Wednesday, June 28, 2006

Inference and the Boundaries of Science

AUTHOR: Hannah Maxson

SOURCE: Evolution and Design

COMMENTARY: Allen MacNeill

The now-notorious Cornell "evolution and design seminar" met for the first time last night, and in my opinion our first meeting was a rousing success. As I had hoped, the participants began to make their opinions and positions known (despite my blathering), and a good time was had by all. We're getting ready to analyze Richard Dawkins' arguments in The Blind Watchmaker, discussion of which will be facilitated by Will Provine (one of our faculty participants).For a brief taste of how things went last night, you should check out the course blog. Here's a sample:

Hannah Maxson (founder of the Cornell IDEA Club) wrote:

In class last night Allen went over inference and his views of the boundaries of science. He gave us the example of an individual coming upon the remains of what appeared to have been a house fire in the past. Without any prior knowledge of the event or eyewitnesses to question, one might infer any of three things (see diagram, above):

1) accidental house fire
2) arson: purposeful house fire
3) no fire at all; setup job (for film, etc.)

A tentative explanatory filter with which to distinguish between those three causes. But he suggested there is a problem from the very beginning. The first question– was this a real fire, or a setup job? can never be definitely answered. Considering a very powerful film crew, for instance, the setup would look almost like a real fire. Extrapolating slightly, given an omnipotent “designer”, could the scene not be exactly the same as what one would expect from a housefire?

Because there is no way of giving a definite answer based on empirical evidence– to which we, as scientists, are limited– we must throw out that whole node on our explanatory filter. Everything above the dotted line, at least, is outside our realm of knowledge.

I had a quarrel with much of this reasoning, though to begin with I ought to make a strong disclaimer that I’m not at all interested in defending “setup jobs”– I think they are highly uninteresting, for one thing, and not worth spending time in. But a “right” or at least convenient answer doesn’t make the logic that goes into an argument sound.

First, can we throw a question out of the realm of science because we will never be able to get a definite answer? Scarcely anything in science will ever be proved or disproved. In general, we don’t look for certain proofs, but simply for empirical evidence that might favor one or the other, so that we can make an inference to the best explanation. If the evidence is not clear, we often make choices based on conventions, such as parsimony.

If we cannot throw it out for lack of a definite answer, can we at least throw out that node for lack of empirical evidence either way? It is true that if the scene was designed (omnipotently) so that there was absolutely no evidence there had been no real fire, science could do nothing with the question. But we cannot assume a priori that all “setup jobs” have no emperical evidence available; there are a great many other possibilities besides an omnipotent designer who works to make things exactly the same. Consider, for example Einstein’s view: “Nature hides her secrets because of her essential loftiness, but not by means of ruse.”; or in another remark: “God is slick, but he ain’t mean.”

So while we can do away with a “absolutely perfect imitation” possibility as an option that could never have any emperical grounds, that is not justification for demarcating the entire first node out of our field of inquiry. In any research project you learn quickly that things are not always as they first appear. What seems on first analysis to be the remains of a fire may turn out on further investigation to hold evidence of a set-up job. What appears to have been designed may in fact be the product of chance and necessity, and what we are used to thinking of as the products of unguided evolution may contain evidence of purposeful design.

Refusing to consider questions is never good practice; we may reject explanations for lack of warrant, but ought never reject the investigation a priori.

To which I replied:

Thanks, Hannah, for the diagram (it’s clearer than mine was last night) and for your analysis, above. However, I still stand by my position that, given a sufficiently powerful “designer,” a house fire (or anything else) can be simulated to such a degree (as Warren [Warren Allman, director of the Paleontological Research Institute and Museum of the Earth here in Ithaca] said, “right down to the subatomic particles) that there would be absolutely no way to distinguish between such a creation ex nihilo and the real thing.

That is, no amount of empirical evidence could make it possible to get past the first branch point in the explanatory filter in the diagram. Indeed, every piece of empirical evidence one could add would simply amplify one’s assertion of the hypothesis of the Designer’s omnipotence (”Amazing, S/He/It can f/make things right down to the quarks!”). For this reason, rather than agonize over our inability to get past the first branch point in the filter via empirical means, we simply agree to skip that step and move down to the second branch point.

I believe that this “agreement” is something with which most ID supporters would concur, as it gets us out of an empirically insoluble dilemma, and moves us along to the question of accident vs design. Darwin did essentially the same thing in the Origin of Species, by bringing in “the Creator” only at the very end, and by relegating Her/Him/It to setting the whole system in motion in the beginning. Having spent many years reading Darwin’s personal writings (correspondence mostly, but also some of the expurgated sections of his autobiography), it appears to me that Darwin became a Deist about the time he wrote the Origin (or in the process of doing so, which took two decades), but then slowly realized that Deism is essentially equivalent to agnosticism/atheism, as the Deity of Deism plays no part in the actual universe at all, beyond setting up the natural laws that govern it. I find myself in the same situation: assuming that the Deity of Deism exists gets one absolutely nowhere at all in science, and so (like most other scientists), I simply don’t go there anymore.

And now I would go further; while it is a good idea to "not reject explanations for lack of warrant, bu never reject the investigation a priori", the point I was trying to make in my reply was that if one can't get by the first branch point in the "explanatory filter" I posited during the discussion, then we can't really do science at all. Furthermore, agreeing that the remains of what looks like a house fire could have been created ex nihilo by a sufficiently powerful entity gets us absolutely nowhere in terms of explaining the origin of the wreckage. In fact, it forestalls the possibility of any kind of empirically verifiable (or falsifiable) hypothesis, and is therefore a "science stopper" of the first order.


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Saturday, June 17, 2006

Identity, Analogy, and Logical Argument in Science (Updated)

AUTHOR: Allen MacNeill

SOURCE: Original essay

COMMENTARY: That's up to you...
"...analogy may be a deceitful guide."
- Charles Darwin, Origin of Species

The descriptions and analysis of the functions of analogy in logical reasoning that I am about to describe are, in my opinion, not yet complete. I have been working on them for several years (actually, about 25 years all told), but I have yet to be completely satisfied with them. I am hoping, therefore, that by making them public here (and eventually elsewhere) that they can be clarified to everyone’s satisfaction.


