Discussion: Analogy, Identity, and Validity
Another topic that has been brought up many times is the question of analogy. What is its role in scientific reasoning? When is an appeal to it justified, when not? In the thread on "Vacuity", Allen writes:
I would be happy to present a more formal analysis of the relationship between analogy, identity, and validity if any of you are interested. I’ve been working on it for several years, and would be curious to see what your reactions might be.
Please!
On a neutral but related topic to help understand how analogy can be overdone by scientists as well as the public, I have a post up on Migrations describing how many cancer biologists falsely describe an aspect of cancer progression as the epithelial-to-mesenchymal transition (EMT).
In short, the cellular changes in cancer progression (aka malignant transformation) resemble a change in morphology to mesenchymal- or ameoboid-like cells, much like a stage in embryonic development. Closer examination reveals that the cells are not switching to a separate differentiated phenotype, their changes are more akin to de-differentiation. This has subtle but significant therapeutic implications, and yet many cancer biologists continue to use the term EMT - some even continue to insist that it is an actual phenomenon.
Such claims aren’t entirely baseless, but they’re aren’t completely accurate either. I find this to be an example of false analogy.
Comment by Dan — June 16, 2006 @ 6:37 pm
Sorry to take so long - my dad has been in the hospital. I will be posting later today (Friday) or tomorrow at the latest.
–Allen
Comment by Allen MacNeill — June 16, 2006 @ 6:39 pm
You and your father are in my prayers.
Comment by Bilbo — June 16, 2006 @ 8:56 pm
Allen– please don’t worry about the post, it can definitely wait.
Comment by Freawaru — June 16, 2006 @ 9:40 pm
Here goes (careful; it’s LONNNNG):
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 improvable premises - 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, several corrolaries may be derived:
CORROLARY 1.1: All analogies that are not identities are necessarily imperfect.
COMMENTARY 1.1: Since only tautologies are prima facie true, this implies that all analogical statements (except tautologies) are false to some degree.
CORROLARY 1.2: 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 1.2: 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,
All forms of logical argument 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 true or false, 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;” 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 an 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. 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 form of logical argument is argument by analogy. 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
A => S
where A is one object or process and S is another (nontautological) object or process. Since there is only one example in the premise in such an argument, to state that there is any degree of confidence in the conclusion is problematic (since it is non-sensical to state that a single example constitutes 95% of anything).
In science, this kind of reasoning is usually referred to as “anecdotal,” 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 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,
A => S
where:
A = green apple
and
S = 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 (see http://www.answers.com/topic/logic-induction), 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. 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. 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; Sir Karl Raimund Popper). For a classic account of inductive arguments see J. S. Mill, System of Logic (1843).
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 => Sn
where:
A1 + A2 + A3 +…An = individual cases of green apples
and
Sn = all 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.
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 William of Ockham, of “Ockham’s razor” fame (see http://en.wikipedia.org/wiki/William_of_Ockham_%28philosopher%29 and http://en.wikipedia.org/wiki/Nominalism ). 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 (see http://www.answers.com/topic/deductive-reasoning-1 ), 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 is contrasted with induction, in which the premises suggest, but do not necessitate a conclusion. Aristotle first laid out a systematic analysis of deductive argumentation in the Organon (see http://en.wikipedia.org/wiki/Organon ). As noted above, Francis Bacon (see http://en.wikipedia.org/wiki/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 a individual cases that applies to all of the 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:
Sn => Ai
where:
Sn = 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 it premised .
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
The newest form of logical argument is argument by abduction. According to the Columbia Encyclopedia (see http://www.answers.com/topic/abductive-reasoning)
abduction (from the Latin ab, meaning “away” and duceré, meaning “to lead”) is the process of reasoning from individual cases to the best explanation(s) for those cases. In other words, it is a reasoning process that starts from a set of facts and derives their most likely explanations. The term abduction is also sometimes used to mean the generation of hypotheses to explain observations or conclusions, but the former definition is more common both in philosophy and computing.
