Induction and creativity

Induction across Two Centuries

Cell Theory as a Creative Hierarchy of Knowledge

From axioms and questions to a contextual certainty, with the errors retained

Author-date citations; bibliography follows the text

Induction is often pictured as a single mind leaping from a handful of facts to a law. The history of the cell theory will not support that picture. Between Hooke’s cork in 1665 and the secure statement that cells arise only from cells, nearly two centuries of questions, new tools, failed generalizations, and renewed searches were required. The result is one of the unifying judgments of biology: living organisms are composed of cells, the cell is the structural and functional unit of life, and all cells arise from pre-existing cells (Wolpert 1996; Wilson 1896). Read against the epistemology of Ayn Rand and the account of embodied structure in Lakoff and Johnson, that long labour is not an exception to induction. It is induction made visible, because the steps were written down.

The metaphysical base on which any such labour stands is not a proved proposition. On the amended metaphysics used here, the axioms are existence, identity, consciousness, causality, mental focus, free will, introspection, space, time, memory, and the validity of the senses. They are grasped in perception and introspection. They are not arranged as corollaries of one another. Rand isolates three of them as axiomatic concepts: an axiomatic concept is “the identification of a primary fact of reality, which cannot be analyzed, i.e., reduced to other facts,” “the fundamentally given and directly perceived or experienced, which requires no proof or explanation, but on which all proofs and explanations rest” (Rand 1990, chap. 6). Existence, identity, and consciousness are perceived directly and grasped conceptually. Something exists of which one is conscious; its identity must be discovered. The other axioms are likewise given. Causality is the fact that entities act in accordance with their identities. Mental focus and free will are the introspective difference between directing awareness and letting it drift. Introspection is awareness turned upon one’s own cognitive acts. Space, time, and memory are the forms in which place, sequence, and retention are encountered. The validity of the senses is the fact that this form of awareness is awareness of existence. Hooke did not deduce the cork chambers from these axioms. He used them. Something was there; it had a repeatable shape; the lens delivered it; memory held one field against the next; a cause was to be sought for the pattern. Without that metaphysical base, the later arguments about artefact, division, and spontaneous generation would have had nothing to contradict.

Above the axioms, ordinary experience is retained as structured wholes. Lakoff and Johnson describe these as image schemata: containment, with interior, boundary, and exterior; path, with source, trajectory, and goal; part and whole; centre and periphery; link and force (Lakoff and Johnson 1980; Johnson 1987). A schema is itself an induction. The particular measurements drop out, and the relation is kept. Rand’s definition of a concept is the same labour in another vocabulary: “a mental integration of two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted” (Rand 1990, chap. 2). The cell theory is a late and explicit use of these early integrations. A cell is grasped as a container. A tissue is grasped as a whole of parts. Division is grasped as a path from one interior to two. The creative step of the cellular induction is not the schema. The creative step is the judgment that these relations, and not fibres, globules, or a free crystallization from fluid, are the identity of living organization.

The method of that judgment is a cycle, not a ceremony. A question is asked. A search is made. What is found prompts a further question, often farther from the starting point than the inquirer expected. Aristotle’s “what is it” is the first form of the question, answered in his account by the concurrence of material, formal, efficient, and final cause: what a thing is made of, the structure by which it is that kind of thing, the agent of its coming to be, and the end toward which the coming to be is directed (Aristotle, Physics II.3). The cell theory is a modern answer to the same question. The material is protoplasm bounded in a unit. The form is the cell, later specified by nucleus, membrane, and chromosome. The efficient cause of a new cell is the division of an old one, not a crystallization out of blastema. The end, so far as biology can state it, is the maintenance and reproduction of the living organization. Each of those clauses was an induction. None was given with the first lens.

The tool (the microscope) came before the theory, and the tool was itself an answer to earlier questions. Spectacle lenses, then magnifiers, then the compound microscope, were searches into the refraction of light. Hooke, in Micrographia (1665), turned the instrument on cork and named the empty compartments cells, from the Latin cella, the small room. He also examined bone and plant tissue and took the spaces for channels of fluid. He did not treat them as the living units of organisms, and Wolpert notes that the significance was not appreciated for nearly two hundred years (Wolpert 1996). Nehemiah Grew described plant tissues as bladders clustered together. Antonie van Leeuwenhoek, with simpler lenses and higher magnification, saw moving animalcules in pond water, sperm, and globules in blood. The observations were vivid. They remained curiosities. The question “what is the unit of a living body” had not yet been stably asked, and so the information could not yet be integrated. A new tool opens a door only if someone spends focus on the question the new field makes askable.

