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Friday, April 16, 2010

Theory vs Theory

This is the third in a series of postings by guest blogger, Arlin Stoltzfus. You can read the introduction to the series at: Introduction to "The Curious Disconnect". The first part is at: The "Mutationism" Myth I. The Monk's Lost Code and the Great Confusion. Arlin is challenging the status quo in modern evolutionary theory. He's not alone in this challenge but it's important to distinguish between kooks who don't know what they're talking about and serious thinkers who have something to say. Arlin is going to explain to you why everything you thought you knew about mutationism is wrong. In this article we learn about theories.

Please pay attention.

The Curious Disconnect

Our journey to map out the Curious Disconnect-- the gap between how we think about evolution and how we might think if we were freed from historical baggage-- began last time with part 1 of The Mutationism Myth.

Before continuing with part 2, I would like to take a detour. Issues surrounding "evolutionary theory", and evolutionary theories, are going to be coming up again and again. In fact, I can see these issues emerging already in The Mutationism Myth. So, before we get bogged down in confusion and disagreement, I would like to begin a discussion of "theory" and "theories". We'll return to the Mutationism Myth next time.

An updated version of the post below will be maintained at (Arlin Stoltzfus, ©2010)

Theory1 vs theory2

What does it mean to invoke "evolutionary theory"? Is "neo-Darwinism" (or "Darwinism") a theory, a school of thought, or something else? What gives a theory structure and meaning (e.g., axioms, themes, formulae)? What is the relationship between mathematical formalisms and other statements of "theory" (e.g., what does it mean for a lecturer to show a key equation of quantitative evolutionary genetics and assert "this is neo-Darwinism")? Who decides how a theory is defined, or redefined (e.g., is Ohta's "nearly neutral" theory an alternative to, or a variant of, Kimura's Neutral Theory of Molecular Evolution)?

Confusion regarding "theory" and "theories" is going to be an ongoing topic of attention in The Curious Disconnect. As noted in the Introduction, we're in an enormous muddle. The way to get out of this muddle is to take some time to build common understanding, learn some useful terms, and establish ground rules.

In this post, we'll begin the process of developing a shared framework for productively discussing "theory" and "theories". We will begin by addressing an ambiguity in the use of the word "theory", partly because this particular ambiguity is important, and partly as an exercise in addressing semantics. 0


Dictionaries provide definitions that can be helpful to clarify the meanings of words and the complications of their usage. Definitions can be descriptive, telling us how a word is used, or prescriptive, telling us how it ought to be used. But, as most of us don't like to be told what we ought to do, I suspect that you share my belief in studying how words are used, in order to determine their denotations (what the word says) and connotations (what the word hints or implies). The English dictionaries used in America typically agree: the definitions that they provide reflect patterns of common usage, not the decrees of authorities.

A difficulty with dictionaries arises given that, within an isolated community, e.g., a scientific discipline, words can take on special meanings. So, dictionaries can be helpful, with the proviso that we need to be sensitive to the special use of terms within a discipline.

The discipline-specific use of a term can be nailed down by looking at examples of usage. For evolutionary biology, the discipline-specific use of a term is to be found in the research literature, and also in the secondary literature of monographs, textbooks, and other disciplinary writings.

Two meanings of "theory"

A good dictionary will distinguish several different senses of the word "theory", including the following two that I believe are the most relevant for our discourse:

1) a major conjecture or systematic hypothesis to account for observed phenomena, as in "prion theory of disease" or "Lamarck's theory of evolution";

2) the body of abstract principles relevant to some discipline, methodology or problem area, as in "music theory" or "population genetics theory"