To begin with, let us define an analogy as “a similarity between separate (but perhaps related) objects and/or processes”. As we will see, this definition may require refinement (and may ultimately rest on premises that cannot be proven - that is, axioms - rather than formal proof). But for now, let it be this:

DEFINITION 1.0: Analogy = Similarity between separate objects and/or processes (from the Greek ana, meaning “a collection” and logos, meaning “that which unifies or signifies.”)

AXIOM 1.0: The only perfect analogy to a thing is the thing itself.

COMMENTARY 1.0: This is essentially a statement of the logical validity of tautology (from the Greek tó autos meaning “the same” and logos, meaning “word” or “information”. As Ayn Rand (and, according to her, Aristotle) asserted:

AXIOM 1.0: A = A

From this essentially unprovable axiom, the following corrolary may be derived:

CORROLARY 1.1: All analogies that are not identities are necessarily imperfect.

AXIOM 2.0: Only perfect analogies are true.

CORROLARY 2.1: Only identities (i.e. tautologies, or "perfect" analogies) are true.

CORROLARY 2.2: Since only tautologies are prima facie "true", this implies that all analogical statements (except tautologies) are false to some degree. This leads us to:

AXIOM 3.0: All imperfect analogies are false to some degree.

AXIOM 3.0: A ≠ notA

CORROLARY 3.1: Since all non-tautological analogies are false to some degree, then all arguments based on non-tautological analogies are also false to the same degree.

COMMENTARY 2.0: The validity of all logical arguments that are not based on tautologies are matters of degree, with some arguments being based on less false analogies than others.

CONCLUSION 1: As we will see in the next sections, all forms of logical argument (i.e. transduction, induction, deduction, and abduction) necessarily rely upon non-tautological analogies. Therefore, to summarize:
All forms of logical argument (except for tautologies) are false to some degree.

Our task, therefore, is not to determine if non-tautological logical arguments are true or false, but rather to determine the degree to which they are false (and therefore the degree to which they are also true), and to then use this determination as the basis for establishing confidence in the validity of our conclusions.


Based on the foregoing, let us define validity as “the degree to which a logical statement is based upon false analogies.” Therefore, the closer an analogy is to a tautology, the more valid that analogy is.

DEFINITION 2.0: Validity = The degree to which a logical statement is based upon false analogies.

COMMENTARY: Given the foregoing, it should be clear at this point that (with the exception of tautologies):
There is no such thing as absolute truth; there is only degrees of validity.

In biology, it is traditional to determine the validity of an hypothesis by calculating confidence levels using statistical analyses. According to these analyses, if a hypothesis is supported by at least 95% of the data (that is, if the similarity between the observed data and the values predicted by the hypothesis being tested is at least 95%), then the hypothesis is considered to be valid. In the context of the definitions, axiom, and corrolaries developed in the previous section, this means that valid hypotheses in biology may be thought of as being at least 95% tautological (and therefore less than 5% false).

DEFINITION 2.1: Confidence = The degree to which an observed phenomenon conforms to (i.e. is similar to) a hypothetical prediction of that phenomenon.

This means that, in biology:
Validity (i.e. truth) is, by definition, a matter of degree.

Following long tradition, an argument (from the Latin argueré, meaning “to make clear”) is considered to be a statement in which a premise (or premises, if more than one, from the Latin prae, meaning “before” and mitteré, meaning “to place”) is related to a conclusion (i.e. the end of the argument). There are four kinds of argument, based on the means by which a premise (or premises) are related to a conclusion: transduction, induction, deduction, and abduction, which will be considered in order in the following sections.

DEFINITION 2.2: Argument = A statement of a relationship between a premise (or premises) and a conclusion.

Given the foregoing, the simplest possible argument is a statement of a tautology, as in A = A. Unlike all other arguments, this statement is true by definition (i.e. on the basis of AXIOM 1.0). All other arguments are only true by matter of degree, as established above.


The simplest (and least effective) form of logical argument is argument by analogy. The Swiss child psychologist Jean Piaget called this form of reasoning transduction (from the Latin trans, meaning “across” and duceré. meaning “to lead”), and showed that it is the first and simplest form of logical analysis exhibited by young children. We may define transduction as follows:

DEFINITION 3.0: Transduction = Argument by analogy alone (i.e. by simple similarity between a premise and a conclusion).

A tautology is the simplest transductive argument, and is the only one that is “true by definition.” As established above, all other arguments are “true only by matter of degree.” But to what degree? How many examples of a particular premise are necessary to establish some degree of confidence? That is, how confident can we be of a conclusion, given the number of supporting premises?

As the discussion of confidence in Section 2 states, in biology at least 95% of the observations that we make when testing a prediction that flows from an hypothesis must be similar to those predicted by the hypothesis. This, in turn, implies that there must be repeated examples of observations such that the 95% confidence level can be reached.

However, in a transductive argument, all that is usually stated is that a single object or process is similar to another object or process. That is, the basic form of a transductive argument is:

Ai => Aa


Ai is an individual object or process


Aa is an analogous (i.e. similar, but identical, and therefore non-tautological) object or process

Since there is only a single example in the premise in such an argument, to state that there is any degree of confidence in the conclusion is very problematic (since it is nonsensical to state that a single example constitutes 95% of anything).

In science, this kind of reasoning is usually referred to as “anecdotal evidence,” and is considered to be invalid for the support of any kind of generalization. For this reason, arguments by analogy are generally not considered valid in science. As we will see, however, they are central to all other forms of argument, but there must be some additional content to such arguments for them to be considered generally valid.

EXAMPLE 3.0: To use an example that can be extended to all four types of logical argument, consider a green apple. Imagine that you have never tasted a green apple before. You do so, and observe that it is sour. What can you conclude at this point?

The only thing that you can conclude as the result of this single observation is that the individual apple that you have tasted is sour. In the formalism introduced above:

Ag => As


Ag = green apple


As = sour apple

While this statement is valid for the particular case noted, it cannot be generalized to all green apples (on the basis of a single observation). Another way of saying this is that the validity of generalizing from a single case to an entire category that includes that case is extremely low; so low that it can be considered to be invalid for most intents and purposes.


A more complex form of logical argument is argument by induction. According to the Columbia Encyclopedia, induction (from the Latin in, meaning “into” and duceré, meaning “to lead”) is a form of argument in which multiple premises provide grounds for a conclusion, but do not necessitate it. Induction is contrasted with deduction, in which true premises do necessitate a conclusion.

