1. Introduction

The reception of Canguilhem in Italy remains largely shaped by his most celebrated work, The Normal and the Pathological[1]. Philosophers of science, historians of medicine, sociologists, and anthropologists draw on it above all for the critique Canguilhem levels at the reduction of the pathological to the normal. ‘Reduction,’ however, is an umbrella term: it encompasses very different operations, applicable to distinct ontological, epistemic, or practical relations among the objects involved. It is also an opaque term, often used interchangeably to refer to a quantitative scaling-down, an ontological conflation, or an epistemic subsumption.

Canguilhem himself is no exception to this plural usage, and he seems well aware of it. It is no accident that in his work he warns the reader of a twofold possible relation between the normal and the pathological — one of continuity and one of alterity — specifying that, in both cases, the pathological can be traced back to the normal through the same epistemic move: its production as an excess or deficiency relative to the normal state.

The first part of The Normal and the Pathological can be read, from this vantage point, as a sustained survey of the different types of reduction of the pathological. In this article I shall attempt to disentangle them, identifying two macro-types: what I shall call epistemic reduction, carried out by Comte and Broussais (and, with certain differences, by Claude Bernard); and statistical reduction, carried out by Quetelet.

To find one’s bearings in Canguilhem’s critique, one must first recognise the architecture of the 1943 first part of The Normal and the Pathological:the Essay on Some Problems Concerning the Normal and the Pathological, which addresses two distinct problems. The first — is the pathological state merely a quantitative modification of the normal state? — directly targets the thesis, upheld by Comte and Bernard, that the physiological and the pathological share an identity of nature and differ only in degree. Comte is concerned with the knowledge of the normal, so the pathological serves him merely as a means of establishing its laws; Bernard is concerned with the knowledge and mastery of the pathological, so physiology serves him as the foundation for rational therapeutic action. The second problem — do sciences of the normal and the pathological exist? — radicalises the first: the question is no longer simply whether the two states differ in degree or in kind, but whether a medical rationality capable of accounting for both is possible, and whether it can do so through the statistical concept of the norm as proposed by Quetelet.

The article is organised in four sections. Firstly, I address the opacity of the concept of reduction, distinguishing it from other operations — quantification, mathematisation, numerisation. Then, I set out the grounds of Canguilhem’s critique of reductionism in general. After, I examine, respectively, epistemic reductionism (Broussais and Comte; — Bernard, whom I shall not discuss for reasons of space —): the attempt to exclude quality as epistemically insignificant and statistical reductionism (Quetelet and Pierre-Charles-Alexandre Louis): the conversion of quality into quantity.

2. Reducing, Quantifying, Mathematising, Numerising: A Preliminary Disambiguation

Anyone who reads The Normal and the Pathological with the intention of reconstructing Canguilhem’s critique of his predecessors — Comte, Broussais, Bernard, Quetelet — soon encounters a conceptual difficulty: the “reduction” of the pathological to the normal covers very different intellectual operations. Sometimes it designates an ontological identification (the pathological is the normal, only varied in degree), sometimes an epistemic inclusion (the pathological is explained from the normal), sometimes a simple numerical treatment (the pathological is measured against the background of the normal). The critical literature has often inherited this ambiguity, treating “mathematisation,” “quantification,” “numerisation,” and “reduction” as interchangeable terms. Canguilhem’s anti-reductionist effort can be properly appreciated only by disaggregating the bundle of operations that fall under this umbrella term. The first three — mathematisation, quantification, numerisation — form, I suggest, a hierarchy of decreasing formal rigour. Reduction requires separate treatment, because its logic is orthogonal to that of the preceding three: it occupies no place on the scale but cuts across it — and it is precisely here that a possible difficulty in reading The Normal and the Pathological arises.

To mathematise is to embed a phenomenon in formal structures — relations, orders, axioms — independently of any use of numerical magnitudes. A valuable contribution in this direction comes from a seldom-discussed text, one closely connected with the themes of The Normal and the Pathological: the paper entitled ‘Quelques distinctions à propos de l’informe et à propos de sa mathématisation’ which Jacques Piquemal[2] — Canguilhem’s student and collaborator — presented in 1972 at the conference on the mathematisation of “informal” doctrines. Piquemal observes that the evolution of mathematics in the twentieth century — in particular the development of the formal theory of relations — has made it increasingly clear that to mathematise does not necessarily mean to quantify. There are perfectly mathematisable domains in which no measurements are taken and to which no real or rational numbers are assigned: mathematisation can consist in the identification of relational structures, orders, and symmetries, without any numerical magnitude entering the picture. The key insight is that a doctrine mathematised at one level may remain “informal” relative to a more demanding mathematisation: a hierarchy of levels thus emerges that cannot be collapsed into a simple quantitative gradation[3].

