The repugnant and the mature in phylogenetic inference: atemporal similarity and historical identity

The significance of ‘‘being similar’’ in the inference of species relationships is refuted once again (see also Hennig, 1966, Phylogenetic Systematics, Univ. of Illinois Press, Urbana, IL). Without merit is Rieppel and Kearney s (Biol. J. Linn. Soc., 2002, 75, 59–82) claim that submitting the relational property of topological similarity, their preferred definition of character, to falsifying tests of similarity benefits that kind of inference. Such a priori uses of similarity, in character analysis, are consistent with observational theory, where a character is defined intensionally in terms of immutable properties. However, the induced hypotheses that follow from this theory, not the deductive test that Rieppel and Kearney wanted, remain controversial, because their predictability is a consequence of circular reasoning, and their projectabality fails empirically from incongruent observation reports. Further, a category mistake is made when the abstract, similarity-defined, group of organisms is reified, as a part of history. In addition, Rieppel and Kearney failed to provide a special theory for similarity, which renders similarity scientifically repugnant (Quine, 1969, Ontological Relativity and Other Essays, Columbia Univ. Press, New York). A return to Hennig s (1966) evolutionary concept of evidence, as transformation series, is urged, and from which a testable character hypothesis can be formulated. There is no one operation for determining character states in this system—it can be anything that leads to the testable hypothesis of synapomorphy, as an historical identity relation. Character compatibility and conjunction, but not similarity, provide a priori tests in phylogenetic character analysis. In turn, the phylogenetic system of inference leads to explanations of homology, as historical identities, which exemplifies the goal of achieving a mature state of historical knowledge (not of Quine, 1969). Such maturity obtains from attempts to falsify hypotheses of species relationships with severely tested evidence, not from induction of ‘‘the’’ observation statement that Rieppel and Kearney sought to justify their true belief in a hypothesis of relationships. 2003 The Willi Hennig Society. Published by Elsevier Inc. All rights reserved. 1 If observation and description constitute science then landscape artists must be scientists. Like Charles Darwin, Willi Hennig attacked the typological thinking of his time and especially that of the German idealistic morphologists/phylogeneticists. In denying evidence of the baupl€ane, i.e., ‘‘typical similarity’’ (e.g., Naef, 1917, p. 16; 1919), Hennig s (1966, p. 9) evolutionary definitions of character and homology were free of idealism and typology, including the explanatory concept of material essentialism (see also * Fax: +734-763-4080. E-mail address: [email protected]. 0748-3007/$ see front matter 2003 The Willi Hennig Society. Published doi:10.1016/S0748-3007(03)00072-0 Mindell and Meyer (2001), but who did not cite Hennig). Indeed, the preeminence of Hennigianism over phenetic and neo-Darwinian systematic approaches has been traced to Hennig s attacks on the significance of being similar (e.g., see Farris, 1977). Why is it then that references to similarity are again becoming commonplace in the systematics literature? Is it merely sloppy language or is it a consequence of some improved According to Hull (1964, p. 317), the three essentialistic tenets of typology are (1) the ontological assertion that forms exist, (2) the methodological assertion that the task of a science is to discern the essences of those things, and (3) the logical assertion concerning definition (i.e., Aristotle s restatement of the inherent essence or nature of a thing). Material (methodological) essentialism is distinct from a purely metaphysical interpretation. by Elsevier Inc. All rights reserved. 3 The contrasting terms acausal/causal, ahistorical/historical, and A.G. Kluge / Cladistics 19 (2003) 356–368 357 insight provided by that kind of science? With regard to the former possibility, Quine (2000, p. 289, my italics; see also Goodman, 1970) offered ‘‘In daily discourse we all do indeed persistently declare things to be similar in various degrees, and a definition of that relation is notoriously lacking.’’ And to which Quine added that ‘‘It is an unconscious projection of perceptual similarity.’’ Earlier, Quine (1969) had made the point that perceived similarity can be well understood only in the context of special circumstances, where the concept of similarity is tied to the notion of natural necessity or lawfulness peculiar to the science at hand; minimally, a theory is required (Goodman, 1970, p. 22). For example, the necessity on which the Periodic Table is now founded is atomic number (the number of positively charged protons in their nucleus), and it is only after a given science s special theory has been hypothesized, which is the case with atomic theory in the above example, that similarity can be tested in light of that necessity. Perhaps it is the increasing emphasis on the supposed critical nature of the ‘‘test’’ that accounts for the mounting references to similarity in phylogenetic inference. Indeed, several authors explored the significance of the test of similarity, including Bock (1977, p. 882), Platnick (1978, p. 366), Patterson (1982a, 1988), and Lipscomb (1992). Most recently, Rieppel and Kearney (2002, hereafter RK) argued at considerable length for formulating and testing character hypotheses in terms of similarity. RK s lengthy contribution will be used as the basis for revisiting character similarity and testability, followed by an evolutionary hypothetico-deductive definition of character and homology, where I ascribe no special significance to similarity, neither conceptually nor operationally. My understanding of the issues relating to similarity has benefited from distinguishing between ‘‘repugnant’’ and ‘‘mature’’ (Quine, 1969). As I will further explain below, scientists must have an aversion to similarity in the absence of a special accompanying theory. Also, according to Quine (1969), once a disposition term is legitimized by defining the relevant similarity standard, with regard to some special theory, the disposition is apt to become known, thereby bypassing the need to refer to similarity. Thus, mature sciences are not expected to retain their highly specific similarity notions, because those notions are not theoretically important. RK s research program concerning similarity will also be evaluated against a theory of scientific progress of this kind. The distinction between abstract and concrete is also important to my position on similarity and testability, for which the following clarifications are offered (see 2 Quine s use of the term ‘‘repugnant’’ is repeated herein, not because it is gratuitous or condescending, but because it underscores the failure of observational theory in science, where pure observation reports are used to erect an inductivist epistemology. also Frost and Kluge, 1994). Various references will be made to abstractions in the text to follow. While ‘‘class’’ will refer to conceptualizations of all ‘‘kinds,’’ ‘‘natural kind’’ is restricted to the kind of class that exhibits nomological, lawful, necessity. A natural kind is defined with regard to properties that are both necessary and sufficient for membership, and its essence involves a generalization that is not accidental and explanatory. Natural kinds are then universals, matters of intensional definition, which are spatio-temporally unrestricted. The concept of essentialism applies to the universal ‘‘Forms’’ of Aristotle, but not to the spatio-temporally restricted thing (Hull, 1964, 1978). Curiously, Mahner and Bunge (1997, p. 221) accepted the nomological necessity of natural kinds, but concluded that ‘‘naturalness comes in degrees’’! With regard to the concrete, these are the spatio-temporally restricted, i.e., empirical things or objects. Things, such as organisms and species, are selfdefining, and reference to them is made with regard to extension. For further details concerning intension and extension see Kluge (2004, Table 1.1; see also Frost and Kluge, 1994). Atemporal similarity RK emphasized the significance of falsification in phylogenetic inference (for this recurrent theme see also Rieppel, 1980b, p. 317; 1988, p. 42, 47, 59, Fig. 4). In particular, they attempted to demonstrate how the data used to test species relationships might be rendered more severely tested by employing a similarity definition of character that is empirically falsifiable. Effectively, their claim was that phylogenetic hypotheses will be more convincingly tested the more effort put toward a priori character analysis involving tests of similarity. The empirically testable nature of the ‘‘critical’’ discussion to which they frequently appealed is undeniable (pp. 61–62; italics in the original). As they stated: ‘‘A meaningful character is thus based upon a character description that can in itself be critically evaluated, tested and potentially rejected. . . . The critical discussion entails attempted refutations, including empirical tests (Popper [1972, p. 80]).’’ Clearly, RK enjoined a falsifying test of similarity in their recognition of a character (see also below). The significance of falsifiability is certainly not a new idea in science (Popper, 1959; see also Farris et al., 2001; Kluge, 2001, 2002, 2003; see, however, Patterson, 1978, atemporal/temporal employed herein follow previous usage (e.g., Rieppel and Grande, 1994, pp. 229–230; Brady, 1994). Acausal/ ahistorical/atemporal and causal/historical/temporal refer not to the nature of the character but to the kind of inference in which the character is used, such as pattern cladistics and phylogenetic systematics, respectively. 