Plato and the Impact Factor

Stephen J Bensman notsjb at LSU.EDU
Fri Feb 18 15:26:17 EST 2011

Below is a section of the book on Hogben's assault on Quetelet, statistics, and the normal paradigm.  Here Hogben elucidates the philosophical bases of statistics, laying the blame on Quetelet.  I think that it is crucial to understand this, so I expanding the sections on Hogben's views.  Although he is a perspecacios writer, you will see that I think that he was probably wrong on the philosophy end.  I would appreciate any comments by philosophers, because philosophy is not my expertise.  I am trying to integrate the history of information science into the general history of science and human knowledge.  Hopefully I am being successful.  You'll like Hogben, because he is a very funny fellow.  A handsome fellow, he is attractive intellectually.  However, for a leading pioneer in experimental biology, his Royal Society photo shows him to be a smoker, but he lived until he was 80




Stephen J. Bensman

LSU Libraries

Louisiana State University

Baton Rouge, LA   70803


notsjb at


Quetelet's Legacy: The Normal Paradigm and Philosophical Transformation of Statistics 

            In his seminal work on scientific revolutions Kuhn (1970) established the concept of the "paradigm."  To do so, he began by defining "normal science" as "research firmly based upon one or more past scientific achievements, achievements that some particular scientific community acknowledges for a time as supplying the foundation for its further practice" (p. 10).  Kuhn named such achievements "paradigms," and, relating this term to normal science, he stated, "By choosing it, I mean to suggest that some accepted examples of actual scientific practice-examples which include law, theory, application, and instrumentation together-provide models from which spring particular coherent traditions of scientific research" (p. 10).  In a postscript to the 2nd edition of his work, he further explained the term "paradigm" by stating it had been used in the book in two different senses: 1) to designate "the entire constellation of beliefs, values, techniques, and so on shared by the members of a given community"; and 2) to denote "one sort of element in that constellation, the concrete puzzle-solutions which, employed as models or examples, can replace explicit rules as a basis for the solution of the remaining puzzles of normal science" (p. 175).  Kuhn considered a scientific revolution to consist of the replacement of one paradigm by another in a process he called the "paradigm shift" (p. 66).

            Quetelet created such a paradigm, which we call the "normal paradigm," because it posited that the frequency distribution of observations taken from a coherent set always fitted the normal curve of error and that, consequently, the normal distribution could be utilized to identify a coherent set.  This paradigm lay at the basis of much subsequent scientific and social research.  However, it was not a universally accepted paradigm but had its ardent opponents.  Keynes (1921) evaluated Quetelet's work thus:

              ... Quetelet belongs ... to the long line of brilliant writers, not yet extinct,

              who have prevented Probability from becoming, in the scientific salon,

              perfectly respectable.  There is still about it for scientists a smack of 

              astrology, of alchemy.  p. 335.

For Keynes, the "suspicion of quackery" raised by Quetelet's writings had not yet disappeared.  In Germany, the normal paradigm was derisively named "Queteletismus" (Hacking, 1990, pp. 125-127), and the noted British economist and statistician Edgeworth (1922) summarized this doctrine thus: 

              ...The theory [of the normal law of error] is to be distinguished from the

              doctrine, the false doctrine, that generally, wherever there is a curve with

              a single apex representing a group of statistics-one axis denoting size, the

              other axis frequency-that curve must be of the "normal" species.  The 

              doctrine has been nicknamed "Quetelismus" [sic], on the ground that 

              Quetelet exaggerated the prevalence of the normal law.  p. 270.

Quetelet's theories were ultimately rejected, and the discovery of the probability structure of scientific information formed in integral part of this paradigm shift.