To quantify is a less demanding operation: it consists in associating numerical values with observable phenomena in a systematic and repeatable way. Unlike mathematisation, which can dispense with numbers, quantification is by definition numerical; but unlike mere numerisation, it presupposes systematicity: measurements must be repeatable and comparable. It does not, however, require a complete theory of the measured phenomenon, only a coherent framework within which to situate it.

To numerise is the least demanding of the three operations: it consists in punctually assigning a number to a phenomenon, without systematicity and without that act being part of a series of comparable measurements. Following Canguilhem, we can easily grasp what is meant: to state that a blood-glucose level above 1.6 grams per litre is a sign of diabetes is not to quantify — still less to mathematise — it is simply to fix a numerical threshold. The example of the arithmetic of occupational disability — which Piquemal develops with explicit reference to Canguilhem’s philosophy of the normal and the pathological — is equally instructive. To assign a percentage rate of incapacity to the loss of a thumb or to a reduction in visual acuity is an act of numerisation that, far from resolving the problem of measuring the pathological, reveals its irreducibility: the underlying biological concepts — functional compensation, the cooperation of synergistic organs — resist formalisation[4]. The number, in such cases, does not explain: it records, and sometimes conceals.

Finally, to reduce is an operation of an altogether different nature from the preceding three, and logically independent of each of them. Everett Mendelsohn, in the discussion following Piquemal’s paper[5], formulated the definition most pertinent to our purposes: to reduce is to reconduct a set of complex statements to another science, deemed more formalised or more fundamental. One can quantify without reducing — as Canguilhem suggests — and one can reduce without quantifying — as Comtean reductionism does, which reconducts the pathological to the normal at the level of principles before ever reaching the level of measurement. One can mathematise without reducing — as Mendel does, whose combinatorial model formalises hereditary relations without claiming to reconduct biology to a more fundamental science — and one can reduce without mathematising. Reduction is neither more nor less demanding than mathematisation or quantification: it is simply something else.

These distinctions make it possible to re-read the first part of The Normal and the Pathological with greater precision. What Canguilhem criticises is not a single operation but a family of operations that share an orientation — reconducting the pathological to the normal — while diverging profoundly in the manner of its execution. The following sections aim to articulate this divergence, beginning with the underlying grounds that sustain Canguilhem’s refusal of reduction.

3. Canguilhem and the Problem of Reduction : Why Life Cannot Be Reduced

As shown in Section 2, “reduction” is an umbrella term applicable to heterogeneous operations — from the reconduction of the pathological to quantitative variations of the normal, to the subsumption of medicine under the laws of physiology, to the statistical translation of biological individuality into an average type. We must now ask: what exactly disturbs Canguilhem about reductionist operations? Canguilhem does not reject quantification as such, nor does he oppose to scientific knowledge a “qualitative” knowledge that would be its rival. His critique targets, more precisely, every attempt to reduce the qualitative to the quantitative — that is, to treat the qualitative dimension of life as an eliminable appearance in favour of metric relations and physico-chemical laws. The target is not measurement, but the identification of measurement with the totality of biological reality.

Two theoretical cores sustain this position: on the one hand, what we may call, with due caution, Canguilhem’s vitalism; on the other, an axiological thesis concerning the nature of the concept of the normal.

3.1 Life and Reason: Vitalism as the Background of The Normal and the Pathological

The first core emerges with particular clarity in a seldom-discussed text: the Note sur la situation faite en France à la philosophie biologique[6], published in the Revue de Métaphysique et de Morale a few years after the drafting of the Essay. In these pages Canguilhem denounces the systematic hostility of the French philosophical tradition — from Cartesianism to the rationalism of Brunschvicg to Marxism — toward what he calls “biological philosophy.” Since Descartes, life has not been recognised as possessing an originality of its own. The living being is treated as a physical and mechanical object whose determinism is not in question, even if its precise formula remains to be found.

The guiding idea of the Note, as C. T. Wolfe[7] has shown, is not a rehabilitation of Romantic Naturphilosophie, but the recognition that certain anti-reductionist demands — reconciling the fracture between subject and nature, acknowledging the autopoietic capacities of organisms — speak to contemporary biology. The positive content of “biological philosophy” is exemplified by works such as Kurt Goldstein’s The Organism[8] and The Normal and the Pathological itself: studies that seek to account for the creative capacities of organisms, rather than treating them as passive and merely receptive mechanisms. Life, in this perspective, is defined all along The Normal and the Pathological as a form of creation, a transformation and sublimation of risks and catastrophic reactions.

Canguilhem’s vitalism, however, is often more fully developed in its critical dimension than in its positive one, here read as metaphysical. What he claims is not a vitalist irrationalism — Canguilhem rejects the “classical” and metaphysical vitalism that would make of the living being an exception to physical laws — but the recognition that life possesses properties found neither in stones nor in atoms or protons: a capacity for creation, for the transformation of risks, for the institution of norms in its relation with the environment.