That is, a theory1 is a grand hypothesis, a conjecture about the actual world, while a theory2 is a collection of principles or models or other formalisms that might apply only in an imagined world. Fisher (1930) famously said that "No practical biologist interested in sexual reproduction would be led to work out the detailed consequences experienced by organisms having three or more sexes; yet what else should he do if he wishes to understand why the sexes are, in fact, always two?" Theoreticians aren't necessarily good with facts, so we'll ignore that the sexes (in the sense of mating types) are not, in fact, always two. Fisher clearly encourages us to work out formalisms for imagined or hypothetical cases. The collection of all these models or formalisms about sexes would constitute the theory2 of sexes. A theory1 of sexes might propose a causal explanation for the actual historic phenomenon of the origin and maintenance of sexual reproduction in animals, addressing such issues as the heterogametic basis of sex determination. 1

These two meanings are not just recognized in dictionaries, but are established in scientific usage. Gilbert's "Exon Theory of Genes" (Gilbert 1987) is the conjecture that genes evolved from exons (i.e., large protein-coding genes emerged by joining primordial exon-minigenes). The prion theory1 of disease clearly revolves around a conjecture that there are actual diseases caused by actual prions. By contrast, population genetics theory2 is not the conjecture that populations have genetics; likewise, the theory2 of stochastic processes is not a conjecture that stochastic processes occur, but consists of a body of abstract principles that might be applicable to such stochastic processes as might occur in some actual or imagined universe.

The use of the abstract noun, as in "let's talk about theory" as opposed to "let's talk about { a | the | this } theory", often signals the use of theory2. For instance, the title of a report by the National Academy of Sciences on "The Role of Theory in Advancing 21st Century Biology" signals a likely emphasis on theory2, and indeed, the report emphasizes the development of formalisms more than conjectures, and says that "a useful way to define theory in biology is as a collection of models", clearly a reference to theory2. The report also mixes in some references to theories1.

Obviously, there is a connection between scientific theories1 and scientific theory2. One way of thinking about the connection is that the abstract principles of theory2, when suitably limited by measurable or observable quantities from the actual world, can provide the basis of a theory1, and conversely, theories1 draw on theory2 for logical structure. Kimura's Neutral Theory (Kimura 1983) provides a clear example because the theory1 and theory2 were developed separately: Kimura combined pre-existing theory2 (of stochastic population genetics) with the concrete assertion that the values of certain quantities (relating to population sizes and mutant effects) were such that, for DNA and protein sequences, neutral evolution by mutation and random fixation would be far more common than anyone had imagined previously. The definition of effectively neutral alleles (perpetually misunderstood by critics) and the probability of fixation under pure drift were known to the canonical founders of population genetics ((Wright 1931); ch. IV of (Fisher 1930); appendix of (Haldane 1932)). Another indication of the distinctness of theory1 and theory2 is that opponents of the Neutral Theory1, who deny the truth of the theory1, are nonetheless quite happy to make use of its theoretical2 infrastructure (Kreitman 1996).

Development and application of theory1 and theory2

We treat the two kinds of "theory" differently, and rightly so.

A theory1 contains a major supposition or unproved conjecture about the world. Kimura's Neutral Theory is the conjecture that most changes at the "molecular level" represent the random fixation of effectively neutral alleles. Darwin proposed, but could not prove, that all large-scale evolutionary changes were built from infinitesimal increments of change that emerged by a process of hereditary "fluctuation". A theory1 takes risks: in Popperian terms, its subject to empirical refutation; in the words of Huxley, a beautiful theory1 can be "killed by an ugly fact."

The relevant standard of validity for theory2 is not verisimilitude (trueness to life), but consistency: the principles derived in the theory are consistent with its assumptions. Importantly, new principles added to a body of theory2 are consistent with previous principles, except in the sense that a body of theory2 may be subdivided into branches that cover non-overlapping universes. If they are not, a logical error has occurred.

While new theory2 is consistent with existing theory2, theories1 often stimulate interest precisely because they conflict with previous theories1. Of course theories1 strive to be internally consistent, but in biology at least, theories1 are not axiomatic, and often encompass ambiguities that make rigorous analysis difficult. A theory1 can be brought down by a contradiction that arises internally, e.g., one part can be found to contradict another part.

