Knowing How We Know That: A New History of Science

Central Thesis

Knowledge is always fully multimediated. It is constituted at once by the body, by relationships with others, by place, by material things, and by symbols. Symbolisation is one constitutive mediation among five. It is not an external addition to a knowledge that already exists without it, and it is not the whole of knowledge either.

This has a further implication the rest of the article depends on. Knowledge spans two very different registers. Some knowing proceeds seamlessly, in the unreflective coordination of a skilled body moving through a familiar world: a surgeon’s hands finding the right pressure before any thought intervenes, a sailor reading a shift in the wind before it has been named.

Call this seamless, being-in-the-world knowing. Other knowing has been made explicit: named, generalised, written down, argued over, taught to strangers who were never present when it was first achieved. Call this symbolised knowledge. Symbolisation reaches only the second register. It stabilises, names, and generalises fragments of what is known; it never fully captures the seamless coordination out of which any explicit articulation is drawn, and it was never going to. That is the boundary this article is concerned with: not a boundary between knowledge and non-knowledge, but a boundary internal to knowledge itself, between what symbols can hold and what remains, irreducibly, outside their reach.

Within symbolisation, however, there exist radically different technologies for stabilising and communicating what has been made explicit. Ordinary language remains permanently nourished by the body, by relationships, by place, and by material life; its meanings are renewed daily by the coordinations that sustain them. Formal systems, mathematics, logic, chemical notation, musical notation, and their kin, are deliberately constructed technologies that, once built, operate largely by rules internal to themselves rather than by constant reference back to bodily, relational, spatial, or material experience. Their purpose is either to describe some aspect of reality with a precision ordinary language cannot achieve, or to coordinate future activity, a meal, a performance, a building, in ways ordinary description was never built to do.

This distinction reframes the philosophy of knowledge, and it also reveals something worth pausing over in contemporary history of science. Over the past half-century the field has done a great deal to broaden what it studies: trust and credibility among early modern scientific communities, laboratory apparatus and embodied witnessing, networks of instruments and inscriptions, the material and institutional culture of scientific practice. It has, in other words, already learned to attend to the body, to relationships, and to material things as constitutive of scientific knowledge, not merely as its backdrop. What the field has not yet turned its attention to is a narrower and more specific question: whether the ordinary language it uses to theorise all of this, the vocabulary in which it talks about knowledge itself, carries a stable and largely unexamined character of its own, drawn overwhelmingly from a single source, industrial production and exchange, however varied the phenomena being studied have become.

The article develops a fully multimediated account of knowledge and symbolisation, uses the history of science as a recurring test case for that account, and opens a comparative programme for studying the many different technologies through which human beings stabilise what they know.

The Hidden Crisis of Knowledge

Begin with a large history-of-science conference: the kind that now convenes hundreds of papers under a single roof, spanning centuries and continents, drawing together historians, philosophers, and sociologists of science from every specialism the discipline has produced. Read the programme of such a gathering and a vocabulary announces itself before any single paper does. Knowledge production. Knowledge circulation. Knowledge transfer. Knowledge exchange. Knowledge infrastructures. Knowledge networks. Knowledge diplomacy. Knowledge legitimacy. Session after session investigates some movement of knowledge: how it travelled from a laboratory to a colony, how it was translated across a language, how it accumulated in an archive, how it was contested in a courtroom, how it was denied to those who produced it and credited to those who did not.

Notice something almost too obvious to notice. The conference investigates every imaginable movement of knowledge. It maps circulation with extraordinary sophistication. And almost nowhere, across the full breadth of a programme this size, does a paper pause

to ask the question that would seem to be logically prior to all the others: what is knowledge, such that it can be produced, stored, circulated, and exchanged in the first place? The field has become extraordinarily sophisticated about knowledge’s biography while remaining largely silent about its constitution. It has a rich vocabulary for what happens to knowledge and almost no vocabulary for what knowledge is made of.

This is not a criticism of any individual scholar or paper; it is a structural observation about a disciplinary vocabulary, and it is the point of departure for this article. If an entire field can produce hundreds of sophisticated studies of something without ever quite specifying what that something is made of, the vocabulary doing the specifying deserves scrutiny in its own right.

The Commodity Vocabulary of Knowledge

The vocabulary is revealing once it is set out plainly. Knowledge, in the standard idiom of the history and sociology of science, is produced. It is stored. It is circulated. It is distributed. It is transferred. It is mobilised. It is accumulated. It is exchanged. Every one of these verbs has a home, and that home is not symbolisation. It is the world of material production.

Factories produce. Warehouses store. Roads and shipping lanes circulate goods. Markets exchange commodities. Supply chains mobilise resources and distribute them across geographies. This is the semantic field from which the entire working vocabulary of knowledge studies has been drawn, largely without notice, because the borrowing happened so long ago and has been so thoroughly naturalised that it no longer reads as borrowing at all. It reads as simply how one talks about knowledge.

This is not merely an instance of capitalism colonising academic language, though it is certainly compatible with that older critique. It is something more specific: a vocabulary built for one dimension of life has been extended, quietly and by habit, to describe a phenomenon that is not primarily made of that dimension at all. Knowledge involves material infrastructure, certainly, laboratories, instruments, archives, printing presses, servers. But the vocabulary does not merely acknowledge that material substrate; it uses the substrate’s own verbs to describe the phenomenon in its entirety, bodily skill, relationships of trust, situatedness in place, and symbolic articulation included. When a field says that knowledge “flows” from a periphery to a centre, it has already decided, at the level of grammar rather than argument, that knowledge behaves like a commodity in transit. Everything the paper subsequently says about that knowledge inherits the assumptions built into the verb before a single piece of evidence has been presented.

It is worth being precise about what is and is not being claimed. The claim is not that historians of science are unaware that knowledge involves bodies, relationships, and places as well as archives and instruments; the following section shows in some detail that they are very much aware of this, and have been for decades. The claim is narrower and, for that reason, harder to dislodge: that the working vocabulary in which their theoretical claims are actually written systematically foregrounds one dimension of knowledge and correspondingly backgrounds the rest, regardless of what any individual scholar would affirm if questioned explicitly. Vocabulary shapes what gets noticed and named long before it shapes what gets consciously believed, and it is at this quiet, grammatical level that the habit described here does its work.

A Field That Broadened Its Objects but Kept Its Vocabulary

It would be a mistake to read the preceding section as a claim that the history and sociology of science have neglected the body, relationships, or material things as objects of study. The opposite is closer to the truth, and the argument is considerably stronger once this is acknowledged directly.

Over the past half-century, the field has done exactly the work that a narrow, text-centred history of ideas was once accused of failing to do. Steven Shapin’s account of trust and gentlemanly credibility in early modern experimental communities is, in substance, an account of how relationships and social standing became constitutive of what counted as reliable knowledge. Simon Schaffer’s work on the air pump and its witnesses is, in substance, an account of how bodily presence, apparatus, and embodied demonstration became constitutive of experimental fact. Bruno Latour’s account of laboratories, instruments, and inscriptions is, in substance, an account of how networks of relationships and material objects together hold a scientific claim in place. Lorraine Daston’s work on the historical construction of objectivity traces how bodily discipline, material technologies of representation, and institutional convention were woven together to produce a specific, historically contingent scientific self. Feminist science studies, in the tradition associated with Sandra Harding and Evelyn Fox Keller, has shown how the social position of the researcher shapes which questions get asked in the first place, a further and distinct kind of contribution this article returns to below. Laboratory ethnography more broadly has spent decades documenting the embodied, improvisational, relationally dense texture of scientific work that formal publications erase.