This vitalist background is precisely what prevents Canguilhem from accepting the reductionist operation. Wolfe[9] has defined it, in a nice way, as an “attitudinal vitalism”: not a postulation of metaphysical vital forces, but an attitude of the living and knowing subject toward life — a refusal to reduce the living being to an inert object, without for all that invoking occult entities. For Canguilhem, vitalism is a permanent demand of life itself within the living being in search of knowledge. As G. Van de Vijver and L. Haeck[10] have specified, this “attitudinal posture” shifts the question of biological organisation beyond ontological commitments regarding the nature of things in themselves, toward epistemological questions concerning the position of the knowing subject, refusing to ontologise the idea of the “vital” so as not to fall into a scientifically untenable ontological vitalism.

If life is this irreducible phenomenon, it is so because it is normative: a normativity that eludes exhaustive rationalisation. The reduction of the pathological to a quantitative variation of the normal is therefore not merely incomplete: it is a mystification of the very workings of life. Such a reduction purports to account for the totality of the vital phenomenon by treating it as a mechanism whose deviation is measured on a scale, with nothing left over.

3.2. The Axiological Argument: Quantity Is Quality Denied but Not Suppressed

The second core of Canguilhem’s critique of reduction is axiological in nature and is stated with the greatest clarity in the chapter of the Essai devoted to Comte and Broussais. Here Canguilhem confronts head-on the determinist presupposition implicit in the identity of the physiological and the pathological: the “reduction”^[11] of quality to quantity. To reduce the difference between a healthy person and a diabetic to a quantitative difference in glucose, to delegate to a renal threshold the task of tracing the boundary between the sick and the well, is to obey the spirit of the physical sciences, which can explain phenomena only by reducing them to a measure.

As E. Meyerson has shown, it is by identifying reality with quantity that the human mind has built its knowledge. But — and this is the crucial point — scientific knowledge, in invalidating qualities that it makes appear illusory, does not for all that annul them. «Quantity is quality denied, not quality suppressed»[12] writes Canguilhem. The example proposed by Canguilhem is illuminating: the qualitative variety of colours perceived by the eye is reduced by science to quantitative differences in wavelength, yet it is the qualitative variety that still persists, in the form of quantitative differences, within the very calculation of wavelengths. And Canguilhem invokes Hegel: quantity, increased or decreased, transforms into quality — which would be entirely inconceivable if a relation to quality did not still persist within the denied quality that goes by the name of quantity[13] (ibid.).

From this standpoint, it is illegitimate to maintain that the pathological state is, really and simply, the plus-or-minus variation of the physiological state in a quantitative sense. Canguilhem’s concern relies on the difference between organism and machine, underwritten by his vitalist conception: a sick organism is not a deviant mechanism. It is a living being that institutes other norms, often narrower, sometimes entirely novel. This axiological production cannot be dissociated from its measurement; although it can be quantified and enumerated, the quality inscribed in the living being’s production of norms — whereby it prefers and excludes — is created together with the norm itself and for this reason cannot be subtracted from it. In this sense Canguilhem suggests in a provocative way that:

to fail to admit that from a biological point of view, life differentiates between its states means condemning oneself to be even unable to distinguish food from excrement. What distinguishes the one from the other is not a physico-chemical reality but a biological value. Likewise, what distinguishes the physiological from the pathological is not a physicochemical objective reality but a biological value[14].

In the second place, if the physiological state is conceived as endowed with a quality and a value for the living being, then it is absurd to extend that value, identical to itself through its variations, all the way to a state whose value marks a contrast with the first. If, on the other hand, what is meant by the physiological state is a mere summary of quantities devoid of biological value, then it possesses no vital quality and cannot be called either healthy, normal, or physiological. Taking again the example of the vision, the normal and the pathological — Canguilhem concludes — have no meaning whatsoever on the scale at which the biological object is decomposed into colloidal equilibria and ionised solutions, without any grasp of what those equilibria are worth, holistically, for the vital activity of the living being[15].

The argument takes the form of a dilemma. Whoever asserts the quantitative identity of the normal and the pathological is forced to choose: either the starting term — the “normal” — is already a value-laden concept, in which case the reduction fails because it cannot account for the qualitative leap that leads to the pathological; or the starting term is a bare metric fact, in which case it can no longer be called “normal” except by an abuse of language, since the word “normal” is by definition value-laden and charge in preferences. In both cases the reduction fails to accomplish what it promises: the elimination of the qualitative. It can only deny it — that is, conceal it beneath the language of measurement. Every type of reduction of life — be it that of Comte, Broussais, or Quetelet — runs up against the same obstacle: the qualitative, driven out through the front door of scientific explanation, comes back in through the window of the concept of norm.