While a theory1 is about the actual world, and thus is judged by verisimilitude, principles of theory2 need not apply to the real world. Indeed, no amount of conflicting data will cause us to discard a principle of theory2 that is properly derived: a beautiful piece of theory2 cannot be killed by an ugly fact. Fisher's fundamental theorem either is logically valid or is not logically valid, independent of any facts.


The distinction between theory1 and theory2 is hidden in the ambiguous word "theory", but I think it comes out more clearly in specific word-derivatives and grammatical usages that seem to favor one meaning more than the other. I mentioned above that the abstract noun typically signals theory2. I'm also convinced that when we refer to a "theoretician", we typically do not mean someone like Tom Cavalier-Smith whose scientific output consists of bold conjectures or systematic hypotheses (we might call such people "theorizers"), but instead someone like Joe Felsenstein whose work focuses on mathematical or algorithmic foundations, i.e., theory2. Its a rare scientist, it seems to me, who is productive both as a theoretician and as a theorizer (e.g., Kimura, Hamilton).

Neither meaning of theory would cause us to relinquish the label "theory" for a proposition that lacks verisimilitude. Clearly the propositions of theory2 do not have to apply to the real world. And a theory1 is a conjecture, not necessarily a true conjecture. Thus, even opponents of the Neutral Theory1, who believe that the theory does not fit the actual world, still refer to it as The Neutral Theory (Kreitman 1996).

I mention this because there is an absurd tendency in the literature of evolution advocacy, e.g., NCSE's screeds, to say that, because scientists reserve the word "theory" only for constructions that have been extensively verified and are accepted as true, the use of "theory of evolution" among scientists means that evolution is well supported.

This argument clearly is false, and the proof does not depend on the theory1 vs. theory2 distinction, but only on the fact that scientists habitually choose to refer to Kimura's theory or Lamarck's theory or Gilbert's theory as a "theory", even if its known to be wrong or is considered deeply suspect. This pattern holds, not just in biology, but in other disciplines. In astronomy, the geocentric theory remains a theory though it has been abandoned; in physics, the phlogiston theory, or the aether theory of light propagation (roughly, the theory that space must be substantive in order for waves to propagate in it) remain theories even though they were abandoned. So, write to the NCSE and tell them to stop using this lame argument. Really, we can do better than that.

The NCSE fallacy seems to arise from mixing together the proposed explanation of phenomena aspect of theory1 and the accepted as valid aspect of theory2. This is suggested from the way that NCSE's screed cites the NAS report on theory2 (the same one that I quoted above) as though it provided a definition of theory qua "well substantiated explanation", which definitely is not the same as "collection of models".

Lets try to sort this out in terms of the distinction between theory1 and theory2. Evolutionists have recourse to a body of theory2 (formalisms or models or principles), ranging from purely phenomenological models of branching and character-state change used in phylogenetics, to the breeder's equation used in quantitative genetics, to detailed formulas for population-genetics processes, and so on. We accept the validity of these abstractions in the theory2 sense of validity, i.e., we accept that they are derived without error, so as to be logically consistent with their assumptions. This body of abstractions, principles, or formalisms (in NAS parlance, this collection of models) is evolutionary theory2.

But saying that this theory2 is valid is not at all the same thing as claiming that its true in the sense of verisimilitude; and claiming that it has verisimilitude is not the same as saying that its complete, in the sense of sufficiently accounting for the phenomena of evolution. For instance, the theory2 of quantitative evolutionary genetics is based on the assumption of infinitesimal variation, but the theory2 itself does not claim that all traits, nor even any single trait, evolved in this manner-- that would be a theory1 issue. Kimura's diffusion equations are a part of population genetics theory2 that provides a way to work out the probability of fixation of alleles under ideal conditions, but it doesn't assert that the results are applicable to any particular case. Got it?