An important form of induction is the process of reasoning from the particular to the general. The English philosopher and scientist Francis Bacon in his Novum Organum (1620) elucidated the first formal theory of inductive logic, which he proposed as a logic of scientific discovery, as opposed to deductive logic, the logic of argumentation. the Scottish philosopher David Hume has influenced 20th-century philosophers of science who have focused on the question of how to assess the strength of different kinds of inductive argument (see Nelson Goodman and Karl Popper).

We may therefore define induction as follows:

DEFINITION 4.0: Induction = Argument from individual observations to a generalization that applies to all (or most) of the individual observations.

EXAMPLE 4.0: You taste one green apple; it is sour. You taste another green apple; it is also sour. You taste yet another green apple; once again, it is sour. You continue tasting green apples until some relatively arbitrary point (which can be stated in formal terms, but which is unnecessary for the current analysis), you formulate a generalization; “(all) green apples are sour.”

In symbolic terms:

A1 + A2 + A3 + …An => As


A1 + A2 + A3 + …An = individual cases of sour green apples


As = green apples are sour

As we have already noted, the number of similar observations (i.e. An in the formula, above) has an effect on the validity of any conclusion drawn on the basis of those observations. In general, enough observations must be made that a confidence level of 95% can be reached, either in accepting or rejecting the hypothesis upon which the conclusion is based. In practical terms, conclusions formulated on the basis of induction have a degree of validity that is directly related to the number of similar observations; the more similar observations one makes, the greater the validity of one’s conclusions.

IMPLICATION 4.0: Conclusions reached on the basis of induction are necessarily tentative and depend for their validity on the number of similar observations that support such conclusions. In other words:
Inductive reasoning cannot reveal absolute truth, as it is necessarily limited only to degrees of validity.

It is important to note that, although transduction alone is invalid as a basis for logical argument, transduction is nevertheless an absolutely essential part of induction. This is because, before one can formulate a generalization about multiple individual observations, it is necessary that one be able to relate those individual observations to each other. The only way that this can be done is via transduction (i.e. by analogy, or similarity, between the individual cases).

In the example of green apples, before one can conclude that “(all) green apples are sour” one must first conclude that “this green apple and that green apple (and all those other green apples) are similar.” Since transductive arguments are relatively weak (for the reasons discussed above), this seems to present an unresolvable paradox: no matter how many similar repetitions of a particular observation, each repetition depends for its overall validity on a transductive argument that it is “similar” to all other repetitions.

This could be called the “nominalist paradox,” in honor of the philosophical tradition founded by the English cleric and philosopher William of Ockham, of “Ockham’s razor” fame. On the face of it, there seems to be no resolution for this paradox. However, I believe that a solution is entailed by the logic of induction itself. As the number of “similar” repetitions of an observation accumulate, the very fact that there are a significant number of such repetitions provides indirect support for the assertion that the repetitions are necessarily (rather than accidentally) “similar.” That is, there is some “law-like” property that is causing the repetitions to be similar to each other, rather than such similarities being the result of random accident.


A much older form of logical argument than induction is argument by deduction. According to the Columbia Encyclopedia, deduction (from the Latin de, meaning “out of” and duceré, meaning “to lead”) is a form of argument in which individual cases are derived from (and validated by) a generalization that subsumes all such cases. Unlike inductive argument, in which no amount of individual cases can prove a generalization based upon them to be “absolutely true,” the conclusion of a deductive inference is necessitated by the premises. That is, the conclusions (i.e. the individual cases) can’t be false if the premise (i.e. the generalization) is true, provided that they follow logically from it.

Deduction may be contrasted with induction, in which the premises suggest, but do not necessitate a conclusion. The ancient Greek philosopher Aristotle first laid out a systematic analysis of deductive argumentation in the Organon. As noted above, Francis Bacon elucidated the formal theory of inductive logic, which he proposed as the logic of scientific discovery.

Both processes, however, are used constantly in scientific research. By observation of events (i.e. induction) and from principles already known (i.e. deduction), new hypotheses are formulated; the hypotheses are tested by applications; as the results of the tests satisfy the conditions of the hypotheses, laws are arrived at (i.e. by induction again); from these laws future results may be determined by deduction.

We may therefore define deduction as follows:

DEFINITION 5.0: Deduction = Argument from a generalization to an individual case, and which applies to all such individual cases.

EXAMPLE 5.0: You assume that all green apples are sour. You are confronted with a particular green apple. You conclude that, since this is a green apple and green apples are sour, then “this green apple is sour.”

In symbolic terms:

As => Ai


As = all apples are sour

Ai = any individual case of a green apple

As noted above, the conclusions of deductive arguments are necessarily true if the premise (i.e. the generalization) is true. However, it is not clear how such generalizations are themselves validated. In the scientific tradition, the only valid source of such generalizations is induction, and so (contrary to the Aristotelian tradition), deductive arguments are no more valid than the inductive arguments by which their major premises are validated.

IMPLICATION 5.0: Conclusions reached on the basis of deduction are, like conclusions reached on the basis of induction, necessarily tentative and depend for their validity on the number of similar observations upon which their major premises are based. In other words:
Deductive reasoning, like inductive reasoning, cannot reveal absolute truth about natural processes, as it is necessarily limited by the degree of validity upon which its major premise is based.

Hence, despite the fact that induction and deduction “argue in opposite directions,” we come to the conclusion that, in terms of natural science, the validity of both is ultimately dependent upon the number and degree of similarity of the observations that are used to infer generalizations. Therefore, unlike the case in purely formal logic (in which the validity of inductive inferences is always conditional, whereas the validity of deductive inferences is not), there is an underlying unity in the source of validity in the natural sciences:
All arguments in the natural sciences are validated by inductive inference.


A somewhat newer form of logical argument is argument by abduction. According to the Columbia Encyclopedia, abduction (from the Latin ab, meaning “away” and duceré, meaning “to lead”) is the process of reasoning from individual cases to the best explanation for those cases. In other words, it is a reasoning process that starts from a set of facts and derives their most likely explanation from an already validated generalization that explains them. In simple terms, the new observation(s) is/are "abducted" into the already existing generalization.

The American philosopher Charles Sanders Peirce (last name pronounced like "purse") introduced the concept of abduction into modern logic. In his works before 1900, he generally used the term abduction to mean “the use of a known rule to explain an observation,” e.g., “if it rains, the grass is wet” is a known rule used to explain why the grass is wet:

Known Rule: “If it rains, the grass is wet.”

