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Aspects of Theory Construction in Biology
ASPECTS OF THEORY CONSTRUCTION IN BIOLOGY
LINDLEY DARDEN Committee on the History and Philosophy of Science University of Maryland, College Park, Maryland, U.S.A.
Philosophers, impressed by the certainty provided by deductive logic, have, in the past, demanded that science provide the same kind of certainty. But arguments to the contrary are persuasive. Duhem claimed : “Unlike the reduction to absurdity employed by geometers, experimental contradiction does not have the power to transform a physical hypothesis into a indisputable truth.” (DUHEM,1914, p. 190). Recognizing these limitations, Stephen Toulmin said: rationality need not be equated with logicality: “A man [or woman] demonstrates his rationality, not by a commitment to fixed ideas, stereotyped procedures, or immutable concepts, but by the manner in which and the occasions on which, he changes those ideas, procedures and concepts.” (TOULMIN,1972, p. x). Other recent philosophers have been concerned to understand the rational factors involved in scientific change, most notably Imre LAKATOS (1970) and Dudley SHAPERE (1974). This paper is within this recent tradition in philosophy of science of understanding the rational means by which science changes. More specifically it is concerned with the question-how are theories constructed and how are they modified in the light of new evidence? Duhem might have been right when he claimed: “NO hypothesis which is a component of a scientific theory T can ever be sufficiently isolated from some set of auxiliary assumptions or other so as to be separately falsifiable by observations.” (QUINN,1974, p. 36). But the truth of such a claim, based on the rigorous demands of certainty, does not negate the possibility of finding rational means, better or worse means, of modifying a theory in the light of conflicting evidence. This paper will argue that procedures 463
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exist for determining which postulates of a theory as opposed to others, are more likely to be in need of modification when evidence necessitates a change. In at least some cases, theory construction is a modular process with specific postulates constructed to account for specific data. Consequently, changes in that data direct the localization of the needed change to the corresponding postulates. Furthermore, as philosophers have often noted (e.g. DUHEM,1914, p. 1851, if a set of postulates is used to make a prediction about new phenomena, not previously investigated, and that prediction is not confirmed, then that set of postulates is in need of modification. But if that set is small and is independent of other postulates of the theory, then the locus and range of modifications may reasonably be judged with some accuracy. In order to substantiate these claims for patterns of reasoning in theory construction and modification, this paper will analyze a case from twentieth century biology, the construction of the theory of the gene, from the rediscovery of Mendel’s work in 1900 to the statement of the theory by T. H. MORGAN in 1926. We will see which postulates accounted for which data and then trace how a subset of the postulates were challenged and modified in the light of new evidence. At the beginning of the field of genetics around 1900, the term “gene” had not come into usage. Instead, the theory was expressed either in terms of differences among germ cells or some kind of “factors” within germ cells. Details about these factors were added as the theory of the gene was modified and augmented. The original postulates were constructed to solve problems posed by empirical regularities, the famous ratios discovered by MENDELin 1866 and rediscovered in 1900. Table 1 presents Mendel’s data, the domain to be explained. Items 1 and 2 present the puzzle, the major problem, that called for a theoretical
. A note on terminology. I am using the word “theory” for a set of “postulates.”
“Hypothesis” is a more flexible word which refers to a claim not yet confirmed, which could be an alternative postulate. I refer to the changing set of postulates as composing the same theory, which is undergoing modification as new hypotheses are proposed and tested. I have not faced the problem of whether there is one (or more) “essential” postulate(s), such that if it (they) were changed the theory would cease to be the same one and would become a different theory. I suspect “purity of the gametes” was such a postulate in the Mendelian case and the scientists tended t o talk as if it were, but I have not examined that carefully. My usage departs from the way philosophers normally talk (e.g. LAKATOS, 1970) in which any change in postulates changes Tn to Tn+,. I prefer discussing the development of a single theory rather than discussing the proposal of a series of new theories because I think it fits the scientific usage more accurately.
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4 explanation: how can something be present (e.g., green color in a parent), disappear for a generation (e.g., all F1 hybrids yellow), and then reappear in a pure form (e.g., pure green in &)? This problem was solved by introducing a new idea, that is, postulating a theoretical entity, a hidden factor, to account for the puzzle. The factors, it was claimed, are transmitted unchanged and thus again produce pure characters. At the outset in theory construction, one needs a simple connection between the theoretical entity and empirically determinable items. One needs a way of easily inferring from empirical items to numbers, types, behaviors of the theoretical entities which are otherwise inaccessible. Theory construction in genetics satisfied this need: one factor was claimed to be associated with one independently variable trait of a character. Information about the behavior of observable characters was used to infer behavior of factors. Table 1 Genetic phenomena to be explained: Irem 1. In artificial breeding experiments involving crosses between varieties of animals or plants differing in the traits of one character, one trait dominates over the other in the hybrid (FJ generation. (For example, yellow and green color are differing traits for the character of pea color; yellow X green peas yield hybrids all of which are yellow.) Item 2. When hybrids from crosses such as those described in Item 1 are allowed to self-fertilize or are crossed with each other, on an average one obtains a ratio of 3 dominants to 1 recessive in the next (F2)generation. (For example, yellow hybrid X yellow hybrid yields 3 yellow: 1 green.) When the recessives from the F, cross are self-fertilized,all offspring are recessive. (For example, green X green yields only green.) When the dominants from the Fp cross are self-fertilized and followed for successive generations, then one third yields pure dominants while two thirds again behave as hybrids. (For example, yellow X yellow yields 1 pure yellow: 2 hybrid yellow.) The 3:l ratio in the F, thus resolves into 1 pure dominant: 2 hybrids: 1 pure recessive. Item 3. In other experiments involving crosses between varieties differing in traits of two characters, the characters behave independently, giving on an average an F, ratio of 9:3:3:1, (For example, yellow tall X short green peas gives hybrids that are yellow and tall: when these are self-fertilized the Fpgives, on an average, 9 yellow tall : 3 yellow short : 3 green tall : 1 green short.)
Once a theoretical entity has been postulated, one may then ask numerous questions about it. For example, where is it located? The genetic data about characters and their numerical relations provided no answer to this question. At this point in theory construction, one may have to turn to other fields in order to answer supplementary problems raised by the postulation of the theoretical entity. In this case, the neighboring field
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of cytology provided the answer: since the germ cells (gametes) alone provide the link between generations, then the factors must be carried in the germ cells, that is, carried in the pollen and egg cells of plants and the sperm and eggs in animals. Table 2 Postulates as of 1900 I
Theoretical assumDtion
1. Traits of characters are produced by factors (elements, pangens, Anlagen, later genes).
I
Simplifying assumption
2. One independently heritable trait of a character is produced by one factor; called unit-character concept.
Interfield connection
3. Since germ cells (i.e., pollen and eggs in plants, eggs and sperm in animals, also called gametes) are the links between generations, the factors are passed from parent to offspring in the germ cells.
Dominancerecessiveness
4. In a hybrid formed by crossing parents that differ in two traits
Segregation
Independent assortment
of a single character, there is some difference between the factors such that one dominates over the other and thus determines that the character in the hybrid resembles one but not the other of the parents. (Let A symbolize the dominant trait which appears; a the recessive which is not apparent.)\
5. The parental factors are not modified as a result of being together the hybrid, nor are any new kinds of factors formed. 6. In the formation of the germ cells of the hybrid, the parental factors separate (segregate) so that the germ cells are of one or other of the parental types. This is called “purity of the gametes” and symbolized by saying that each germ cell carries A or a but not both. 7. The two different types of germ cells are formed in equal numbers in the hybrid. 8. When two similar hybrids are fertilized (or self-fertilization occurs), the differing types of germ cells combine randomly. (A+a)(A+a) = AA+ZA+aa; appearance 3A:la.