It is precisely this result that justifies the survey of the diverse forms of reduction attempted in the first part of The Normal and the Pathological. Canguilhem does not refute them all in the same way, because they do not all operate in the same way. But the specific form that reduction assumes in each case — and the specific way in which the qualitative makes its return — can emerge only from analysis. In the sections that follow we shall examine the two principal forms: that of Broussais and Comte, and that of Quetelet.

4. Epistemic Reduction: Broussais and Comte

4.1. The Broussais Principle

With the framework in place, we can now turn to the reduction that Canguilhem targets most insistently: the so-called Broussais principle, as Comte inherited it, reformulated it, and elevated it to a dogma. According to this principle, the pathological state does not differ radically from the physiological state: it is merely a prolongation, an extension of the limits of variation — by excess or deficiency — proper to each phenomenon of the normal organism. No genuinely new phenomenon arises in disease; there is always and only a modification of intensity.

Broussais’s pathological theory can be reconstructed from De l’irritation et de la folie[16] — the work that Comte knew best and from which he drew the principle that would bear the surgeon’s name. For Broussais, excitation is the primordial vital fact: the human being exists solely by virtue of the excitation exerted upon its organs by the environments in which it is compelled to live. To apply the physiological doctrine to pathology is to investigate how such excitation can deviate from the normal state. All deviations are reducible to two poles: deficiency and excess. Irritation differs from excitation only in terms of quantity.

Now, as Canguilhem shows, this theory harbours a constitutive ambiguity. Broussais conflates cause and effect: a cause can vary quantitatively and continuously, yet produce qualitatively different effects — an increased excitation can bring about a pleasant state immediately followed by pain, two sensations that, as Canguilhem stresses, no one would wish to confuse[17]. Canguilhem further shows that Broussais’s vocabulary is only apparently quantitative. The terms “excess” and “deficiency” retain an implicitly qualitative and normative character: it is in relation to a norm that excess or deficiency obtains. To define the abnormal by the too-much or the too-little is already to acknowledge the normative character of the so-called normal state. Broussais’s “quantification” is not quantification in the strong sense. If we employ the distinctions proposed in Section 2, it amounts at most to an implicit numerisation: a quantitative intention that is never translated into metric operations.

It is instructive according to Canguilhem to compare this outcome with the doctrine of the Scottish physician John Brown, from whom Broussais draws the idea of excitation as the primordial fact. Brown had claimed to evaluate numerically the variable disposition of organs to be excited, and his pupil Lynch had constructed a veritable scale of degrees of incitation. As Canguilhem notes, one is entitled to smile at this «caricature of mathematisation of the pathological phenomenon»[18] yet the doctrine follows through on the demands of its postulates, with a conceptual consistency that is not found in Broussais. Brown had carried the quantitative identification of the normal and the pathological to its logical conclusion: if the difference is of degree and not of kind, then it must be measurable on a scale. The outcome is caricatural, but logically coherent.

Broussais, by contrast, inherits from Brown the quantitative intention but contaminates it with another legacy, that of X. Bichat. In the Recherches sur la vie et la mort[19] (1800), Bichat contrasts the object and methods of physiology with those of physics: instability and irregularity are essential characters of vital phenomena, and to force the latter into the rigid framework of metric relations is to denature them. The result is that Broussais’s doctrine inhabits a no man’s land between quantity and quality: it asserts the quantitative identity of the normal and the pathological, but lacks — and does not wish to possess — the instruments to translate that assertion into measurements. It is precisely this doctrine that Comte elevates to a universal principle — and this Bichatian legacy, as we shall see, will persist and grow stronger in the Comtean conception.

4.2. The Comtean Reduction

Auguste Comte not only adheres to the Broussais principle but never ceases to elevate it, extending its scope well beyond the field of pathology. As Canguilhem suggests[20], Comte broadens above all the horizon of application: the principle is destined to be extended to the intellectual and moral faculties, and ultimately to the collective organism, society. The principle of classification of the normal and the pathological is invested with universal authority: since the real interest in the theory of the normal and the pathological was for Comte anything but biological, the principle has for him the character of a dogma to apply to the social dimension.

