Darwin’s two theories, 1844 and 1859

Darwin’s first two, relatively complete, explicit articulations of his theorizing on evolution were his Essay of 1844 and On the Origin of Species published in 1859. A comparative analysis concludes that they espoused radically different theories despite exhibiting a continuity of strategy, much common structure and the same key idea. Both were theories of evolution by means of natural selection. In 1844, organic adaptation was confined to occasional intervals initiated and controlled by de-stabilization events. The modified descendants rebalanced the particular “plant and animal forms … unsettled by some alteration in their circumstances.” But by 1859, organic adaptation occurred continuously, potentially modifying the descendants of all organisms. Even natural selection, the persistent core of Darwin’s theorizing, does not prove to be a significant basis for theory similarity. Consequently, Darwin’s Origin theory cannot reasonably be considered as a mature version of the Essay. It is not a modification based on adjustments, further justifications and the integration of a Principle of Divergence. The Origin announced a new “scientific paradigm” while the Essay did little more than seemingly misconfigure the operation of a novel mechanism to extend varieties beyond their accepted bounds, and into the realm of possible new species. Two other collections of Darwin’s theorizing are briefly considered: his extensive notes of the late 1830s and his contributions to the famous meeting of 1 July 1858. For very different reasons, neither constitutes a challenge to the basis for this comparative study. It is concluded that, in addition to the much-debated social pressures, an unacknowledged further reason why Darwin did not publish his theorizing until 1859, could have been down to his perceptive technical judgement: wisely, he held back from rushing to publish demonstrably flawed theorizing.     

Infinite Graphs in Systematic Biology, with an Application to the Species Problem

We argue that C. Darwin and more recently W. Hennig worked at times under the simplifying assumption of an eternal biosphere. So motivated, we explicitly consider the consequences which follow mathematically from this assumption, and the infinite graphs it leads to. This assumption admits certain clusters of organisms which have some ideal theoretical properties of species, shining some light onto the species problem. We prove a dualization of a law of T. A. Knight and C. Darwin, and sketch a decomposition result involving the internodons of D. Kornet, J. Metz and H. Schellinx. A further goal of this paper is to respond to B. Sturmfels’ question, “Can biology lead to new theorems?”     

What is a species? Essences and generation

Arguments against essentialism in biology rely strongly on a claim that modern biology abandoned Aristotle’s notion of a species as a class of necessary and sufficient properties. However, neither his theory of essentialism, nor his logical definition of species and genus (eidos and genos) play much of a role in biological research and taxonomy, including his own. The objections to natural kinds thinking by early twentieth century biologists wrestling with the new genetics overlooked the fact that species have typical developmental cycles and most have a large shared genetic component. These are the “what-it-is-to-be” members of that species. An intrinsic biological essentialism does not commit us to Aristotelian notions, nor even modern notions, of essence. There is a long-standing definition of “species” and its precursor notions that goes back to the Greeks, and which Darwin and pretty well all biologists since him share, that I call the Generative Conception of Species. It relies on there being a shared generative power that makes progeny resemble parents. The “what-it-is-to-be” a member of that species is that developmental type, mistakes in development notwithstanding. Moreover, such “essences” have always been understood to include deviations from the type. Finally, I shall examine some implications of the collapse of the narrative about essences in biology.     

Mayr's view of Darwin: was Darwin wrong about speciation?

We commonly read or hear that Charles Darwin successfully convinced the world about evolution and natural selection, but did not answer the question posed by his most famous book, ‘On the Origin of Species …’. Since the 1940s, Ernst Mayr has been one of the people who argued for this point of view, claiming that Darwin was not able to answer the question of speciation because he failed to define species properly. Mayr undoubtedly had an important and largely positive influence on the study of evolution by stimulating much evolutionary work, and also by promoting a ‘polytypic species concept’ in which multiple, geographically separated forms may be considered as subspecies within a larger species entity. However, Mayr became seduced by the symmetry of a pair of interlocking ideas: (1) that coexistence of divergent populations was not possible without reproductive isolation and (2) reproductive isolation could not evolve in populations that coexist. These beliefs led Mayr in 1942 to reject evidence of the importance of intermediate stages in speciation, particularly introgression between hybridizing species, which demonstrates that complete reproductive isolation is not necessary, and the existence of ecological races, which shows that ecological divergence can be maintained below the level of species, in the face of gene flow. Mayr's train of thought led him to the view that Darwin misunderstood species, and that species were fundamentally different from subspecific varieties in nature. Julian Huxley, reviewing similar data at the same time, came to the opposite conclusion, and argued that these were the intermediate stages of speciation expected under Darwinism. Mayr's arguments were, however, more convincing than Huxley's, and this caused a delay in the acceptance of a more balanced view of speciation for many decades. It is only now, with new molecular evidence, that we are beginning to appreciate more fully the expected Darwinian intermediates between coexisting species. © The Author. Journal compilation © 2008 The Linnean Society of London, Biological Journal of the Linnean Society, 2008, 95 , 3–16.     