9. The factors in hybrids formed from parents differing in two traits of two characters assort so that all pairwise combinations are found in the germ cells. (AB, Ab, aB, ab) 10. The four different types of germ cells are formed in equal numbers. 11. When two similar hybrids are fertilized (or self-fertilization occurs) the four different types of germ cells combine randomly. (ABS Ab+ aB+ ab)* = complicated array which in appearance reduces to 9AB:3Ab:3aB:lab.
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With the theoretical assumption of hidden factors (Postulate 1 of Table 2), the simplifying assumption of one unit-one character (Postulate 2) and the interfield connection linking factors to germ cells (Postulate 3), the further postulates to give specific explanations of the domain item could be constructed. Table 2 is my attempt to lay out more clearly than was done at the time the separable assumptions made by the theory as of 1900. Note that no explanation of Item 1, dominance-recessiveness, is given by Postulate 4: some difference, not known, between factors was claimed to be responsible. This was easily dropped when exceptions were found. Postulates 5-8 together accounted for the 3:l ratios (Item 2) and were collectively usually called “segregation” or “Mendel’s first law”. However, each postulate was separable assumption that was challenged historically. Postulate 6 was often called the “essence” of segregation; the “purity of the gametes” was often cited as the essential discovery of Mendel. DARWINin 1868, not knowing of Mendel’s work, had postulated that hybrid units were formed in the hybrid. Mendel’s 3:l ratios could not easily be explained on such an assumption, but pure parental factors with no hybrid units easily explained the data. Postulates 9-1 1 explain the 9 :3 :3 :1 ratios (Item 3) and were collectively referred to as “independent assortment” or “Mendel’s second law” (although they were not clearly laid out as postulates separate from segregation until after 1900). Postulates 9-1 1 were all challenged and subsequently modified. The theory as of 1900 was rather different from the statement of the theory of the gene given by Morgan in 1926: The theory [of the gene] states that the characters of the individual are referable to paired elements (genes) in the germinal material that are held together in a definite number of linkage groups; it states that the members of each pair of genes separate when their germ-cells mature in accordance with Mendel’s first law, and in consequence, each germcell comes to contain one set only: it states that the members belonging to different linkage groups assort independently in accordance with Mendel’s second law: it states that an orderly interchang-rossing over-also takes place, at times between the elements in corresponding linkage groups: and it states that the frequency of crossing-over furnishes evidence of the linear order of the elements in each linkage group and of the relative position of the elements with respect to each other. (MORGAN, 1926,p. 25.)
A number of changes had been made. Dominance-recessiveness was no longer included among the postulates. Segregation had withstood all the tests to which it was subjected. Independent assortment was substantially modified by the discovery and explanation of linkage. It is too
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lengthy a task for this paper to trace all the challenges and modifications in the theory. Instead we will focus only on the unit-character assumption, Postulate 2, and segregation, Postulates 5-8. The unit-character concept, Postulate 2, was a simplifying assumption important for obtaining empirical access to the hidden factors. But the direct relation of one trait of a character produced by one factor was too simple, and working out the more complicated relations aided in both the conceptual development of the theory and extended the domain to which it applied. JOHANNSEN (1903, 1909) did experiments in which he selected traits which continuously varied in populations, e.g., the size of beans. Such “continuous” or quantitative variation was not part of the original domain of Mendelism and had been thought to need a different theory to explain it. Johannsen showed that selection was effective only in sorting out different genotypes (a term he coined) which produced the statistically varying characters of the phenotypes. With a clearer understanding of genotype and phenotype, other workers (e.g., EAST, 1910) followed up BATESON’S suggestion (1902) that multiple factors interacted to produce seemingly ‘‘continuous’’ variation. The unit-character concept thus gave way to knowledge of more complicated relations between genes and characters and the domain of the theory was enlarged to include what had once been thought to be an exception. The central claims of the theory are expressed by Postulates 5 and 6, namely that factors are not modified by being together in the hybrid and gametes consist of pure parental factors. These postulates underwent extensive tests with W. E. Castle as their strongest critic. Yet, after years of experiments, he finally came to accept them as a result of a crucial experiment. Since, at the outset, Castle accepted a strong connection between units and characters (Postulate 2), he reasoned in the following way: variation is found in traits which were once present together in the hybrid; thus, the units producing those traits may be inferred to vary also. By selecting individuals with one or other of the extremes of the variation, CASTLE(and PHILLIPS,1914) claimed to be selecting modified units. H. J. MULLER(1914) provided an alternative interpretation: the multiple factor hypothesis already proposed (modification of Postulate 2) could be invoked to postulate “modifying” factors which interacted to produce the variation and which Castle was sorting out into pure lines by selection. Castle recounted the events and issues: Investigations with rats were made by us primarily to ascertain whether Mendelian characters are, as generally assumed, incapable of modification by selection.. My own
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early observations indicated that they were modifiable, and to this view I stubbornly adhered, like Morgan in his early opposition to Mendelism, until the contrary view was established by a crucial experiment. (CASTLE,1951, p. 71.)
Experiments were carried out on rats with a black and white pattern, called “hooded” and known to segregate as a Mendelian character. In separate series of experiments, Castle selected in both directions, toward more white and toward more black. Castle continued : The fact of modifiability of the hooded pattern was thus firmly established, but its interpretation was still doubtful. Two interpretations were possible: (1) that the unit character, or unit factor, or gene for the hooded pattern, as it had successively been designated, was itself fluctuating, or (2) that the observed modification had been effected by a modifying influence of other genes than the gene for hooded pattern. Such hypothe tical genes might be designated modifying. Their reality in other genetic material became increasingly clear from 1911 on. (CASTLE,1951, pp. 71-72.)
With hindsight Castle was willing to give the hypothesis of modifying genes more credence than he did while opposing it. In 1919, discussing modifying genes, he said: In some cases [the modyfying genes] are known to have other functions also. Thus the gene proper of one character may function also as a modifying gene for another character. But in the majority of cases the only ground for hypothecating the existence of modifying genes is the fact that characters are visibly modified. As an alternative to the theory of modifying genes, the theory has been considered that genes may themselves be variable and if so, genes purely modifying in function might be dispensed with. (CASTLE,1919, p. 127.)
Castle is here appealing to a criticism of modifying genes as being ad hoc addition to the theory in order to save Postulate 5, namely that genes are not modified by hybridization. He advocated, instead, dropping that postulate in favor of modifiable genes, a hypothesis that may be argued to be the simpler of the two since it fulfills the dictum not to multiply entities beyond necessity. But Muller’s counter to these arguments was that the multiple factor hypothesis was to be preferred because it was consistent with previous work and did not involve the “radical” denial of the conclusion to which “all our evidence points”, namely “the conclusion that the vast majority of genes are extremely constant”, and change only by occasional mutation (MULLER,1914, pp. 61-62). Castle saw very clearly what was needed to perform a test to choose between the hypotheses:
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Since the supposed “factors” of inheritance are invisible, we cannot hope to deal with them directly by experiment, but only indirectly. Our method obviously should be to eliminate all environmental factors so far as possible and also all factors of inheritance except one.. . But it is very difficult to apply this method to specific cases, since when variation is observed it is alway possible to suppose that all factors but one have yet 1916, p. 95.) been eliminated. (CASTLE,
Despite the difficulties, Castle designed and carried out the crucial experiment. He took hooded rats which had been selected and crossed them with another race which lacked the hooded character. If the original hooded trait reappeared in the new hybrids, it was predicted, then selection had not modified the factors ; instead, modifying genes were eliminated by the cross and the original factor was once again producing the hooded trait. The prediction was confirmed. Castle accepted the results as crucial and changed his views: The fact that the hooded gene itself had not been changed as a result of long continued selection was thus demonstrated, but, incidentally mutation had been observed to occur in the hooded gene itself in a single instance. Thus we now knew that in mammals color patterns may be. modified by selection (1) through cumulation of modifying genes, and (2) much more rarely, by isolation of mutations in the particular pattern gene itself. (CASTLE, 1951, p. 72.)