None of this amounts to a field that ignores the body, relationships, or material things. It amounts to a field that has, over several decades, dramatically broadened which aspects of scientific life it treats as worth studying. That broadening is real, and it should be credited as such.

What none of this scholarship has done, however, and what this article is actually concerned with, is turn the same scrutiny on the field’s own theoretical vocabulary: on the words historians reach for when they step back from a case study and say what knowledge, in general, is and does. That vocabulary, production, circulation, storage, transfer, exchange, has remained remarkably stable across exactly the period in which the objects of study diversified so dramatically. A historian steeped in Shapin’s account of trust, or Schaffer’s account of embodied witnessing, or Latour’s account of material networks, will nonetheless very often reach for “circulation” and “production” the moment the discussion turns from a specific case to a general claim about knowledge as such. The issue, then, is not that the field has neglected the mediations. It is that it has increasingly diversified the phenomena it studies while leaving remarkably stable the ordinary-language vocabulary through which it theorises those phenomena in general terms. That is a considerably more precise claim than a charge of neglect, and it is the claim this article develops.

Knowledge Is Fully Multimediated

The alternative on offer here begins by rejecting a much older assumption, one the historyof-science vocabulary inherits without examining: the assumption, running through most of the Western philosophical tradition since at least the seventeenth century, that knowledge just is a symbolic or propositional achievement, a justified true belief, a well-formed statement, a proposition that stands in the right relation to the world.

Knowledge is always fully multimediated: it is simultaneously bodily, relational, material, situated in place, and symbolic, constituted across all five of these at once, never reducible to the symbolic dimension alone, and never excluding it either. Symbols do not stand outside knowledge, waiting to describe it from a distance. Whenever symbolisation is part of a coordination, it is constitutive of the knowledge that coordination amounts to, exactly as the body, relationships, place, and material things are constitutive when they are involved. A surgeon’s knowledge of an operation is not contained in the textbook description of the procedure, but it is not independent of that description either; it is distributed across the surgeon’s trained hands, the years of apprenticeship under more senior surgeons, the layout and instrumentation of the operating theatre, and the symbolic articulation, in protocol, in case notes, in the language exchanged with colleagues, through which the procedure is reviewed, taught, and revised. Remove any one of these and something different, not merely something smaller, is left behind.

This is where the boundary claim set out at the start becomes important. The point is not that knowledge is somehow prior to symbols, sitting complete and finished before language arrives to describe it from outside. The point is narrower and more exact: symbolisation only ever reaches part of what knowing involves. Some knowing proceeds seamlessly, registered and acted on without needing to be put into words at all; call this the unreflective register. Other knowing has been made explicit, named, generalised, and stabilised in a form that can travel beyond the situation that produced it; call this the articulated register. Symbolisation constitutes knowledge whenever it is present, but it is only ever present, as the primary carrier, in the second register. It cannot fully colonise the first, and treating a symbolic account as though it exhausted the knowing it describes is precisely the error the commodity vocabulary of Section II encourages, because a vocabulary of production and circulation implicitly treats knowledge as though it were entirely made of the portable, articulated kind, the kind that actually can be produced, stored, and exchanged, and has nothing to say about the unreflective register that never fully enters that economy at all.

There is no contradiction, incidentally, in an article that makes this argument being itself a piece of symbolic articulation. Symbolisation was never claimed to be external to knowledge, only partial with respect to it. This article is a contribution, in the articulated register, to an ongoing coordination that also includes the unreflective, embodied, relational habits of the people who read and use it; it does not claim to replace that coordination, only to describe its shape more accurately than the commodity vocabulary does.

One further precision closes a gap this formulation would otherwise leave open. Wherever symbolisation is part of a coordination, it is constitutive of the knowledge that coordination amounts to. Its absence does not make a coordination fall short of being knowledge; it simply makes that coordination non-articulable in the register symbols reach. A fox reading a landscape, a dog anticipating a familiar walk, a human infant recognising a caregiver before either has language for it: these are coordinations across the body, place, material things, and often relationship, without symbolisation playing any constitutive role at all, and nothing in this account requires calling them lesser knowledge, still less non-knowledge, for that reason. What can be said is only that such coordinations remain, permanently, outside the reach of the articulated register this article is chiefly concerned with, not that they fall short of what knowing is.

The justified-true-belief tradition, and its many descendants and critics within analytic epistemology, largely accepted a propositional starting point even while disputing what should be added to true belief to make it knowledge. Gettier cases, reliabilism, virtue epistemology, each of these debates operates on the assumption that the object under analysis is, at bottom, a proposition or a believing of a proposition, and asks what further condition converts mere true belief into knowledge proper. This article does not enter that debate on its own terms, because it rejects the shared premise that makes the debate possible: that knowledge is, in the first instance, a propositional attitude to be analysed rather than a multimediated coordination, only part of which is ever propositional in form.

The practical consequence of relocating knowledge in this way is significant for any discipline that studies knowledge historically. If knowledge just were propositional content, the historian’s task would reduce, in principle, to tracing which propositions were believed, by whom, and when, a task the vocabulary of circulation and transfer describes reasonably well. If knowledge is fully multimediated, and only partly articulated at that, the historian’s task is considerably larger: it requires attending to bodily skill that rarely survives in textual archives, to relationships of trust and apprenticeship that leave only fragmentary traces, to the specific material instrumentation without which a given coordination could not have occurred, and to a situatedness in place that shaped what could be discovered there and nowhere else. Much of this is, in practice, irrecoverable for historical periods beyond living memory. That irrecoverability is not a reason to pretend the missing dimensions were not there; it is a reason for the field to be considerably more modest about how much of “what was known” a documentary archive alone can actually reconstruct. A field that describes knowledge as something produced and circulated has, without quite meaning to, mistaken the articulated residue for the whole of what it is studying.

What Each Dimension Contributes to Knowing

If knowledge is fully multimediated, each of its five constituting dimensions must be shown to make an irreducible contribution to it, one that cannot be absorbed into any of the others.

The body contributes perception, skill, attunement, and recognition: the trained eye of the field geologist who sees a fault line where a novice sees only rock, the potter’s hands that know the clay is ready before any measurement confirms it, the clinician’s sense that something is wrong before the symptoms have been named. Relationships with others contribute apprenticeship, trust, authority, correction, and shared attention: knowledge is transmitted through relationships of trust between teacher and student, through the correction of error by a more experienced colleague, through the shared attention that a research group directs at a shared problem. Material things contribute tools, instruments, and infrastructure: the telescope, the assay, the archive, the server, each of which does not merely record knowledge already achieved elsewhere but actively participates in making certain forms of knowing possible and others impossible. Place contributes orientation, affordance, and situatedness: knowledge of a landscape is inseparable from having been oriented within it, and much traditional ecological knowledge is knowledge precisely because it is inseparable from a place rather than a portable claim about one. Symbolisation contributes stabilisation, reflection, communication, and the capacity to fix a piece of knowing in a form that survives the death of the knower, that can be argued over, revised, and transmitted to those who were never present at its original discovery.