Observation: “The grass is wet.”

Conclusion: “The grass is wet because it has rained.”

Peirce later used the term abduction to mean “creating new rules to explain new observations,” emphasizing that abduction is the only logical process that actually creates new knowledge. He described the process of science as a combination of abduction, deduction and implication, stressing that new knowledge is only created by abduction.

This is contrary to the common use of abduction in the social sciences and in artificial intelligence, where Peirce's older meaning is used. Contrary to this usage, Peirce stated in his later writings that the actual process of generating a new rule is not hampered by traditional rules of logic. Rather, he pointed out that humans have an innate ability to correctly do logical inference. Possessing this ability is explained by the evolutionary advantage it gives.

We may therefore define abduction as follows (using Peirce's original formulation):

DEFINITION 6.0: Abduction = Argument that validates a set of individual cases via a an explanation that cites the similarities between the set of individual cases and an already validated generalization.

EXAMPLE 6.0: You have a green fruit, which is not an apple. You already have a tested generalization about green apples that states that green apples are sour. You observe that since the fruit you have in hand is green and resembles a green apple, then (by analogy to the case in green apples) it is probably sour (i.e. it is analogous to green apples, which you have already validated are sour).

In symbolic terms:

(Fg = Ag) + (Ag = As) => Fg = Fs


Fg = a green fruit

Ag = green apple

As = sour green apple


Fs = a sour green fruit

In the foregoing example, it is clear why Peirce asserted that abduction is the only way to produce new knowledge (i.e. knowledge that is not strictly derived from existing observations or generalizations). The new generalization (“this new green fruit is sour”) is a new conclusion, derived by analogy to an already existing generalization about green apples. Notice that, once again, the key to formulating an argument by abduction is the inference of an analogy between the green fruit (the taste of which is currently unknown) and green apples (which we already know, by induction, are sour).

IMPLICATION 6.0: Conclusions reached on the basis of abduction are, like conclusions reached on the basis of induction and deduction, are ultimately based on analogy (i.e. transduction). That is, a new generalization is formulated in which an existing analogy is generalized to include a larger set of cases.

Again, since transduction, like induction and deduction, is only validated by repetition of similar cases (see above), abduction is ultimately just as limited as the other forms of argument as the other three:
Abductive reasoning, like inductive and deductive reasoning, cannot reveal absolute truth about natural processes, as it is necessarily limited by the degree of validity upon which it premised.


The newest form of logical argument is argument by consilience. According to Wikipedia, consilience (from the Latin con, meaning “with” and saliré, meaning “to jump”: literally "to jump together") is the process of reasoning from several similar generalizations to a generalization that covers them all. In other words, it is a reasoning process that starts from several inductive generalizations and derives a "covering" generalization that is both validated by and strengthens them all.

The English philosopher and scientist William Whewell (pronounced like "hewel") introduced the concept of consilience into the philosophy of science. In his book, The Philosophy of the Inductive Sciences, published in 1840, Whewell defined the term consilience by saying “The Consilience of Inductions takes place when an Induction, obtained from one class of facts, coincides with an Induction obtained from another different class. Thus Consilience is a test of the truth of the Theory in which it occurs.”

The concept of consilience has more recently been applied to science in general and evolutionary biology in particular by the American evolutionary biologist Edward_O._Wilson. In his book, Consilience: the Unity of Knowledge, published in 1998, Wilson reintroduced the term and applied it to the modern evolutionary synthesis. His main point was that multiple lines of evidence and inference all point to evolution bynatural selection as the most valid explanation for the origin of evolutionary adaptations and new phylogenetic taxa (e.g. species) as the result of descent with modification (Darwin's term for "evolution").

To extend the example for abduction given above, if the grass is wet (and rain is known to make the grass wet), the road is wet (and rain is known to make the road wet), and the car in the driveway is wet (and rain is known to make the car in the driveway wet), then rain can make everything outdoors wet, including objects whose wetness is not yet verified to be the result of rain.

Independent Observation: “The grass is wet.”

Already validated generalization: "Rain makes grass wet."

Independent Observation: “The road is wet.”

Already validated generalization: "Rain makes roads wet."

Independent Observation: “The car in the driveway is wet.”

Already validated generalization: "Rain makes cars in driveways wet."

Conclusion: “Rain makes everything outdoors wet.”

One can immediately generate an application of this new generalization to new observations:

New observation: "The picnic table in the back yard is wet."

New generalization: “Rain makes everything outdoors wet.”

Conclusion: "The picnic table in the back yard is wet because it has rained."

We may therefore define consilience as follows:

DEFINITION 7.0: Consilience = Argument that validates a new generalization about a set of already validated generalizations, based on similarities between the set of already validated generalizations.

EXAMPLE 7.0: You have a green peach, which when you taste it, is sour. You already have a generalization about green apples that states that green apples are sour and a generalization about green oranges that states that green oranges are sour. You observe that since the peach you have in hand is green and sour, then all green fruits are probably sour. You may then apply this new generalization to all new green fruits whose taste is currently unknown.

In symbolic terms:

(Ag = Sa) + (Og = Os) + (Pg = Ps) => Fg = Fs


Ag = green apples

Sa = sour apples

Og = green oranges

Os = sour oranges

Pg = green peaches

Ps = sour peaches

Fg = green fruit

Fs = sour fruit

Given the foregoing example, it should be clear that consilience, like abduction (according to Peirce) is another way to produce new knowledge. The new generalization (“all green fruits are sour”) is a new conclusion, derived from (but not strictly reducible to) its premises. In essence, inferences based on consilience are "meta-inferences", in that they involve the formulation of new generalizations based on already existing generalizations.

IMPLICATION 7.0: Conclusions reached on the basis of consilience, like conclusions reached on the basis of induction, deduction, and abduction, are ultimately based on analogy (i.e. transduction). That is, a new generalization is formulated in which existing generalizations are generalized to include all of them, and can then be applied to new, similar cases.

Again, since consilience, like induction, deduction, and abduction, is only validated by repetition of similar cases, consilience is ultimately just as limited as the other forms of argument as the other three:
Consilient reasoning, like inductive, deductive, and abductive reasoning, cannot reveal absolute truth about natural processes, as it is necessarily limited by the degree of validity upon which it premised.