            Despite the ultimate failure of his ideas, Quetelet transformed the philosophical bases of statistics.  This was, perhaps, inevitable in the transfer of using probability from calculating astronomical error to analyzing mass socioeconomic phenomena, and it is certainly implicit in the way Quetelet combined Poisson's strong version of the law of large numbers with Bernoulli's weak version to accomplish this transfer.  Perhaps the most cogent critique of the philosophical and logical bases of modern inferential statistics was written by Lancelot Hogben (1957), who was one of Britain's leading experimental biologists.  Born in 1895, Hogben was the son of an impoverished evangelical Methodist minister, and he was the first student from a London County Council secondary school to win a scholarship to Cambridge (Trinity College), where his lower class origins distinguished him from the other undergraduates.  At Cambridge Hogben became a Fabian socialist and Quaker.  He was an ardent pacifist, and, during World War I, when conscription was introduced in 1916, he deliberately gave up his exemption as a Quaker to serve time in Wormwood Scrubs in protest of this act.  Throughout his life, according to Bud (2004), "Hogben displayed a brilliance whose rewards were undermined with 'a sheer genius for making enemies'" (p. 556).  Given this personality, it is not surprising that Hogben made numerous career changes, working successively in the 1920s at the University of Edinburgh, McGill University, and the University of Cape Town.  In 1930 Hogben (1998) became in his own words "the first, last and only professor of social biology" (p. 120) at the London School of Economics in a position funded by the Rockefeller Foundation and lasting seven years.  He finished his academic career at the University of Birmingham, where he was first a professor of zoology (1941-1947) and then of medical statistics (1947-1961).  In 1923 Hogben was a founder of the Society for Experimental Biology and in 1936 became a Fellow of the Royal Society.

            Hogben did not become seriously interested in the theory underlying statistics until relatively late in his career.  This interest began during World War II, when he was given the job of overhauling British Army medical statistics, and it was heightened after the war, when the British government decided to establish the National Health Service and fund a chair of medical statistics at the University of Birmingham.  This post was offered to Hogben (1998), who accepted it, realizing, as he reported in his autobiography, that "acceptance would commit me to undertake a critical evaluation of the credentials of current mathematical statistics" (p. 190).  Hogben began this evaluation by writing a two-volume introduction to probability using visual models entitled Chance and Choice by Cardpack and Chessboard, which, he stated, "provided me with what William Blake called mental work for Jerusalem" (p. 190).  This last was a reference to Blake's poem, Jerusalem, whose last stanza reads: "I will not cease from mental fight, Nor shall my sword sleep in my hand, Till we have built Jerusalem, In England's green and pleasant land."   Hogben's textbook received a somewhat mixed reception from professional statisticians.  For example, Snedecor (1951) gave the first volume a very favorable review, stating, "The professional statistician will be interested in the polemics as well as in the originality of the viewpoint" (p. 256), whereas David (1956) dismissed the volumes as "of little use to the research worker in other fields who wishes to learn a little statistical method" but did state that "serious students of mathematical statistics" would find "a certain freshness of exposition which will possibly help them when they come to revise what they already know," even though she thought the chapter on significance revealed "a certain naivety of outlook on the part of the author" (p. 236). 

            With the groundwork prepared by the textbook, Hogben (1957) published his main assault in a work his son, Adrian (himself a medical doctor and leading researcher in physiology), considered as "perhaps Lancelot's stellar intellectual achievement" (Hogben, 1998, p. xvi).  Entitled Statistical Theory, its logical and philosophical approach was summed up in its lengthy subtitle, The Relationship of Probability, Credibility and Error: An Examination of the Contemporary Crisis in Statistical Theory from a Behaviourist Viewpoint.  Hogben's behaviorist approach is extremely complex, and his explanation of it is rather perfunctory in the book.  Therefore, it is necessary to dig more deeply into his intellectual history in order to understand more fully philosophical bases of his critique.  Hogben's development of his behavioral approach to science originated from his participation in a joint discussion held in 1929 at the meeting of the British Association for the Advancement of Science in South Africa by the Physiology Section together with the other biological sections.  The meeting was entitled "The Nature of Life," and the scientific journal, Nature (South Africa Meeting, 1929a; 1929b; 1929c), reported, "The discussion...was more than usually interesting, since it indicated a swing of the pendulum towards the vitalistic view of the nature of life" (1929b, p. 205).  Blackburn (2005) succinctly defined "vitalism" as a philosophical doctrine thus:

               The doctrine that there is some feature of living bodies that 

                prevents their nature from being entirely explained in physical

                or chemical terms.  This feature may be the presence of a 

                further "thing" (such as a soul), but it may also be simply the

   emergence of special relations or principles of organization arising 

   from the complexity of the biological organism .... p. 383.    