None of these five can become knowledge by itself. A perfectly stabilised symbolic proposition with no bodily skill behind it, no relational transmission, no material instrumentation, and no situatedness in a working environment is not knowledge in any sense a working scientist, craftsperson, or practitioner would recognise; it is at best a claim awaiting the coordination that would make it actionable.

The irreducibility of each dimension can be tested by subtraction. Remove bodily skill from a laboratory’s coordination and the instruments remain, the protocols remain, the archive remains, but nobody is left to run the assay, calibrate the equipment against its drift, or notice the anomaly that does not match the expected trace; what remains is inert infrastructure, not knowledge in operation. Remove relationships and a solitary researcher can still perceive, handle instruments, and write, but has lost the apprenticeship through which technique was originally transmitted and the correction through which error is normally caught before publication; knowledge produced this way is demonstrably more fragile than knowledge sustained within a working relational field. Remove material things and bodily skill, trust, and situated orientation may all remain intact, but there is no telescope, no assay, no instrument through which any of that can act on, or register anything about, a world beyond immediate reach. Remove place and a research group can retain its instruments, its relationships, and its skills, yet lose the orientation within a specific field site or institutional landscape that made a given set of anomalies visible in the first place; the field sciences in particular are barely coherent as practices once severed from the places whose particularities they were built to register. Remove symbolisation last, and everything else may remain, but nothing can be stabilised beyond the working lifetime of those immediately involved, transmitted to distant collaborators, or subjected to the kind of sustained scrutiny that turns competent individual practice into a shared and revisable body of knowledge.

Each subtraction produces a genuinely different kind of deficiency, not a smaller amount of the same thing. The five dimensions are not five overlapping ways of describing a single underlying capacity that could, in principle, be fully captured by any one of them given enough elaboration; they are five independent contributions, and a coordination that is fully intact along four of them while damaged along the fifth is not eighty per cent as good as full coordination. This is why a vocabulary built almost entirely from the language of production and exchange can never, on its own terms, register what has gone missing when bodily skill, relationships, or place drop out of a historical account of knowledge. A field that can say a manuscript was produced and circulated has no comparably fluent way of saying that the apprenticeship behind it collapsed, or that the site that generated its anomalies has since been destroyed.

Lakoff and Johnson Were Right, but About Only One Source

George Lakoff and Mark Johnson’s account of conceptual metaphor made a genuine and lasting contribution: abstract thought is structured by metaphors drawn from concrete experiential domains, and those metaphors are not decorative but constitutive of how abstract concepts are actually reasoned about. This insight deserves to be preserved.

But their account has a limitation that becomes visible once knowledge is understood as fully multimediated: for Lakoff and Johnson, experience effectively collapses into the body. Their source domains are overwhelmingly bodily: containers, paths, forces, verticality, balance. This article asks a question their theory never quite poses: where do metaphors actually come from, across the full range of what constitutes experience? The answer is that they come from all four non-symbolic dimensions of knowing, the body, relationships, place, and material things, not from the body alone. This multiplies the explanatory reach of the theory of conceptual metaphor without discarding its central insight. Metaphor is still experientially grounded. What changes is the recognition that experience itself has more than one source, and a theory of metaphor built on one source will necessarily misdescribe metaphors whose origin lies elsewhere.

Where Ordinary Language Gets Its Metaphors

Once this reframing is in place, every ordinary-language metaphor can be traced to one of four sources. Bodily metaphors supply grasp, see, balance, stand, and the entire vocabulary of physical orientation applied to abstract thought, “I see what you mean,” “grasping an argument,” “a balanced view.” Relational metaphors supply trust, follow, agreement, authority, “following an argument,” “trusting the data,” “an authoritative source.” Material metaphors supply build, produce, construct, circulate, the entire industrial vocabulary already diagnosed in Sections II and III, but now recognisable as one source among several rather than the whole of ordinary language. Metaphors of place supply field, ground, ground truth, path, home, horizon, “a field of study,” “grounding a claim,” “a research path,” terms so naturalised in scholarly prose that their spatial origin is rarely noticed.

The upshot is that ordinary language continuously draws on all four of these sources at once. It is never nourished by the body alone, or by material things alone, or by place alone; it draws promiscuously on all of them, often within a single sentence, and this promiscuous drawing is precisely what keeps ordinary language semantically alive, tethered to the coordinations that generate and sustain meaning.

This has a consequence worth making explicit, because it explains why ordinary language, despite its imprecision relative to formal systems, has proven so durable across the entire span of human history and so resistant to replacement. A formal system, once its internal rules are fixed, gains inferential power precisely by cutting loose from constant dependence on bodily, relational, spatial, or material reference; but this same cut is what makes a formal system brittle outside the narrow domain it was built for, and unable, on its own, to renew its meanings when the surrounding coordinations change. Ordinary language pays for its comparative imprecision with an offsetting flexibility: because it keeps drawing new metaphorical resources from the body, from relationships, from place, and from material life as those things themselves change historically, it can absorb and articulate genuinely novel coordinations that no formal system anticipated. A community that has never encountered a given new technology nonetheless finds ordinary-language resources, however imperfect, to talk about it within a generation.

The claim that metaphors come from four different sources rather than from the body alone is not merely a tidier taxonomy than Lakoff and Johnson’s; it makes predictions that can be checked. It predicts that communities whose working life is organised primarily around material production, industrial modernity’s academic and administrative registers among them, will recruit their abstract vocabulary disproportionately from building, construction, and circulation, exactly the pattern already traced through the history-of-science conference. It predicts that traditions whose life is organised primarily around place, many land-based and Indigenous traditions among them, will recruit their abstract vocabulary disproportionately from orientation, terrain, and seasonal cycle rather than from industrial process. It predicts that traditions whose life is organised primarily around relationships with others, many religious and ritual traditions among them, will recruit their abstract vocabulary disproportionately from trust, covenant, obedience, and address. And it predicts that economic language, organised around material exchange specifically, will recruit a vocabulary of flow, accumulation, and circulation strikingly similar to the vocabulary already diagnosed in the history of science, which is itself no coincidence: both are drawing on the same source.

This is a considerably larger claim than a single chapter can properly test, and it points toward a project of its own, a systematic comparison of metaphor sources across different discourse communities, historical periods, and languages, one this article can only gesture toward here before returning to its narrower argument about knowledge and the history of science.

Ordinary Language Is One Technology Among Many

This is the major shift the article now needs to make explicit, because it is a shift the entire philosophical tradition, including Lakoff and Johnson at their most ambitious, has quietly declined to make. Their implicit assumption, inherited from a much longer philosophical habit, is that ordinary language simply is symbolisation: that to have a theory of metaphor in natural language is to have, in essence, a theory of symbols as such.

This article rejects that assumption. There are dozens of distinct technologies for stabilising and communicating what is known, and ordinary language is only one of them. Mathematics is another. Chemical notation is another. Musical notation is another. Cartography is another.

Formal logic is another. Programming languages are another. Recipes are another. Architectural plans are another. Double-entry accounting is another. Dance notation is another. Phylogenetic trees are another. Legal codes and contracts are another, an internally coherent system of definitions, precedents, and rules of interpretation that only partly depends on ordinary meaning once it has been stabilised. Religious liturgies and ritual sequences are another, governed by canonical order and rules of valid performance rather than by everyday semantics alone. Each of these evolved under different pressures, serves a different purpose, and relates to the body, relationships, place, and material life in a fundamentally different way than ordinary language does. Treating ordinary language as the paradigm case of symbolisation, and generalising conclusions drawn from it to symbolisation as such, mistakes one technology, however important, for the whole field.