However, there is an increasing degree of confidence involved in the five forms of logical argument described above. Specifically, simple transduction produces the smallest degree of confidence, induction somewhat more (depending on the number of individual cases used to validate a generalization), deduction more so (since generalizations are ultimately based on induction), abduction even more (because a new set of observations is related to an already existing generalization, validated by induction), and consilience most of all (because new generalizations are formulated by induction from sets of already validated generalizations, themselves validated by induction).


Transduction relates a single premise to a single conclusion, and is therefore the weakest form of logical validation.

Induction validates generalizations only via repetition of similar cases, the validity of which is strengthened by repeated transduction of similar cases.

Deduction validates individual cases based on generalizations, but is limited by the induction required to formulate such generalizations and by the transduction necessary to relate individual cases to each other and to the generalizations within which they are subsumed.

Abduction validates new generalizations via analogy between the new generalization and an already validated generalization; however, it too is limited by the formal limitations of transduction, in this case in the formulation of new generalizations.

Consilience validates a new generalization by showing via analogy that several already validated generalizations together validate the new generalization; once again, consilience is limited by the formal limitations of transduction, in this case in the validation of new generalizations via inferred analogies between existing generalizations.

• Taken together, these five forms of logical reasoning (call them "TIDAC" for short) represent five different but related means of validating statements, listed in order of increasing confidence.

• The validity of all forms of argument are therefore ultimately limited by the same thing: the logical limitations of transduction (i.e. argument by analogy).

• Therefore, there is (and can be) no ultimate certainty in any description or analysis of nature insofar as such descriptions or analyses are based on transduction, induction, deduction, abduction, and/or consilience.

• All we have (and can ever have) is relative degrees of confidence, based on repeated observations of similar objects and processes.

• Therefore, we can be most confident about those generalizations for which we have the most evidence.

• Based on the foregoing analysis, generalizations formulated via simple analogy (transduction) are the weakest and generalizations formulated via consilience are the strongest.

Comments, criticisms, and suggestions are warmly welcomed!


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Tuesday, June 13, 2006

Are Adaptations "Real?"

AUTHOR: Allen MacNeill

SOURCE: Original essay

COMMENTARY: That's up to you...

In an ongoing thread at Design Paradigm, Salvador Cordova wrote:

“There are many designed features in biology that make no sense in terms of natural selection but make complete sense in terms of design.”

This statement demonstrates a profound misunderstanding of both the concept of “design” and of “natural selection,” a misunderstanding which lies at the heart of the evolution/design debate. What is “design” anyway? Note that I’m not asking the question that Dr. Dembski thought he was answering, i.e. how can we tell if something has been designed. Before one can even ask that question (much less attempt to answer it), one must first agree on what “design” is.

This is not a trivial problem. Michael Ruse, in Darwin and Design: Does Evolution Have a Purpose?, asserts that one of the most important contributions of Darwin’s theory was that it put “design” back into nature (from which it had been removed by the “Newtonians”). To Ruse, “design” is essentially equivalent to “adaptation,” in that adaptations “solve” problems of biological function.

But the problem here is one that Lewontin and Gould addressed almost 30 years ago in their landmark paper “The Spandrels of San Marco...”. Lewontin and Gould pointed out two things: (1) not all of the characteristics of living organisms are adaptations (i.e. some of them are the result of pure “chance,” not necessity), and (2) even the characteristics that are clearly adaptive don’t have to have arisen because they are adaptive, nor will they continue to exist for the same reason. They coined the term “exaptation” to refer to characteristics of organisms that are not necessarily adaptive, but which nonetheless are biologically significant.

I would go much further than Lewontin and Gould: just as Darwin suggested (but did not come right out and say) that there are no such things as “species” (see "Origin of the Specious" in this blog), I believe that in nature there are no such things as “adaptations,” at least not insofar as such "adaptations" are "solutions" to biological "problems." That is, although there are characteristics of organisms that are correlated with relatively high reproductive success (and would therefore be considered by most evolutionary biologists to qualify as “adaptations”), it becomes problematic to decide exactly which of those characteristics are the “real” adaptations and which are merely “accidental.” Indeed, if one is serious about the variation/inheritance/fecundity/differential reproductive success model of evolution (i.e. the genuine article, not the RM+NS straw-man attacked by most IDers), then all of the characteristics of living organisms are “accidental” insofar as their origin cannot be shown to have been “intended” or “pre-destined” ahead of time.

Here is the real crux of the disagreement, as PvM has pointed out: what qualifies as an “adaptation” in biology can only be determined retrospectively, insofar as it has the practical result of causing increased relative survival and reproduction. No characteristics of living organisms can be shown to have come into being because they would eventually have that result; indeed, I would assert that to even make this claim is non-sensical in the extreme. What characteristics of living organisms currently alive will eventually result in their assendance or demise? We have absolutely no way of knowing, nor even of imagining a way of knowing. At some point in the future, we can look back and say “son-of-a-gun, those funny looking scales are correlated with increased survival and reproduction because they allow the animals that have them to fly, and therefore escape predators and capture prey more effectively,” but until this actually happens (and absolutely nothing in nature guarantees that it will), we can’t make any statements about the “value” of any of the characteristics of organisms now living.

This, rather than the rather vapid speculations Salvador cited for the future of genetic engineering, is the real value of genetic engineering to evolutionary biology (and vise versa). We now have the ability to selectively delete individual characteristics from many different organisms. This makes possible something that natural selection does not: the precise determination of the selective “value” of particular characteristics. This has already been done, and the surprising outcome has been that even some gene sequences that were thought to have been very important in selection (due to having been “conserved” over deep evolutionary time) are apparently insiginificant or even useless. We know this because knocking them out of the genome has no discernible effect on the survival or reproduction of the “knock-out” progeny. If one is the kind of “pan-adaptationist” that Lewontin and Gould criticized, this outcome should come as a severe shock, as it should to every IDer. But, if one is a true “Darwinian” (i.e. a devotee to that tradition which questions absolutely all assumptions, including the very existence of “adaptations” and “species”), it should come as no surprise at all.



Gould, S. J. and Lewontin, R. C. (1974) "The Spandrels of San Marco and the Panglossian Paradigm: A Critique Of The Adaptationist Programme" Proceedings Of The Royal Society of London, Series B, Vol. 205, No. 1161, pp. 581-598.

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Tuesday, June 06, 2006

Random Mutation and Natural Selection Revisited

AUTHOR: Allen MacNeill

SOURCE: Original essay

COMMENTARY: That's up to you...

