Reductio ad reductionem

Atomic force microscopy image
Atomic force microscope image of a single molecule, courtesy Bruno Schuler

Reduction is a powertool of rationality. It accounts for some of the most spectacular scientific success stories. Outstanding examples include the kinetic theory of gases, set theory, and the whole of computer science.1

Dazzled by such cases, some rationalists say we can do this for everything. Overall, rationalism seeks a rational theory of rationality, preferably based on a criterion which guarantees correctness. Could reduction form that criterion? Reduction certainly is rational, so reducing rationality to reduction would fulfill the rationalist program. On this view, if a theory is not reductive, it is not rational.

The dream is that reduction could deliver absolute truths about the eggplant-sized world, by explanation through a series of levels. The rationalist’s reflex, when confronted with nebulosity, is to retreat to the most fundamental physics: quantum field theory. That, she says, is definitely not nebulous; there is absolute truth there.2 Based on this unshakable foundation, we can find absolute truths about atoms, which are just assemblages of quanta. And we can reduce molecules to atoms (chemistry), and cells to molecules (molecular biology), and eggplants to cells (phytotomy); and finally, triumphantly, prove beyond any possibility of doubt the absolute truth that eggplants are fruits (reproductive biology).

Empirically, this metaphysical fantasy is a bad theory of actually-existing rationality. It’s simply false to facts.

We are routinely rational, in practice, in domains in which reduction is not currently feasible. Neuroscience is mostly not, in practice, reducible to molecular biology. We don’t have sufficiently detailed and accurate models of neurons to make that feasible. Psychology is not, in practice, reducible to neuroscience. We don’t understand in detail what individual neurons do, and we don’t know in detail how groups of neurons form functional structures. Cases of completely successful scientific reductions, in which one domain has been fully explained in terms of another, are very rare, and perhaps non-existent.3 Partial reductions do not enable absolute truth to bubble up from lower to higher levels.

When you point this out, rationalists often fall back on “well, reduction must be possible in principle.” If this metaphysical claim were true,4 it would be irrelevant. A useful understanding of rationality needs to explain how it does work in practice, not how it should work according to philosophical theory, or could work in a distant, ideal future.

“Sometimes this way of reasoning wins big” does not imply “this is the only way to do it,” nor “it always works.”5 A good theory of rationality may treat reduction among other topics. As it happens, The Eggplant’s alternative treatment of rationality doesn’t. “What role does reduction play in rationality?” is a valid and interesting question, but it’s not central enough to give space in this book.

For much of the twentieth century, most philosophers of science did believe reduction was essential to science, or even its essence. They developed several complex, conflicting stories about what reduction is and how and why it works, including taxonomies of different types of reduction. Unfortunately, none of these theories survived testing against diverse specific cases of scientific progress. In this century, most philosophers have reluctantly accepted that reduction is nebulous (impossible to define), and that most science is not reductive.6

Whether or not reduction is theoretically possible is irrelevant to whether reductionism is a useful theory of rationality. However, it’s helpful to understand some obstacles to reduction that arise in practice. You may then suspect that they are also obstacles in principle as well. I’ll sketch two issues here:

  1. The terms used at one level of description cannot be defined in terms of the next lower level, as required.
  2. Levels of description have patchy holes in them, so lower levels show through, and higher levels get sucked in.

These could be summarized as: nebulosity blurs reduction, so it cannot propagate absolute truth upward.


Reduction should redefine entities at one abstraction level in terms of combinations of those at the next lower one. These definitions must be precise to propagate absolute truth. In physics, this may be possible. Atoms are combinations of electrons and nucleons. Light spectra are combinations of photons of different wavelengths.

In biology, reduction is mainly impossible in practice.7 In fact, it’s usually impossible to define biological entities at all; certainly not precisely, or in terms of chemistry. Cells, for example, are a central category, but there’s no definite criterion for what counts as a cell. If you attempt to find one, you rapidly bog down in a maze of exceptions. You might start with something like “a self-reproducing living unit carrying a single copy of the organism’s DNA within a membrane.” But red blood cells don’t self-reproduce and have no DNA. Mitochondria are not cells, but they self-reproduce using their own DNA within a membrane. Muscle cells have multiple nuclei, each with a separate complete copy of the DNA. Some algae have life stages in which they have no cell membranes. And so on indefinitely.8

The next chapter explores many reasons absolutely precise definitions are difficult or impossible, particularly in biology.

In most cases, translating terms from one level of description to a lower one would be meaningless and useless even if it were possible. Imagine you had a precise chemical definition of “cell.” Start with some particular cell, and imagine randomly adding or removing individual molecules. (There are several trillion of them per cell, mostly water; on the order of a hundred million proteins and a billion lipid molecules.) At some point, a single-molecule change must switch the entity from a cell to a non-cell. What could that possibly signify? (It wouldn’t be the transition from living to dead, even if “living” were definable and single molecule made the difference; a dead cell is a cell. It wouldn’t be the transition from able to reproduce to not able; red blood cells can’t reproduce regardless. And so on.)

Some rationalists might say that if biologists can’t define “cell,” they are sciencing wrong. If “cell” isn’t reducible to quantum theory, at least in principle, nothing biologists say about cells can be absolutely true or false, and therefore it’s all meaningless. Biology will have to get fixed by people who know what they are doing. Scientists can only meaningfully ask questions that can be cashed out in unambiguous physical terms.

But, this is impossible currently. So then, rationally speaking, we do not currently have any genuine knowlege of biology. Here there is a fork in the road… Taking this seriously leads to post-rationalist nihilism, the despairing realization that rationality cannot deliver on rationalism’s promises. By rationalism’s standards, knowlege is mostly impossible. We’ll explore this nihilism, and ways to avoid the rage and depression it entails, at the end of Part One.