But what exactly does Comte accomplish when he “reduces” the pathological to the normal? If we take up the grid of distinctions proposed in Section 2, we can specify that the Comtean reduction is neither a mathematisation, nor a quantification, nor a numerisation: Comte does not assign numbers to phenomena, does not construct scales, does not propose thresholds. He carries out neither experiments nor any of the observations he so prizes in principle. What he does is apply one and the same theory systematically across the domains of biology and sociology alike — and it is this very systematicity that reveals the nature of his operation. For what Comte accomplishes is, in the strict sense proposed by Mendelsohn, a reduction: a reconduction of one set of complex statements to another science deemed more fundamental. But the more fundamental science is not physics or chemistry — Comte, as we have seen, is actively hostile to the mathematisation of biology and grants it a genuine autonomy within his encyclopaedic hierarchy. The science to which the pathological is ultimately reduced is sociology: the theory of order and progress. The identity of the normal and the pathological matters to Comte not because it illuminates disease, but because it guarantees that political crises are mere variations of a stable social order. The rare numerical figure that surfaces in his account — when it surfaces at all — is not the product of a systematic theory of disease; it is an echo of Broussais’s vocabulary. What Comte accomplishes is a denial of the epistemic significance of the qualitative without measuring. The pathological is not to be measured as quantitatively identical to the normal; it is simply to be declared irrelevant as a distinct entity. The qualitative difference between health and disease is not translated into a quantitative difference — it is put out of play, excluded from the framework of what a positive science can and should take into account. It is a reduction by exclusion, not by translation.

Four elements converge in support of this characterisation.

The vaguely quantitative vocabulary. The pathological is defined by Comte according to Canguilhem, as a «simple prolongation, more or less extensive, of the limits of variation» of the normal. But the terms actually employed, as Canguilhem has shown, are only vaguely and mildly quantitative and retain a qualitative resonance that betrays their metric insufficiency[21]. As J-F. Braunstein has observed, the principle is formulated without medical examples to support it, without precise concepts to render it operational[22]. Canguilhem has insisted on this lacuna: Comte proposes no criterion that would make it possible to recognise that a phenomenon is normal, and uses the notions of normal state, physiological state, and natural state interchangeably[23]. He does not count, does not measure, does not propose scales. Better still: when called upon to define the limits of pathological disturbances compatible with the existence of organisms, Comte identifies those limits with those of a harmony of various influences, both external and internal — so that the concept of the normal, at last clarified by means of the concept of harmony, «is traced back to a qualitative and polyvalent concept, still more aesthetic and moral than scientific»[24]. The normal that should serve as a quantitative benchmark is itself defined in qualitative terms. Comte does not translate the qualitative into the quantitative: he denies it in pathology and finds it again, intact, in the very definition of the normal.

The hostility to statistics and to the mathematisation of biology. Comte not only fails to quantify: he is positively hostile to every attempt to do so. Canguilhem recalls this in The Normal and the Pathological[25] by referring to lesson XL of the Cours de philosophie positive[26]. Here the Bichatian legacy is systematised into a principled position. Comte insists on the necessity of differentiating the study of living organisms from such disciplines as geometry, physics, and astronomy, concluding that no idea of fixed numbers, still less of numerical laws, and above all of mathematical investigation, can be considered compatible with the fundamental character of biological inquiry[27].

A Comtean vitalism? This anti-metric stance belongs to a broader conception of life. As Canguilhem has shown in La philosophie biologique d’A. Comte[28], Comte’s admiration for Gall reveals a principled hostility to sensualism and mechanistic determinism: Comte found in Gall an argument in favour of the spontaneity of the organism against Cartesian automatism and mechanism. Canguilhem notes that Comte inherited from Bichat, through Blainville, a resolute hostility toward every mathematisation of biology, and that «however discreet, balances the profound logical requirements of the assertion of the identity between physiological and pathological mechanisms»[29].

The paradox of Comtean moral medicine. Finally, the Comtean conception of medicine confirms that the reduction carried out by Comte does not consist in making the pathological numerically tractable, but in denying it significance as an autonomous entity. As F. Dupin has shown (2010), for Comte biology is anti-reductionist in principle and synthetic in method. Medicine is not the application of physiological truths but an “art social.” The Comtean conception of life is built around the concept of milieu and of harmony — the very concept that, as Canguilhem has shown, is intrinsically normative and axiological. Harmony is not observed: it is evaluated. Hence the paradox. Comte denies the pathological any qualitative status of its own — pathologies result solely from deficiencies or excesses — but the entire edifice of his medicine rests on irreducibly qualitative concepts. By defining health as an essentially moral phenomenon, Comte makes the brain the central object of medical theory and subjects cerebral life to a triple determination — physical, physiological, and social. The physician must not separate disease from morality, nor therapeutics from education. The qualitative, declared irrelevant in pathology, thus re-enters from every side: in the definition of the normal as harmony, in the conception of health as moral hygiene, in therapeutics as education. Comte’s “enemy” is not the qualitative as such — indeed, the qualitative is the very instrument of the cure — but the qualitative as the epistemic significance of the pathological: the claim that disease is a qualitatively other entity relative to health, endowed with laws of its own and irreducible to a variation of the normal. And the qualitative, driven out through the front door of pathology, comes back in through the window of therapeutics.