Promoters of "intelligent design theory" and other forms of creationism often assert that random mutation plus natural selection (RM+NS) are insufficient to explain the diversity of life on Earth. In particular, people like William Dembski assert that RM+NS cannot work fast enough (even given billions of years) to produce the complex living organisms we observe around us.

In so doing, they attack evolutionary theory using a "straw-man argument," because modern evolutionary theory is not limited to RM+NS alone to produce adaptations, nor to explain the diversity of life on Earth. In particular, while there is no empirical evidence that would lead one to believe that mutations are produced by an "intelligent designer," it is also not true that mutations alone must supply the variation necessary for evolution by natural selection.

In particular, while it is true that any given mutation is random (as far as we can tell), a series of mutations which are then preserved as the result of natural selection aren't really random at all, at least not in the way that is often depicted by critics of evolutionary theory. In classical evolutionary theory, as first mathematically formalized by R. A. Fisher, the variation that is necessary for the raw material for natural selection is the result of a large number of individual alleles, all producing variations of the same trait, such as height or skin color in humans. In this model, a normal distribution of heights or skin colors are produced by combinations of different alleles, each influencing some fraction of the overall height, producing what Fisher and others called "continuous variation." Selection then preserved one or a few of the various allele combinations by preserving the individuals that carried the controlling alleles.

In this model, evolutionary change would necessarily be slow and gradual, as changes in the overall mean value for any trait would require the gradual accumulation of mutations in each of the many alleles that controlled the trait. Since the observable mutation rate is very low (at least, the rate of mutations that significantly affect most phenotypic traits is very low), the argument was that directional change in any given trait was something like a wagon train: only as fast as its slowest constituent. That is, change in the overall distribution of the trait (such as height) depended on the rate of mutation of all of the alleles controlling it, and required that a sufficient proportion of the alleles that were preserved by selection mutate and then be selected in the same "direction" (e.g. for greater height).

However, subsequent field and laboratory investigations into the genetic and developmental control of such variable traits have shown the multiple allele/continuous variation model upon which the "modern synthesis" was based is, in fact, not the way most traits apparently evolve. For example, consider a mutation that causes an increase in size of a particular anatomical feature (e.g. a finch's beak). Most such features are regulated by a set of genes that are themselves regulated by a homeotic gene (or a few such homeotic genes; in the case of Darwin's finches, the controlling homeotic gene is called bmp4, for "bone morphology protein 4") [1]. Homeotic genes, like many but not all genes, do not produce a purely monotonic trait (i.e a trait with no variation). Instead, they produce a trait that varies somewhat between individuals, in what approximates a normal distribution. In the case of finch beaks, this means that in any population of finches, there are some individuals with small beaks, some with large beaks, and most with intermediate beaks. All of these finches could easily have the same allele for the homeotic gene controlling the trait. The variation in beak size would therefore be the result, not of the expression of different alleles, but rather of the different outcomes of the expression of the same allele of the homeotic gene, developing differently in different individuals as the result of a combination of chance and environmental conditions (this is how humans differ in heights, for example).

Now consider a situation in which an environmental change (for example, a drought), selected for individual finches with larger beaks. At the level of the controlling homeotic gene, this could mean one of two things: either the larger beaks are still within the developmental limits of the original allele, or another allele (i.e a mutant) has arisen, with an overlapping developmental pattern but a higher mean value for beak size. If the former is the case, then a return to the original environment would result in a return to the original mean beak size.

However, if the latter were the case, then there would be a built-in bias toward finches with larger beaks in the resulting population. This would also mean that the "base" allele - i.e. the new mutant allele - would start out producing a larger mean beak size along with the usual normal distribution of beak sizes. If the environmental change persisted, new alleles might arise, but they would begin with a "norm of reaction" that would produce significantly larger mean beak sizes, along with a normal distribution with significantly larger beaks at the upper tail of the distribution.

In other words, the existing alleles for such a trait would bias subsequent mutations in the "direction" of larger beaks, simply because the pool of potential new alleles would already start out biased in that direction. Therefore, the mutations and developmental changes that were available from one generation to the next would be biased in the direction of whatever phenotypic trait resulted in the highest reproductive success.

This process, called genetic accommodation [2], is part of the new science of evo-devo, which renders much of the classical "evolutionary synthesis" obsolete, and at the same time explains how such phenomena as punctuated equilibria can be integrated into a unified theory of evolutionary development. In particular, genetic accommodation and similar processes can explain how natural selection alone can produce both rapid and directional change in phenotypes over time, thereby making any resort to "intelligent design" unnecessary and irrelevant.


[1] Pennisi, E. (2004) Bonemaking protein shapes beaks of Darwin's finches. Science, Vol. 305. no. 5689, p. 1383, available at :

[2] West-Eberhard, M. J. (2003) Developmental Plasticity and Evolution. Oxford, UK, Oxford University Press. See especially pages 147 to 158.


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Monday, June 05, 2006

Detailed Syllabus for Cornell Evolution/Design Course

BioEE 467/B&Soc 447/Hist 415/S&TS 447: Seminar in History of Biology

Summer 2006 - Syllabus

PREREQUISITES: None (introductory course in evolutionary biology recommended, but not required)

CREDIT HOURS: 4 (does not count toward evolution distribution requirement in biological sciences)

CLASS TIMES: Tuesdays and Thursdays 6-9 PM

CLASS LOCATION: Whittaker Seminar Room, 409 Corson-Mudd Hall.

COURSE FORMAT: The format for each class will be a 90 minute interactive discussion/seminar, in which all participants present their interpretations and opinions of the concepts and readings under consideration. Participants will also have the opportunity to make presentations of their original work. Grades will be based on the quality of a term research paper, due at the end of the course, plus attendance and class participation.

GRADE BASED ON: Attendance and participation in seminar discussions, plus a letter grade on the final research paper (maximum length = 20 pages), for a total of 100 points (electronic/email submission encouraged, but not required):

Course Grade Components................Due On

Proposal for final research paper.......Fri07Jul06
Draft/outline of research paper.........Thu20Jul06
Final research Paper:= 75 points.......Thu03Aug06
Attendance..............= 10 points........overall
Participation............= 15 points........overall

COURSE TITLE: Evolution and Design: Is There Purpose in Nature?

COURSE DESCRIPTION: This seminar addresses, in historical perspective, controversies about the cultural implications of evolutionary biology. Discussions focus upon questions about gods, free will, foundations for ethics, meaning in life, and life after death. Readings range from Charles Darwin to the present (see reading list, below).