358 A.G. Kluge / Cladistics 19 (2003) 356–368 1982c) nor is the point of view that similarity may be an operational part of character analysis (e.g., Wiley, 1975, p. 235; Bock, 1977, p. 882; Platnick, 1978, p. 366; 1982, p. 283; Cracraft, 1979, p. 33; Rieppel, 1980b, p. 315; Patterson, 1982a, pp. 46, 47, 1988; Lipscomb, 1992; Brower, 2000a,b; Whiting et al., 2003). What is novel in RK s thesis is their claim that a character is both definable and falsifiable with regard to similarity (pp. 61–63, 66, and elsewhere). Consider RK s definition of character (p. 61): ‘‘a logical relation established between intrinsic attributes of two or more organisms that is rooted in observation.’’ This is what I will call an operational/phenetic definition of character, where the datum, dp, is an observed property of an organism, a property instantiated by an organism (pace Woodger, 1952). This definition is an ordinary categorical proposition, which follows from facts—simple atomic propositions, such as ‘‘Olivier likes wine.’’ As for an example of a more complex proposition, one familiar to comparative biologists, ‘‘organism A has part X with property 1,’’ or more specifically, ‘‘this snake has a caudal vertebra with a hemapophysis,’’ or ‘‘this snake s ND2 gene sequence has an adenine at nucleotide position 297.’’ So defined, a character involves a basic statement (proposition), which is sensed and becomes the content of a declarative sentence employed in its typical form. As an aside, these examples illustrate a basis for distinguishing a character (part X) from its states (property) (contra Bock, 1973, p. 387; Patterson, 1982a, p. 25; Platnick, 1979). The theory of propositions concerns only the nature of the subject and the predicate, which in the case of a phylogenetic character refer to the organism and the particular property and which are logically connected by referring to some part of the organism. A predicate is, by extension, the class of objects that it describes. For example, the extension of hemapophysis is the class of hemapophysis things. On the other hand, the properties of an object are intensional. Intension is the action that picks out precisely definable circumstance(s), the condition(s) in the present circumstance that must be satisfied to be described by the predicate. For example, the intension of hemapophysis might involve any number of assessments, as per intrinsic properties (e.g., mass, composition, development), relational properties (e.g., topological), primary properties (does not require a sentient power), secondary properties (phenomenal; requires a sentient power), qualitative properties, quantitative properties, etc. (there is no generally agreed upon list or classification of properties). 4 This definition is incomplete without reference to some property to which similarity can be referred. RK made such references elsewhere in their paper, such as repeatedly stating their preference for the relational property of topological similarity (p. 64). A claim that one observes two or more organisms with similar properties is to maintain that those organisms are members of the same intensionally defined class, Dp. Mahner and Bunge (1997, pp. 219–220) used not only the ‘‘scopes of properties’’ to delimit such classes but also the concomitance of different properties as the basis for claiming the lawfulness of those that are natural kinds (see, however, Sober, 1981). Projectability, a property of predicates, is the degree to which past instances can be taken as guides to future ones. For example, that all those individuals of the class dog that have been observed thus far are four-legged is considered a plausible basis for predicting that all dogs observed in the future will have four legs. Thus, fourleggedness is a projectable predicate. Whether it is ‘‘kinds’’ or ‘‘natural kinds,’’ an intension of similarity is involved in the classification. Each usage of a proposition is true or false, which is not known in any particular instance. ‘‘Testing’’ dp usually begins with what the predicate is, with regard to its relational and/or intrinsic (e.g., topological and developmental) properties, followed by what that predicate s relation is among organisms, Dp. In the sense of the theory of propositions, character analysis is concerned with both individual and generic properties— what makes an organism an organism and what makes an organism a member of a class of equivalent organisms of some kind, respectively. It is on the basis of this brief review of observational theory (see also Kluge, 2004) that the details of RK s thesis, that similarity constitutes the basis for character formulation and its falsifiability, will be evaluated. RK argued the need for testing observation statements, because those propositions are the only basis for determining object-level reality, what a character is, and what the relation of a character is among organisms. According to these authors then, only by having attempted to falsify dp and Dp can the results of phylogenetic analysis be justified, such as provided by a character congruence analysis. What RK suggested, as character analysis, is an exercise in the Popperian logic of scientific discovery (Popper, 1972, p. 80; Kluge, 2002), and there can be no recourse to the ‘‘interpretation functions’’ and ‘‘truth values’’ (truth table) of the theory of propositions. The falsifying tests of dp and Dp must come from the observation hypotheses themselves, i.e., the properties and the relation of those properties among organisms. RK s definition of character is not unique in systematics or phylogenetic inference more specifically. For example, as Lipscomb (1998, p. 53, boldface in the original; see also Grande and Rieppel, 1994, p. 261; Rieppel, 2002, p. 195) stated, ‘‘[t]he observable parts, or attributes, of organisms which can be examined for similarity or difference are called characters.’’ Likewise, Kitching et al. (1998, p. 201) held a A.G. Kluge / Cladistics 19 (2003) 356–368 359 character to be ‘‘an observable feature of an organism used to distinguish it from another.’’ Even the pheneticists definition is much the same, that a character is operationally homologous if the states are ‘‘very much alike in general and in particular’’ (Sokal and Sneath, 1963, p. 70). RK argued that character hypotheses (what they called primary conjectures of homology; see de Pinna, 1991) should be based on the classical observational techniques of comparative morphology, emphasizing the relational property of topological similarity (see also Russell, 1916, p. 246; Jardine, 1969, p. 328), and less often according to the ‘‘subsidiary’’ techniques of assessing special similarity and intermediate form (see also Hennig, 1966, p. 94), because those three techniques provide a priori tests, with the unfalsified shared similarities becoming more severely tested evidence. Paraphrasing (p. 72), RK s favored test of similarity of primary homology involved the establishment of one-to-one relationships of structures observed on organisms, and a falsifying test was ‘‘the lack of topological correspondence’’ (p. 70). Summarizing their position (p. 72), they stated that ‘‘[t]he type of testing described above for conjecturing [primary] homology is rigorous and requires in-depth and timeconsuming study of structural complexity, which is at odds with recent trends that diminish the role of careful character analysis in morphological systematics.’’ In the present context, complexity is understood (usually) with regard to the relational properties of an organism s anatomical parts, the more such relations can be specified the greater is the recognized degree of complexity. The authors intention to provide more severely tested evidence in phylogenetic inference, not casually identified relational properties or systematically biased basic statements, is considered laudable (e.g., see Rieppel et al., 2002). However, significant problems exist in what they, and many others, have emphasized as significant in the definition of character and its tests, namely similarity. Also, there is the more general philosophical issue of whether their research program is really concerned with ‘‘knowing’’ in the objective knowledge sense of Popper or whether it is just another exercise in justifying true belief in a hypothesis of relationships, with regard to knowing the ‘‘truth value’’ of characters. 5 The term ‘‘connectivity’’ is often associated with the concept of topology, but not always with the same meaning. As RK (p. 66; see also Rieppel, 1980a, p. 85; 1989, p. 54) stated, ‘‘[a]s ontogeny adds a dynamic component to topology, the latter becomes connectivity,’’ whereas according to Rieppel (1990, p. 302; 1994, pp. 71–72), the connectivity of topology originated with Geoffroy Saint-Hilaire s explanation ‘‘principe des connexions’’—compensated change in structures due to the constancy of blood volume. Normative problems RK were not always clear that similarity resides in the properties of organisms. Even their character definition lacks that necessary reference (p. 61). This deficiency is also true of many other character definitions (e.g., Grande and Rieppel, 1994; Kitching et al., 1998; Lipscomb, 1998; Rieppel, 2002). The problem is this: things do not contain similarity. It is the particular properties in a similarity relation that gives meaning to the comparison. As Ghiselin (1966, pp. 212–213) succinctly put it: ‘‘It is one thing to say x is similar to y in possessing property a. It is another to say that x is more similar to y than to z, or that x is twice as similar as y. Without reference to intrinsic properties, these latter two statements are pure nonsense.’’ In other words, the proposition must be complete, as in ‘‘organism A has part X with property 1.’’ Likewise, RK s basic thesis with regard to the testability of observation proposition is flawed fundamentally, because those statements are not falsifiable, neither dp nor Dp. It is the inductive power of similarity—prediction and projectability—that is emphasized in tests of observation hypotheses (e.g., Goodman, 1965, 1970, p. 23; see, however Sober, 1981, p. 159), not their Popperian falsification, to which RK repeatedly referred. The testability of a Popperian hypothesis has to do with its improbability, not the likelihood of it being verified (Kluge, 2001; contra de Queiroz and Poe, 2003). However, even if RK had settled for a test of induction (see p. 66), those kinds of observation hypotheses come with the well-known criticism of circularity—the idea of similarity is understood with regard to shared properties, and the idea of predictive power is understood with regard to the capacity to facilitate inference of additional properties. Furthermore, similarity and predictive power do not necessarily distinguish a real property from a pseudoproperty (Goodman, 1965). As Sober and Lewontin (1982, pp. 176–177) pointed out, ‘‘a predicate can pick out a real (causally efficacious) property in one context and fail to do so in another,’’ and ‘‘the point is that a certain natural interpretation of a biological phenomenon helps to indicate how we ought to understand a rather abstract metaphysical issue,’’ such as this. Returning to Quine (1969; see also Goodman, 1970; Sober, 1981), what is necessary for a realistic interpretation of similarity is a special theory that can explain similarities. Also, as will be discussed further, projectability fails, because it does not cover the observed patterns of similarity that are inconsistent. For example, the projectable predicate of four-leggedness of the class dogs does not predict a three-legged dog. Unfortunately, RK did not specify a special theoretical meaning in their definition of character, and therefore it is difficult, if not impossible, to evaluate the application of any kind of definition of character and 360 A.G. Kluge / Cladistics 19 (2003) 356–368 test that they might have proposed. Such a significant lapse is curious, because RK did point out (p. 62; see also Rieppel, 1989, pp. 54, 56; 1991, p. 93; 1994, pp. 69–70) that ‘‘theory . . . always precedes observation.’’ Nonetheless, the relation that RK had in mind was something that they argued is to be discovered by empirical test, and therefore a theoretical basis for the observation of similarity must be specified a priori, as part of the explanans of whatever scheme of inference is involved. Without an underlying theory of similarity, their thesis of testing it can have no real merit (Nagel, 1979, pp. 79–105; Beatty, 1982, p. 31; Grant, 2002, p. 96; see also Brady, 1983, pp. 57–58). Clearly, a temporal/historical, transformational relation among character states (e.g., Hennig, 1966; Platnick, 1979, 1982)—an evolutionary interpretation of character—was not part of RK s definition of character (see also Rieppel, 2002; Patterson, 1982b,c). To be sure, as they emphasized (pp. 77–79), their definition of character is purified of that assumption (see also Rieppel, 1980a, 1991, p. 94, 98; 1992, 2002; Patterson, 1982a,b,c, 1988, p. 304; Brady, 1983, p. 59; Lipscomb, 1992; Brower, 2000a,b), since it is only after the observed similarities among organisms have been corroborated with character congruence that an atemporal relation may be ‘‘hypothetically explained as an historical relation.’’ This is the familiar pattern cladistic thesis (e.g., Rieppel, 1991, p. 98; 1992, p. 713; see also Brady, 1983; Patterson, 1982a,b, p. 306; 1983, 1988; Brady, 1985, p. 119; Brower, 2000a,b, 2002). Reiterating RK s position, the theory and practice of establishing an atemporal (acausal) relation in evidence precedes that of establishing temporal (causal) historical relationships among species, where the former is based on intensionally defining a character and testing it in terms of similarity. The crux of this normative problem, as Quine (2000) explained, is that there is no general theory of causal determination for similarity/similarities, contrary to what one might think, given the terms frequent use in ordinary, technical, and even scientific discourse. Finally, RK (pp. 59–60, 64, 70) repeatedly mentioned that recognizing a character, dp, involved the problem of ‘‘abstraction.’’ Their concern is well founded, of course, but the abstraction for which they expressed concern comes from having intensionally defined characters on 6 Some pattern cladists (e.g., Brower, 2002, p. 223) have denied making the assumption of ‘‘descent with modification,’’ only to follow with the claim that ‘‘the [pattern] cladistic method is based upon the minimization of ad hoc hypotheses of observed character state transformation . . .’’ What ‘‘transformation’’ means in the context of species relationships, if not evolution, remains a mystery (e.g., see also Brower, 2000b, p. 13, 15). 7 An especially clear and concise description of pattern or transformed cladism can be found in a little-cited paper by Patterson (1982b, pp. 304–306). 