The discussion was dominated by the ideas of the South African statesman and soldier, Jan Smuts, and the English astrophysicist, Arthur Eddington.  Smuts opened the discussion by developing his theory of "holism," a word, which the Oxford English Dictionary (2002) states he introduced into the English language with his book entitled Holism and Evolution.  Smuts (1927) opened this book by stating that it dealt with problems falling within the debatable borderland between science and philosophy.  According to him, recent advances in physical and biological science had revealed that there was operative in this borderland a very important factor or principle, which he called "Holism."  Smuts (1927) then summarized what his book would endeavor to show about the operation and role of this principle thus:

   ...Holism...underlies the synthetic tendency in the universe,

    and is the principle which makes for the origin and progress

    of wholes in the universe. An attempt is made to show that 

    this whole-making or holistic tendency is fundamental in nature, 

    that it has a well-marked ascertainable character, and that Evolution

    is nothing but the gradual development and stratification of 

    progressive series of wholes, stretching from the inorganic

    beginnings to the highest levels of spiritual creation .... p. ix

With this concept, Smuts merged the material with the spiritual into the whole, promising to deal with the primary concepts of matter, life, mind, and personality from this perspective.  For his part, in a book entitled The Nature of the Physical World containing his 1927 Gifford Lectures, Eddington (1929) based modern physics on philosophical idealism, which Blackburn (2005) generically defined as: "Any doctrine holding that reality is fundamentally mental in nature" (p. 177).  According to Eddington, the theoretical advances made by Einstein and Rutherford at the beginning 20th century fundamentally changed our ideas not only of time and space but also matter, causing the downfall of classical Newtonian physics.  In his view, the stuff of the world is "mind-stuff," and he stated, "The realistic matter and fields of force of former physical theory are altogether irrelevant-except in so far as the mind-stuff has itself spun these imaginings" (p. 276).  Eddington declared, "It is necessary to keep reminding ourselves that all knowledge of our environment from which the world of physics is constructed,

has entered in the form of messages transmitted along the nerves to the seat of consciousness" (p. 277), asserting that "it is only our own ends of the [nerve] fibres that we actually know" (p. 278).  

            The scientific journal, Nature (South Africa Meeting), reported that Hogben responded to such ideas by stating that he was "not prepared to believe anything not amenable to experiment" (1929b, p. 205), and it considered him as representing the "extreme behaviourists or bio-mechanists" (1929c, p. 397) at the conference.  Hogben had been asked to deliver a 35-minute talk at the conference, but he considered the topic too formidable for such a short presentation.  Instead he decided to publish a book, because other contributors at the conference had already published their philosophical views in book form.  Hogben (1930) entitled his book The Nature of Living Matter

-the title suggesting a biologist's riposte to the astrophysicist Eddington's idealistic The Nature of the Physical World. 

In his book Hogben (1930) regarded the history of philosophy as continuous controversy between those who had confidence in the testimony of human receptor organs and others who mistrusted the evidence of the senses.  According to him, the only permanent feature of philosophical discussion was the impossibility of effecting a permanent reconciliation between those called themselves at different periods of history "materialists and idealists, nominalists and realists, empiricists and transcendentalists, mechanists and vitalists, to emphasize some new aspect of a fundamental incompatibility" (pp. 220-221).  A key element in this struggle was played by the concept of "universals," which the Oxford English Dictionary (2002) defines thus for philosophy and logic:

   That which is predicated or asserted of all the individuals or species

   of a class or genus, or of many things which are regarded as forming a class;

   an abstract or general concept regarded either as having an absolute, mental,

   or nominal existence....