5. Statistical Reduction: Quetelet and the Numerical School

5.1. Quetelet and the Ontological Production of the Average Man

The reduction carried out by A. Quetelet is profoundly different in nature from the Comtean one. Where Comte denied the pathological any epistemic significance — declaring it a mere variation of the normal without translating that declaration into metric operations — Quetelet performs an inverse and complementary operation: he constructs the normal as a statistical reality and produces, through calculation, a new entity — the average man (l’homme moyen) — that functions simultaneously as an arithmetic mean, a representative type, and a norm. Here the reduction is not by exclusion but by construction: from already quantitative data — measurements of stature, of chest circumference, of bodily proportions — Quetelet produces an object that claims ontological consistency. Crucially, Quetelet does not translate qualitative characteristics into numbers. His starting point is already numerical. What he does, rather, is confuse the norm with the mean: he takes a statistical regularity — a quantitative fact — and mistakes it for a normative one, treating the most frequent value as though it expressed a law of nature rather than the outcome of a qualitative normativity operating beneath the numbers.

As Canguilhem reconstructs, Quetelet — an astronomer and mathematician of considerable talent — had discovered around 1843 that many measurable human characters are distributed according to the Gaussian error curve. Studying variations of stature within a homogeneous population, he had established the existence of a frequency polygon with a vertex at the maximum ordinate and a symmetry about it. The “bell curve” became for Quetelet proof of the existence of a type of the human species, of which individual differences would be nothing but accidental fluctuations[30].

This is, as Piquemal has noted[31], a composite notion that amalgamates without the slightest critical scrutiny three distinct concepts: the arithmetic average man (likened to the centre of gravity in mechanics), the average man as the typical being of a population, and the average man as the individual in the “right measure.” Quetelet will never call this fusion into question: the discovery of the Gaussian distribution will not become for him the starting point of a rigorous mathematisation, but the crowning achievement of what appears to us today as an initial confusion. Quetelet reads the mean as if it were itself a norm, when in fact it is the statistical shadow of a normativity — vital, social, historical — that is irreducibly qualitative in character.

The interest of Quetelet’s conception, Canguilhem writes, lies in the fact that he identifies within his notion of the true mean the notions of statistical frequency and of norm[32]. But the direction of inference is reversed with respect to what one would expect. Quetelet does not present the mean as the empirical foundation of the norm: he explicitly presents an ontological regularity as expressing itself through the mean. The average man is not just a proper statistical abstraction: for Quetelet, he is a real entity, and the regularity that the mean reveals is a law of nature[33]. The existence of the mean is the sign of the existence of a regularity — and for Quetelet this regularity has an ultimately divine foundation.

5.2. Canguilhem’s Reversal: The Normative Precedes the Normal

The critical analysis that Canguilhem conducts of Quetelet’s position, drawing on the examination by Halbwachs[34], is not limited to denouncing the metaphysical naïveté of this construction. It targets the very logic of the reductive operation.

Halbwachs had shown that Quetelet errs when he treats the distribution of human statures as a phenomenon to which the laws of chance can be applied. The principal condition for such application is that the realisations be mutually independent. Now, this is untenable in the human domain, where social norms interfere with biological laws: the human individual is the product of a coupling that obeys customary and legislative prescriptions. Heredity and tradition, habit and custom constitute so many obstacles to an adequate use of the calculus of probabilities[35].

But Canguilhem goes beyond Halbwachs’s critique. Even conceding that Quetelet was mistaken in attributing to the mean the value of a divine norm, this happened only insofar as he specified the norm, not insofar as he interpreted the mean as the sign of a norm. If the human body is in a certain sense a product of social activity, it is not absurd to suppose that the constancy of certain traits depends on conscious or unconscious fidelity to certain norms of life. Consequently, in the human species, statistical frequency expresses not only a vital normativity but also a social one. And it is here that Canguilhem delivers the formula that overturns the entire Queteletian construction: «a human trait would not be normal because frequent but frequent because normal, that is, normative in one given kind of life»[36].

The reversal is radical. Where Quetelet made the mean the source of the norm, Canguilhem shows that it is vital and social normativity that produces statistical regularity. The mean does not found the norm: it reflects it. If a given stature is the most frequent in a given population, this is not because nature has produced an ideal type around which individuals distribute themselves by chance, but because a certain way of life — with its dietary norms, its marriage customs, its working conditions — has selected and favoured certain traits at the expense of others. Statistical regularity is the effect of a normativity, not its cause.

The Queteletian reduction thus reveals itself, in Canguilhem’s reading, as a reduction that produces an ontological reality — the average man — from a statistical operation, but in so doing inverts the relation between norm and mean. The error is not in calculating means: it is in conflating the mean with the norm, frequency with value, statistical regularity with the law of life. Which amounts, to return to the Hegelian formula of Section 3.2, to a particularly effective form of denial of the qualitative: no longer a declaration of irrelevance, as in Comte, but a substitution by means of statistics — biological value is replaced by frequency, the norm is absorbed into the mean, and the qualitative difference between the healthy and the sick becomes a numerical deviation from an ontological type.