Thus, Castle’s tests of the central claims of the theory (Postulates 4 and 5 ) resulted in their retention. More evidence for the multiple factor hypothesis led to further evidence against the one unit-one character concept. Furthermore, “modifying genes” became part of the multiple factor repertoire. Referring to Table 2, Postulates 5 and 6 were tested and confirmed but those tests led to further change and development of Postulate 2, namely a change from the one unit-one character concept to the proposal of the interaction of multiple factors. Postulates 6, 7 and 8, collectively often called segregation, came under found an exception to the 3:1 ratios that those fire when C U ~ N O(1905) T postulates were constructed to explain. On breeding yellow mice with those having other colors, yellow was dominant. However, when the hybrids were bred, the percentage of yellow in the F, generation was smaller than expected by 2.55 per cent, that is, the ratios were between 2:1 and 3:l. When CuCnot bred the yellows so produced, he was unable to obtain any homozygous yellows, i.e., no pure dominants (no AA) were produced. CASTLEand LITTLE(1910) tested CuCnot’s results with a larger sample and showed that the ratio was closer to 2:l. It was agreed that Postulates 6-8 were the locus of th problem, but CuCnot, Castle
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and Morgan proposed different modifications in the postulates to account for this exception which occupy a scale from a radical change to little change of postulates. Morgan’s entailed the most fundamental modification, a denial of the purity of the gametes in general (Postulate a), with this case providing evidence for their impurity. CU~NOT (1905) left Postulate 6 intact but modified Postulate 8 by proposing a selective fertilization. Castle’s explanation involved the least modification: he left all postulates intact and explained away the exceptional data as an unusual case of inviability of some gametic combinations. The differences among the proposed modifications are instructive, so we will examine these alternatives in more detail. In 1905, as a critic of Mendelism, MORGAN(1905) used CuCnot’s exceptional results to provide evidence against purity of the gametes. He proposed that the factors never segregate into pure parental forms but that the hybrid produces gametes with both dominant and recessive factors present. However, in half the gametes the dominant is latent; in the other half the recessive is latent. In future generations, Morgan predicted, the effect of the hybridization would be evident, some of the previous grandparental characters would reappear. In CuCnot’s exceptional yellow mice such appearances occurred sooner than is usually the case. Morgan, it should be noted, here is giving a theoretical explanation which accords with intuitive suspicions. The Mendelian phenomena are puzzling: is it really possible that a hybrid yellow pea can give rise to a pure breeding green strain that will never show the effects of having been produced by a yellow hybrid? Purity of the gametes entails that result. But when MORGAN(1909) tested his prediction with other strains of mice, he did not find the predicted reappearance of dominants in the recessive strains. His conclusion: “It is evident that the hypothesis failed when tested and must therefore be abandoned.” (MORGAN,1911). CuCnot’s modification left the postulate of purity of the gametes (Postulate 6) intact and instead modified Postulate 8. Not all gametes combine randomly, he claimed ; sometimes selective fertilization occurs. In this case the gametes bearing factors for yellow selectively combine with gametes bearing different factors, but not with each other. (In the symbolism used here: (A+a)(A+a) = no AA, only 2Aa : laa.) MORGAN (1909) criticized Cutnot’s hypothesis of selective fertilization as “a conception entirely foreign to the whole Mendelian scheme. There is no evidence of selective fertilization in this sense known elsewhere and it seems a very questionable advantage to introduce the factor [an unfortunate
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choice of word here] into the Mendelian process.” (MORGAN, 1909,p. 503). Bateson and Punnett also criticized selective fertilization by countering that it would not even explain the exceptional ratios. Since more sperm are found than eggs, there would be sufficient numbers of “non-yellow” sperm to fertilize all the “yellow” eggs so one would expect a 3:l ratio of yellow to other color (e.g., 3Aa : laa) even though no pure yellows were among the proportion of yellows. (BATESON,1909, p. 119.) The lack of pure yellows still required an explanation and Castle’s explanation proved to be the best: the embryos formed by the mating of two gametes with yellow factors were inviable, thus one expects the 2:l ratio that was found. CASTLE(and LITTLE,1910) appealed to smaller numbers of young produced as evidence for this hypothesis and also pointed out that decreased viability had been found in other cases. By 1941 (e.g., MORGAN, 1914) Castle’s explanation of Cudnot’s results had been accepted. Once again, the purity of the gametes and the other segregation postulates survived severe challenges to remain unmodified. Such was not the case with the independent assortment postulates (9-11) which were extensively modified as numerous cases of linkage were found. But a discussion of those modifications is too lengthy for consideration here. A number of features of this case may be noted. The original domain resulting from Mendel’s work with peas was very simple in that it consisted of results from a single species with clear cut character differences. It was a good model system for seeing the need to postulate pure units not interacting in the hybrid. Furthermore, the technique of artificial breeding provided a means of developing a line of research to test the generality of the postulates. The promise of this new theory marked the emergence of the field of genetics to carry out tests of generality. (See DARDEN,1977, 1978 for further discussion.) But, as might have been expected, hereditary phenomena were more diverse. (As in fact Darwin had already known; Darwin did not discover Mendel’s laws, it is plausible to claim, because he knew too much.) Experimental results expanded the domain, necessitating modifications in the postulates. Some were straight forward “complications”, i.e., the original postulate was too simple and was expanded. The change from the unit-character concept to multiple factors is an example. In some cases, that the particular data required modification in a particular postulate was not debated. The postulate had been introduced to account for an item in the domain when that item was modified in the light of new evidence, then the postulate; constructed to explain it was modified.
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In other cases, however, debate focused on which of two postulates to modify. Castle, for example, accepted Postulate 2 that a tight connection existed between the unit and character and argued that variability of character implied variability of the gene, thereby denying Postulate 5. Muller countered by retaining Postulate 5 and denying a strict version of Postulate 2 by postulating effects of modifying genes on a character. This was a legitimate debate about where the locus of modification should be and both modifications had arguments in their favor. Appeals were made to ad hocness, simplicity, and consistency with other results. A crucial experimental test ruled in favor of Muller’s alternative. When Cuenot found an exception to the 3:1 ratios, there was agreement as to which set of postulates needed modifying: Postulates 5-8 which had been constructed to account for the 3:1 ratios. But debate occurred as to which should be modified. The modifications ranged from a very fundamental change to leaving the postulates intact and explaining the case away as an unusual one. Fundamentality here is analyzed as that which would require the most extensive modification of other postulates. If, for example, Morgan’s denial of purity of the gametes had prevailed, it would have had consequences for the postulate claiming that genes are not modified by being together in the hybrid (Postulate 5). However, Cudnot’s proposal of selective fertilization (modification of Postulate 8) left Postulate 5 intact. Castle’s explanation of the exceptions to 3:l ratios left all the postulates intact and explained the particular case as due to an exceptional occurrence. Deviations from the 3:l ratios were not common, lending credence to Castle’s less fundamental change.