A Delicate Adjustment: Wallace and Bates on the Amazon and “The Problem of the Origin of Species”

For over a century it has been believed that Alfred Russel Wallace and Henry Walter Bates set out for the Amazon in 1848 with the aim of “solving the problem of the origin of species”. Yet this enticing story is based on only one sentence. Bates claimed in the preface to his 1863 book that Wallace stated this was the aim of their expedition in an 1847 letter. Bates gave a quotation from the letter. But Wallace himself never endorsed or repeated this story. Many writers have acknowledged that this letter still survives. Yet the wording is different from that quoted by Bates and the letter says nothing of an expedition. It is argued that the sentence given by Bates is not a genuine quotation from this or any other Wallace letter but was modified by Bates to promote his own reputation. More significantly, this leads to the conclusion that there was a very sudden and dramatic shift in the way species were thought of and discussed after Darwin’s Origin of species appeared. Something called “the problem of the origin of species” (and similar variants) never occurred before Darwin’s book but exploded in frequency immediately after it. A profound change in how species origins were discussed happened which no one seemed to notice.     

Darwin,the amphibians,and the natural selection

A critical review of Darwin's publications shows that he did not dissert much about amphibians, in comparison with the other tetrapods. However, in “A Naturalist's Voyage round the World”, Darwin described for the first time several amphibian species and was surprised by their peculiar way of life, terrestrial or euryhaline. These amphibian observations around the world led Darwin to discuss evolutionnary notions, like developmental heterochronies or evolving convergences, and later to illustrate his famous natural selection theory. This is confirmed, for example, by the publication of “On the Origin of Species” where Darwin ironically questioned creation theory, trying to explain the absence of amphibians on oceanic islands. Lamarck also considered amphibians as relevant material to illustrate his theory of acquired character heredity. These historical uses of lissamphibians as evolutionary models have been mostly realized before any amphibian fossil discovery, i.e. out of a palaeontological context.     

Darwin's species category realism

Ever since Charles Darwin's On the Origin of Species was published, the received view has been that Darwin literally thought of species as not extra-mentally real. In 1969 Michael Ghiselin upset the received view by interpreting Darwin to mean that species taxa are indeed real but not the species category. In 1985 John Beatty took Ghiselin's thesis a step further by providing a strategy theory to explain why Darwin would say one thing (his repeated nominalistic definition of species) and do another (hold that species taxa are real). In the present paper I attempt to take this line of interpretation to a new level. Guided by the principle of charity, I provide and analyze a considerable amount of evidence from Darwin's mature writings (both private and published) to show that (contra Ghiselin and Beatty) Darwin did not simply accept the species delimitations of his fellow naturalists but actually employed, repeatedly and consistently, a species concept in a thoroughly modern sense, albeit with an implicit definition, a concept uniquely his own and fully in accord with his theory of evolution by natural selection. This implicit concept and definition is carefully reconstructed in the present paper. A new strategy theory is then provided to account for why Darwin would define species (both taxa and category) nominalistically on the one hand but delimit species realistically on the other.     

Microbiology and the species problem

This paper examines the species problem in microbiology and its implications for the species problem more generally. Given the different meanings of ‘species’ in microbiology, the use of ‘species’ in biology is more multifarious and problematic than commonly recognized. So much so, that recent work in microbial systematics casts doubt on the existence of a prokaryote species category in nature. It also casts doubt on the existence of a general species category for all of life (one that includes both prokaryotes and eukaryotes). Prokaryote biology also undermines recent attempts to save the species category, such as the suggestion that species are metapopulation lineages and the idea that ‘species’ is a family resemblance concept.     