The wikipedia entry on theory ( has a "List of Notable Theories" that clearly mixes up theories1 or grand conjectures (the cell theory, the phlogiston theory) with theories2 or bodies of abstract principles (music theory, extreme value theory). What are some other clear examples of theory1 and theory2 in this list? Which examples are difficult to classify (and what does one learn from those)?

Who, besides Kimura and Hamilton, was productive as both a theoretician and as a theorizer?

Think of a few theories in science, ideally in life sciences. I'm going to assert that they are not axiomatic, i.e., they are not completely encompassed by precisely stated propositions. Given this, how do we really know what defines the theory? If we know a theory from the verbal statements in a body of literature (i.e., "things people say"), what is the relationship of an individual expression (e.g., a paper, a monograph, a quotation) to the theory? Is it the instantiation of a platonic form or essence? How do we get to the essence? Is the distribution of expressions of a theory its "reaction norm", representing environmental noise in the expression of an underly structure (the theory's "genotype")?

The Modern Synthesis as theory1: into the memory hole

The folks at NCSE and wikipedia are not the only ones blurring the issues. The Modern Synthesis or modern neo-Darwinism 2 was put forth originally as a falsifiable theory1 of evolution, but evolutionists themselves don't treat it that way anymore. For instance, in Maynard Smith's defense of "neo-Darwinism" (Maynard Smith 1969), the only kinds of falsifying observations he can imagine are cases that seem to introduce supernatural forces, e.g., if the spots on a fish always appeared in prime numbers, he says this would contradict neo-Darwinism. He does not imagine variation-induced trends, discontinuous jumps based on individual mutations, or extensive neutral evolution as contradictions of "neo-Darwinism", though these ideas were rejected by the architects of modern neo-Darwinism. Maynard Smith makes the claim in regard to the Neutral Theory that "I have never seen any reason why, as a naive Darwinist, I should reject this theory" (Maynard Smith 1995). It seems that, for Maynard Smith, "neo-Darwinism" is not a theory1 at all, but merely indicates a commitment to scientific materialism, i.e., seeking natural causes through observation and experiment.

Other authoritative sources suggest that the Modern Synthesis is no longer viewed as a falsifiable conjecture. In Hull's Encyclopedia of Evolution article on the history of evolutionary thought (Hull 2002), the Modern Synthesis is presented as an open-ended "theory" that merely assumes the principle of selection and the rules of genetics, and which has swallowed up the neutral theory along with all other useful ideas:

"Any criticism of the synthetic theory that turned out to have some substance was subsumed in a modified version of this theory. Instead of being a weakness, this ability to change is one of the chief strengths of the synthetic theory of evolution. As in the case of species, scientific theories evolve" (p. E16)

Hull's conception of the Modern Synthesis sounds more like an extensible set of principles, theory2, than the theory1 of Mayr, Simpson, Ayala, etc (which is extensible in some ways but closed and falsifiable in others). I'm not necessarily going to say its wrong for scientists to decide that the Modern Synthesis is no longer a theory1, but can someone please tell me when, and on what basis, did we make this decision? Is there a citation for that? And who decided that we wouldn't tell Richard Dawkins, leaving the poor fellow stuck in a time warp defending the original Modern Synthesis? 3

But I'm getting ahead of myself. I started The Curious Disconnect with the The Mutationism Myth because 1) most evolutionists don't understand how the Modern Synthesis came into existence as a theory1 that entails risky conjectures, and 2) the mutationist challenge provides the definitive historical proof that the Modern Synthesis is a theory1 and not just a commitment to selection and the rules of genetics. The historical record will show clearly that the mutationists or "Mendelians" presented a workable synthesis of selection and the rules of genetics, and that their view was rejected by the architects of the Modern Synthesis. Once we find out why, we will understand what makes the Modern Synthesis a theory1.

Literature cited

Dawkins, R. 2007. Review: The Edge of Evolution. Pp. 2. International Herald Tribune, Paris.