The current debate over "intelligent design theory" is only the latest phase in the perennial debate over the question of design in nature. Beginning with Aristotle's "final cause," this idea was the dominant explanation for biological adaptation in nature until the publication of Darwin's Origin of Species. Darwin's work united the biological sciences with the other natural sciences by providing a non-teleological explanation for the origin of adaptation. However, Darwin's theory has been repeatedly challenged by theories invoking design in nature.

The latest challenge to the neo-darwinian theory of evolution has come from the "intelligent design movement," spearheaded by the Discovery Institute in Seattle, WA. In this course, we will read extensively from authors on both sides of this debate, including Francisco Ayala, Michael Behe, Richard Dawkins, William Dembski, Phillip Johnson, Ernst Mayr, and Michael Ruse. Our intent will be to sort out the various issues at play, and to come to clarity on how those issues can be integrated into the perspective of the natural sciences as a whole.

In addition to in-class discussions, course participants will have the opportunity to participate in online debates and discussions via the instructor's weblog at Students registered for the course will also have an opportunity to present their original research paper(s) to the class and to the general public via publication on the course weblog and via THE EVOLUTION LIST.

INTENDED AUDIENCE: This course is intended primarily for students in biology, biology and society, history, philosophy, and science & technology studies. The approach will be interdisciplinary, and the format will consist of in-depth readings across the disciplines and discussion of the issues raised by such readings. Although there are no prerequisites, a knowledge of evolutionary biology (equivalent to BioEE 207 and/or BioEE 278) is highly recommended. In addition to registered students, course participants will also include invited guests from the Department of Ecology & Evolutionary Biology, the Paleontological Research Institute, and the Cornell IDEA Club. Members of the general public may only attend class discussions with prior permission of the instructor.

REQUIRED TEXTS: (all texts will be available at The Cornell Store,

Behe, Michael (2006) Darwin's black box: The biochemical challenge to evolution. New York, NY, Free Press, 352 pages.

Dawkins, Richard (1996) The blind watchmaker: Why the evidence of evolution reveals a universe without design. New York, NY, W. W. Norton (reissue edition), 400 pages.

Dembski, William (2006) The design inference : Eliminating chance through small probabilities. Cambridge, UK, Cambridge University Press, 272 pages.

Johnson, Phillip E. (2002) The wedge of truth: Splitting the foundations of naturalism. Downers Grove, IL, InterVarsity Press, 192 pages.

Ruse, Michael (2006) Darwin and design: Does evolution have a purpose? Cambridge, MA, Harvard University Press, 384 pages.

OPTIONAL TEXTS: (all texts will be available at The Cornell Store,

Darwin, Charles (1859) On the origin of species by means of natural selection, or the preservation of favoured races in the struggle for life, 1st Edition (E. Mayr, ed.), Cambridge, MA, Harvard University Press, 513 pages.
Available online at:

Darwin, Charles (E. O. Wilson, ed.) (2006) From so simple a beginning: Darwin's four great books. New York, NY, W. W. Norton, 1,706 pages.
Available online at:

Dembski, William & Ruse, Michael (2004) Debating design: From darwin to DNA. Cambridge, UK, Cambridge University Press, 422 pages.

Forrest, Barbara & Gross, Paul R. (2004) Creationism's trojan horse: The wedge of intelligent design. New York, NY, Oxford University Press USA, 416 pages.

Graffin, Gregory W. (2004) Evolution, monism, atheism, and the naturalist world-view. Ithaca, NY, Polypterus Press (P.O. Box 4416, Ithaca, NY, 14852), 252 pages.
Can be purchased online at:

Perakh, Mark (2003) Unintelligent design. Amherst, NY, Prometheus Books, 459 pages.

Ruse, Michael (2000): The evolution wars: A guide to the debates. New Brunswick, NJ: Rutgers University Press. 326 pages.

COURSE PACKET: (all items will be available online at the course website)

Ayala, F. (1970) Teleological explanations in evolutionary biology. Philosophy of Science, Vol. 37: pages 1-15.

Binswanger, H. (1992) Life-based teleology and the foundations of ethics. The Monist, pages 84-103.

Behe, M. (2002) Intelligent design as an alternative explanation for the existence of biomolecular machines. Unpublished manuscript.

Dembski, W. (2005) What every theologian should know about creation, evolution, and design. Orthodoxy Today. Available online at:

Discovery Institute (1999) The wedge. Available online at:

Kitzmiller v. Dover Area School District (2005) Complete trial documents and references. Available online at:

Mayr, E. (1974) Telological and teleonomic: A new analysis. Boston Studies in the Philosophy of Science, XIV, pages 91 to 117.

Nagel, E. (1977) Teleology revisited: Goal-directed processes in biology. Journal of Philosophy. Vol. 74, No. 5, pages 261-301.

As noted in the Course Format (above), each class will be a 90 minute discussion/seminar, in which all participants will have an opportunity to present their interpretations and opinions of the concepts and readings under consideration. Only the first two classes will depart somewhat from this format. In these, the instructor will lay out the ground rules for the course and present some basic information on evolution and some of its philosophical implications. Notice that two classes have been *rescheduled* due to holidays and time conflicts. Also note that there is an optional picnic/campfire scheduled for Friday 28 July 2006 at the instructor’s home.

DAY & DATE: Tuesday 27 June 2006
6:00-7:30 Course ground rules and an introduction to evolution, "Darwin's dangerous idea"
7:30-9:00 The Natural Selection Game and discussion of the results and implications


DAY & DATE: Friday 30 June 2006 *Rescheduled from Thursday 29 June*
Dawkins/The Blind Watchmaker
Ruse/Darwin and Design: Does Evolution Have a Purpose? chapters 1 & 2
6:00-7:30: Natural selection and scientific reasoning
7:30-9:00: Discussion of natural selection, scientific method, and philosophy of science


DAY & DATE: Thursday 6 July 2006
Dawkins/The Blind Watchmaker
Ruse/Darwin and Design: Does Evolution Have a Purpose? chapter 3 & 4

DAY & DATE: Friday 7 July 2006 *Rescheduled due to Independence Day Holiday*
Dawkins/The Blind Watchmaker
Ruse/Darwin and Design: Does Evolution Have a Purpose? chapters 5 & 6