’ Dudley Shapere in a recent paper discussed another case (the problem of solar neutrinos)
and made a penetrating comment relevant to this question of fundamentality : If the predictions of our hypotheses disagree with our observations (as they have in the case of solar neutrinos), it is not necessarily the hypothesis under examination (in that case, hypotheses about the processes of stellar energy production) which is at fault; it may be any portion of the theoretical and instrumental ingredients which form the background of the experiment. The point is, of course, not new: but what needs to be made clear and precise is that there exists a rough rationale for the order in which we subject the ingredient accepted ideas to suspicion, and correlatively, an order in which we propose new alternatives. We begin by suspecting those ingredients which are most likely to be a fault, and least costly to give up; if the difficulty persists, the threat penetrates deeper and deeper into the structure of accepted beliefs involved 1980, p. 79). in the purported observation and background. (SHAPERE,
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Conclusion I have examined one case from the history of biology in detail. What
can be concluded on the basis of only one case? I cannot prove that I have found general patterns of reasoning in science. Nor do I have a basis for prescribing how successful science is to be done, a worthy, but perhaps unattainable, goal of philosophy of science. But this case does belie the general claim that one never has any reasons for believing that one rather than another postulate of a theory is in need of modification in the light of new evidence. Furthermore, the reasoning patterns found in this case serve as examples which can be looked for in other cases to test their generality and which suggest strategies for achieving certain goals in theory construction and modification. By viewing theory construction as a modular process, one can see particular postulates are related to particular domain items. If the item changes, then the first locus to be considered for possible modification is the postulate or postulates which account for that item. The case examined shows that scientists usually agree on one or a few postulates as those in need of modification. The task then becomes to devise and choose among alternative ways of modifying that localized postulate. Devising alternatives is the process of discovery ; choosing among them involves various aspects of theory choice or confirmation. Both are intimately connected in producing a modified theory. Although no algorithm is known for producing correct modifications, we can imagine a scientist (more likely a computer program these days) who employs a systematic strategy when faced with exceptions. Several goals are chosen. First, the theory must account for the domain items ; exceptions or additions to the domain may thus necessitate changes in the theory. Secondly, a consistent set of postulates must result from any modification. Thirdly, an exhaustive list of alternative modifications should be devised. In actual practice it is often hard to find one or two, much less produce an exhaustive set. Usually one scientist devises only one alternative and argues for it against competitors proposed by another scientist. However, more expansive minds devise their own alternative hypotheses (e.g., see a recent article by Francis CRICK(1979) on the possible mechanisms for eliminating intervening sequences from genes
*
Work along these lines is being done by Bruce Buchanan of the Computer Science Department at Stanford University, for example in his recent paper (BUCHANAN, 1978).
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prior to their expression). For pragmatic reasons (or maybe something stronger, such as, we can only gain new knowledge when we have a base of older, better established knowledge) an economy of effort is desirable: make the least fundamental modifications first, then proceed to more fundamental ones. With these goals and directives, we can devise a systematic strategy for modifying a theory to account for an exception to a domain item. Such a strategy is given in Table 3. Table 3 Strategy for theory modification I
These steps should be taken in the order given. When an exception to a theory arises: (i) Confirm the experimental results to be sure it is an exception. (ii) See if such a n exception arises only in the system studied (e. g., one character in one species) or whether it is found in other systems (e. g., other characters, other species). (iii) Locate the postulate constructed to account for the domain item to which it is an exception. See if the postulate can be “complicated” to explain the exception (e. g., add another variable). (iv) If (iii) failed to locate only one postulate, then examine the two or more postulates involved. Devise an exhaustive list of modifications possible, making sure that a consistent set of postulates results from each modification. Choose the modification that has least effect on the other postulates and test it experimentally. If it fails, then make the next least fundamental modification, test, and so on. (v) If a modification cannot be used to make new predictions by which it can be tested, because it only accounts for the exception for which it was devised, then it is to be shelved as an unacceptable ad hoc modification.
In summary, this paper has examined questions about reasoning in scientific change. More specifically, it has focused on theory construction and modification and argued that in some cases, at least, rational procedures exist for localizing parts of a theory in need of modification in the light of exceptions. Furthermore, it has suggested a strategy for carrying out those modifications, given certain goals of science, such as accounting for the data and devising consistent theories. Acknowledgment This research was supported by the History and Philosophy of Science Program of the U.S.National Science Foundation (Grant SOC77-23476).
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References BATESON, W., 1902, Mendel's principles of heredity-A defense (University Press, Cambridge, England) BATESON, W., 1909, Mendel's principles of heredity (University Press, Cambridge, England) BUCHANAN, B., 1978, Steps toward mechanizing discovery, Proceedings from a Conference on Logic of Discovery and Diagnosis in Medicine, Pittsburgh, October 1978 (Stanford Heuristic Programming Project Memo HPP-79-28) CASTLE, W. E., and C. C. LIITLE, 1910, On a modified Mendelian ratio among yellow mice, Science, vol. 32, pp. 868-870 CASTLE, W. E., and J. C. PHILLIPS,1914, Piebald rats and selection: An experimental test of the effectivenessof selection and of the theory of'gametic purity in Mendelian crosses, Carnegie Institute of Washington Publication, No. 196, pp. 51-55 CASTLE,W. E., 1916, Pure lines and selection, Journal o f Heredity, vol. 5, pp. 93-97 CASTLE, W. E., 1919, Piebald rats and the theory of genes, Proceedings of the National Academy of Sciences, vol. 5, pp. 126-130 CASTLE,W. E., 1951, The beginnings of Mendelism in America, in: Genetics in the 20th Century, ed. Leslie C. Dunn (New York, Macmillan), pp. 59-76 CRICK, F., 1979, Split genes and RNA splicing, Science, vol. 204, pp. 264-271 CU~NOT, L., 1905, Les racespures et Ieurs combinaisons chez les souris, Archives de Zoologie Experimkntale et Gtntrale, 4 Strie, T. 11 1, pp. CXXIII-CXXXII DARDEN, L., 1974, Reusoning in scientific change: The field of genetics at its beginnings, Ph. D. Dissertation. (The University of Chicago, Chicago, Illinois) L., 1976, Reasoning in scientific change: Charles Darwin, Hugo de Vries, and the DARDEN, discovery of segregation, Studies in the History and Philosophy of Science, vol. 7, pp. 127-169 DARDEN, L., 1977, William Bateson and the promise of Mendelism, Journal of the History of