The philosopher Charles Peirce introduced abduction into modern logic. In his works before 1900, he mostly uses the term 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.”
He later used the term 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 the old meaning is used. Contrary to this use, Peirce stated that the actual process of generating a new rule is not hampered by traditional logic rules. Rather, he pointed out that humans have an innate ability to correctly do inference; possessing this ability is explained by the evolutionary advantage it gives. Pierce’s second use of ‘abduction’ is most similar to induction.
We may therefore define abduction as follows:
DEFINITION 6.0: Abduction = Argument that validates a set of individual cases via a new explanation that best explains the similarities between all of the individual cases.
EXAMPLE 6.0: You have a green fruit, which when you taste it, is sour. You already have a generalization about green apples that states that green apples are sour. You observe that since the fruit you have in hand is green and sour, then all green fruits are probably sour.
In symbolic terms:
(Ag = Sa) + (Fi = Sf) => Fn = Sn
where:
Ag = green apples
Sa = sour apples
Fi = a green fruit
Sf = sour fruit
Fn = all green fruits
and
Sn = all sour fruit
In the foregoing example, it is clear why Pierce 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 (“all green fruits are sour”) is a new conclusion, derived from (but not strictly reducible to) its premises.
IMPLICATION 5.0: Conclusions reached on the basis of abduction are, like conclusions reached on the basis of induction deduction, 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 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 .
CONCLUSIONS:
• the validity of all forms of argument are limited by the same thing: the logical limitations of transduction.
• Induction validates generalizations only via repetition of similar cases, the similarity of which is validated by transduction.
• Deduction validates individual cases, but is limited by the induction required to formulate generalizations and by the transduction necessary to formulate individual cases.
• Abduction validates new generalizations via analogy between individual cases; however, it too is limited by the formal limitations of transduction, in this case in the formulation of new generalizations.
Comments, criticisms, and suggestions are warmly welcomed!
Comment by Allen MacNeill — June 17, 2006 @ 9:38 pm
P.S. Sorry I couldn’t figure out how to use subscripts in the long post on analogy and identity.
Comment by Allen MacNeill — June 17, 2006 @ 9:39 pm
A cleaner version of this essay, with typos corrected, more hot links added, and a nifty picture of Piaget, Bacon, Aristotle, and Pierce is now up at http://evolutionlist.blogspot.com/2006/06/identity-analogy-and-logical-argument.html.
Comment by Allen MacNeill — June 18, 2006 @ 2:04 am
I’m not sure I followed you on abduction. At first, I thought you were saying it was an argument to the best explanation (e.g., the best explanation for the observed movements of the planets is the heliocentric theory, with elliptical orbits of the planets). But then you seemed to suggest that it was a way to make a more generalized argument (e.g., from green apples being sour, to green fruit being sour). Those seem to be different types of arguments.
Comment by Bilbo — June 19, 2006 @ 1:11 am
Bilbo wrote:
“I’m not sure I followed you on abduction.”
Indeed, and there lies the “incompleteness” that I alluded to in the beginning of the essay. Peirce (turns out I spelled his name wrong) formulated two different (but related) versions of what he called “abduction,” which correspond to the two different versions you alluded to in your comment. His earlier version was just as you describe it: “argument to the best explanation”, in which a set of observations that are initially apparently unrelated are shown to be related by virtue of an already existing generalization that applies to them all.
However, in his later writings Peirce introduced the concept of “new generalizations”, which do not exist until a set of existing observations are “unified” under a more general “covering law” (to use Hempel’s terminology) that applies to all of them.
It is my impression (which I admit is not formally worked out…yet) that the difference between these two versions of “abduction” is that in the first version the “covering law” is already known, and simply “abducts” the disparate observations by subsuming them under a more general statement that explains them all, whereas in his second version the “covering law” is essentially “induced” de novo.