This list should not be read as decoration. It is close to the article’s real subject. Everything said here about knowledge, about the history of science, about metaphor, is an application of a single underlying claim: that symbolisation is not a single, uniform activity but a landscape of distinct technologies, each deserving its own account. The remainder of the article develops that landscape through a small number of cases, chiefly the contrast between ordinary language and formal mathematical notation, but the argument being built is general, and knowledge is simply the first domain rich enough to force the distinction into view.

It is worth being clear about what kind of claim this is, because it is easy to misread as a

claim about how scientists think. It is not. No scientist reasons only in equations, any more than a musician reasons only in notation. Working scientific practice is constantly multitechnological: a physicist moves between ordinary conversation, a diagram sketched on a whiteboard, an equation, a gesture indicating orientation in space, a line of code, and hands-on adjustment of an instrument, often within the same few minutes, and the fluent translation between these technologies is itself one of the central, and most underdescribed, achievements of scientific training. The claim developed here concerns the technologies themselves, what each one can and cannot do, not the cognitive processes of the people who move between them.

The Central Bifurcation

Here is the decisive claim this article exists to establish. Symbolisation, often treated as a single, unified activity, in fact splits into two fundamentally different kinds of technology.

Ordinary language continually draws on the body, relationships, place, and material life, as the previous sections have shown. It never fully detaches from them; its meanings are perpetually renewed by, and answerable to, the coordinations those dimensions sustain. This is not a limitation of ordinary language. It is the source of its extraordinary flexibility and its capacity to remain intelligible across radically different situations of use.

Formal systems do something categorically different. They construct internally coherent systems whose combinatorial possibilities are governed by rules internal to the system itself, rules that no longer depend on ordinary meaning for their validity. A step in an algebraic derivation is valid or invalid according to the internal rules of algebra, not according to whether it “sounds right” against bodily, relational, spatial, or material experience. This is not abstracted ordinary language, a more careful version of the same technology. It is a different kind of technology altogether, one that trades the constant renewal available to ordinary language for an internally policed precision ordinary language cannot achieve and was never trying to achieve.

It matters to be precise about what kind of change this involves, because it is easy to overstate the contrast as one of change versus changelessness, which it is not. Ordinary language changes continuously, by daily use, drift, and improvisation, absorbed almost without anyone deciding it should happen. Formal systems change too, mathematics has grown enormously since antiquity, chemical notation has been revised more than once, but they change episodically, through deliberate reconstruction: a new axiom proposed and debated, a new notation designed and adopted, a new rule of inference argued for and formally incorporated. The contrast that matters is therefore not openness against closure. It is continuous, informal renewal against episodic, deliberate revision, two entirely different mechanisms of change, and mistaking one for a slower version of the other misses what is actually distinctive about each.

This distinction should be read as a claim about which mechanism dominates, not as an absolute divide with no exceptions on either side. Ordinary language does undergo deliberate revision: legal definitions are drafted on purpose, a term like misinformation is coined and pushed into circulation by identifiable actors. Formal systems do undergo informal drift: the shorthand physicists scribble on a whiteboard bends the rules long before anyone formalises the bend, and a theorem’s meaning shifts slightly each time it is taught to a new cohort of students. Neither observation undoes the distinction; it only means the diagnostic question has to be asked case by case: for this piece of symbolisation, which mechanism is doing most of the work of change, the constant informal renewal characteristic of ordinary language, or the episodic, deliberate revision characteristic of a formal system? The answer sorts a given instance of symbolisation into one camp or the other far more reliably than asking whether it changes at all, since everything changes.

A single comparison makes the bifurcation vivid. Consider two ways of expressing a relationship between quantities that change together. In ordinary language: “the faster the wind blows, the harder the wave breaks.” In algebraic notation: a functional relationship between wind velocity and wave energy, expressed as an equation relating the two through specified exponents. The ordinary-language sentence remains fully tethered to bodily experience, anyone who has stood on a shoreline in a storm understands it immediately, and it draws simultaneously on place, the shoreline itself, and on the sedimented conventions of relationship that make “the harder” an intelligible comparison between speakers who have never measured anything together. It is also, however, radically underdetermined: it says nothing about the precise mathematical form of the relationship, cannot be used to predict wave energy at a wind speed nobody has directly observed, and cannot be checked for internal consistency against other quantitative claims about fluid dynamics. The algebraic expression achieves exactly what the sentence cannot: it can be manipulated, combined with other equations, used to predict values far outside anyone’s direct experience of storms, and checked for consistency using rules that have nothing to do with what wind or waves feel like. It has bought this power by cutting loose from the shoreline, from the community of speakers, from the felt experience of breaking waves, retaining only a relational skeleton that a reader anywhere, with the requisite training, can operate on identically.

Neither expression is a degraded version of the other. The sentence is not a sloppy approximation of the equation waiting to be formalised; it does real work, communicating a felt regularity between people who share a shoreline and a language, that the equation cannot do on its own. The equation is not a richer version of the sentence; it is silent about everything the sentence conveys about the felt, shared experience of a stormy coastline. Each is the right technology for a different task, and mistaking one for a more or less developed version of the other is among the most common errors in popular accounts of what mathematics actually does for scientific understanding.

The same error, transposed, is what a vocabulary of production and circulation commits when it is used to describe knowledge in general. A field that has, in effect, only the ordinary-language pole of this bifurcation available to it, since production and circulation are themselves ordinary-language metaphors, has no vocabulary at all for the formal pole: for what happens when a domain of knowing migrates out of everyday description and into an internally coherent system of its own. That migration is exactly what the following section takes up.

Scientific Revolutions as Technological Revolutions inSymbolisation

This bifurcation gives history of science a more precise object of study than “new theories” or “new experiments,” the vocabulary the field currently relies on to describe its central transformations.

What the Scientific Revolution actually accomplished, on this account, was a migration of inference: a sustained and cumulative movement of reasoning out of ordinary language and into a series of newly constructed, internally coherent systems. Algebra migrated inference about unknown quantities out of prose description and into a self-contained system with its own combinatorial rules. Chemical notation migrated inference about substances and their transformations out of qualitative description and into a system whose formulae could be manipulated according to conservation rules no ordinary-language account of “mixing” or “combining” could enforce. Cartesian coordinates migrated geometric reasoning out of diagrammatic intuition and into an algebraic system where spatial relationships became manipulable as equations. The calculus migrated reasoning about continuous change out of the vocabulary of “faster” and “slower” and into a system capable of inferences no naturallanguage description of motion could support. Formal logic migrated inference about validity itself out of rhetorical argument and into a system whose validity conditions are, in principle, mechanically checkable.

Reconceived this way, the Scientific Revolution is not primarily a story about new facts discovered or new experiments performed, though both certainly occurred. It is, at the level this article is concerned with, a story about several new technologies for stabilising and manipulating knowledge being constructed in rapid succession, each one relocating a domain of inference out of the constant, informal renewal of ordinary language and into a system whose inferential reach vastly exceeded what ordinary language, however carefully deployed, could ever have achieved.

