Williamson and Why Understanding Educational Potential As Modal Structure Debunks Performative Education

One of the most pervasive but least examined assumptions in contemporary educational systems is that what is actual, what is observed, what is measurable, provides an adequate basis for judging what a learner is and can become. This assumption underwrites the entire apparatus of performativity, the dense network of assessment regimes, accountability structures, data dashboards, progress measures, and evaluative categories that now organise schooling in many contexts (Ball 2003; Biesta 2010). The student writes, speaks, solves, submits, and is then rendered legible through scores, levels, grades, and descriptors. From these actualised performances, the institution infers ability, potential, trajectory, and worth.

The philosophical weakness of this picture is rarely interrogated with sufficient depth. Critiques of performativity often focus on its social and political effects, narrowing of curriculum, teaching to the test, instrumentalisation of learning, but they typically leave intact a more basic epistemological assumption, namely that actual performance, suitably aggregated and standardised, provides a reliable window onto the learner’s capacities. It is precisely this assumption that Williamson’s work allows us to destabilise at a much deeper level, not by appealing to vague notions of complexity or individuality, but by reconstructing the logical and metaphysical structure of what it means to ascribe capacity, ability, or knowledge at all.

Williamson’s anti luminosity argument is an important starting point (Williamson 2000). The argument, in its most general form, shows that even if a condition obtains, it does not follow that one is in a position to know that it obtains. The key idea is that knowledge requires a form of modal stability. If one knows that p, then p must be true not only in the actual case, but in nearby cases as well. If small variations in the situation would easily lead to error, then the claim to knowledge is undermined. This is formalised through what Williamson calls the safety condition: roughly, if one knows p, then in all nearby possible worlds in which one believes p in the same way, p is true.

Williamson rejects what he calls exceptionalism about logic. To understand this, imagine the traditional picture many philosophers have had. Logic is often treated as a special domain. It is supposed to deal with truths that are certain, self evident, or grounded purely in meaning. It is not supposed to depend on empirical facts, and it is not supposed to be revised in light of theoretical considerations in the way that physics or biology might be. On that picture, logic sits above the rest of inquiry.

Williamson wants to dismantle that. He is saying that logic is not methodologically isolated. The same kinds of considerations that apply in other domains, coherence, explanatory power, comparison of rival theories, also apply in logic. To helpus see this he introduces a distinction between two different activities that are often conflated. The first is the metatheory of modal logic. The second is the use of modal logic as a language to talk about reality.

Metatheory is, in effect, mathematics. When logicians study modal systems formally, they define symbols, rules, models, and then prove theorems about them. They ask questions like, which formulas are valid in which systems, how different systems relate to each other, whether certain proof systems are complete? All of this is carried out in an ordinary mathematical language. There are sets, functions, structures, and so on. Crucially, the symbols for necessity and possibility, the box and the diamond, do not appear in that metalanguage in the sense that matters for interpretation. The logician is not, at that stage, talking about what is necessary or possible in reality. They are manipulating mathematical objects.

This leads to a slightly surprising observation. Modal logic, which is supposed to be about modality, is studied at the metatheoretical level in a non modal way. The machinery is mathematical. That already supports the anti exceptionalist stance. The metatheory of modal logic is just another branch of mathematics.But then there is the second activity. We take a modal language and we interpret it. We say what its symbols mean. Now the box and diamond are supposed to represent something, perhaps metaphysical necessity and possibility, or perhaps some more restricted notion like physical possibility. At this point we are no longer just doing mathematics. We are doing theory about the world.

This is where things become more delicate. A natural idea is that to interpret a formal language, we specify a model. In model theory, a model is a mathematical structure that assigns meanings to the symbols. For example, we might say that the domain of quantification is a certain set, that predicates pick out subsets of that set, and that modal operators are interpreted using a structure of possible worlds connected by an accessibility relation. This is standard Kripke semantics.Williamson points out that this approach runs into trouble when we try to use it for metaphysics. Why so? Well, metaphysics often aims at total generality. When a metaphysician says “everything”, they mean absolutely everything. But in standard mathematics, and specifically in standard set theory, there is no set of absolutely everything. This is tied to well known paradoxes such as Russell’s paradox. If you try to form the set of all sets, contradictions arise.

So if the intended interpretation of our language requires a domain that includes absolutely everything, we cannot simply identify that domain with a set in the usual way. That means that no ordinary model, understood as a set theoretic structure, can straightforwardly serve as the intended interpretation for metaphysical discourse. The point is that the structure of set theory constrains what counts as a model, and metaphysical ambition exceeds that structure.
Williamson’s response is to change how we think about interpretation. Instead of saying that the meaning of the language is given by a specific model, he suggests that we give an informal explanation. We say, in ordinary language, how the symbols are to be understood. In the metaphysical case, the quantifiers are to be understood as ranging over absolutely everything, without restriction, and the modal operators are to be understood as expressing metaphysical possibility and necessity.