This is why Peirce argued that the second (i.e. later) version of “abduction” is the only form of logic that can actually produce “new” knowledge. However, I would argue that Peirce’s second version is reducible to induction, as implied by the treatment in the Wikipedia article linked in my essay.
I would go further than this: it seems to me (and again I have no formal way of “proving” this) that induction is the only form of logic that can produce genuinely new generalizations, and that Peirce’s second version of “abduction” is simply a kind of “meta-induction” in which the new generalization that subsumes (i.e. “abducts”) the disparate observations is “induced” by the “realization” (and I mean that literally) that a more general covering law unites all of them.
Comment by Allen MacNeill — June 19, 2006 @ 3:30 pm
One of the most famous analogies in the history of science is Darwin’s “natural selection.”
Darwin borrowed the term from the breeders—a trait is said to be naturally selected if the breeder is incapable of exercising any effective control over (“selection”) its expression.
So natural selection is the effective limiting case of artificial selection.
Darwin’s analogical argument is interesting for several reasons. Most interesting to me are his “limiting case” arguments.
The first question to ask is what exactly is being compared? Needless to say, it is the comparison artificial selection natural selection. However if selection = selection, logically and empirically, that is not the analogical part of the argument.
All of Darwin’s “limit” arguments wrt selection have dissolved due to the advance of science and technology. E.g., one of Darwin’s (“limiting case”) arguments was that we select solely for our own benefit or for whatever strikes our “fancy” (Darwin), whereas natural selection selects only for the benefit of the individual (-> species). That is no longer true.
W/o elaborating further, I believe that all of Darwin’s limit arguments are now invalid. There is nothing that natural selection can do that we can’t do. Indeed, Darwin (in 1883. The Variation of Animals and Plants Under Domestication, 2nd Ed. Appleton. NY. “XXVIII Concluding Remarks.”), perhaps unwittingly, dissolves the differences between artificial and natural selection himself!
So it is only the parentheticals that are compared, analogized. Darwin’s analogical argument, the theory of natural selection, is a direct comparison of artificial and natural. The like terms, selection, on both sides of the inequality drop out and all that remains to compare is artificial and natural.
Professor MacNeill makes a good point (if I understood correctly and in my own words) analogical arguments are not logical arguments. But that’s OK because scientific arguments are not logical arguments either, but empirical arguments. Analogical arguments are empirical arguments insofar as they reduce to quantitiative limiting case arguments. This is true of Darwin’s analogy, because we can make a direct experiemtnal, quantitative test of the analogy. We can compare artificial and natural selection experimentally.
Indeed, if there is not a direct, quantitative, experiemtnally determinable and positive comparison then a lot of biologists have been wasting their time.
There remains only the analogy artificial natural. We could reject out of hand any positive comparison. Or refer it to the philosophers. But that would hardly be an acceptable solution to the problem the analogy poses for evolutionary-theoretic biology.
I have noticed before, in these arguments with IDers and other creationists, that we tend to be a bit selective (so to speak) in our criticisms of analogical arguments. Analogical arguments are common in science, and have more than demonstrable heuristic value, as in the case of natural selection, they can made testable hypotheses.
As long as we accept the force of Darwin’s famous analogy we have no in principle objection to the analogies of IDers.
We should rather request the IDers do, what Darwin never really did, and that is make the analogies concrete, qunatitiative, and empirically testabley hypotheses.
Apart from the broader issue of comparing natural and artificial there are some intersting related matters. E.g., another one of the most famous analogies in the history of science, sparking a “Biological Revolution,” is the biologists comparison of the DNA molecule with a “code.” In this case the analogy, originally qualitative, or maybe even only illustrative in some sense, does admit quantitative comparison, but one has to wonder just how meanigful empirically such quantitative comparisons are. This is really an analogy that depends upon a formal definition. DNA isn’t just a code by analogy, but on the basis of a formal definition of what a code is. DNA is identically, definitively, a code so its not really an analogy at all!