This reframing carries a historiographical consequence worth stating plainly. If what changed most fundamentally in the seventeenth century was the construction of new technologies for reasoning rather than simply the discovery of new facts, then the central historical question becomes: how, precisely, was each of these systems built, out of what prior resources, by whom, and under what conditions that made the construction possible at that moment and not earlier? That is a question about the deliberate construction of technologies, closely related to but distinct from the question of who discovered what fact when, and a vocabulary that already assumes knowledge is a discrete, portable thing that gets moved around is not well designed to ask it, because that vocabulary treats the technology as already given and asks only how its products circulated.

A history of science oriented around circulation looks for evidence of a new fact or theory spreading, citation counts, translations, correspondence networks. A history of science oriented around the construction of new symbolic technologies looks instead for evidence of a new system of notation and rule stabilising, being taught, being extended by a growing community of users who share its internal rules rather than merely its conclusions, and gradually demonstrating an inferential reach ordinary-language argument in the same domain could not match. These are not incompatible lines of evidence, but they direct attention to different archival traces, and a field trained mainly in the vocabulary of circulation will systematically underweight the second kind of evidence relative to the first. A session on the circulation of a scientific idea will trace who read what and when; comparatively few will trace the harder and more interesting question of how the notation the idea depended on was itself constructed, taught, and stabilised in the first place. The migration of inference is the revolution. The circulation of its conclusions is only ever the revolution’s aftermath.

Formal Systems Are Built, Not Stripped Down

There is a natural but mistaken way to picture how formal systems like algebra or chemical notation came into being: as though they arose by progressively stripping the body, relationships, place, and material life away from an ordinary-language starting point until only a residue of pure symbol remained.

This is the wrong picture. Formal systems are constructed, deliberately and often laboriously, as new technologies with their own internal architecture, built by identifiable historical actors solving specific inferential problems that ordinary language could not solve. Their independence from ordinary-language meaning is the effect of a formal system once it has been built and has stabilised, not the process by which it comes into being. Algebra was not ordinary language slowly worn down to symbols; it was invented, by identifiable people, as a new technology for reasoning about unknown quantities. Once established, a formal system operates largely independently of ordinary-language meaning; it does not arrive at that independence by gradual subtraction.

This matters practically as well as conceptually: it means that the history of a formal system’s construction, who built it, for what problem, drawing on what prior resources, is a legitimate and necessary object of historical study in its own right, even though the system, once built, no longer requires that history to function.

Each Formal System Builds Its Own World

Every formal technology develops its own internal world once constructed: a set of rules, an internal syntax, and a bounded space of inferential possibilities generated by that syntax. Mathematics has its own, governed by axioms and proof. Formal logic has its own, governed by validity and consistency. Chemical notation has its own, governed by conservation and valence. Musical notation has its own, governed by pitch, duration, and the conventions of a given tradition. Programming languages have their own, governed by syntax and computability. Double-entry accounting has its own, governed by the requirement that debits and credits balance. Legal codes have their own, governed by precedent, definition, and rules of interpretation that can diverge sharply from an ordinary-language reading of the same words. Religious liturgies have their own, governed by canonical sequence and rules of valid performance that determine, independently of any single participant’s ordinary understanding, whether a rite has been correctly enacted.

Each of these constitutes, in a meaningful sense, its own symbolic world: a space of wellformed expressions and valid transformations that can be explored, extended, and tested on terms internal to the system, without constant recourse to the body, relationships, place, or material things that ordinary language never stops consulting. This is precisely what makes formal systems powerful, and precisely what makes them dangerous when their outputs are read back into ordinary language without the translation being marked as a translation, a danger the discussion of a well-known case in biology, in Section XVIII, examines directly.

Formal Systems Slice Reality; They Do Not Simplify It

A persistent misdescription of formal systems holds that they simplify reality, that mathematics or chemical notation gives a stripped-down, lower-resolution version of a

richer reality better captured by ordinary experience. This gets the relationship backwards.

Formal systems do not simplify reality in the sense of giving a coarser picture of the same thing ordinary experience already grasps. They selectively slice reality: each system achieves extraordinary, often unprecedented fit to one narrow relational dimension of the world, while remaining entirely silent about, rather than crudely simplifying, everything outside that dimension. Mathematics slices quantitative and structural relations with a precision no other technology approaches, and says essentially nothing, within its own rules, about the qualitative, relational, or historical dimensions of what it quantifies. Logic slices valid inference, independent of the truth or falsity of any particular premise. Chemical notation slices molecular transformation, abstracting entirely from the biography or social meaning of the substances involved. Accounting slices financial relations, rendering an organisation’s entire bodily, relational, and material life visible only insofar as it can be represented as a movement of value between accounts. Musical notation slices intervallic and rhythmic relations, leaving timbre, phrasing, and the entire embodied experience of performance outside its formal vocabulary, which is why notation and performance remain distinct, a distinction the next section develops at length.

Each formal system, in other words, deliberately narrows its field of view to one relational dimension, and it is precisely this narrowness that generates its extraordinary fit to that dimension. Narrowness is not a deficiency here; it is the source of the power. The danger lies not in the narrowness of a formal system but in the later misapplication of a narrow, purpose-built concept to a situation that in fact requires the full range of what constitutes it.

This also explains a pattern that has otherwise puzzled philosophers of science: why formal systems constructed for one purpose so often turn out, unexpectedly, to fit domains their inventors never had in mind. Non-Euclidean geometries, developed initially as internally consistent explorations with no evident application, later turned out to slice the structure of physical spacetime with startling accuracy. Group theory, developed to study the internal symmetries of algebraic equations, later turned out to slice the structure of subatomic particle interactions. If formal systems were simplified pictures of a single, already-familiar reality, this kind of transfer would be a happy coincidence needing separate explanation each time. If formal systems are relational slices, extracting a pattern of structure and leaving everything else silent, then it becomes considerably less surprising that a slice extracted from one domain should recur in another, because what is being matched is not two pictures of the same content but two instances of the same relational skeleton, wherever in reality that skeleton happens to recur. The famous puzzle of the unreasonable effectiveness of mathematics in the natural sciences becomes considerably less mysterious once mathematics is understood as a technology for slicing relational structure as such, rather than a picture of any one domain that structure happens to inhabit.

The same slicing logic explains why formal systems built for adjacent domains so often fail to transfer. Accounting’s apparatus, built to slice financial relations under a strict conservation constraint, debits must equal credits, does not transfer to slicing ecological relations, where the analogous constraints, energy and matter flowing through a system, are real but follow entirely different formal rules; attempts to force ecological accounting into financial accounting’s shape, treating a wetland as a balance sheet, are a recurring source of exactly this kind of mismatch, where a concept built for one relational slice is extended, often for institutional convenience, to a domain whose structure it was never built to capture.

Music: Performance and Notation

Music is a useful test case for everything argued so far, because music exists simultaneously as two entirely different kinds of phenomena that are routinely conflated: a fully multimediated performance, and a formal system for stabilising some of what a performance does.

Musical performance is one of the most fully multimediated phenomena human beings produce: it involves bodily skill of extraordinary refinement, the relational attunement of an ensemble listening and adjusting to itself in real time, the acoustic particularity of a space that shapes what is even possible to play, the material presence of instruments built from specific woods, metals, and strings, and a symbolic dimension that is present but subordinate to the sounding event itself.