Biology, vol. 10, pp. 87-106 DARDEN, L., and N. MAULL,1977, Interfield theories, Philosophy of Science, vol. 44, pp. 43-64 DARDEN, L., 1978, Discoveries and the emergence of new fields in science, P S A 1978, vol. 1, Philosophy of Science Association (East Lansing, Michigan), pp. 149-160 DARDEN, L., Theory construction in genetics, in: Scientific Discovery Case Studies, ed. T. Nickles (Reidel Dordrecht) (forthcoming) DARWIN,C., 1868, Provisional hypothesis ofpangenesis, in: The Variation of Animals and Plants Under Domestication, vol. 2, ch. 27 (Orange Judd and Co., New York) DUHEM, P., 1914, The aim and structure of physical theory, trans. F. P. Wiener, 1962 (Atheneum, New York) EAST,E., 1910, A Mendelian interpretation of variation that is apparently continuous, American Naturalist, vol. 44, pp. 65-82 JOHANNSEN, W., 1903, Heredity in populations andpure lines, selectionstrans. and reprinted in: Classic Papers in Genetics, ed. James A. Peters (Prentice Hall, Engelwood Cliffs, N. J., 1959), pp. 20-26 JOHANNSEN, W., 1909, Elemente der Exakten Erblichkeitslehre (G. Fischer, Jena) LAKATOS, I., 1970, Falsification and the methodology of scientific research programmes, in: Criticism and the Growth of Knowledge, ed. I. Lakatos and Alan Musgrave (The University Press, Cambridge, England), pp. 91-195
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MENDEL,G., 1866, Experiments on plant hybrids, reprinted in: The Origin of Genetics, A Mendel Source Book, eds. Curt Stern and Eva Shenvood (W. H. Freeman and Company, San Francisco), pp. 1-48 MORGAN, T. H., 1905, The assumedpurity of the germ cells in MendeIian results, Science VOI. 22, pp. 877-879 MORGAN,T . H., 1909, Recent experiments on the inheritance of coat colors in mice, American Naturalist, vol. 43, pp. 494-510 MORGAN,T. H., 1911, The influence of heredity and of environment in determining the coat colors in mice, New York Academy of Science Annals, voI. 21, pp. 87-1 17 MORGAN,T. H., 1914, Multiple allelomorphs in mice, American Naturalist, vol. 48, pp. 449-58 MORGAN, T. H., 1926, The theory of the gene (Yale University Press, New Haven) MULLER,H. J., 1914, The bearing of the selection experiments of Castle and Phillips on the 1962, pp. 61-69 variability of genes, American Naturalist 48, reprinted in: MULLER, MULLER,H. J., 1962, Studies in genetics, The selected papers of H. J. Muller (Indiana University Press, Bloomington) QUINN, P., 1974, What Duhem really meant, in: Methodological and Historical Essays in the Natural and Social Sciences, Proceedings of the Boston Colloquium for the Philosophy of Science 1969-1972, eds. R. S. Cohen and M. Wartofsky, vol. XIV (Reidel, Dordrecht), pp. 33-56 SHAPERE, D., 1974, Scientific theories and their domains, in: The Structure of Scientific Theories, ed. Frederick Suppe (University of Illinois Press, Urbana), pp. 518-565 SHAPERE, D., 1980, The character of scientific change, Scientific Discovery, Logic, and Rationality, pp. 61-101, ed. T. Nickles (Reidel, Dordrecht) TOULMIN, S., 1972, Human understanding, vol. I (Princeton University Press, Princeton)
LINDLEY DARDEN Committee on the History and Philosophy of Science University of Maryland, College Park, Maryland, U.S.A.
Philosophers, impressed by the certainty provided by deductive logic, have, in the past, demanded that science provide the same kind of certainty. But arguments to the contrary are persuasive. Duhem claimed : “Unlike the reduction to absurdity employed by geometers, experimental contradiction does not have the power to transform a physical hypothesis into a indisputable truth.” (DUHEM,1914, p. 190). Recognizing these limitations, Stephen Toulmin said: rationality need not be equated with logicality: “A man [or woman] demonstrates his rationality, not by a commitment to fixed ideas, stereotyped procedures, or immutable concepts, but by the manner in which and the occasions on which, he changes those ideas, procedures and concepts.” (TOULMIN,1972, p. x). Other recent philosophers have been concerned to understand the rational factors involved in scientific change, most notably Imre LAKATOS (1970) and Dudley SHAPERE (1974). This paper is within this recent tradition in philosophy of science of understanding the rational means by which science changes. More specifically it is concerned with the question-how are theories constructed and how are they modified in the light of new evidence? Duhem might have been right when he claimed: “NO hypothesis which is a component of a scientific theory T can ever be sufficiently isolated from some set of auxiliary assumptions or other so as to be separately falsifiable by observations.” (QUINN,1974, p. 36). But the truth of such a claim, based on the rigorous demands of certainty, does not negate the possibility of finding rational means, better or worse means, of modifying a theory in the light of conflicting evidence. This paper will argue that procedures 463
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exist for determining which postulates of a theory as opposed to others, are more likely to be in need of modification when evidence necessitates a change. In at least some cases, theory construction is a modular process with specific postulates constructed to account for specific data. Consequently, changes in that data direct the localization of the needed change to the corresponding postulates. Furthermore, as philosophers have often noted (e.g. DUHEM,1914, p. 1851, if a set of postulates is used to make a prediction about new phenomena, not previously investigated, and that prediction is not confirmed, then that set of postulates is in need of modification. But if that set is small and is independent of other postulates of the theory, then the locus and range of modifications may reasonably be judged with some accuracy. In order to substantiate these claims for patterns of reasoning in theory construction and modification, this paper will analyze a case from twentieth century biology, the construction of the theory of the gene, from the rediscovery of Mendel’s work in 1900 to the statement of the theory by T. H. MORGAN in 1926. We will see which postulates accounted for which data and then trace how a subset of the postulates were challenged and modified in the light of new evidence. At the beginning of the field of genetics around 1900, the term “gene” had not come into usage. Instead, the theory was expressed either in terms of differences among germ cells or some kind of “factors” within germ cells. Details about these factors were added as the theory of the gene was modified and augmented. The original postulates were constructed to solve problems posed by empirical regularities, the famous ratios discovered by MENDELin 1866 and rediscovered in 1900. Table 1 presents Mendel’s data, the domain to be explained. Items 1 and 2 present the puzzle, the major problem, that called for a theoretical
. A note on terminology. I am using the word “theory” for a set of “postulates.”
“Hypothesis” is a more flexible word which refers to a claim not yet confirmed, which could be an alternative postulate. I refer to the changing set of postulates as composing the same theory, which is undergoing modification as new hypotheses are proposed and tested. I have not faced the problem of whether there is one (or more) “essential” postulate(s), such that if it (they) were changed the theory would cease to be the same one and would become a different theory. I suspect “purity of the gametes” was such a postulate in the Mendelian case and the scientists tended t o talk as if it were, but I have not examined that carefully. My usage departs from the way philosophers normally talk (e.g. LAKATOS, 1970) in which any change in postulates changes Tn to Tn+,. I prefer discussing the development of a single theory rather than discussing the proposal of a series of new theories because I think it fits the scientific usage more accurately.