The eighteenth century shows what an unsettled induction looks like. Albrecht von Haller took the elementary fibre as the structural unit of the body, “what the line is for a geometer.” Globulists held that tissues were built of similar corpuscles. Milne-Edwards concluded in 1826 that the most complicated animal, like the simplest, is formed from a greater or lesser number of these corpuscles. Henri Dutrochet in 1824, and François-Vincent Raspail in 1833, argued that animals and plants share a cellular structure, and both were critical of vitalism (Wolpert 1996; Duchesneau 1987). Epistemologically, these claims were possible. They had evidence, and they had rivals. Many reported globules were optical artefacts, as Hodgkin and Lister showed in 1827 with the achromatic microscope. Animal tissues, full of vessels, tendons, and muscle, did not look like walled plant cells. The fibre theory and the globule theory could each cite observations. Neither had eliminated the other, and neither had a secure account of origin. On the scale later set out by Leonard Peikoff in the Objectivist theory of knowledge, an idea is possible when some evidence supports it while alternatives remain; it is not yet probable, and it is not certain (Peikoff 1991, chap. 5). That was the standing of cellular organization in 1830.

The synthetic step was a fresh question asked of a shared mark, a cellular nucleus. Robert Brown identified the nucleus in plant cells in 1831. Matthias Schleiden, turning from law to botany, treated the organism as a society of cells and asked how they arise. Theodor Schwann, in Müller’s laboratory in Berlin, had seen a similar body in the cells of the notochord. At dinner in October 1837 Schleiden pointed out the role of the nucleus in plant cells. Schwann later wrote that he at once recalled the notochord and “grasped the extreme importance” of showing that the nucleus played the same role in animals (quoted in Wolpert 1996). The question crossed a kingdom boundary. The search that followed produced Schwann’s Mikroskopische Untersuchungen (1839): nature does not join molecules directly into fibres and tubes, but first fashions a cell, and transforms that cell into the adult elements of structure. With Schleiden’s botanical conclusion of 1838, the first two tenets acquired a systematic statement. Plants and animals are composed of cells. The cell is the unit of development and of organization. The integration omitted the particular measurements of cork, cartilage, and leaf, and kept the unit. It was new knowledge. It was also, on the evidence then in hand, probable rather than certain. A common principle had been found. The cause of new cells had not.

The error of the founders of this theory is the clearest exhibit of an epistemologically possible idea that fails to become probable. Schleiden, observing the endosperm of seeds, in which nuclei multiply before walls form, generalized from that atypical tissue. He held that cells arise de novo from a mass of minute granules, the cytoblastema, the nucleus forming first and the wall condensing about it as a crystal forms from solution (Schleiden 1838; Wolpert 1996). Schwann extended the free formation to animal tissues, even where no wall could be seen, and defined a cell by nucleus, fluid content, and wall. The crystallization metaphor was not arbitrary. It was an available gestalt, a container precipitating from a fluid, and it organized real observations of nuclei appearing before partitions. It was possible. It became a block when it was treated as the general cause. Von Mohl had already, in 1837, watched a partition form in a green filamentous alga. Trembley had described division in protozoa in 1744. Cleavage of early embryos had been seen. None of these was yet identified as the division of cells, in part because the egg itself was not yet grasped as a cell. Kölliker could describe the cleavage of Ascaris and still, in his Manual of Human Histology, treat endogenous origin as frequent (Wolpert 1996). A failed induction is often a partial one: a real relation, taken from the wrong sample, and then protected by the authority of the men who had just unified the field.

The correction had the same form as the original claim, and a higher ethical cost. Robert Remak, an orthodox Jew trained in Berlin and barred from an academic post, did not accept Schwann’s origin story. He traced successive division in frog embryos from the germ to cartilage and muscle. “The extracellular cell creation as postulated by Schwann cannot be proved,” he wrote; the cells of the germ multiply by continuous division, beginning at the nucleus (Remak, quoted in Wolpert 1996). The question was “how does a new cell come to be,” asked against the textbook answer. The search was embryological and repeated. The integration omitted the particular tissue and kept the path from cell to cell. Rudolf Virchow, in 1855, captured the corrected understanding in the sentence Omnis cellula e cellula, all cells from cells. Wolpert’s judgment is that Virchow was probably influenced by Remak. The historical controversy is sharper than that clause. Remak had published the evidence; Virchow, the more powerful figure, popularized the formula in a setting where Remak’s standing was already narrowed by institutional exclusion, and the credit attached to the phrase rather than to the observations. Whether one calls the episode plagiarism or appropriation, the epistemic point is the same. The induction was Remak’s labour of focus. The public certainty was delayed, and misassigned, by a barrier to enquiry. An ethic or a profession that sidelines the person who asks the unwanted question slows the passage from the possible to the probable.