Musical notation, whatever specific system is at issue, is something categorically different from the performance it stabilises: an internally symbolic system whose elements are defined relationally, within the system, rather than by direct reference to the body, relationships, place, or material things. A given pitch or duration exists, within a notational system, as what it is by virtue of its relations to the other elements of that system, not by virtue of any bodily, social, or material fact about a particular performance. This is true whatever the specific geometry of the notation happens to be, as three quite different traditions make clear.

Consider first a formal notation built on entirely different principles from the Western staff.

Korean court music developed jeongganbo, a grid-based mensural notation in which time is divided into square cells, jeonggan, arranged in columns, with a pitch symbol placed inside each cell according to where in the cell’s internal subdivisions the note falls. Pitch and precise rhythmic duration are therefore encoded together, within a single spatial unit, in a way the Western staff, which separates pitch on the vertical axis from duration in noteshape, does not attempt. Jeongganbo is every bit as much an internally coherent, rulegoverned symbolic system as staff notation, one that slices the same general domain, pitch and time, along a different internal geometry, and it is a formal system in exactly the sense this article has been developing: once its cells and conventions are fixed, a musician can read, transmit, and reconstruct a piece from it without needing to have heard the piece performed.

Consider next a tradition that relies far less on fixed notation and far more on the coordinative technologies described in Section XVI. Balinese gamelan ensembles transmit a great deal of their repertoire aurally, through apprenticeship, but the coordination of a large ensemble, particularly the interlocking drumming that leads the group through changes of tempo and section, is guided by mnemonic syllables, spoken drum-pattern vocables that a leader can call out or a student can chant while learning a part. These syllables are symbols, but they are coordinative rather than descriptive in exactly the sense of Section XV: their job is not to represent the music accurately for later analysis but to bring about a correctly coordinated performance in real time, and, in the most skilled players, the syllables disappear into the playing itself, precisely the pattern Section XVI identifies as the signature of a successful coordinative technology.

Only against this background is it worth turning to the Western tradition, where staff notation enabled a very particular kind of combinatorial construction: counterpoint, fugue, large-scale polyphony, achievements made possible once notation had developed sufficient internal combinatorial richness to support them, richness performance alone, however skilled, could never have generated or preserved across generations of composers who never met one another. A fugue in four voices, each independently constrained by rules of harmonic and melodic relation that a composer can check, revise, and combine on the page long before any voice sounds, is not something an oral tradition without a comparably rich internal notation could have produced and transmitted with the same combinatorial complexity intact across centuries. This is a real and specific achievement of one formal system, not a general property of notation as such, and it sits alongside jeongganbo’s different slicing of pitch and time and gamelan’s different balance of oral transmission and coordinative mnemonic, as one case among several rather than the paradigm the others are measured against.

The point generalises further still. Classical traditions of Hindustani and Carnatic music developed, largely without a comparably prescriptive notational apparatus, an extraordinary combinatorial sophistication of a different kind: improvisational systems of raga and tala that unfold in real time within a shared framework transmitted primarily through apprenticeship, achieving a rhythmic and melodic flexibility that staff notation is poorly equipped to capture at all. Classical Arabic maqam traditions developed sophisticated systems of modal organisation and microtonal inflection that a notational system built around equal temperament has no symbols for. West African polyrhythmic traditions achieve layered rhythmic complexity through embodied, relationally transmitted practice that has no comparably economical fixed notation and arguably needs none. Each of these traditions, jeongganbo and gamelan among them, solved a different symbolic and combinatorial problem, using a different balance between formal notation and embodied, relationally transmitted practice, and each achieved a form of sophistication the others did not prioritise. The comparison between traditions is therefore not a comparison of more against less developed music, and no single tradition supplies the master case the others illustrate. It is a comparison of which combination of formal notation and embodied transmission a given tradition relied on to build and preserve its own particular kind of complexity.

The Voyager Golden Record pushes the formal-symbolic logic to its limit: it is an attempt to construct a system, built largely from mathematical and physical relations rather than ordinary language, capable of being understood in principle by a listener who shares none of the bodily, relational, material, or spatial coordinations of the community that produced it. Music, among symbolic technologies, was judged to have the best chance of surviving that total absence of shared context, precisely because its formal, relational core, intervals, ratios, periodicities, does not depend on the body, relationships, place, or material life for its internal coherence in the way that a spoken greeting or a photograph of a familiar landscape would. Whether that judgement was correct is a separate and genuinely open question; what matters here is that the reasoning behind including music at all is a direct, if informal, application of the bifurcation this article has been developing.

Two Different Jobs Symbols Do

Gilbert Ryle’s distinction between knowing-that and knowing-how has organised a large portion of twentieth-century epistemology, and it captures something real. But once knowledge itself is understood as fully multimediated rather than primarily propositional, Ryle’s distinction can no longer do the work it was asked to do, because both knowing-that and knowing-how, on this account, are equally multimediated achievements; neither is more purely symbolic than the other.

What actually differs, once the distinction is placed correctly, is not a property of knowledge but a property of the symbolic technologies used to articulate it: the kind of endpoint toward which each is directed. This article proposes replacing know-that and know-how with two functions symbols can perform: describing and coordinating. Descriptive systems, physics, chemistry, cartography, taxonomy, are built to terminate in an accurate symbolic account of some domain; their success is measured by fidelity of description. Coordinative systems, recipes, musical scores, assembly manuals, computer programs, architectural plans, choreographic notation, are built to terminate in something outside symbolisation altogether: a meal cooked, a piece performed, a structure built, a shelf assembled, a movement executed. Their purposes differ fundamentally, and confusing the two, treating a recipe as if its point were an accurate description of food, or a physical theory as if its point were to be cooked, is a category error the older vocabulary was never equipped to diagnose.

Symbolic Systems Whose Point Is Not Description

This distinction deserves to be developed in its own right, because coordinative systems occupy a place in the study of symbols that has been badly undertheorised. Coordinative systems are not primarily representational, even though they are made of symbols and can be read, studied, and analysed as texts. Their genuine endpoint lies outside symbolisation entirely: they exist in order to bring about a piece of coordinated activity, a specific meal, a specific performance, a specific structure, a specific sequence of movement, and their success is judged by whether that activity is achieved, not by whether the symbolic account is elegant, complete, or internally consistent on its own terms.

In the most successful cases, the symbols of a coordinative system disappear into the practice they generate. An experienced cook barely consults the recipe; an experienced musician internalises the score to the point where performance no longer requires conscious reading of notation; an experienced builder works from a plan that has become second nature. This disappearance is not a failure of the symbolic system. It is the sign of its success: the most successful coordinative symbolisation is the kind that no longer needs to be consulted, because it has already done its work of shaping practice. This identifies an entire category of symbolic technology, arguably the majority of symbolic technologies actually in daily use across human history, whose function has been persistently mismodelled by philosophical traditions that took descriptive, propositional language as the paradigm case of symbolisation as such.

A vocabulary of production and circulation has no real place for this category at all. A recipe is not usefully described as “produced, circulated, and exchanged”; a recipe is enacted, and its success is measured in the kitchen, not in its rate of transmission. A history of science built exclusively from descriptive assumptions about symbolisation will systematically misdescribe every coordinative dimension of scientific practice: laboratory protocols, standard operating procedures, calibration routines, all of which are coordinative rather than descriptive technologies, all of which such a vocabulary quietly mistranslates into propositions to be produced and circulated rather than instructions to be enacted.

