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.

--Allen

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.

SECTION ONE: ON ANALOGY

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.

SECTION TWO: ON VALIDITY, CONFIDENCE, AND LOGICAL ARGUMENT

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.

SECTION THREE: ON TRANSDUCTION

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

where:

Ai is an individual object or process

and

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

where:

Ag = green apple

and

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.

SECTION FOUR: ON INDUCTION

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

where:

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

and

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.

SECTION FIVE: ON DEDUCTION

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

where:

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.

SECTION SIX: ON ABDUCTION

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

where:

Fg = a green fruit

Ag = green apple

As = sour green apple

and

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.

SECTION SEVEN: ON CONSILIENCE

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

where:

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).

CONCLUSIONS:

• 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!

--Allen

More on Parsimony in Biology

AUTHOR: Robert Skipper

SOURCE: Cladistic Parsimony and Ockham's Razor

COMMENTARY: Allen MacNeill

Robert Skipper has a report on his participation in the Southern Society for Philosophy and Psychology conference last weekend. He delivered a paper on Cladistic Parsimony and Ockham's Razor, a subject about which both he and I have blogged in the past. In a previous post, Skipper comes to the following (admittedly tentative) conclusions:

At the moment, my thinking is that cladistic parsimony is a special case of simplicity (if it is a case at all). But I won't make the case for that here....One thing I think we can say, from the examples, is that when we're in a situation in which we must choose among competing hypotheses or theories, and empirical evidence isn't definitive, use simplicity to make the choice.

Each of [the authors cited] urge us to run with the simplest model among the relevant alternatives unless we're forced to abandon that model for a more complicated one. What does the forcing is empirical evidence. Indeed, none of the biologists I quoted above said anything about the fact that simplicity is truth-indicative. Burnet in fact said that because the clonal theory is simplest, it's probably false! So, simplicity doesn't indicate the truth of some hypothesis or model or theory. Rather, it's a strategy that directs us toward the truth....At least we can say we've eliminated some fruitless paths of inquiry.

COMMENTARY:

I think it would be helpful to consider two possibilities vis-a-vis the application of parsimony in science:

1) Parsimony is merely "useful" in the sense that it reduces the complexity of hypotheses to a level at which they are empirically testable. When I teach my students about how science is usually done, I give them the "hypothetico-deductive" model first, and then point out that this model doesn't give you criteria for formulating testable hypotheses, it only gives you a method for testing them once they have been formulated. To formulate testable hypotheses requires an additional step: one must "mentally" test one's hypothesis to determine if:
• it's empiirically testable, and
• the emipirical test that one is considering can distinguish between it and alternative hypotheses
If the answers to these two questions are both "yes," then one is ready to actually run the experiment/make the observations to test the predictions that flow from the hypothesis.

In this view, parsimony is simply "useful" in that it is more likely (on average) to yield testable hypotheses whose empirical results are more likely to unambiguously validate or falsify one's predictions.

2) Parsimony might actually be an intrinsic feature of "natural causation" itself. In evolutionary psychology (my field, BTW) there is a concept known as "computational overload (CO)." Basically, CO is used as an argument against the "blank slate" hypothesis for human cognition and motivation. That is, if the mind is a "blank slate" (i.e. relies entirely on "trail and error/reinforcement" algorithms), CO rapidly overwhelms even the largest and fastest computer imagineable. Therefore, EPs like me assume that the brain is modularized, and that each module has a fairly stringent "perceptual filter" that limits inputs as a way of minimizing CO (such filters and modules having evolved by natural selection).*

The same concept could be applied to nature, and especially biology. Biological systems are fiendishly complex, much more so than physical or chemical systems. This complexity, if not minimized in some way, would result in biological systems "seizing up" as the result of CO (where "computation" is interpreted broadly as the binary and higher level interactions between multiple influences, some competing and some complementary).

Natural selection, in other words, has resulted in the evolution of biological systems in which "parsimony" has been encoded into the interactive structure of living organisms and systems of living organisms themselves, as a way of minimizing CO and maximizing effective interaction with one's environment.

Indeed, I would be tempted to argue that (1) may even be a consequence of (2), as our minds themselves are already adapted to minimizing CO, and therefore are predisposed to parsimonious solutions to problems in general, and therefore also scientific problems. In our interactions with nature as in our science, therefore, "good enough for now" is "good enough for all".
--Allen

*I also suspect that this phenomenon is the basis for the "Fundamental Attribution Error (FAE)" in humans, as a predisposition for making FAEs would be selected for as long as the results of doing so were as often adaptive as deleterious (i.e. a tendency toward "false positives" in making FAEs would simply be a kind of "worse case analysis", which is almost always adaptive...especially in a dangerous world such as ours, in which even paranoids have real enemies ;-)

Incommensurate Worldviews

AUTHOR: Allen MacNeill

SOURCE: Original essay

COMMENTARY: That's up to you...