The third tenet did not stand alone. It had to be integrated with the wider rejection of spontaneous generation, the doctrine that living things arise from non-living matter. Francesco Redi, in 1668, showed that maggots appear on meat only where flies can reach it. The microscope then revived the doctrine at a smaller scale. John Needham, in the 1740s, found organisms in briefly boiled broth and inferred a vital force. Lazzaro Spallanzani boiled longer, sealed the vessels, and found sterility; critics answered that he had destroyed the force in the air. Louis Pasteur’s swan-neck flasks, in 1859–1862, let air in and kept dust out. The broth stayed clear until the neck was broken or the trapped particles were washed back. John Tyndall’s later account of heat-resistant spores explained why some boiled infusions had still grown. Omne vivum ex vivo, life only from life, then stood on evidence that had eliminated the rivals. In Peikoff’s scale, an idea is certain when, in a given context, the evidence is conclusive: what is known supports it, and no evidence supports an alternative (Peikoff 1976; Peikoff 1991, chap. 5). Certainty is contextual. It is not omniscience. The cell theory after Remak, Virchow, and Pasteur met that standard for the context they had. It did not yet include mitosis, the lipid membrane, or the neuron.

Later questions show how a secure integration opens new ones rather than closing the subject. Walther Flemming, working with large salamander cells and new stains, linked the stainable substance of the resting nucleus to the chromosomes at division, described the longitudinal split, and followed one half of each chromosome to each pole (Wolpert 1996). The number of chromosomes was then found to be constant, and the individuality of the chromosome became a further induction. Overton, in 1895, distinguished membrane from wall by physiological means: cane sugar plasmolyzed plant cells, while some substances of the same osmotic pressure did not, and lipid-soluble substances entered more readily. The membrane, long disputed because it could not be seen, was identified by what it did. In the nervous system the reticular theory of Gerlach and Golgi treated the tissue as a continuous net, because boundaries were hard to see. Santiago Ramón y Cajal, using Golgi’s stain against Golgi’s interpretation, showed neurons as separate cells. The cell theory was thereby extended to the tissue that had seemed to refute it. Each of these was a new search, prompted by a tool or by a remaining contradiction, and each omitted measurements that did not bear on the identity being sought.

The path was not a single sequence, and that is why induction looks chaotic. One might have begun from Dutrochet’s drawings, or from von Mohl’s alga, or from cleavage, or from the dinner in Berlin. Several of those beginnings were in fact taken, and for a time they diverged. Globules, fibres, free formation, and division were all answers to “what is it.” They converged only as questions were renewed and as negative evidence was reclassified. Optical globules were set aside as artefacts. Endosperm was set aside as a special case, not as the type. The vital force was set aside once air without dust produced no growth. What remained could be integrated with the rest of biological knowledge: development, pathology, and, later, genetics. E. B. Wilson judged that no biological generalization except organic evolution had brought so many phenomena under a common point of view (Wilson 1896, cited in Wolpert 1996). Wolpert records a further moral, which belongs to the theory of induction itself. Ideas later found to include much that is incorrect can still be highly productive of advance. Schleiden and Schwann were wrong about origin and right about the unit. The wrong clause was a possible idea that organized inquiry until a better search retired it. Rejection is not a failure of the method. It is the method, once contrary evidence is allowed to count.

The creativity in this history is the production of identifications the world did not hand over already labeled. Rand’s formula applies to the theory as well as to the first concepts: knowledge is “neither revealed nor invented, but produced by man’s consciousness in accordance with the facts of reality” (Rand 1990). Hooke invented the name. He did not invent the compartments. Schwann did not copy a universal out of cartilage. He produced it by integrating plant nucleus and animal nucleus while omitting the measurements of each tissue. Remak produced the causal clause by following one embryo through many divisions. Pasteur produced a decisive contrast by bending glass until the rival hypothesis had to predict a result it could not save. Surprise sits in the middle of the cycle. Each new question takes the search further from what was already known. The microscope was built to enlarge. It delivered animalcules, then a unit of life, then a constraint on how life can begin. That is creativity in the cognitive sense: a new whole, constrained by the facts, and not contained in any one of the facts.