5.3. Louis’s Numerical School: Statistical Reduction in Clinical Practice

If Quetelet had constructed the average man as the type of the species on the basis of the Gaussian distribution of anatomical characters, the numerical method of Pierre-Charles-Alexandre Louis, a physician trained under A.-F. Chomel in Paris, carries the reductive operation into the heart of clinical practice. Louis does not derive from Quetelet: his numerical school arises in parallel, as a response to the same lacuna that we identified in Broussais — the absence of a genuine quantitative rationality in physiological medicine. But where Broussais and Comte had evaded the problem by declaring the qualitative irrelevant, Louis proposes to translate the qualitative into the quantitative systematically, rendering the former homogeneous with the latter and thus calculable. It marks a further step toward ontological reduction: the reality of disease is transformed into a numerical reality by conversion.

The principle of the numerical method is simple: to integrate anatomo-pathological studies with a systematic collection of data. Statistics, for Louis, is not an ornament of clinical practice but its foundation — a systematic form of data collection capable of placing medicine on the same scientific footing as chemistry.

Now, statistics demands homogeneity of data — and here lies the crux of the matter. For clinical data to be comparable, everything the physician observes must receive numerical expression. Louis intended to replace the qualitative adverbs then current in medicine — “often,” “rarely,” “occasionally” — with precise numerical ratios[37]. The presupposition is that qualitative phenomena can be rendered homogeneous with quantitative data by transforming the former into the latter. This is not a mere methodological expedient: it is an ontological assumption — the conviction that the conversion of the qualitative into the quantitative loses nothing essential, that the number can take the place of quality without remainder[38].

From this presupposition there follows a consequence that Canguilhem will not fail to note: the loss of the individuality of the patient — the very individuality that he will define as the patient’s own normativity. In the numerical method, patients cease to represent distinct individuals capable of unique adaptive responses to disease; they become anonymous cases within larger groups, identified with their pathologies[39]. The collection of individual data and their subsequent quantification and depersonalisation transform the single patient into a case belonging to a pathological category — thereby completing the process of abstraction that Quetelet had inaugurated at the anthropometric level.

The difference between the two forms of reduction analysed in this article now emerges in full clarity. In Comte, the qualitative is denied: declared irrelevant as an explanatory category in pathology, excluded from the framework of positive science, yet not replaced by any metric operation — so that it returns, intact, through the window of therapeutics, in the definition of the normal as harmony, in the conception of health as moral hygiene. In statistics, the qualitative is transformed. From this transformation new objects arise that claim to occupy the place of the eliminated qualitative. Where Comte drove the qualitative out through the front door of pathology and found it again at the window of therapeutics, Louis absorbs it into the mean and into frequency: what returns, this time, is not the qualitative itself but its quantitative simulacrum — the norm disguised as a mean, biological value disguised as a statistical datum. Both reductions run up against the same obstacle identified by Canguilhem: the qualitative, driven out through the front door of scientific explanation, comes back in through the window of the concept of norm. But it does so in different ways, and recognising this diversity — such is the thesis this article has sought to argue — is the condition for appreciating the scope and precision of Canguilhem’s critique.

6. Conclusion

This article has sought to show that Canguilhem’s critique of the reduction of the pathological to the normal does not target a single operation but a family of heterogeneous operations that the term “reduction” tends to conflate. The disambiguation proposed in Section 2 offered the conceptual grid for re-reading with greater precision the cases examined by Canguilhem; Section 3 made explicit the underlying grounds of Canguilhem’s refusal: an attitudinal vitalism that recognises in life an irreducible normativity, and an axiological argument from which it follows that quantity is quality denied but not abolished. On this basis, Sections 4  and 5 argued the central thesis. The Comtean reduction is a reduction by exclusion: the qualitative is not translated into quantity; it is declared devoid of epistemic significance — but, driven out through the front door of pathology, it comes back in through the window of therapeutics. The Queteletian reduction and the numerism of Louis is, by contrast, an ontological reduction by translation: the qualitative is converted into quantity through the calculation of means, and from this conversion new objects arise — the average man, the patient as a case within a pathological category — that claim to replace it, yet restore it as their own quantitative simulacrum. In both cases the qualitative cannot be wholly eliminated: it can be denied or transformed, but it cannot vanish, because the concept of norm itself is irreducibly qualitative and axiological. Distinguishing the different modalities through which reduction attempts this suppression is not an exercise in terminological hair-splitting: it is the condition for understanding why The Normal and the Pathological remains, more than eighty years after its drafting, a text whose critique has lost none of its pertinence.