I am beginning to understand more about the differences between the physical sciences (such as astronomy, chemistry, and physics) and the biological sciences, and why the worldview of a physical scientist with a strongly mathematical predilection is apparently so different from mine and that of most other biologists (at least, of those biologists of whom I have personal and/or reputable knowledge). Furthermore, it seems to me that these differences are central to the apparent inability of non-biologists to fully comprehend the "darwinian" worldview upon which much of biology (and all of evolutionary theory) has been constructed (and vice versa, of course).

To me, these appear to be the basic differences that inform our worldviews:

1) CONTINGENCY: The biological sciences (i.e. anatomy & physiology, parts of biochemistry, botany, development & embryology, ecology, ethology, evolution, genetics, marine biology, neurobiology, and the allied subdisciplines), like the "earth sciences" (i.e. atmospheric sciences, geology, etc.) are both contingent and historical. That is, they cannot be derived from "first principles" in the way that algebra, calculus, geometry (both euclidean and non-euclidean), probability, symbolic logic, topology, trigonometry, and other "non-empirical" sciences can be. As both Ernst Mayr and Karl Popper have pointed out, historical contingency is inextricably intertwined with biological causation, in a way that it is not in mathematics and the physical sciences. This would appear to be true, by the way, for both "darwinist" and ID models of biological evolution and the fields derived from them. Indeed, even the Judeo-Christian-Muslim worldview is contingent and historical, in ways antithetical to both mathematics and pre-"big bang" cosmological physics.

2) UNIVERSALITY: The biological sciences are also not "universal" in the way that chemistry and physics are. We assume that the processes described by physical "laws" are universal and ahistorical. that is, we assume that they are the same regardless of where, when, and by whom they are investigated. Furthermore, it is tacitly assumed by physical scientists that the "laws" they discover apply everywhere and everywhen, without empirical verification that this is, in fact, the case. It seems to me that this assumption is reinforced by the mathematical precision with which physical processes can be analyzed and described.

By contrast, the entities and processes studied by biologists are necessarily "messy" and often "non-quantifiable," in the sense that they cannot be entirely reduced to purely mathematical abstractions. The great beauty and elegance of Newton's physics and Pauling's chemistry are that the objects and processes they describe can be so reduced, and when they are, they reveal an underlying mathematical regularity, a regularity so precise and so elegant that one is tempted to believe that the mathematical formalism is what is "real" and the physical entities and processes that they describe are, at best, somewhat imperfect expressions of the underlying perfect regularities.

To me, however, what has always been appealing about biology is its very "messiness." As the so-called Law of Experimental Psychology states "Under carefully controlled conditions, the organism does whatever it damn well pleases." Biological entities and processes are not quantifiable in the same way that physical ones are. This is probably due to the immensely greater complexity of biological entities and processes, in which causal mechanisms are tangled and often auto-catalytic.

3) STOCHASTICITY: The biological sciences are irreducibly statistical/stochastic, in ways that neither the physical nor mathematical sciences generally are (although they are becoming moreso as they intrude deeper into biology). R. A. Fisher was not only the premier mathematical modeler of evolution, he was also the founder of modern statistical biometry. This is no accident: both field and laboratory biology (but not 19th century natural history) depend almost completely on statistical analysis. Again, this is probably because the underlying causes for biological processes are so multifarious and intertwined.

Physicists, chemists, and astronomers can accept hypotheses at confidence levels that biologists can never aspire to. Indeed, until recently the whole idea of "confidence levels" was generally outside the vocabulary of the physical sciences. When you repeatedly drop a rock and measure its acceleration, the measurements you get are so precise and fit so well with Newton's descriptive formalism that the idea that one would necessarily need to statistically verify that they do not depart significantly from predictions derived from that formalism seems superfluous. Slight deviations from the predicted behavior of non-living falling objects are considered to be just that: deviations (and most likely the result of observer error, rather than actual deviant causation). Rarely does any physical scientist look at such deviations as indicative of some new, perhaps deeper formalism (but consider, of course, Einstein's explanation of the precession of the orbit of Mercury, which did not fit Newton's predictions).

4) FORMALIZATION: There are many processes in biology, and especially in organismal (i.e. "skin out" biology) that are so resistant to quantification or mathematical formalization that there is the nagging suspicion that they cannot in principle be so quantified or formalized. It is, of course, logically impossible to "prove" a negative assertion like this - after all, our inability to produce a Seldonian "psychohistory" that perfectly formalizes and therefore predicts animal (and human) behavior could simply be the result of a deficiency in our mathematics or our ability to measure and separately analyze all causative factors.