Knowing How We Know That

This is the article’s title chapter, and it is where its deepest move finally becomes explicit. It would be easy to read what follows as a revision of Ryle: a proposal to replace his distinction with a better one, describing in place of knowing-that, coordinating in place of knowinghow. That reading is not wrong, but it understates what is actually happening here.

The real point is not a better answer to Ryle’s question. It is the discovery that the question philosophy has asked for centuries, what is knowledge?, was never well posed, because it silently fused two questions that can now be held apart. The first is: what is knowledge? The second is: how do symbolic technologies stabilise knowledge, once it exists? Philosophy has largely treated these as a single question, answerable by a single theory, because it never had a way of separating a fully multimediated achievement, only part of which is ever articulated, from the technologies that intermittently stabilise fragments of it. Ryle’s distinction between knowing-that and knowing-how is a symptom of this fusion, not a solution to it: it locates a real and important difference, but it locates it inside knowledge, as if knowledge itself came in two kinds, propositional and practical, when the difference in fact belongs to the technologies used to articulate a single, uniformly multimediated kind of achievement.

Once this is seen, the article’s actual subject comes into focus. It has not, for most of its length, been offering a theory of knowledge in competition with justified-true-belief accounts, reliabilism, or virtue epistemology. It has been offering an account of the different technologies through which fragments of what is known get made explicit, using knowledge as the domain rich enough, and philosophically prestigious enough, to force the two questions apart. Knowing how we know that is therefore not, in the end, a question about a cognitive achievement called knowledge-that. It is a question about the symbolic technology, descriptive, formal, portable across situations, through which certain fragments of unreflective, embodied coordination get made explicit as articulated claims in the first place, and about what is lost, and what is gained, in that process.

Knowledge, whether it concerns riding a bicycle or Newton’s laws of motion, is uniformly multimediated: both require bodily skill, both are transmitted through relationships of trust and correction, both depend on material instrumentation of one kind or another, both are situated in place, and both are, at some point, symbolically articulated. What actually differs between “knowing how to ride a bicycle” and “knowing that force equals mass times acceleration” is not the underlying structure of the knowledge itself but the purpose of the symbolic technology through which each is, at some point, articulated. Riding a bicycle is coordinated through embodied practice directly, with symbolisation playing at most a minor role, “lean into the turn,” said once, by a parent, and then rendered unnecessary by practice, a coordination that barely needs to be made explicit at all. Newton’s second law is stabilised through a descriptive formal system whose entire purpose is precision about force and motion, independent of whether any particular reader has ever felt acceleration in their own body, a coordination, Newton’s own bodily and instrumented investigation of falling bodies and orbits, that has been almost entirely absorbed into a formalism portable enough to be taught to students who will never repeat the original investigation themselves.

The distinction that matters, in other words, is not epistemological. It concerns the technology used to make something explicit, and how much of the original, unreflective coordination survives that process. Knowing how we know that turns out to require asking not what kind of knowledge we have, but what kind of symbolic technology we are using to articulate it, and how much of the coordination it was drawn from remains outside its reach. Philosophy asked what is knowledge for centuries without asking how symbolic technologies stabilise it. This article proposes that the second question was the one worth asking all along, and that the first question only ever looked answerable because the second question kept quietly answering it in its place.

Three Different Kinds of Bias, and Where Each One Lives

Emily Martin’s landmark analysis of the gendered metaphors used to describe fertilisation in biology textbooks, active, questing sperm and passive, waiting eggs, remains one of the most influential demonstrations that scientific language is never metaphor-free, that even the most technical biological description carries ordinary-language freight capable of encoding social assumptions about gender.

This argument becomes considerably sharper once three different levels are kept apart, levels that discussions of bias in science too often run together. The first is bias in ordinarylanguage description: the metaphors used to explain a finding to students or the public, which is what Martin’s analysis is actually about. The second is bias in the formal symbolic systems in which the underlying reasoning is conducted: the molecular and biochemical notation itself, which does not, on its own terms, encode gender at all, and which is a different object from the prose used to gloss it. The third is bias in which research questions get asked and funded in the first place, the level addressed by the tradition of feminist science studies associated with Sandra Harding and Evelyn Fox Keller, which concerns whose interests and assumptions shape a research programme’s priorities rather than either its explanatory prose or its formal apparatus.

Martin’s metaphors belong to the first level. They are best understood as an interface: a point of contact between the formal system in which the actual reasoning is conducted and the ordinary language in which that reasoning must eventually be communicated to students, journalists, and the wider public. The metaphor of questing sperm is not, on this account, the inferential engine of the science itself; the inferential engine runs largely inside a formal system of chemical and molecular notation that has no symbols for gender at all. The metaphor operates at the interface, in the translation back into ordinary language, which is exactly the point at which ordinary language’s constant openness to relational and social experience, where gendered assumptions live, makes it vulnerable to importing precisely this kind of bias.

This should not be read as a claim that the formal level is neutral in every sense that matters. A formal system has no symbols for gender, but it can still be built around ontological presuppositions, that molecular interactions are fundamentally competitive, that the relevant entities are best modelled as target-seeking agents, that are themselves historically contingent choices about how to model a domain, not logical necessities forced by the mathematics alone. Those presuppositions are not gender bias encoded in a variable; they are closer to the third level, decisions about how a research programme frames its object, than to the first. But they are real, and a defender of a formal system’s neutrality who stops at “there is no symbol for gender here” has answered a narrower question than the one a serious critic is usually asking. The three-level distinction this section proposes is meant to sharpen exactly where such a critique should land, not to declare formal systems immune from it.

This does not diminish the importance of Martin’s finding; it sharpens the diagnosis of where the remedy needs to be applied. If the gendered metaphor were located inside the formal biochemical system itself, correcting it would require revising the formal system, its notation, its accepted derivations, a far more demanding undertaking than correcting a textbook’s prose. Locating the bias at the interface instead means the remedy is available at comparatively low cost: revise the ordinary-language gloss that accompanies the formal account, without needing to touch the underlying molecular biology at all, since the bias was never a feature of that biology’s own formal representation. This is, in fact, closer to what happened historically once Martin’s critique was absorbed: textbook language changed considerably faster than any underlying biochemical model did.

Nothing here denies that ideological assumptions can shape which formal systems get built and which research questions get pursued in the first place; of course they can, and the feminist science studies tradition mentioned above has documented this at length. That is a claim about the third level, research priorities, and it is different in kind from a claim that the formal syntax of a completed system itself encodes bias. Keeping the three levels apart, bias in explanatory prose, bias in formal systems, and bias in research priorities, matters because each requires a different remedy, and conflating them, treating every instance of loaded ordinary-language communication as evidence of bias inside a science’s own formal reasoning, both overstates the difficulty of some corrections and understates the depth of others.

Returning to the Conference

Return, with all of this now in place, to the conference with which the article began. Its blind spot can now be named with some precision. The field has, as Section III showed, learned to study the body, relationships, and material things as constitutive of scientific knowledge, not merely its backdrop. What it has not yet turned its attention to is its own theoretical vocabulary: whether the words it reaches for when generalising about knowledge, produced, circulated, exchanged, themselves carry a stable and largely unexamined character, drawn overwhelmingly from one dimension of life regardless of how varied the objects of study have become.