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4 explanation: how can something be present (e.g., green color in a parent), disappear for a generation (e.g., all F1 hybrids yellow), and then reappear in a pure form (e.g., pure green in &)? This problem was solved by introducing a new idea, that is, postulating a theoretical entity, a hidden factor, to account for the puzzle. The factors, it was claimed, are transmitted unchanged and thus again produce pure characters. At the outset in theory construction, one needs a simple connection between the theoretical entity and empirically determinable items. One needs a way of easily inferring from empirical items to numbers, types, behaviors of the theoretical entities which are otherwise inaccessible. Theory construction in genetics satisfied this need: one factor was claimed to be associated with one independently variable trait of a character. Information about the behavior of observable characters was used to infer behavior of factors. Table 1 Genetic phenomena to be explained: Irem 1. In artificial breeding experiments involving crosses between varieties of animals or plants differing in the traits of one character, one trait dominates over the other in the hybrid (FJ generation. (For example, yellow and green color are differing traits for the character of pea color; yellow X green peas yield hybrids all of which are yellow.) Item 2. When hybrids from crosses such as those described in Item 1 are allowed to self-fertilize or are crossed with each other, on an average one obtains a ratio of 3 dominants to 1 recessive in the next (F2)generation. (For example, yellow hybrid X yellow hybrid yields 3 yellow: 1 green.) When the recessives from the F, cross are self-fertilized,all offspring are recessive. (For example, green X green yields only green.) When the dominants from the Fp cross are self-fertilized and followed for successive generations, then one third yields pure dominants while two thirds again behave as hybrids. (For example, yellow X yellow yields 1 pure yellow: 2 hybrid yellow.) The 3:l ratio in the F, thus resolves into 1 pure dominant: 2 hybrids: 1 pure recessive. Item 3. In other experiments involving crosses between varieties differing in traits of two characters, the characters behave independently, giving on an average an F, ratio of 9:3:3:1, (For example, yellow tall X short green peas gives hybrids that are yellow and tall: when these are self-fertilized the Fpgives, on an average, 9 yellow tall : 3 yellow short : 3 green tall : 1 green short.)
Once a theoretical entity has been postulated, one may then ask numerous questions about it. For example, where is it located? The genetic data about characters and their numerical relations provided no answer to this question. At this point in theory construction, one may have to turn to other fields in order to answer supplementary problems raised by the postulation of the theoretical entity. In this case, the neighboring field
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of cytology provided the answer: since the germ cells (gametes) alone provide the link between generations, then the factors must be carried in the germ cells, that is, carried in the pollen and egg cells of plants and the sperm and eggs in animals. Table 2 Postulates as of 1900 I
Theoretical assumDtion
1. Traits of characters are produced by factors (elements, pangens, Anlagen, later genes).
I
Simplifying assumption
2. One independently heritable trait of a character is produced by one factor; called unit-character concept.
Interfield connection
3. Since germ cells (i.e., pollen and eggs in plants, eggs and sperm in animals, also called gametes) are the links between generations, the factors are passed from parent to offspring in the germ cells.
Dominancerecessiveness
4. In a hybrid formed by crossing parents that differ in two traits
Segregation
Independent assortment
of a single character, there is some difference between the factors such that one dominates over the other and thus determines that the character in the hybrid resembles one but not the other of the parents. (Let A symbolize the dominant trait which appears; a the recessive which is not apparent.)\
5. The parental factors are not modified as a result of being together the hybrid, nor are any new kinds of factors formed. 6. In the formation of the germ cells of the hybrid, the parental factors separate (segregate) so that the germ cells are of one or other of the parental types. This is called “purity of the gametes” and symbolized by saying that each germ cell carries A or a but not both. 7. The two different types of germ cells are formed in equal numbers in the hybrid. 8. When two similar hybrids are fertilized (or self-fertilization occurs), the differing types of germ cells combine randomly. (A+a)(A+a) = AA+ZA+aa; appearance 3A:la.
9. The factors in hybrids formed from parents differing in two traits of two characters assort so that all pairwise combinations are found in the germ cells. (AB, Ab, aB, ab) 10. The four different types of germ cells are formed in equal numbers. 11. When two similar hybrids are fertilized (or self-fertilization occurs) the four different types of germ cells combine randomly. (ABS Ab+ aB+ ab)* = complicated array which in appearance reduces to 9AB:3Ab:3aB:lab.
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With the theoretical assumption of hidden factors (Postulate 1 of Table 2), the simplifying assumption of one unit-one character (Postulate 2) and the interfield connection linking factors to germ cells (Postulate 3), the further postulates to give specific explanations of the domain item could be constructed. Table 2 is my attempt to lay out more clearly than was done at the time the separable assumptions made by the theory as of 1900. Note that no explanation of Item 1, dominance-recessiveness, is given by Postulate 4: some difference, not known, between factors was claimed to be responsible. This was easily dropped when exceptions were found. Postulates 5-8 together accounted for the 3:l ratios (Item 2) and were collectively usually called “segregation” or “Mendel’s first law”. However, each postulate was separable assumption that was challenged historically. Postulate 6 was often called the “essence” of segregation; the “purity of the gametes” was often cited as the essential discovery of Mendel. DARWINin 1868, not knowing of Mendel’s work, had postulated that hybrid units were formed in the hybrid. Mendel’s 3:l ratios could not easily be explained on such an assumption, but pure parental factors with no hybrid units easily explained the data. Postulates 9-1 1 explain the 9 :3 :3 :1 ratios (Item 3) and were collectively referred to as “independent assortment” or “Mendel’s second law” (although they were not clearly laid out as postulates separate from segregation until after 1900). Postulates 9-1 1 were all challenged and subsequently modified. The theory as of 1900 was rather different from the statement of the theory of the gene given by Morgan in 1926: The theory [of the gene] states that the characters of the individual are referable to paired elements (genes) in the germinal material that are held together in a definite number of linkage groups; it states that the members of each pair of genes separate when their germ-cells mature in accordance with Mendel’s first law, and in consequence, each germcell comes to contain one set only: it states that the members belonging to different linkage groups assort independently in accordance with Mendel’s second law: it states that an orderly interchang-rossing over-also takes place, at times between the elements in corresponding linkage groups: and it states that the frequency of crossing-over furnishes evidence of the linear order of the elements in each linkage group and of the relative position of the elements with respect to each other. (MORGAN, 1926,p. 25.)
A number of changes had been made. Dominance-recessiveness was no longer included among the postulates. Segregation had withstood all the tests to which it was subjected. Independent assortment was substantially modified by the discovery and explanation of linkage. It is too
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lengthy a task for this paper to trace all the challenges and modifications in the theory. Instead we will focus only on the unit-character assumption, Postulate 2, and segregation, Postulates 5-8. The unit-character concept, Postulate 2, was a simplifying assumption important for obtaining empirical access to the hidden factors. But the direct relation of one trait of a character produced by one factor was too simple, and working out the more complicated relations aided in both the conceptual development of the theory and extended the domain to which it applied. JOHANNSEN (1903, 1909) did experiments in which he selected traits which continuously varied in populations, e.g., the size of beans. Such “continuous” or quantitative variation was not part of the original domain of Mendelism and had been thought to need a different theory to explain it. Johannsen showed that selection was effective only in sorting out different genotypes (a term he coined) which produced the statistically varying characters of the phenotypes. With a clearer understanding of genotype and phenotype, other workers (e.g., EAST, 1910) followed up BATESON’S suggestion (1902) that multiple factors interacted to produce seemingly ‘‘continuous’’ variation. The unit-character concept thus gave way to knowledge of more complicated relations between genes and characters and the domain of the theory was enlarged to include what had once been thought to be an exception. The central claims of the theory are expressed by Postulates 5 and 6, namely that factors are not modified by being together in the hybrid and gametes consist of pure parental factors. These postulates underwent extensive tests with W. E. Castle as their strongest critic. Yet, after years of experiments, he finally came to accept them as a result of a crucial experiment. Since, at the outset, Castle accepted a strong connection between units and characters (Postulate 2), he reasoned in the following way: variation is found in traits which were once present together in the hybrid; thus, the units producing those traits may be inferred to vary also. By selecting individuals with one or other of the extremes of the variation, CASTLE(and PHILLIPS,1914) claimed to be selecting modified units. H. J. MULLER(1914) provided an alternative interpretation: the multiple factor hypothesis already proposed (modification of Postulate 2) could be invoked to postulate “modifying” factors which interacted to produce the variation and which Castle was sorting out into pure lines by selection. Castle recounted the events and issues: Investigations with rats were made by us primarily to ascertain whether Mendelian characters are, as generally assumed, incapable of modification by selection.. My own
.