Darwin's principles of divergence and natural selection: Why Fodor was almost right

Darwin maintained that the principles of natural selection and divergence were the “keystones” of his theory. He introduced the principle of divergence to explain a fundamental feature of living nature: that organisms cluster into hierarchical groups, so as to be classifiable in the Linnaean taxonomic categories of variety, species, genus, and so on. Darwin’s formulation of the principle of divergence, however, induces many perplexities. In his Autobiography, he claimed that he had neglected the problem of divergence in his Essay of 1844 and only solved it in a flash during a carriage ride in the 1850s; yet he does seem to have stated the problem in the Essay and provided the solution. This initial conundrum sets three questions I wish to pursue in this essay: (1) What is the relationship of the principle of divergence to that of natural selection? Is it independent of selection, derivative of selection, or a type of selection, perhaps comparable to sexual selection? (2) What is the advantage of divergence that the principle implies—that is, why is increased divergence beneficial in the struggle for life? And (3) What led Darwin to believe he had discovered the principle only in the 1850s? The resolution of these questions has implications for Darwin’s other principle, natural selection, and permits us to readjust the common judgment made about Jerry Fodor’s screed against that latter principle.     

Darwin's sexual selection: Understanding his ideas in context

Darwin's writings need to be seen in their fullness, as opposed to quote-mining individual sentences without the context of his passages. Sometimes Darwin wrote at length, apparently favorably, about ideas that he subsequently undermined, replacing them with a more integrative view that reflected his own broad compass. Darwin understood that nature is not simple, that not all members of a group may have evolved under the same selective regime, and that variation of all kinds is fundamental to selection in its several forms. Sexual selection requires sexual dimorphism; it is not centred on variation within sexes but on selection for the ability to acquire mates. “Mutual sexual selection” was rejected by Darwin for every species except humans. Mating success is not a matter of mere numbers but of the transmission of the most attractive features to the opposite sex. The term “sexual selection” should only be used when one sex uses a feature not present in the other sex to attract mates or repel rivals for mates.     

The individuality of the species: A Darwinian theory? — from Buffon to Ghiselin, and back to Darwin

Since the 1970s, there has been a tremendous amount of literature on Ghiselin's proposal that “species are individuals”. After recalling the origins and stakes of this thesis in contemporary evolutionary theory, I show that it can also be found in the writings of the French naturalist Buffon in the 18th Century. Although Buffon did not have the conception that one species could be derived from another, there is an interesting similarity between the modern argument and that of Buffon regarding the “individuality of species’. The analogy is strong enough to force us to recognize that genuine evolutionary (or Darwinian) questions might be of secondary importance in the discussion. In consequence, the third section of the paper proposes an alternative schema for the “logical structure” of the Darwinian concept of species. Darwin distinguished the problem of the designation of a concrete species, and the problem of its signification of species within his theory of descent? The resulting notion of species involves a logical structure based on the fusion of the logical operations of classification and ordering. The difficulty — and interest — is that this interpretation of species does not entail any precise operational definition of species; it can only tell us what the ultimate signification of classification is within the theory of descent with modification through natural selection.     

A commentary on “The Formal Darwinism Project”: there is no grandeur in this view of life

The Formal Darwinism Project is an attempt to use mathematical theory to prove the claim that fitness maximization is the outcome of evolution in nature. Grafen’s (2014, p. 12) conclusion from this project is that “….there is a very general expectation of something close to fitness maximisation, which will convert into fitness-maximisation unless there are particular kinds of circumstances—and further, that fitness is the same quantity for all genetic architectures.” Grafen’s claim appears to mean to him that natural populations are expected to contain individuals whose traits are optimal, i.e., any given trait outperforms all reasonable alternatives. I describe why Grafen’s attempt can never provide a meaningful expectation as to the ubiquity of optimal traits in nature. This is so because it is based upon a misconception of the relationship between theory and empirical analysis. Even if one could use theory in the way Grafen proposes, I describe how his theory is causally incomplete. Finally, I describe how Grafen’s conceptual framework is ambiguous. The Formal Darwinism Project has been inspired by “On The Origin of Species” by Darwin. The great lesson of this book was Darwin’s demonstration of the necessary dialog between theory and data, with each influencing and being influenced by the other. Grafen’s Formal Darwinism Project, an attempt to create understanding of nature by removing data from this dialog, reflects a failure to understand Darwin’s great lesson.     