Due to frequency theory of probability, which requires the definition of coherent sets, it is the classificatory role of universals that is of the most importance for the history of statistics.   The debate over the status of universals stems from the ancient Greek theory of Forms or Ideas, which Plato held to have real existence distinct from their manifestations in individual objects, i.e., "redness" as a concept must exist before manifesting itself "red" things.  Aristotle, on the other hand, argued that universals were not "before the thing" as Plato posited but "in the thing."  The Middle Ages were marked by a controversy between Realism, which in its exaggerated form held that universals exist in the mind and nature, and Nominalism, which denied the existence of universals and regarded them merely as adjectival names to describe particular things and events.  There was a third position called Conceptualisim advanced, among others, by Abelard and William of Ockham.  Conceptualism admitted the existence within us of abstract and universal concepts but held that it is not known whether the mental objects have any foundation outside our minds.

            In his discussion of these matters as they pertained to science, Hogben (1930) proceeded within the Cartesian framework of "mechanism," as this term has been thus defined by Honderich (1995):  

               In the philosophy of mind, the doctrine that we are machines.

               Descartes held that other animals are machines, but only to emphasize

               his own view that human beings are not machines because they have

               minds, which he supposed to be non-physical....  p. 543. 

Thus, according to Hogben (1930, pp. 232-235), Cartesian philosophy did not attempt mix metaphysics and science in a uniform system of nature but defined separate spheres of autonomy for the scientist and metaphysician.  Thus, he wrote:

               ...With his propositions and demonstrations "which establish the existence

               of God and the distinction between the mind and body of man disposed in 

               geometrical order" Descartes stumbled upon the felicitous notion that 

               God ordained the investigation of nature according to strictly mechanistic 

               principles....  p. 232

In his summarization of vitalism and mechnanis that opened the book, Hogben noted that physicists had assumed the leading role in the question of the relationship of science to moral philosophy that had arisen from the uneasy recognition of the conflict between science and common sense, but he asserted that the question could not be settled until the contribution of biology to natural philosophy had been taken into consideration.  Hogben (1930) then asserted, "The merits of a mechanistic or vitalistic outlook in biology have been too often discussed from an ontological rather than an epistemological standpoint" (p. 1).    According to Hogben, there was a similarity of method in physics and biology, particularly in physiology, and he summed up the underlying theoretical bases of his argumentation, noting the philosophical consequences of the work of the noted Russian physiologist, Ivan Pavlov, on conditioned reflex, thus:

               ...Traditional mechanistic physiology has accepted the Cartesian dualism

               of mind and matter.  The modern physiology of the conditioned reflex

               has undermined the distinction between reflex and voluntary behaviour.

               There this thus no nicely defined boundary at which physiology ends and

               philosophy begins.  Biology is annexing regions of enquiry which have 

               hitherto remained the province of moral philosophy.  As a concept of 

               biology Mind is replaced by Behviour.... p. 1 

As a result of this intrusion, Hogben saw no limit to the reduction of behavior to purely physico-chemical hypotheses, and he regarded as the significant issue not the completeness of the mechanistic solution but whether there existed any definable method of arriving at a more complete solution that the mechanistic outlook permitted. 

            The perceived merger of mind and matter resulting from Pavlovian theory caused Hogben (1930) to change the emphasis of the discussion from the problem of being (ontology) to the problem of knowledge (epistemology).  This is evident in the following summarization by him of his conclusions:

                  When the conclusions of physicists are supplemented by the enquiries

               of the biologist we are led to a schematization of experience which

               permits us to discuss the nature of matter and life on a neutral ground.  This

               neutral ground is the public world of science.  It represents what is 

               significant for the purpose of discourse.  Idealistic philosophers have

               assumed the nature of reality as the goal of philosophy; but the 

               concept of reality is essentially equivocal.  For the purpose of discourse

               we have to assume that the neutral ground is the real thing.  In private

               we are at liberty to reject this view.  Temperament decides which of 

               these alternatives we adopt.  There is therefore no hope of arriving at

              universal agreement in discussing the nature of reality.  To the introvert

               reality resides in the domain of mystic experience.  To the extrovert the 

               public world is the nearest approach to a complete representation of 

               reality which our limited range of receptor organs permits us to

               construct.  The belief that philosophy can settle the nature of reality,

               and that it is possible to arrive at universal conclusions independently

               of the methods of science and mathematics arose in the period of

               decadence of Greek philosophy.  It developed in modern Europe under

\              influence of ecclesiasticism.  Freed from the bondage of clerical control,