Which illustrates what I intended to convey: Someimes analogies are not what they seem. They are not “analogies” at all, but scientifically testable hypothesis.
Dembski’s argument is intersting to me because what he says, as I understand, is that comparison/distinction, artificial/natural, is testable.
Just some food for thought. (Hopefully not too confused.)
(BTW, Professor MacNeill, it is conventional to denote subscripts in HTML by the underscore, such A_i.)
Comment by Rock — June 19, 2006 @ 3:35 pm
Sorry for the typos, etc. For some reaon my computer can’t find the spellchecker. Is MS a POS, or what?!
Comment by Rock — June 19, 2006 @ 3:39 pm
Rock:
Thanks for the comments, and for the tip about subscripts.
And yes, I agree with your evaluation of the status of analogies in science, and especially your analysis of Darwin’s analogy between artificial and natural selection in Ch. 1 & 2 of the Origin. I have had my students in Evolution analyze his argument from analogy, and some have come to the same conclusion that you do.
In the context of the essay, therefore, I would say that Darwin’s argument is perhaps abductive (in the second sense used by Peirce), in that he “abducts” both artificial and natural selection under the more general covering law of “selection” (which, BTW, he wanted to call “preservation” but did not because of its connotations of intentional action in nature).
However, I really have to question your analogy:
MS = POS
In my opinion,
MS = AOE
where
MS = MicroSoft
and
AOE = axis of evil
;-)
Comment by Allen MacNeill — June 19, 2006 @ 4:08 pm
LOL And a peculiarly insidious form evil at that. A famous rabbi wrote that the very personfication of evil manifests itself as an “angel of light,” a beauty to behold! The face of evil (MS), Bill Gates, although certainly a face only a mother could love, hardly bears the stamp of malevolence. It is the very face of the “banality of evil.”
Of course, I don’t believe that. Prof. MacNeill’s right, its just an analogy. I don’t believe Bill Gates is any more “evil” than the average power-mad plutocrat with his thumb over virtually every aspect of my personal life.
Thanks for the response, Professor. And I appreciate the effort you put into your logical analysis. I’m not aware that anyone has ever really attempted a thoroughgoing formal logical analysis of analogical arguments. And if not it truly is a significant neglect. Usually logical analyses of “illogical” arguments are in the endeavor to correct common logical errors in argumentation. But an analogical argument really is something else altogether.
(Man! Absence makes the heart grow fonder and I never really appreciated how much I releid [LOL] upon Bill Gates clunky spellchecker and the MS version of the English language.)
Comment by Rock — June 19, 2006 @ 5:41 pm
Perhaps there’s a way to unify the two meanings of abduction:
We’ve induced that all green apples are sour. Now we want an explanation for why that is. So we posit the generalization:
“All green fruit is sour.”
This is not an induction. This is a hypothesis, that we can then go out and test. And we find out that honeydew mellon falsifies our hypothesis. So we abandon our hypothetical generalization, and look for some other generalization that will “cover” the fact that all green apples are sour.
I think it probably gets more complicated when we come up with competing hypotheses that explain or “cover” our original inductive generalizations.
By the way. I’m guessing that at some point (now or in your class) you’re going to use this in analyzing and evaluating ID. Am I wrong?
Comment by Bilbo — June 19, 2006 @ 9:14 pm
Bilbo wrote:
“I’m guessing that at some point (now or in your class) you’re going to use this in analyzing and evaluating ID.”
I am indeed, although I’m not sure where or when. This is an ongoing project, and as I indicated in the essay, I haven’t reached clarity on all of it myself.
Comment by Allen MacNeill — June 20, 2006 @ 2:11 am
Once again, I envy your students.
Comment by Bilbo — June 20, 2006 @ 8:15 pm
Allen,
In every system of thought a degree of faith is required. This was famously formalized by mathematician Kurt Godel when he actually tried to establish Bertrand Russel and Alfred North Whitehead’s aim in Prinicipia Mathematica that significant ultimate truths could be established without any sort of self-reference or faith.