Alternatively, you can acknowledge that actually-existing biological research is rational, and so some different and better understanding of rationality must be possible. Meta-rationalism is that.

Levels of description are nebulous

The levels proposed by reductionism were not ordained by God, nor granted perfect cohesion by Him. Apart from fundamental physics, they all turn out to be layers of patchy clouds. In computer science terms, they are “leaky abstractions,” that fail to fully “encapsulate” lower levels, which show through.

Level-skipping is common. Some properties “show through” all the way from quantum field theory to the eggplant-sized world. Color is an example. Starting around 1800, chemistry restricted itself to investigating properties of molecules that can be derived from the atoms that make them up. But you can’t derive most properties of molecules—including color—from their constituent atoms, so color was explicitly excluded from chemistry’s consideration.

Starting in the mid-20th century, color became a chemical property again, due to the development of quantum molecular orbital theory. That considers the relationship of individual electrons to the whole molecule. In a molecule, electrons are “delocalized,” so only global computations over the whole system, at the quantum level, give meaningful results.9 Quantum mechanics “shows through” the atomic abstraction. In the case of color, it is still feasible to make approximate but predictive level-skipping calculations.

On the other hand, chemical reactions cannot generally be predicted just from molecular orbital theory, because that considers molecules in a vacuum. Most reactions occur in an environment—such as water—that modulates reactivity. In biochemistry, taking this a step further, many reactions are only enabled by the active site of an enzyme, which provides the exquisitely specific spatial distribution of electron density required. Enzyme function is often regulated by additional molecules—activators and inhibitors—that alter this geometry. Those are often regulated in turn by complex cellular processes, ultimately under control of genetic feedback loops.

And it doesn’t stop there; the metabolism of individual cells is regulated by signals from neighboring cells, and up through to the organization of the whole organism, which interacts with its environment, which… which means that a fully predictive model of an individual biochemical reaction would suck in all the descriptive levels above it, as well as below it, and therefore would require a quantum simulation of the entire organism and its environment. As a matter of metaphysics, this may be possible in principle, but it has no implications for any conceivable practice.

  1. 1.The kinetic theory explains the relationship between the pressure, volume, and temperature of eggplant-sized quantities of gas in terms of the behavior of individual gas molecules. It’s only approximately true, but highly accurate in practice. Set theory reduces all of mathematics to a handful of simple axioms about a single type of object. Computer software generally comes in many layers, each providing a different abstract vocabulary that is implemented in terms of the next one down in the stack. Eventually you reach a machine language program, which is directly executed by the hardware. That, in turn, is understood as many layers of abstraction, with registers and multipliers implemented as gates, implemented as circuits, implemented as a physical chip that is understood partly in terms of quantum mechanics. Each layer in this stack is fully explained by reduction to the one below. Until you get to the semiconductor device level, anyway. Transistors are modeled partly with quantum mechanics, but the reduction is incomplete, and involves empirically derived parameters of bulk materials. Complete quantum mechanical reduction is not feasible there.
  2. 2.Even this point is dubious. It’s unlikely there’s any absolute truth in actually-existing fundamental physics, at least. Half a century ago, it seemed that the Standard Model and general relativity were absolute truths, but since then anomalies have piled up. The reflex to treat physics as certain is left over from the Newtonian worldview. Taking actually-existing physical theory (rather than a fantasy of an ultimate correct one) as absolute doesn’t work anymore; but it’s a cultural habit ingrained in many rationalists.
  3. 3.For an argument that there are zero examples of completely successful scientific reductions, with a recognition that imperfect reductions are important nevertheless, see Kenneth F. Schaffner’s “Reduction: the Cheshire cat problem and a return to roots,” Synthese (2006) 151: 377–402. A classic argument against reductionism is “More Is Different” by physicist Philip W. Anderson, who made the case that small molecules, and even large atomic nuclei, cannot be understood quantum mechanically. Science, 177:4047 (Aug. 4, 1972), pp. 393-396.
  4. 4.Certainty that reduction is possible in principle seems to be proven by proceeding backwards, in steps of emotional necessity. There must exist a way to gain reliable knowledge, or else the universe would be ultimately awful, and we might as well kill ourselves. Rationality is, by definition, the only way to gain reliable knowledge; so rationality must always work. Rationality requires absolute truth; therefore absolute truths must always exist. Fundamental physics has absolute truths; if theory A is absolutely true and we can reduce theory B to theory A, then theory B is also absolutely true; so we must be able to reduce everything to fundamental physics. QED.
  5. 5.There’s a tendency among working scientists to confuse mechanistic understanding (which is widely available) with theory level reduction (which is not). Reduction is not just any explanation, or causal explanation, or mechanical explanation. We also have no coherent definition or specific theory of what an explanation or cause is, so if it were just those things, “reduction” wouldn’t explain anything, and wouldn’t be an adequate account of rationality.
  6. 6.The Stanford Encyclopedia of Philosophy’s “Scientific Reduction” article is a good review.
  7. 7.See Schaffner’s “Reduction” paper cited above. He also explains, with nice examples, how good biological explanations typically include aspects from many levels of description, rather than reducing one level (even in part) to the next-lower one.
  8. 8.Sharrock, Randall, and Greiffenhagen’s 2011 “Engineering the Scientific Corpus: Routine Semantic Work in (Re)constructing a Biological Ontology” describes a team of experts in biological ontology attempting to find a definition for “cell” and failing; and then attempting to find a coherent taxonomy of types of cells, and achieving only limited, provisional, negotiated success.
  9. 9.Taking this to 11, quantum mechanics predicts that gold would have almost the same color as silver. Gold’s yellow depends on its electrons increasing in mass due to traveling at more than half light speed, and its color can only be predicted from a combination of quantum mechanics and relativity.