However, my own experience as a field and laboratory biologist (I used to study field voles - Microtus pennsylvanicus - and now I study people) has instilled in me what could be called "Haldane's Suspicion:" that biology "is not only queerer than we imagine, but queerer than we can imagine." That is, given the complexity and interlocking nature of biological causation, it may be literally impossible to convert biology into a mathematically formal science like astronomy, chemistry, or physics.

But that's one of the main reasons I love biology so much. Mathematical formalisms, to me, may be elegant, but they are also sterile. The more perfect the formalism, the more boring and unproductive it seems to me. The physicists' quest for a single unifying "law of everything" is apparently very exciting to people who are enamored of mathematical formalism for its own sake. But to me, it is the very multifariousness – one could even say "cussedness" – of biological organisms and processes that makes them interesting to me. That biology may not have a single, mathematical "grand unifying theory" (yes, evolution isn't it ;-)) means to me that there will always be a place for people like me, who marvel at the individuality, peculiarity, and outright weirdness of life and living things.

5) PLATONIC VS. DARWINIAN WORLDVIEWS: It seems to me that many ID theorists come at science from what could be called a "platonic" approach. That is, a philosophical approach that assumes a priori that platonic "ideal forms" exist and are the basis for all natural forms and processes. To a person with this worldview, mathematics are the most "perfect" of the sciences, as they literally deal only with platonic ideal forms. Astronomy, chemistry, and physics are only slightly less "prefect," as the objects and processes they describe can be reduced to purely mathematical formalisms (without stochastic elements, at least at the macroscopic level), and when they are so reduced, the predictive precision of such formalisms increases, rather than decreases.

By contrast, I come at science from what could be called a "darwinian" approach. Darwin's most revolutionary (and subversive) idea was not natural selection. Indeed, the idea had already been suggested by Edward Blythe. Rather, Darwin's most "dangerous" idea was that the variations between individual organisms (and, by extension, between different biological events) were irreducibly "real." As Ernst Mayr has pointed out, this kind of "population thinking" fundamentally violates platonic idealism, and therefore represents a revolutionary break with mainstream western philosophical traditions.

I am and have always been partial to the "individualist" philosophical stance represented by darwinian variation. It informs everything I think about reality, from the idea that every individual living organism is irreducibly unique to the idea that my life (and, by extension, everybody else's) is irreducibly unique (and non-replicible). Such a philosophical position might seem to lead to a kind of radical "loneliness," and indeed there have been times when that was the case for me. But since all of us are equal in our "aloneness," it paradoxically becomes one of the things we universally share.

And so, I don't think a "darwinian worldview" applies to the physical sciences (and certainly does not apply to non-empirical sciences, such as mathematics), for the reasons I have detailed above. In particular, it seems clear to me that although it may be possible to mathematically model microevolutionary processes (as R. A. Fisher and J. B. S. Haldane first did back in the early 20th century), it is almost certainly impossible to mathematically model macroevolutionary processes. The reason for this impossibility is that macroevolutionary processes are necessarily contingent on non-repeatable (i.e. "historical") events, such as asteroid collisions, volcanic eruptions, sea level alterations, and other large-scale ecological changes, plus the occurrence (or non-occurrence) of particular (and especially major) genetic changes in evolving phylogenies. While it may be possible to model what happens after such an event (e.g. adaptive radiation), the interactions between events such as these are fundamentally unpredictable, and therefore cannot be incorporated in prospective mathematical models of macroevolutionary changes.

It's like that famous cartoon by Sidney Harris: "Then a miracle occurs..." The kinds of events that are often correlated with major macroevolutionary changes (such as mass extinctions and subsequent adaptive radiations) are like miracles, in that they are unpredictable and unrepeatable, and therefore can't be integrated into mathematical models that require monotonically changing dynamical systems (like newtonian mechanics, for example).

So, to sum up, I believe that the "darwinian worldview" applies only to those natural sciences that are both contingent and intrinsically historical, such as biology, geology, and parts of astrophysics/cosmology. Does this make such sciences less "valid" than the non-historical (i.e. physical) sciences? Not at all; given that physical laws now appear to critically depend on historical/unrepeatable events such as the "big bang," it may turn out to be the other way around. In the long run, even the physical sciences may have to be reinterpreted as depending on contingent/historical events, leaving the non-empirical sciences (mathematics and metaphysics) as the only "universal" (i.e. non-contingent/ahistorical) sciences.

To summarize it in a bullet point:

• Platonic/physical scientists describe reality with equations, whereas darwinian/biological scientists describe reality with narratives.

--Allen

P.S. Alert readers may recognize some of the hallmarks of the so-called Apollonian vs. Dionysian dichotomy in the preceding analysis. That such characteristics are recognizable in my analysis is not necessarily an accident.

P.P.S. It is also very important to keep in mind, when considering any analysis of this sort, that sweeping generalizations are always wrong ;-)