When mapping mathematical analogies to physical systems, or describing one system as an anology to another, my math professor said their is no way to prove the analogy is accurate or demonstrate the absolute efficacy of the analogy. One can falsify the fidelity of an analogy, but one can not formally prove it. This is actually consistent with the Popperian conception of science.
Thus anaologies are accepted by and large by faith, but they are open to falsification. There really is no “confidence” level in the conclusion. The sun has risen every day of my life. I expect the analogy of the past to be reasonably applicable to tomorrow, but there is no guarantee the sun will rise tomorrow and that a thousand years of analogical expectation will hold.
Salvador
Comment by Salvador T. Cordova — June 22, 2006 @ 6:45 pm
Salvador writes: “I expect the analogy of the past to be reasonably applicable to tomorrow”
Ah, but the interesting question is: What makes it reasonable?
Comment by Bilbo — June 22, 2006 @ 8:02 pm
A bit less well known than Darwin’s analogy “natural selection,” is the analogy that is assumed in much (almost all) traditional popgen models:
“Consider the mechanical adaptation of an instrument such as a microscope, when adjusted for distinct vision. If we imagine a derangement of the system by moving a little each of the lenses, either longitudinally or transversely, or by twisting through an angle, by altering the refractive index and transparency of the different components, or the curvature, or the polish of the interfaces, it is sufficiently obvious that any large derangement will have a very small probability of improving the adjustment, while in the case of alterations much less than the smallest of those intentionally effected by the maker or operator, the chance of improvement should be almost exactly one half (Fisher, R.A. 1930. The Genetical Theory of Natural Selection. Oxford Univ. Press. Oxford. p. 40.).”
There are several problems with Fisher’s analogy. Not the least of which is that it lacks the virtue of transparency, of a comparison that is readily apprehensible. It has one thing and one thing only going for it, in that unlike Darwin’s analogy, Fisher formalizes his design analogy with his famous “geometric model” of evolutionary adaptation. And unlike Darwin’s powerfully intuitive heuristic analogy, Fisher’s analogy, despite its formalization and having become a “central dogma” in population genetics, may, in the end, prove to be profoundly misleading.
It might be interesting to observe where Fisher may have gone wrong here, to explore Fisher’s equally influential analogy, which has heretofore received little critical attention, in comparison with Darwin’s analogy, which has been the source of much critical analysis, most of it bad. E.g., notice the many causal factors Fisher includes as possibly contributing to the magnitude of the effect. Yet the formalization does not include multiple factors, but assumes the effective independence (additivity) of factors, each contributing independently and each of small magnitude of effect. Little of what was formalized seems to be suggested directly by the analogy!
It might be interesting to compare the fate of these two analogies.
See:
Towards a theory of evolutionary adaptation
Daniel L. Hartl & Clifford H. Taubes
Genetica 102/103: 525–533, 1998.
Copyright 1998 Kluwer Academic Publishers.
http://www.oeb.harvard.edu/hartl/lab/publications/pdfs/Hartl-98-Genetica.pdf
And for a nice historical review see also (and the citations therein):
THE GENETIC THEORY OF
ADAPTATION: A BRIEF HISTORY
H. Allen Orr
VOLUME 6 | FEBRUARY 2005 | 119-127
http://www.maths.lth.se/matematiklth/personal/mario/orr.pdf
And a simulation by the same author:
The evolutionary genetics of adaptation: a simulation study
Genet. Res., Camb. (1999), 74, pp. 207-214.
(This is available online.)