RESEARCH PROPOSAL DUE: All students must submit a tentative proposal on Friday 7 July 2006

DAY & DATE: Tuesday 11 July 2006
Behe/"Intelligent Design as an Alternative Explanation for the Existence of Biomolecular Machines" (provided in course packet)
Behe/Darwin’s Black Box
Ruse/Darwin and Design: Does Evolution Have a Purpose? chapter 7

DAY & DATE: Thursday 13 July 2006
Behe/Darwin’s Black Box
Ruse/Darwin and Design: Does Evolution Have a Purpose? chapter 8

DAY & DATE: Tuesday 18 July 2006
Dembski/”What Every Theologian Should Know About Creation, Evolution, and Design” (provided in course packet)
Dembski/The Design Inference
Ruse/Darwin and Design: Does Evolution Have a Purpose? chapters 9 & 10

DAY & DATE: Thursday 20 July 2006
Dembski/The Design Inference
Ruse/Darwin and Design: Does Evolution Have a Purpose? chapters 11 & 12

DRAFT/OUTLINE DUE: All students must submit an outline and references on Thursday 20 July 2006

DAY & DATE: Tuesday 25 July 2006
Discovery Institute/The wedge. Available online at:
Johnson/The Wedge of Truth
Ruse/Darwin and Design: Does Evolution Have a Purpose? chapter 13

DAY & DATE: Thursday 27 July 2006
READINGS: Johnson/The Wedge of Truth
Ruse/Darwin and Design: Does Evolution Have a Purpose? chapter 14

DAY & DATE: Friday 28 July 2006
Optional barbeque/picnic and campfire at professor's home, beginning at 6 PM

DAY & DATE: Tuesday 1 August 2006
Ayala/Teleological explanations in evolutionary biology.
Binswanger/Life-based teleology and the foundations of ethics.
Mayr/Teleological and teleonomic: A new analysis.
Nagel/Teleology revisited: Goal-directed processes in biology.

DAY & DATE: Thursday 3 August 2006
Kitzmiller v. Dover Area School District (2005) Judge Jones’ decision.
Ruse/Darwin and Design: Does Evolution Have a Purpose? chapter 15

RESEARCH PAPER DUE: All assigned written work due by 6:00 PM on Thursday 3 August 2006

PROFESSOR: Allen D. MacNeill
G-24 Stimson Hall

For logistical reasons, there are two course websites.

The Course Blog is located online at This website is administered and moderated by the course instructor (Allen MacNeill,, in cooperation with the blog webmaster Hannah Maxson (, founder and president of the Cornell IDEA Club. The course blog is open to the public and contains articles, commentary, papers, etc. by students in the course and participants online. Both the moderator and the webmaster are great admirers of the traditional values of the academy: intellectual freedom, personal responsibility, and respect for others. Therefore, the course blog has several rules, which will be strictly enforced:

1. Ad hominem attacks, blasphemy, profanity, rudeness, and vulgarity will not be tolerated (although heresy will always be encouraged). However, vigorous attacks against a member's position are expected and those who cannot handle such should think twice before they post.

2. Long-running debates that are of interest only to a small number of individuals should be taken elsewhere, preferably via private email (i.e. if the moderator gets tired of reading posts concerning the population density [N] of terpsichorean demigods inhabiting ferrous microalpine environments, the posters will be encouraged to "settle it outside").

3. Pseudonyms are permitted but real names are preferred. However, if the moderator suspects that someone is posting under multiple aliases or pretending to be someone else, they will be permanently banned from the blog.

4. Mutual respect and sensitivity towards those with opposing views is essential. In particular, posts containing what the moderator feels is "creation-bashing" by evolutionists or "evolution-bashing" by creationists, will not be tolerated.

The Course Website is located online at This website is the source for course packets and lecture notes. All students registered for the course should also register at (just follow the onscreen instructions), where they can then download the course readings packet and lecture notes (some course packet items require payment before downloading; these items will also be on free reserve).

In addition to the course blog and website, the following websites are recommended as sources of information:

Access Research Network (information & research/intelligent design):
Adventures in Ethics & Science (blog/evolutionist):
Answers in Genesis (news & commentary digest/young-Earth creationist)
Anthro-L list at SUNY Buffalo (anthropology listserve/evolutionist):
Austringer, The (blog/evolutionist):
Concerned Scientist (blog/evolutionist):
Cornell Idea Club (information/intelligent design):
Creation News (news & commentary digest/young-Earth creationist):
Darwinian Conservatism (blog/politics/evolutionist):
Design Paradigm (blog/intelligent design):
Discovery Institute (news & commentary digest/intelligent design):
Dispatches from the Culture Wars (blog/evolutionist):
Evolgen (blog/evolutionist):
Evolution at PBS (TV series/evolutionist):
Evolution at (encyclopedia-wiki):
EvolutionBlog (blog/evolutionist):
Evolution List (blog/evolutionist):
Evolution News (news & commentary digest/intelligent design):
Evolution Update (links & sources/evolutionist):
Evolutionary Psychology (listserve/evolutionist):
Evolving Thoughts (blog/evolutionist):
EvoWiki (encyclopedia-wiki/evolutionist):
Hpb. Etc/ (blog/history & philosophy of biology):
ID in the United Kingdom (Blog/intelligent design):
iDesign at UCI (blog/intelligent design):
Indian Cowboy (blog/evolutionist):
Intelligent Design at Wikipedia (encyclopedia-wiki):
Intelligent Design The Future (blog/intelligent design):
International Society for Complexity, Information, & Design (info/intelligent design):
Intersection, The (blog/evolutionist):
Loom, The (blog/evolutionist):
National Center for Science Education (news & commentary digest/evolutionist):
Nature (news, commentary, original research/scientist):
New York Times/Science Online (commentary digest):
Panda's Thumb, The (blog/evolutionist):
Pew Forum on Religion and Public Life (links & sources)
Pharyngula (blog/evolutionist): (online research/intelligent design):
Science (news, commentary, original research/scientist):
Science & Technology Daily News (news & commentary digest):
Science & Theology Daily (news digest):
Scientific American (news, commentary, original research/scientist):
Society for the Study of Evolution (information & links/evolutionist):
Stranger Fruit (blog/evolutionist):
Talk.Origins (online FAQs/evolutionist):
Telic Thoughts (blog/intelligent design):
Terra Daily News (news digest):
Understanding Evolution (museum website/evolutionist):

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