[1] G. Canguilhem, The Normal and the Pathological (1966), Zone Books, New York 1991.

[2] J. Piquemal, Quelques distinctions à propos de l’informe et à propos de sa mathématisation, in G. Canguilhem, La mathématisation des doctrines informes, 24–26 Juin 1970, Hermann, Paris 1972, pp. 157–190.

[3] Ibid., pp. 154-160.

[4] Ibid., pp. 160-164.

[5] Ibid., p. 178.

[6] G. Canguilhem, Note sur la situation faite en France à la philosophie biologique in «Revue de Métaphysique et de Morale», 52(3/4), 1947, pp. 322–332.

[7] C.T. Wolfe, A Note on the Situation of Biological Philosophy, in «Revue internationale de philosophie», 307, 1, 2024, pp. 95–110.

[8] K. Goldstein, The Organism: A Holistic Approach to Biology Derived from Pathological Data in Man, American Book Company, New York 1939.

[9] C. T. Wolfe, From Substantival to Functional Vitalism and Beyond: Animas, Organisms and Attitudes, in «Eidos», 14, 2011, pp. 212–235.

[10] G. Van de Vijver, L. Haeck, Canguilhem’s Divided Subject. A Kantian Perspective on the Intertwinement of Logic and Life, in G. Bianco, C.T. Wolfe, and G. Van de Vijver (eds.), Canguilhem and Continental Philosophy of Biology, Springer, Cham 2023, pp. 123–146.

[11] It is important to note that the reduction here is an epistemic one, not yet statistical. See part 4 and 5.

[12] G. Canguilhem, The Normal and the Pathological, cit., p. 110.

[13] Ibid.

[14] Ibid., p. 220.

[15] Ibid., p. 110.

[16] F. J.V. Broussais, De l’irritation et de la folie, Chez Mlle Delaunay, Paris-Bruxelles 1828.

[17] G. Canguilhem, The Normal and the Pathological, cit., p. 55.

[18] Ibid., p. 60.

[19] X. Bichat, Recherches physiologiques sur la vie et la mort, Brosson, Paris 1800.

[20] G. Canguilhem, La philosophie biologique d’Auguste Comte et son influence en France au XIXe siècle, in «Bulletin de la Société française de philosophie» in numéro spécial: Célébration du centenaire de la mort d’Auguste Comte, 1958, pp. 13–26.

[21] G. Canguilhem, The Normal and the Pathological, cit., p. 52.

[22] J.-F. Braunstein, Canguilhem, Comte et le positivisme, in F. Bing, J.-F. Braunstein, and É. Roudinesco (eds.), Actualité de Georges Canguilhem. Le normal et le pathologique, Les Empêcheurs de penser en rond, Le Plessis-Robinson 1998, pp. 95–120.

[23] G. Canguilhem, The Normal and the Pathological, cit., pp. 52-53.

[24] Ibid., p. 53.

[25] Ibid., p. 61.

[26] A. Comte, Cours de philosophie positive, Baillière et Fils, Paris 1869³.

[27] Ibid., pp. 291-292.

[28] G. Canguilhem, La philosophie biologique d’A. Comte, in La philosophie biologique d’Auguste Comte et son influence en France au XIXe siècle, Bulletin de la Société française de philosophie, numéro spécial: Célébration du centenaire de la mort d’Auguste Comte, 1958, pp. 13–26.

[29] Id., The Normal and the Pathological, cit., p. 64.

[30] Ibid., pp. 157-158.

[31] J. Piquemal, Quelques distinctions à propos de l’informe et à propos de sa mathématisation, in «La mathématisation des doctrines informes», 24–26 Juin 1970, Hermann, Paris 1972, pp. 157–190.

[32] G. Canguilhem, The Normal and the Pathological, cit., p. 158.

[33] A. Quetelet, Anthropométrie ou mesure des différentes facultés de l’homme, C. Muquardt, Bruxelles 1871.

[34] M. Halbwachs, La théorie de l’homme moyen : essai sur Quetelet et la statistique morale, Félix Alcan, Paris 1913.

[35] G. Canguilhem, The Normal and the Pathological, cit., p. 161.

[36] Ibid., p. 160.

[37] P.-C.-A. Louis, De l’examen des malades et de la recherche des faits généraux, in «Mémoires de la Société Médicale d’Observation», 1, pp. 1–63.

[38] Id., Généralités sur l’enseignement de la médecine clinique, ou idée succincte de la méthode à suivre dans l’examen des malades et dans la recherche des faits généraux, Lachevardière, Paris 1831.

[39] G. Canguilhem, La statistique médicale en France dans la première moitié du XIXe siècle, in Centre d’archive en philosophie, histoire et éditions des sciences – Paris 1963 – CAPHES, GC 24.9.10, p. 7.