“Summary
It is now clear that the genetic basis of adaptation does not resemble that assumed by the
infinitesimal model. Instead, adaptation often involves a modest number of factors of large effect
and a greater number of factors of smaller effect. After reviewing relevant experimental studies, I
consider recent theoretical attempts to predict the genetic architecture of adaptation from ®rst
principles. In particular, I review the history of work on Fisher’s geometric model of adaptation,
including recent studies which suggest that adaptation should be characterized by exponential
distributions of gene effects. I also present the results of new simulation studies that test the
robustness of this finding. I explore the effects of changes in the distribution of mutational effects
(absolute versus relative) as well as in the nature of the character studied (total phenotypic effect
versus single characters). The results show that adaptation towards a fixed optimum is generally
characterized by an exponential effects trend.”
Comment by Rock — June 25, 2006 @ 8:55 pm
A bit less well known than Darwin’s analogy “natural selection,” is the analogy that is assumed in much (almost all) traditional popgen models:
“Consider the mechanical adaptation of an instrument such as a microscope, when adjusted for distinct vision. If we imagine a derangement of the system by moving a little each of the lenses, either longitudinally or transversely, or by twisting through an angle, by altering the refractive index and transparency of the different components, or the curvature, or the polish of the interfaces, it is sufficiently obvious that any large derangement will have a very small probability of improving the adjustment, while in the case of alterations much less than the smallest of those intentionally effected by the maker or operator, the chance of improvement should be almost exactly one half (Fisher, R.A. 1930. The Genetical Theory of Natural Selection. Oxford Univ. Press. Oxford. p. 40.).”
There are several problems with Fisher’s analogy. Not the least of which is that it lacks the virtue of transparency, of a comparison that is readily apprehensible. It has one thing and one thing only going for it, in that unlike Darwin’s analogy, Fisher formalizes his design analogy with his famous “geometric model” of evolutionary adaptation. And unlike Darwin’s powerfully intuitive heuristic analogy, Fisher’s analogy, despite its formalization and having become a “central dogma” in population genetics, may, in the end, prove to be profoundly misleading.
It might be interesting to observe where Fisher may have gone wrong here, to explore Fisher’s equally influential analogy, which has heretofore received little critical attention, in comparison with Darwin’s analogy, which has been the source of much critical analysis, most of it bad. E.g., notice the many causal factors Fisher includes as possibly contributing to the magnitude of the effect. Yet the formalization does not include multiple factors, but assumes the effective independence (additivity) of factors, each contributing independently and each of small magnitude of effect. None of what was formalized seems to be suggested directly by the analogy!
It might be interesting to compare the fates of these two analogies so central to evolutionary theory.
See:
Towards a theory of evolutionary adaptation
Daniel L. Hartl & Clifford H. Taubes
Genetica 102/103: 525–533, 1998.
Copyright 1998 Kluwer Academic Publishers.
http://www.oeb.harvard.edu/hartl/lab/publications/pdfs/Hartl-98-Genetica.pdf
And for a nice historical review see also (and the citations therein):
THE GENETIC THEORY OF
ADAPTATION: A BRIEF HISTORY
H. Allen Orr
VOLUME 6 | FEBRUARY 2005 | 119-127
http://www.maths.lth.se/matematiklth/personal/mario/orr.pdf
And a simulation by the same author:
The evolutionary genetics of adaptation: a simulation study
Genet. Res., Camb. (1999), 74, pp. 207-214.
(This is available online.)
“Summary
It is now clear that the genetic basis of adaptation does not resemble that assumed by the
infinitesimal model. Instead, adaptation often involves a modest number of factors of large effect
and a greater number of factors of smaller effect. After reviewing relevant experimental studies, I
consider recent theoretical attempts to predict the genetic architecture of adaptation from ®rst
principles. In particular, I review the history of work on Fisher’s geometric model of adaptation,
including recent studies which suggest that adaptation should be characterized by exponential
distributions of gene effects. I also present the results of new simulation studies that test the
robustness of this finding. I explore the effects of changes in the distribution of mutational effects
(absolute versus relative) as well as in the nature of the character studied (total phenotypic effect
versus single characters). The results show that adaptation towards a fixed optimum is generally
characterized by an exponential effects trend.”
Comment by Rock — June 25, 2006 @ 8:59 pm