               philosophy must undertake the more modest task of discussing what

               characteristics of belief determine their communicability or publicity, and

               and indicating how the problems of existence can be resolved into their public

               and private components.  From this standpoint educational theory must be based

               on a recognition of the respective spheres of publicity and privacy....  p. 217.

Thus, for Hogben, the important question was not what is exists but what is knowable, and, in order to be knowable, it must be communicable.

            It was from this philosophical platform that Hogben launched his critique of modern inferential statistics.  In his book Statistical Theory Hogben (1957) accused statistics of committing the philosophical crime of "Platonism," regarding this discipline as dealing with "the Platonic empyrean of universals with an infinite population of the Normal Man" (p. 180) and as having recourse to "Platonic constructs" (p. 476).  His attitude toward such a philosophical basis can be inferred from his statement that "few persons outside a mental home would defend thoroughgoing Platonic idealism" (p. 10).  Hogben traces the source of this Platonism back to Quetelet.  According to one reviewer of this book, Plackett (1958), Quetelet was "seen as the skeleton in the cupboard of contemporary statistics" (p. 244).  To make his case, Hogben published a translation of a critique of Quetelet by the French mathematician, Joseph Bertrand, that captured the full Voltairean flavor of the original (pp. 172-174).  In this critique Bertrand accused Quetelet of unknowingly resolving the long-forgotten medieval debate about universals-of "[w]andering over the schoolmen's ancient battlefield."  This debate pitted the Nominalists, who rejected the existence of universals, holding the view that things denominated by the same name share nothing except that fact, against the Realists, who believed in line with Plato that there are universals that are related to but exist apart from the individual objects in the world.  Bertrand wrote that Quetelet "in a book stuffed full of judiciously collected facts, would have us accept a precise definition of the word Man, independently of human beings whose particularity can be considered accidental."  After noting that Quetelet defined his "specimen" by attributing to him the arithmetic mean of every element that varies from one man to another, Bertrand focused on Quetelet's use of the physical measurements of military conscripts to lampoon him.  Bertrand first wrote on Quetelet's finding that the mean height of 20,000 conscripts was 1 m 75:

               In this comparison M. Quetelet sees an identity.  Our inequalities of height

               are, in his eyes, the result of inept measurements taken by Nature on an

               immutable model in whom alone she reveals her secrets.  1 m 75 is the 

               normal height.  A little more makes no less a man, but the surplus or deficit

               in each individual is nature's error, and thus monstrous.  p. 173

Then, after a short disquisition in solid geometry, Bertrand drove the dagger home:

               ...Men's shapes unfortunately can vary, and M. Quetelet profits therefrom.

               By combining the mean weight of 20,000 conscripts with their mean height, 

               we should produce an absurdly fat man and, whatever Reynolds might have

               saids, a poor model for an artist.  pp. 173-174. 

With one shot, Bertrand had, thus, hit Quetelet the statistician and Quetelet the aspiring artist.

            Central to Bertrand's critique was the significance and accuracy of the arithmetic mean, which for Quetelet represented the epitome that identified the Platonic type.  Hogben (1957, pp. 227-231) shared Bertrand's doubts on this matter and emphasized this in a section of his book entitled "The Tyranny of Averages."  Here he gave the following quote from writings of the great 19th-century French physiologist, Claude Bernard, who, Hogben stated, had been provoked by "Quetelet's disciples inspired with the new evangel of averages":

      By destroying the biological character of phenomena, the use of averages

   in physiology and medicine usually gives only apparent accuracy to the 

   results....  If, for instance, we observe the number of pulsations and the degree

               blood pressure by means of the oscillations of a manometer throughout one day, and

               if we take the average of all our figures to get the true or average blood pressure

               and to learn the true or average number of pulsations, we shall simply have

               wrong numbers.....   p. 227. 