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early observations indicated that they were modifiable, and to this view I stubbornly adhered, like Morgan in his early opposition to Mendelism, until the contrary view was established by a crucial experiment. (CASTLE,1951, p. 71.)
Experiments were carried out on rats with a black and white pattern, called “hooded” and known to segregate as a Mendelian character. In separate series of experiments, Castle selected in both directions, toward more white and toward more black. Castle continued : The fact of modifiability of the hooded pattern was thus firmly established, but its interpretation was still doubtful. Two interpretations were possible: (1) that the unit character, or unit factor, or gene for the hooded pattern, as it had successively been designated, was itself fluctuating, or (2) that the observed modification had been effected by a modifying influence of other genes than the gene for hooded pattern. Such hypothe tical genes might be designated modifying. Their reality in other genetic material became increasingly clear from 1911 on. (CASTLE,1951, pp. 71-72.)
With hindsight Castle was willing to give the hypothesis of modifying genes more credence than he did while opposing it. In 1919, discussing modifying genes, he said: In some cases [the modyfying genes] are known to have other functions also. Thus the gene proper of one character may function also as a modifying gene for another character. But in the majority of cases the only ground for hypothecating the existence of modifying genes is the fact that characters are visibly modified. As an alternative to the theory of modifying genes, the theory has been considered that genes may themselves be variable and if so, genes purely modifying in function might be dispensed with. (CASTLE,1919, p. 127.)
Castle is here appealing to a criticism of modifying genes as being ad hoc addition to the theory in order to save Postulate 5, namely that genes are not modified by hybridization. He advocated, instead, dropping that postulate in favor of modifiable genes, a hypothesis that may be argued to be the simpler of the two since it fulfills the dictum not to multiply entities beyond necessity. But Muller’s counter to these arguments was that the multiple factor hypothesis was to be preferred because it was consistent with previous work and did not involve the “radical” denial of the conclusion to which “all our evidence points”, namely “the conclusion that the vast majority of genes are extremely constant”, and change only by occasional mutation (MULLER,1914, pp. 61-62). Castle saw very clearly what was needed to perform a test to choose between the hypotheses:
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Since the supposed “factors” of inheritance are invisible, we cannot hope to deal with them directly by experiment, but only indirectly. Our method obviously should be to eliminate all environmental factors so far as possible and also all factors of inheritance except one.. . But it is very difficult to apply this method to specific cases, since when variation is observed it is alway possible to suppose that all factors but one have yet 1916, p. 95.) been eliminated. (CASTLE,
Despite the difficulties, Castle designed and carried out the crucial experiment. He took hooded rats which had been selected and crossed them with another race which lacked the hooded character. If the original hooded trait reappeared in the new hybrids, it was predicted, then selection had not modified the factors ; instead, modifying genes were eliminated by the cross and the original factor was once again producing the hooded trait. The prediction was confirmed. Castle accepted the results as crucial and changed his views: The fact that the hooded gene itself had not been changed as a result of long continued selection was thus demonstrated, but, incidentally mutation had been observed to occur in the hooded gene itself in a single instance. Thus we now knew that in mammals color patterns may be. modified by selection (1) through cumulation of modifying genes, and (2) much more rarely, by isolation of mutations in the particular pattern gene itself. (CASTLE, 1951, p. 72.)
Thus, Castle’s tests of the central claims of the theory (Postulates 4 and 5 ) resulted in their retention. More evidence for the multiple factor hypothesis led to further evidence against the one unit-one character concept. Furthermore, “modifying genes” became part of the multiple factor repertoire. Referring to Table 2, Postulates 5 and 6 were tested and confirmed but those tests led to further change and development of Postulate 2, namely a change from the one unit-one character concept to the proposal of the interaction of multiple factors. Postulates 6, 7 and 8, collectively often called segregation, came under found an exception to the 3:1 ratios that those fire when C U ~ N O(1905) T postulates were constructed to explain. On breeding yellow mice with those having other colors, yellow was dominant. However, when the hybrids were bred, the percentage of yellow in the F, generation was smaller than expected by 2.55 per cent, that is, the ratios were between 2:1 and 3:l. When CuCnot bred the yellows so produced, he was unable to obtain any homozygous yellows, i.e., no pure dominants (no AA) were produced. CASTLEand LITTLE(1910) tested CuCnot’s results with a larger sample and showed that the ratio was closer to 2:l. It was agreed that Postulates 6-8 were the locus of th problem, but CuCnot, Castle
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and Morgan proposed different modifications in the postulates to account for this exception which occupy a scale from a radical change to little change of postulates. Morgan’s entailed the most fundamental modification, a denial of the purity of the gametes in general (Postulate a), with this case providing evidence for their impurity. CU~NOT (1905) left Postulate 6 intact but modified Postulate 8 by proposing a selective fertilization. Castle’s explanation involved the least modification: he left all postulates intact and explained away the exceptional data as an unusual case of inviability of some gametic combinations. The differences among the proposed modifications are instructive, so we will examine these alternatives in more detail. In 1905, as a critic of Mendelism, MORGAN(1905) used CuCnot’s exceptional results to provide evidence against purity of the gametes. He proposed that the factors never segregate into pure parental forms but that the hybrid produces gametes with both dominant and recessive factors present. However, in half the gametes the dominant is latent; in the other half the recessive is latent. In future generations, Morgan predicted, the effect of the hybridization would be evident, some of the previous grandparental characters would reappear. In CuCnot’s exceptional yellow mice such appearances occurred sooner than is usually the case. Morgan, it should be noted, here is giving a theoretical explanation which accords with intuitive suspicions. The Mendelian phenomena are puzzling: is it really possible that a hybrid yellow pea can give rise to a pure breeding green strain that will never show the effects of having been produced by a yellow hybrid? Purity of the gametes entails that result. But when MORGAN(1909) tested his prediction with other strains of mice, he did not find the predicted reappearance of dominants in the recessive strains. His conclusion: “It is evident that the hypothesis failed when tested and must therefore be abandoned.” (MORGAN,1911). CuCnot’s modification left the postulate of purity of the gametes (Postulate 6) intact and instead modified Postulate 8. Not all gametes combine randomly, he claimed ; sometimes selective fertilization occurs. In this case the gametes bearing factors for yellow selectively combine with gametes bearing different factors, but not with each other. (In the symbolism used here: (A+a)(A+a) = no AA, only 2Aa : laa.) MORGAN (1909) criticized Cutnot’s hypothesis of selective fertilization as “a conception entirely foreign to the whole Mendelian scheme. There is no evidence of selective fertilization in this sense known elsewhere and it seems a very questionable advantage to introduce the factor [an unfortunate
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choice of word here] into the Mendelian process.” (MORGAN, 1909,p. 503). Bateson and Punnett also criticized selective fertilization by countering that it would not even explain the exceptional ratios. Since more sperm are found than eggs, there would be sufficient numbers of “non-yellow” sperm to fertilize all the “yellow” eggs so one would expect a 3:l ratio of yellow to other color (e.g., 3Aa : laa) even though no pure yellows were among the proportion of yellows. (BATESON,1909, p. 119.) The lack of pure yellows still required an explanation and Castle’s explanation proved to be the best: the embryos formed by the mating of two gametes with yellow factors were inviable, thus one expects the 2:l ratio that was found. CASTLE(and LITTLE,1910) appealed to smaller numbers of young produced as evidence for this hypothesis and also pointed out that decreased viability had been found in other cases. By 1941 (e.g., MORGAN, 1914) Castle’s explanation of Cudnot’s results had been accepted. Once again, the purity of the gametes and the other segregation postulates survived severe challenges to remain unmodified. Such was not the case with the independent assortment postulates (9-11) which were extensively modified as numerous cases of linkage were found. But a discussion of those modifications is too lengthy for consideration here. A number of features of this case may be noted. The original domain resulting from Mendel’s work with peas was very simple in that it consisted of results from a single species with clear cut character differences. It was a good model system for seeing the need to postulate pure units not interacting in the hybrid. Furthermore, the technique of artificial breeding provided a means of developing a line of research to test the generality of the postulates. The promise of this new theory marked the emergence of the field of genetics to carry out tests of generality. (See DARDEN,1977, 1978 for further discussion.) But, as might have been expected, hereditary phenomena were more diverse. (As in fact Darwin had already known; Darwin did not discover Mendel’s laws, it is plausible to claim, because he knew too much.) Experimental results expanded the domain, necessitating modifications in the postulates. Some were straight forward “complications”, i.e., the original postulate was too simple and was expanded. The change from the unit-character concept to multiple factors is an example. In some cases, that the particular data required modification in a particular postulate was not debated. The postulate had been introduced to account for an item in the domain when that item was modified in the light of new evidence, then the postulate; constructed to explain it was modified.