At home among strangers: Alfred Russel Wallace in Russia

Alfred Russel Wallace (1823–1913) was an influential figure within Russian pre-Synthetic evolutionary biology, i.e. the time period before the Synthetic Theory of Evolution was established (ca. 1880–1930s). His major works were translated into Russian and his general ideas were read and discussed by both insiders and outsiders of scientific evolutionism. At the same time, Wallace played a controversial role in the growth of Darwinism in Russia, and Charles Robert Darwin (1809–1882) has eclipsed Wallace in his influence on Russian evolutionary thinking. In this paper we briefly outline Wallace’s impact on Russian pre-Synthetic scientific evolutionism and its general intellectual climate. We demonstrate that both Russian pro-Darwinian evolutionists and anti-Darwinians (scientific anti-Darwinians as well as creationists) were fully aware of Wallace’s contributions to the development of evolutionary theory. Yet, Wallace’s radical selectionism, as well as his controversial arguments for “design in nature”, predetermined his special place within the Russian intellectual landscape.     

The proximate/ultimate distinction in the multiple careers of Ernst Mayr

Ernst Mayr's distinction between “ultimate” and “proximate” causes is justly considered a major contribution to philosophy of biology. But how did Mayr come to this “philosophical” distinction, and what role did it play in his earlier “scientific” work? I address these issues by dividing Mayr's work into three careers or phases: 1) Mayr the naturalist/researcher, 2) Mayr the representative of and spokesman for evolutionary biology and systematics, and more recently 3) Mayr the historian and philosopher of biology. If we want to understand the role of the proximate/ultimate distinction in Mayr's more recent career as a philosopher and historian, then it helps to consider hisearlier use of the distinction, in the course of his research, and in his promotion of the professions of evolutionary biology and systematics. I believe that this approach would also shed light on some other important “philosophical” positions that Mayr has defended, including the distinction between “essentialism: and “population thinking.”     

The origin of Darwin’s “abominable mystery”

The phrase “Darwin’s abominable mystery” is frequently used with reference to a range of outstanding questions about the evolution of the plant group today known as the angiosperms. Here, I seek to more fully understand what prompted Darwin to coin the phrase in 1879, and the meaning he attached to it, by surveying the systematics, paleobotanical records, and phylogenetic hypotheses of his time. In the light of this historical research, I argue that Darwin was referring to the origin only of a subset of what are today called angiosperms: a (now obsolete) group equivalent to the “dicotyledons” of the Hooker and Bentham system. To Darwin and his contemporaries, the dicotyledons’ fossil record began abruptly and with great diversity in the Cretaceous, whereas the gymnosperms and monocotyledons were thought to have fossil records dating back to the Carboniferous or beyond. Based on their morphology, the dicotyledons were widely seen by botanists in Darwin’s time (unlike today) as more similar to the gymnosperms than to the monocotyledons. Thus, morphology seemed to point to gymnosperm progenitors of dicotyledons, but this hypothesis made the monocotyledons, given their (at the time) apparently longer fossil record, difficult to place. Darwin had friendly disagreements about the mystery of the dicotyledons’ abrupt appearance in the fossil record with others who thought that their evolution must have been more rapid than his own gradualism would allow. But the mystery may have been made “abominable” to him because it was seen by some contemporary paleobotanists, most notably William Carruthers, the Keeper of Botany at the British Museum, as evidence for divine intervention in the history of life. Subsequent developments in plant systematics and paleobotany after 1879 meant that Darwin’s letter was widely understood to be referring to the abrupt appearance of all angiosperms when it was published in 1903, a meaning that has been attached to it ever since.     

The Haeckelian hijack of Darwinian deism

ABSTRACT

Ernst Haeckel (1834–1919) is most recalled in the history of biology for his Recapitulation Theory and the allegedly fudged illustrations of embryos that he presented in support of that case. Less well known is his contribution to abiogenesis theory, which he incorporated into evolutionary theory. In so doing, Haeckel, a vitriolic atheist, was instrumental in inserting atheism into the evolutionary mindset. While anti-evolution propaganda commonly makes Darwin out to be the villain of the piece, the association of evolution in the broad sense of the word with atheism arises more from the Haeckelian legacy than from Darwin’s initially conciliatory deism or Huxley’s non-committal agnosticism.     