Hogben emphasized that Bernard was writing as an experimentalist.           

            Bertrand's and Hogben's assessments of Quetelet's work from the viewpoint of philosophical idealism were negative, but that of Desrosières (1998) from the same philosophical standpoint was quite positive.  In a chapter entitled "Averages and the Realism of Aggregates" Desrosières places his evaluation of Quetelet's work within the same philosophical framework of the medieval debate between Nominalism and Realism as did Bertrand.  Desrosières' summary of Quetelet's accomplishments is as follows:

                 But it was Quetelet who, in the 1830s and 1840s, largely disseminated

              the argument connecting the theory of probability and statistical 

  observations.  This construct held together both the random, unpredictable 

  aspect of individual behavior and the contrasting regularity (and consequent

  predictability) of the statistical summation of these individual acts, 

  through the notion of the average man.  It was based both on the

  generality of [the] Gaussian probability distribution (the future "normal

  law") and on sets of "moral statistics" (marriages, crimes, suicides)

  developed by the bureaus of statistics.  This form of argument would

  long send probability theory swinging from its subjective, epistemic side, 

  expressed in terms of "reason to believe," toward its objective, frequentist 

  side: the  regularity of averages, opposed to the chaos and unpredictability of 

  individual acts, provided an extremely powerful tool of objectification.  p. 10.   

Thus, in Desrosières' opinion, Quetelet played an extremely important role in the historical development of the statistical tools used for objectifying the social world. 

            Of the above assessments of the significance of Quetelet's work from the philosophical standpoint, that of Desrosières can be said to be the most valid.  In a review of Hogben's book appearing in the Journal of the Royal Statistical Society, Smith (1958) pointed out that the author did not put forward any coherent alternative system to statistical theory and practice as they then stood and even suggested pessimistically at the end of the book that there may be no such system.  It will be seen that much of probabilistic and statistical theory is still based on Platonism and other forms of philosophical idealism.  This is also true of information science, and this applies not only to such obvious matters as the delineation of scientific disciplines but also to the definition of bibliographic entities.   At present there is being designed and tested a new, unified cataloging standard to replace the present Anglo-Anglo American Cataloging Rules (2nd ed.) presently in use.  The new standard is called RDA: Resource Description & Access, and it is conceptually based upon a study of the functional requirements for bibliographic records done under the auspices of the International Federation of Library Associations and Institutions (IFLA) (1998), commonly known the FRBR.  Central to the FRBR is a group of entities, whose purpose is to represent the products of intellectual or artistic endeavor described by bibliographic records.    The FRBR briefly defines these entities thus:

            ...The entities defined as work (a distinct intellectual or artistic creation) 

and expression (the intellectual or artistic realization of a work) reflect 

intellectual or artistic content. The entities defined as manifestation (the 

physical embodiment of an expression of a work) and item (a single

exemplar of a manifestation), on the other hand, reflect physical form.  p. 12  


The most important of these entities is the "work," which the FRBR describes in the following manner:

A work is an abstract entity; there is no single material object one can point to

as the work. We recognize the work through individual realizations or expressions

of the work, but the work itself exists only in the commonality of content between

and among the various expressions of the work. When we speak of Homer's Iliad 

as a work, our point of reference is not a particular recitation or text of the work, but 

the intellectual creation that lies behind all the various expressions of the work.   p.16.

On the basis of the FRBR even Plato's Republic can be conceived of as a Platonic construct.  On this basis Bensman and Leydesdorff (2009) have shown that scientific journals are being re-conceptualized by library catalogers as Platonic constructs that instantiate themselves in reality under different titles, in different formats, etc.  To push the analogy further, the value of a scientific journal is commonly epitomized by the "impact factor," which is the arithmetic mean of the citations to its articles and suffers from the same faults Hogben pointed out for the arithmetic mean applied in biology.            









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