The energy required is ethical because the cycle is chosen. “Reason does not work automatically; thinking is not a mechanical process; the connections of logic are not made by instinct” (Rand 1961, 120). Focus is the volitional act on which the rest depends. In this history the act is visible. It is Schwann holding a dinner remark long enough to reopen his slides. It is Remak continuing a trace that the dominant theory said was unnecessary, without a post from which to speak. It is Pasteur designing the flask so that the objection about air was met rather than evaded. It is also the energy that was not spent: the decades in which cleavage was drawn and not identified, because the egg was not asked about as a cell. The virtues involved are ordinary and strict. Independence asks the question the evidence requires. Honesty registers the artefact and the exception. Persistence keeps the search open after the first integration has become famous. Integrity refuses to let a phrase outrun the observations, and refuses to drop an observation because its author is unwelcome. Where a culture or a profession penalizes the question, the same lenses yield less knowledge. The hierarchy does not change. The labour that climbs it is refused.

Cell theory, then, is not a monument placed beside the account of induction. It is an instance of it, long enough to show the stages. Isolated observations were possible and unintegrated. Globules and fibres were possible and in competition. The cellular unit of plants and animals became probable when the nucleus gave the two kingdoms a common mark. Free formation was a possible cause that failed when division was followed and when life from non-life was closed off. Omnis cellula e cellula became contextually certain in the knowledge of the mid-nineteenth century, and then became the base of further inductions about chromosomes, membranes, and neurons. The order of questions was not fixed. The form of the labour was: ask, search, integrate, and ask again. The products were created. The cost was focus, sustained in particular persons, and sometimes blocked by the institutions around them.

Bibliography

Aristotle. Physics. Book II. Standard editions; the four causes are set out at II.3.

Duchesneau, François. 1987. Genèse de la théorie cellulaire. Paris: Vrin.

Dutrochet, Henri. 1824. Recherches anatomiques et physiologiques sur la structure intime des animaux et des végétaux. Paris: J.-B. Baillière.

Hooke, Robert. 1665. Micrographia. London: Jo. Martyn and Ja. Allestry.

Johnson, Mark. 1987. The Body in the Mind: The Bodily Basis of Meaning, Imagination, and Reason. Chicago: University of Chicago Press.

Lakoff, George, and Mark Johnson. 1980. Metaphors We Live By. Chicago: University of Chicago Press.

Pasteur, Louis. 1861. “Mémoire sur les corpuscules organisés qui existent dans l’atmosphère.” Annales des sciences naturelles, partie zoologique, 4th ser., 16: 5–98.

Peikoff, Leonard. 1976. “Certainty.” Lecture 6 of The Philosophy of Objectivism. Recorded lecture series. Later incorporated into Peikoff 1991.

Peikoff, Leonard. 1991. Objectivism: The Philosophy of Ayn Rand. New York: Dutton.

Rand, Ayn. 1961. For the New Intellectual. New York: Random House. “Galt’s Speech,” reprinted from Atlas Shrugged (1957).

Rand, Ayn. 1964. The Virtue of Selfishness: A New Concept of Egoism. New York: New American Library.

Rand, Ayn. 1990. Introduction to Objectivist Epistemology. Expanded 2nd ed., edited by Harry Binswanger and Leonard Peikoff. New York: Meridian.

Remak, Robert. 1855. Untersuchungen über die Entwicklung der Wirbelthiere. Berlin: G. Reimer. Related papers from 1852.

Schleiden, Matthias Jacob. 1838. “Beiträge zur Phytogenesis.” Archiv für Anatomie, Physiologie und wissenschaftliche Medicin, 137–176.

Schwann, Theodor. 1839. Mikr

oskopische Untersuchungen über die Uebereinstimmung in der Struktur und dem Wachsthum der Thiere und Pflanzen. Berlin: Sander.

Virchow, Rudolf. 1855. “Cellular-Pathologie.” Archiv für pathologische Anatomie und Physiologie und für klinische Medicin 8: 3–39.

Wilson, Edmund B. 1896. The Cell in Development and Inheritance. New York: Macmillan. First edition 1896; Wolpert cites the 1892 date used in some discussions of the argument.

Wolpert, Lewis. 1996. “The Evolution of ‘the Cell Theory.’” Current Biology 6 (3): 225–228. Abridged from Philosophical Transactions of the Royal Society B 349 (1995): 227–233.