8 This does not deny perceptual theory. the basis of the similarity of properties, i.e., their determination of an abstract (class) concept. As I will emphasize below, abstraction does not accompany all approaches to character delimitation, such as those concerned with historical things. Descriptive problems The descriptive issues relating to RK s position concern the nature of similarity and the definition of the kind of quality space (the parameters of the similarity space), the totality of the space, and the identification of the paradigm object (what is being compared for their similarities—x and y are more similar to each other than either is to z, etc.). As already noted above, to make a similarity comparison is problematic, because similarity is ‘‘merely the subjective impression of resemblance . . . similarities are real, similarity is subjective’’ (Ghiselin, 1966, p. 213). Moreover, even quantified similarity may be judged subjective, because it is without extensive orderings, which is to say that similarity, as such, does not obey the associative or commutative laws of mathematics. Repeatability, including that which is judged from the consensus of opinion that is expected from intersubjectivity (Rieppel, 2002), does not necessarily overcome the subjective nature of what is claimed in a similarity relation. For example, while there may be subjective agreement as to redness, not all instances of red are precisely the same. Also, as noted above, RK argued the significance of three similarity space qualities—the relational property of topological similarity, special similarity, and intermediate form. Here a problem obtains whether those qualities are used separately or whether some overall quality of the similarity space is specified, as for example Carine and Scotland (1999) employed in their modified version of three-taxon analysis (Kluge and Farris, 1999). To begin with, the basis for topology being considered the most important property on which to evaluate similarity, as argued by RK (see review by Rieppel, 1980b, p. 315), has yet to be justified with regard to it actually having a lower error rate in the identification of homologues, not withstanding Brady s (1994) attempt to define ‘‘transformation’’ in static terms, with the principle of ‘‘topological invariance’’ as its cause. But, in any case, as Russell (1916; see also Riedl, 1975; Rieppel, 1988, pp. 45, 52) pointed out, the relational property of topology presupposes the same measure of similarity— that of similarity of position—and that leads to a methodological regress, arguably an infinite one. Thus, any particular relational property of topology is in principle founded on a notion of overall (topological) similarity. To involve the qualities of special similarity and intermediate form in induction, including that of A.G. Kluge / Cladistics 19 (2003) 356–368 361 connectivity (the ontogenesis kind, not that of topological invariance, sensu Geoffroy Saint-Hilaire, 1818, p. xxvi), some measure of topological correspondence among organisms must have already been established. That being the case, I fail to see how RK can have argued that, with the failure of the test of character hypotheses according to the relational property of topological similarity, the ‘‘other’’ techniques can be used as tests. Logically at least, what they claimed as ‘‘beyond topology’’ cannot be divorced from suppositions of the relational property of topological similarity (pp. 75–77). My point is that the tests of connectivity (ontogenesis), special similarity, and intermediate form that RK advocated are not independent of their test of the relational property of topological similarity. If there is to be real meaning to discovery in a priori character analysis then all tests must be independent, and the more the better (Kluge, 1989, 2003). Arguably, RK can claim only one ‘‘test,’’ one of overall (topological) similarity. That the ‘‘frame of reference’’ for the relational property of topological similarity (Rieppel, 1988) may be defined by connectivity (ontogenesis), special similarity, and intermediate form does not mean that there are additional, independent, tests of similarity involved. While some may be satisfied with metaphor and simile in perceptual theory (see, however, Goodman, 1970, p. 22), the scientific recognition of what a character is requires testing, and the independence of those tests is critical. If the similarity space were to be defined in more than one dimension, as discussed above and as might be summarized by a multivariate statistic such as principal components, then it would be an n-dimensional kind of similarity. However, with regard to the totality of such a similarity space, the problems of holism are confronted, as is the arbitrariness of selecting just some part of that space to observe and describe. A fundamental question that RK did not address is how much similarity is enough when a relational property of topological similarity is stated? As Popper (1957, p. 77) discussed, If we wish to study a thing, we are bound to select certain aspects of it. It is not possible for us to observe or to describe a whole piece of the world, or a whole piece of nature; in fact, not even the smallest whole piece may be so described, since all description is necessarily selective. . . . [For example,] a piece of the world, such as a sparrow nervously fluttering about, may be described by the following widely different propositions, each corresponding to a different aspect of it: This bird is flying!— There goes a sparrow! — Look, here is an animal! — Something is moving here. — Energy is being transformed here. — This is not a case of perpetual motion. — The poor thing is frightened! It is clear that it can never be the task of science to attempt the completion of such a list, which is necessarily in-