that has to be tackled in such a perspective is the relation between causal reduction and theoretical autonomy. Mathematics plays the fundamental role here. Indeed, the formal equivalent to causal reduction is mathematical deduction. But deducibility is a syntactic property and doesn't entail any evident conceptual derivation (it is for that very reason that mathematics constitutes an authentically “synthetic” knowledge even if proofs are “analytical”). Therefore the fact that the structures and properties of the macro level can be mathematically deduced from the micro level doesn't mean that the representational content of its conceptual description can be reduced to the representational content of the microlevel. A very spectacular example is that found in statistical physics where magnetic critical behaviors can be classified, via the renormalization group, in universal classes independent of the specific fine-grained physical structure of the substrate. The renormalization group is a dynamic method that enables us to define these universal behaviors as attractors of a certain dynamics on the space of Hamiltonians. Near the critical temperature (T = T_c) the macro variables of the system (magnetization, specific heat, magnetic susceptibility, etc.) follow power laws (ΔT)^α (where α is called the critical exponent of the variable). Empirical data have shown that there exist universal classes of critical exponents linked by very precise relations. These universal classes depend only on very general abstract dimensional and symmetry properties of the substrate and not on its detailed physical structure. The point is that if you prove mathematically that such a critical phenomenon arises from a symmetry breaking of an order parameter, this doesn't mean that this macro and abstract symmetry breaking modeled via group theory, has something to do with the concept of a spin of a particle. Causal reduction that parallels mathematical deduction is not a conceptual reduction. Moreover, the universality of critical exponents—that is the existence of invariants—proves that the emerging critical phenomenon under consideration has some measure of autonomy and belongs to an autonomous level of reality.

As the physical examples of reductionism are very well known, and because we think that it is always better to discuss precise examples, we will focus in some detail on two examples. The first belongs to cognitive sciences and concerns phenomenology of perception and visual neurosciences. The second belongs to social sciences and concerns Hayek's catallaxy and evolutionary game theory.

II
COGNITIVE SCIENCES

In cognitive sciences, reductionism concerns in particular the reducibility of mental states, representations, contents, structures, events, and processes to neural activity. The most difficult challenge is that of the reduction of consciousness. For materialists such as Dan Dennett, mind is epiphenomenal and without any causal efficiency, and must be reduced to neurobiology. Conversely, for philosophers such as David Chalmers, phenomenal consciousness is irreducible and there will always remain an “explanatory gap.”

Let us recall very briefly the classical op...

Table of contents

• Series Title
• Introduction
• SESSION I Reductionism in Social Science
• SESSION II Emergence and Complex Systems
• SESSION III Reduction and Emergence …
• SESSION IV Organizers' Opening Remarks