Development of the amentiferous concept

The amentiferous concept developed in pre-Linnaean times, and early botanists clearly recognized the topical similarities among plants bearing aments. Among the amentiferous plants placed side by side in early times were many that would not be so situated today—e.g., gymnosperms intermixed with dicotyledons. By the time of Linnaeus, only dicotyledons were included among the ament-bearing groups. J. G. Gmelin was first to recognize ament-bearing plants (including some gymnosperms) under a single category, “Amentaceae.” Linnaeus, A. L. de Jussieu, W. J. Hooker, Lindley, and Eichler, at one time or another, placed these plants in a separate amentaceous category, but never under the term “Amentiferae.” The name was never used by Engler although he did place the ament-bearing plants among the first families of his Archichlamydeae. The category “Amentiferae” appears to have entered the literature in British publications and through British/English translations from the German.     

Humboldt,Darwin, and population

Conclusions I have attempted to clarify some of the pathways in the development of Darwin's thinking. The foregoing examples of influence by no means include all that can be found by comparing Darwin's writings with Humboldt's. However, the above examples seem adequate to show the nature and extent of this influence. It now seems clear that Humboldt not only, as had been previously known, inspired Darwin to make a voyage of exploration, but also provided him with his basic orientation concerning how and what to observe and how to write about it. An important part of what Darwin assimilated from Humboldt was an appreciation of population analysis as a tool for assessing the state of societies and of the benefits and hardships which these societies can expect to receive from the living world around them.Darwin exhibited in his Journal of Researches a casual interest in the economic and political conditions of the countries he visited, but these considerations were much less important to him than to Humboldt. Instead, Darwin, with the assistance of Lyell's Principles of Geology, shifted from Humboldt's largely economic framework to a biological one built around the species question. This shift led Darwin away from a consideration of how the population biology of animals was related to man's economy to focus instead upon how population biology fitted into the economy of nature.Humboldt's Personal Narrative served very well as a model for Darwin's Journal of Researches, thereby helping Darwin gain scientific eminence. The Journal of Researches, like virtually all of Humboldt's writings, was a contribution to scientific orthodoxy. But Darwin had, along the way, acquired an urge to do more than just add his building blocks to the orthodox scientific edifice. He decided to rearrange those blocks of knowledge into a different structure, and for that task neither Humboldt's Personal Narrative nor any other of his works could serve as a model. Humboldt had lacked the confidence which Darwin needed that biogeography and the origin of species could be understood. Humboldt had not explored very far the possible connections between biology and geology. Nor had he provided a general synthetic account of population biology. Had he done so, he might have been more explicit about the extent of his endorsement of Malthus. But even if he had, Humboldt's strong orientation toward cooperation would probably have inhibited his recognition of the importance of competition in nature.Lyell, who had also benefited from reading Humboldt, gave Darwin insights that were lacking in Humboldt's Personal Narrative. Lyell admirably demonstrated how stratigraphy, paleontology, biogeography, and population biology could be interrelated, and his reasons for doing so were essentially the same as Darwin's. Lyell's understanding of biogeography and ecology came from the writings of Augustin-Pyramus de Candolle as much as from Humboldt's, and from the former Lyell derived an appreciation for the importance of competition and also a confidence that the mysteries of biogeography could be explained.¹¹⁷ Furthermore, Lyell's discussion of all these subjects and also of evolution in his Principles of Geology is a good synthetic argument that was the ideal model for Darwin's greatest book.Darwin, having become convinced that species change through time, was able to synthesize in his mind the contributions which he had derived from the writings of Humboldt and Lyell as they applied to the species question. When Darwin wrote his Journal of Researches there were two large gaps in his thinking about evolution that bothered him—the mechanism of evolution and the causes of extinction. It was only after reading Malthus in 1838 that he realized, as Lyell had more or less pointed out, how important was competition in nature. He now had the general outlines for his theory, and in the 1845 abridged edition of his Journal, now retitled The Voyage of the Beagle, he inserted a fuller discussion of competition in nature which showed his awareness of its importance as an ecological factor.¹¹⁸ An abridged version of this paper was presented at the meeting of the History of Science Society in Washington, D.C., on 29 December 1969.     