Fisher, R. A. 1930. The Genetical Theory of Natural Selection. Oxford University Press, London.

Gilbert, W. 1987. The exon theory of genes. Cold Spring Harbor Symp. Quant. Biol. 52:901-905.

Haldane, J. B. S. 1932. The Causes of Evolution. Longmans, Green and Co., New York.

Hull, D. L. 2002. History of Evolutionary Thought. Pp. E7-E16 in M. Pagel, ed. Encyclopedia of Evolution. Oxford University Press, New York.

Kimura, M. 1983. The Neutral Theory of Molecular Evolution. Cambridge University Press, Cambridge.

Kreitman, M. 1996. The neutral theory is dead. Long live the neutral theory. Bioessays 18:678-683.

Maynard Smith, J. 1969. The Status of Neo-Darwinism. Pp. 82-89 in C. H. Waddington, ed. Towards a Theoretical Biology 2. Sketches. Edinburgh Universeity Press, Edinburgh.

Maynard Smith, J. 1995. Life at the Edge of Chaos? Pp. 28-30. New York Review of Books, New York.

Wright, S. 1931. Evolution in Mendelian populations. Genetics 16:97.


0 I thank Dr. Mike Coulthart for originally drawing my attention to the importance of this distinction.

1 If we were to propose just that the sexes are always 2 in number, simply because that is what we have seen in the past, I would call this an empirical generalization or "law". Sometimes "theory" is used for such a generalization, but that usage does not correspond to either meaning of "theory" addressed here.

2 I'm using "modern neo-Darwinism" as a synonym for "Modern Synthesis". Neo-Darwinism (for our purposes, Darwinism 1.2) is the pre-Mendelian theory of Weissman and Wallace emphasizing the supreme power of selection and infinitesimal variation to build adaptation (and rejecting Darwin's reliance on Lamarckism). The Modern Synthesis (Darwinism 2.0) comes from this tradition and is often called "neo-Darwinism", though "modern neo-Darwinism" is clearer.

3 Kidding aside, its quite useful to have a scholar still defending the actual Modern Synthesis. For instance, in his attempt to rebut Behe (Dawkins 2007), Dawkins claims that mathematical geneticists "have repeatedly shown that evolutionary rates are not limited by mutation" and that Behe's critique based on the idea that evolution depends on specific mutations would mean that "the entire corpus of mathematical genetics, from 1930 to today, is flat wrong". In making this claim, Dawkins is correctly representing the Modern Synthesis view that (due to the buffering effect of the "gene pool") evolution does not depend on the rate of new mutations, a principle that he believes to be an infallible theoretical result.


Mike from Ottawa said...

"Think of a few theories in science, ideally in life sciences. I'm going to assert that they are not axiomatic, i.e., they are not completely encompassed by precisely stated propositions."

I don't think the term you want is "axiomatic". Since theories are subject to falsification, they are inherently not axiomatic. The term I'd suggest, to borrow from math, is "well-defined". A mathematical set is well-defined when its definition includes all elements of the set and nothing that isn't an element of the set.

A theory would be well-defined if its expression set out all that was included within the theory and captured nothing that wasn't.

That would seem to fit with the content of your post.

Marcello Pucciarelli said...

A complication with theories1 is that their defense is based on argumentation -- rational arguments, but less constrained than logical or deductive demonstrations. Thus, a bold conjecture can in principle be falsifiable, but an actual falsification may require an agreement on what counts as evidence for or against the theory.

Given this complication, however, it is easy to loose sight of the very important point you are making -- that bold conjectures are falsifiable after all. The details may be messy, but they don't fall exclusively in the domain of the sociology of science.

I would only caution against taking "falsification" too strictly, as a relation involving a theory(1) and some experimental results. I think it's more a process of accumulation, where the weight of the evidence against a theory can only be gauged by a workable alternative theory.