This is not a minor omission. A field that talks about knowledge exclusively in the vocabulary of production and exchange will, almost without choosing to, continue to reach for that vocabulary the moment a case study gives way to a general claim, even after decades of case studies that have shown, in exquisite detail, how much of scientific knowledge is bodily, relational, and situated in place. The gap is not between what the field studies and what actually matters. It is between what the field has learned to study, in its best and most detailed work, and the more general, less examined language it falls back on whenever it steps back to say what knowledge, as such, is.

The remedy this article proposes is not a call to abandon the vocabulary of circulation and exchange altogether; those words describe something real about how stabilised, articulated claims move through institutions, and abandoning them would leave the field without a vocabulary for a genuine phenomenon. The remedy is narrower: to treat that vocabulary as accurate for the articulated residue of knowledge, publications, patents, formal claims, while developing an equally rigorous vocabulary for the unreflective, bodily, relational, and situated coordination that residue only ever partially records. A history of science that could move fluently between both vocabularies, naming when it is discussing the circulation of a stabilised claim and when it is attempting to reconstruct the coordination that claim was drawn from, would no longer be captured by a single dimension of its object.

Toward a Comparative Study of Symbolic Technologies

The argument developed here opens onto a considerably larger comparative programme than this single article can complete. If symbolisation genuinely splits into ordinary language and formal systems, and if formal systems themselves subdivide into descriptive and coordinative kinds, each with its own purpose and its own history of deliberate construction, then each of the technologies named in Section VIII deserves the kind of dedicated treatment this article has begun to give to mathematics, chemical notation, and musical notation in passing.

A study of mathematics would ask what quantitative relations it slices, and what it is compelled to leave silent. A study of musical notation would extend Section XIV’s brief treatment into a full account of the historical construction of Western notation as a formal system. A study of programming would treat code as a coordinative formal system whose endpoint is computation rather than description, closely related to but distinct from the recipe and the score. A study of accounting would examine how double-entry bookkeeping slices financial relations and ask what it renders invisible. A study of maps would examine cartography as a descriptive formal system whose relation to place is more intimate, and more fraught, than its relation to anything else. A study of recipes would develop Section XVI’s account of coordinative symbolisation through the single most universally practised example of the genre. A study of architecture would examine the plan as a coordinative system whose endpoint is a built environment that then becomes, in its own right, a place to inhabit. A study of formal logic would ask what, precisely, its slice of valid inference leaves out, and what has historically gone wrong when that slice was mistaken for the whole of reasoning. A study of legal codes would examine how they construct an internally coherent system out of ordinary-language materials, and what is gained and lost when a dispute migrates from lived grievance into that system’s own categories. A study of religious liturgy would examine ritual sequence as a coordinative technology whose endpoint is not belief but correctly enacted relationship. And a full comparative study of metaphor sources, anticipated in Section VII, would test the prediction that material, place-based, relational, and exchange-based communities recruit systematically different sources for their abstract vocabulary, a comparative project considerably larger than conceptual metaphor theory has so far attempted.

A criticism worth taking seriously at this point is that a comparative programme of this kind risks being unfalsifiable, a descriptive vocabulary flexible enough to accommodate any case after the fact. The concern is reasonable, and it has a concrete answer. The claims made in Sections VI and VII generate a testable research design, not merely an interpretive stance. Call it metaphor-source analysis: take a corpus of texts from a given discourse community, a conference programme, a set of journal abstracts, a body of religious or legal writing. Code every abstract, general-level metaphor used to describe the field’s central object. Classify each metaphor by its source: bodily, relational, material, or spatial. Measure the relative frequency of each source within the corpus. Then compare corpora: across disciplines, across historical periods, across languages, across institutional settings. The prediction is specific enough to fail: corpora drawn from communities organised primarily around material production and exchange should show a measurably higher proportion of materialsource metaphors than corpora drawn from communities organised primarily around place or relationship. The null hypothesis is equally specific, and stating it plainly is the right way to close this objection: if industrial and administrative discourse communities show no higher proportion of material-source metaphors than land-based or kinship-based communities, once source is coded blind to the hypothesis and checked for inter-coder agreement, the claim made in Sections VI and VII is false, not merely unconfirmed. The history-of-science conference programme with which this article began is exactly such a corpus, and the pattern traced informally in Sections I and II is, in principle, precisely what metaphor-source analysis would either confirm or disconfirm at scale.

Each of the studies proposed above is a distinct project, not a subsection of a single unified theory of symbols. That plurality is itself the point: symbolisation is not one thing, and an account of knowledge that treats it as one thing will keep making the error this article has spent its length diagnosing. Ordinary language, mathematics, formal logic, musical notation, accounting, programming, legal codes, recipes, architectural plans, maps, choreography, and ritual sequence each turn out to have their own history of construction, their own purpose, their own relationship to the body, relationships, place, and material things, and their own internal system of rules. That is the article’s real scale: not one more application of a theory of knowledge, but the discovery that symbolisation, so often treated as a single, uniform capacity, is in fact a wide and internally varied field, and that knowledge is simply the first place this variety became impossible to ignore.

Conclusion: Knowing How We Know That

Return to the title, once more and for the last time. For centuries philosophy asked: what is knowledge? This article has argued that the question was never well posed, because it fused a question about a fully multimediated achievement with a question about the technologies that intermittently make fragments of it explicit. Held apart, the two questions become: what is knowledge? And how do different symbolic technologies articulate it? The second question, not the first, is where this article’s real contribution lies. It is not, in the end, a work of epistemology that happens to touch on symbols. It is an account of symbolic technologies that happens to use knowledge, and the history of science’s peculiar blindness to its own theoretical vocabulary, as its opening case.

Knowledge is never merely symbolic, and it is never independent of symbols either; it is fully multimediated, constituted by the body, by relationships, by place, by material things, and, wherever it is present, by symbolisation, which reaches only the articulated part of what is known and never the unreflective coordination that articulation is always drawn from. Symbols are technologies that either describe some aspect of reality with a precision ordinary language cannot achieve, or coordinate future activity in ways ordinary description was never built to do. The deepest irony uncovered along the way is that the history of science has devoted itself to understanding the history of knowledge while, even after decades of learning to take the body, relationships, and material things seriously as objects of study, remaining captive to a single, historically contingent vocabulary for talking about knowledge in general, one borrowed wholesale from industrial production and exchange and never subjected to the same scrutiny the field has learned to apply to everything else it studies.

A genuinely comparative account of symbolisation begins only when that vocabulary itself becomes an object of inquiry rather than a transparent window onto its subject, and it need not stop at interpretation: metaphor-source analysis, coding a corpus of texts for the mediational source of its abstract vocabulary and comparing the results across disciplines, periods, and languages, turns that inquiry into a method with a stated null hypothesis, capable of being wrong. From there, symbolisation ceases to look like a single, uniform capacity and becomes a wide comparative field of distinct technologies, each with its own logic, its own relationship to the rest of what constitutes a life, and its own distinctive contribution to human understanding. That expansion, from a single assumed capacity into an entire field with its own internal variety, is, of all the claims this article has advanced, its most ambitious, and its most original.