Das Triplett aus zwei Monophyla und einem Paraphylum als Baustein des phylogenetischen Systems

The triplet consisting of two monophyletic taxa and one paraphyletic taxon as constructive element of the phylogenetic system Evolution has produced very many novelties (apomorphies). Most of them are small and relatively inconstant, these are more or less indicative of the phylogenetic relationships between closely related species. They cannot be the constitutive character of a supraspecific taxon that exists since a long time and comprises many diversified species. Such a taxon of higher rank can only be characterized by an improbable, rare novelty that has developed only once and has been preserved in all descendent species. Two consecutive apomorphies of this persistent type (‘fixed apomorphies’) characterize three supraspecific taxa, the triplet “A”, “B” and “A minus B” (Fig. 1). The group “A minus B” is rejected in Hennig's theory because it is ‘paraphyletic’, but it is not an artefact created by the systematicist. It is an inevitable mathematical consequence of the differentiatison of the group “B” within the group “A”. Being the result of a subtraction, it is necessarily associated with the two monophyletic partners in the triplet, as it is delimited on one side by the synapomorphy of the group “A”, of which it is a part, and on the other side by the autapomorphy of the separate group “B”. Traditional classifications often include paraphyletic groupings that are inconsistent with phylogenetics, e. g. the Reptilia and the Apterygota. The fault in such cases is that these groups are extended beyond the limits of a triplet and cover more than a single interval between consecutive monophyletic taxa. Paraphyletic groups are admitted in the phylogenetic system only for bridging the gaps in our cladistic information. According to HENNIG'S theory, all supraspecific taxa should be arranged two by two as sister-groups originating from one ancestral species and comprising all descendents of that species. The fixed evolutionary novelties which characterize higher supraspecific taxa are, however, rare and scattered. It is highly improbable that they have developed in sister species, therefore the taxa marked by them cannot be sister-groups (except in very rare cases). In HENNIG'S earlier papers, e. g. in his system of Lepidoptera (1953: 46–49), the alleged ‘sister-groups' are, in reality, the groups “B” and “A minus B” of a triplet (see Fig. 2). In his revised concept (1957 and later), two autapomorphic groups which are most closely related in the recent fauna (“B” and “C” in Fig. 3) are called ‘sister-groups’. But these have originated independently from different ancestors in a plesiomorphic complex of extinct species and are more closely related to parts of this complex than to each other. True sister-groups (“Bx” and “Cx” in Fig. 4) would be formed if these related plesiomorphic species were included, but this extension of the ’backward‘ border of the taxon is not justified by synapomorphy (in the terms of logic, it is a ’metabasis‘), and it would make the classification of fossil species impossible, unless these show at least one synapomorphy with either “B” or “C”. In the system of the recent fauna the sister-groups are identical with the autapomorphic groups, because the plesiomorphic species are extinct. The natural system based on synapomorphies and autapomorphies is the triplet-system as outlined in Figure 6. It is not a new type of classification, but its theoretical foundation was missing, and precise instructions were needed for its use in phylogenetics. The information obtained by HENNIG'S method is entirely preserved in this system and can be retrieved from it, and both recent and extinct species can be classified together. The disadvantage of the triplet-system is that it contains twice as many taxa as HENNIG'S classification. This complexity will limit its use in the practice of taxonomy, but it may be simplified by transforming the system into a sequence of paraphyletic taxa terminating in a single monophylum.     

The Other Edge of Ockham’s Razor: The A-PR Hypothesis and the Origin of Mind

Charles Darwin’s theory of evolution characterized all life as engaged in a “struggle for existence”. To struggle requires internal data processing to detect and interpret patterns to guide behavior, a mechanism to struggle for existence. The cognitive bootstrapping A-PR cycle (Autonomy | Pattern Recognition) couples the origin of life and mind, enabling their symbiotic co-evolution. Life processes energy to create order. Mind processes data to create meaning. Life and mind co-evolve toward increased functional effectiveness, using A-PR feedback cycles that reflect the two Laws deduced from Ockham’s Razor. The Law of Parsimony is only one of two laws that have emerged from debate about Ockham’s Razor. Less well known is the “other edge of Ockham’s Razor”, the Law of Succinctness which, when viewed through the lens of Charles Darwin’s theory of evolution, enables the A-PR Hypothesis to fulfill the criteria of Ockham’s Razor.