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In other cases, however, debate focused on which of two postulates to modify. Castle, for example, accepted Postulate 2 that a tight connection existed between the unit and character and argued that variability of character implied variability of the gene, thereby denying Postulate 5. Muller countered by retaining Postulate 5 and denying a strict version of Postulate 2 by postulating effects of modifying genes on a character. This was a legitimate debate about where the locus of modification should be and both modifications had arguments in their favor. Appeals were made to ad hocness, simplicity, and consistency with other results. A crucial experimental test ruled in favor of Muller’s alternative. When Cuenot found an exception to the 3:1 ratios, there was agreement as to which set of postulates needed modifying: Postulates 5-8 which had been constructed to account for the 3:1 ratios. But debate occurred as to which should be modified. The modifications ranged from a very fundamental change to leaving the postulates intact and explaining the case away as an unusual one. Fundamentality here is analyzed as that which would require the most extensive modification of other postulates. If, for example, Morgan’s denial of purity of the gametes had prevailed, it would have had consequences for the postulate claiming that genes are not modified by being together in the hybrid (Postulate 5). However, Cudnot’s proposal of selective fertilization (modification of Postulate 8) left Postulate 5 intact. Castle’s explanation of the exceptions to 3:l ratios left all the postulates intact and explained the particular case as due to an exceptional occurrence. Deviations from the 3:l ratios were not common, lending credence to Castle’s less fundamental change.
’ Dudley Shapere in a recent paper discussed another case (the problem of solar neutrinos)
and made a penetrating comment relevant to this question of fundamentality : If the predictions of our hypotheses disagree with our observations (as they have in the case of solar neutrinos), it is not necessarily the hypothesis under examination (in that case, hypotheses about the processes of stellar energy production) which is at fault; it may be any portion of the theoretical and instrumental ingredients which form the background of the experiment. The point is, of course, not new: but what needs to be made clear and precise is that there exists a rough rationale for the order in which we subject the ingredient accepted ideas to suspicion, and correlatively, an order in which we propose new alternatives. We begin by suspecting those ingredients which are most likely to be a fault, and least costly to give up; if the difficulty persists, the threat penetrates deeper and deeper into the structure of accepted beliefs involved 1980, p. 79). in the purported observation and background. (SHAPERE,
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Conclusion I have examined one case from the history of biology in detail. What
can be concluded on the basis of only one case? I cannot prove that I have found general patterns of reasoning in science. Nor do I have a basis for prescribing how successful science is to be done, a worthy, but perhaps unattainable, goal of philosophy of science. But this case does belie the general claim that one never has any reasons for believing that one rather than another postulate of a theory is in need of modification in the light of new evidence. Furthermore, the reasoning patterns found in this case serve as examples which can be looked for in other cases to test their generality and which suggest strategies for achieving certain goals in theory construction and modification. By viewing theory construction as a modular process, one can see particular postulates are related to particular domain items. If the item changes, then the first locus to be considered for possible modification is the postulate or postulates which account for that item. The case examined shows that scientists usually agree on one or a few postulates as those in need of modification. The task then becomes to devise and choose among alternative ways of modifying that localized postulate. Devising alternatives is the process of discovery ; choosing among them involves various aspects of theory choice or confirmation. Both are intimately connected in producing a modified theory. Although no algorithm is known for producing correct modifications, we can imagine a scientist (more likely a computer program these days) who employs a systematic strategy when faced with exceptions. Several goals are chosen. First, the theory must account for the domain items ; exceptions or additions to the domain may thus necessitate changes in the theory. Secondly, a consistent set of postulates must result from any modification. Thirdly, an exhaustive list of alternative modifications should be devised. In actual practice it is often hard to find one or two, much less produce an exhaustive set. Usually one scientist devises only one alternative and argues for it against competitors proposed by another scientist. However, more expansive minds devise their own alternative hypotheses (e.g., see a recent article by Francis CRICK(1979) on the possible mechanisms for eliminating intervening sequences from genes
*
Work along these lines is being done by Bruce Buchanan of the Computer Science Department at Stanford University, for example in his recent paper (BUCHANAN, 1978).
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prior to their expression). For pragmatic reasons (or maybe something stronger, such as, we can only gain new knowledge when we have a base of older, better established knowledge) an economy of effort is desirable: make the least fundamental modifications first, then proceed to more fundamental ones. With these goals and directives, we can devise a systematic strategy for modifying a theory to account for an exception to a domain item. Such a strategy is given in Table 3. Table 3 Strategy for theory modification I
These steps should be taken in the order given. When an exception to a theory arises: (i) Confirm the experimental results to be sure it is an exception. (ii) See if such a n exception arises only in the system studied (e. g., one character in one species) or whether it is found in other systems (e. g., other characters, other species). (iii) Locate the postulate constructed to account for the domain item to which it is an exception. See if the postulate can be “complicated” to explain the exception (e. g., add another variable). (iv) If (iii) failed to locate only one postulate, then examine the two or more postulates involved. Devise an exhaustive list of modifications possible, making sure that a consistent set of postulates results from each modification. Choose the modification that has least effect on the other postulates and test it experimentally. If it fails, then make the next least fundamental modification, test, and so on. (v) If a modification cannot be used to make new predictions by which it can be tested, because it only accounts for the exception for which it was devised, then it is to be shelved as an unacceptable ad hoc modification.
In summary, this paper has examined questions about reasoning in scientific change. More specifically, it has focused on theory construction and modification and argued that in some cases, at least, rational procedures exist for localizing parts of a theory in need of modification in the light of exceptions. Furthermore, it has suggested a strategy for carrying out those modifications, given certain goals of science, such as accounting for the data and devising consistent theories. Acknowledgment This research was supported by the History and Philosophy of Science Program of the U.S.National Science Foundation (Grant SOC77-23476).
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