When Williamson talks about metaphysical necessity, he is not talking about what we can know without experience, which would be the a priori. Nor is he talking about what is necessary given the laws of physics, which would be physical necessity. He is talking about the strongest kind of objective necessity. Objective here means that it is about how reality is, not about our knowledge of it. Metaphysical necessity is supposed to be stronger than any more restricted kind of necessity. If something is metaphysically necessary, it could not have been otherwise in any objective sense. Conversely, if something is possible in any objective sense, then it is metaphysically possible.

This way of thinking is influenced by Kripke, but Williamson presents it in a more general way. The important point is that we are now treating the modal operators as expressing something about reality itself. That is what turns the formal language into a tool for metaphysics. Once we have fixed this interpretation, we can start to formulate principles in the language and ask whether they are true. He gives as an example the dispute between necessitism and contingentism. The formula Williamson introduces, which he abbreviates as NNE, says, in effect, that necessarily everything is necessarily something. 

The inner part, “everything is something”, is trivial in ordinary logic. It just says that for every object, there is some object identical to it. That is a way of saying that everything exists. When we put necessity operators around this, we get a stronger claim. We are saying that it is necessary that everything necessarily exists. There is no possible situation in which something fails to be something. In other words, there is no contingency in what exists.

That is the position Williamson calls necessitism. Its opponent, contingentism, denies this. The contingentist says that there are things that could have failed to exist altogether. Not merely that they could have been different, or located elsewhere, but that they could have been nothing at all.
It is very tempting to think that the two sides must be talking past each other, using the words “exists” or the quantifiers in different ways. Williamson insists that both sides can agree that the quantifiers are unrestricted and that the modal operators express metaphysical necessity and possibility. They share a language and a meaning. They disagree about what is true in that language.

This is a key anti exceptionalist move. The principles at stake are not analytic truths that anyone who understands the language must accept. They are theoretical claims. They are like hypotheses in science. One can understand them perfectly well and still reject them. That is why Williamson compares the dispute to disagreements in physics or biology. We can use the same concepts and still disagree about the world.

This also affects how we think about axioms. In formal logic, axioms are often presented as basic truths. Here, Williamson says that axioms in applied modal logic are more like postulates. They are starting points for theories. They are not self evident, and they are not guaranteed by meaning. They are to be evaluated by looking at their consequences and seeing how well they fit with the rest of our understanding.
Necessitists and contingentists tend to favour different kinds of models. Necessitists prefer constant domain models, where the same objects exist in every possible world. Contingentists prefer variable domain models, where different worlds can have different objects. But Williamson emphasises that this difference in models is not the fundamental issue. The fundamental issue is the interpretation. The models are tools that help us explore the consequences of the theories, not the source of their meaning.

He introduces an important criticism of taking model theory too literally. Consider the contingentist claim that there could have been something that does not actually exist, for example a child that Wittgenstein could have had but did not. In a Kripke model, we represent this by having a world whose domain contains an object not in the actual world’s domain. That object represents the merely possible child.

But the model itself is a mathematical structure that actually exists. The object representing the possible child is itself an actual object in that structure. So we are representing a non actual object by means of an actual object. From the point of view of mathematics, this is perfectly fine. From the point of view of metaphysics, it shows that the model is only a representation, not a literal picture. It simulates modality using non modal resources.

This is why Williamson says that, especially from a contingentist perspective, Kripke models cannot be taken as fully faithful representations of modal reality. They are extremely useful for working out what follows from what, but they do not directly reveal the structure of reality. This is a warning against a common philosophical temptation, to treat semantic models as if they were ontological blueprints.
When we state principles like those of modal logic, we often use schematic letters such as “P”. For example, the S5 principle says that if possibly P, then necessarily possibly P. But if we want to treat this as a genuine claim about reality, we need to understand it as saying something about all possible propositions. In other words, it is a universal generalisation over all formulas.

To express that explicitly, we need to quantify not just over objects, but over predicates or sentences. This is what is meant by higher order logic. In first order logic, quantifiers range over individuals. In higher order logic, they can range over properties, relations, and propositions. Williamson’s point is that if we want to state general modal laws as single claims that can be true or false, we need this higher order machinery. It is required by the kind of generality we are aiming for.

A similar point arises with infinitary logic. If we want to represent inferences that involve infinitely many premises, we may need a language that allows infinitely long conjunctions. Again, this is driven by theoretical need. The logic expands because the phenomena we want to describe demand it.
Williamson challenges the idea that science is purely non modal because it is expressed mathematically. He argues that modality is often present implicitly in scientific theories, even if it is not explicitly marked. His main example is dynamical systems. A dynamical system consists of a set S of states. Each state represents a possible condition of a physical system. There is also a set T of times, which can be thought of as integers or real numbers, representing moments or intervals. Then there is a family of functions. For each time T, there is a function that takes a state and tells us what state the system will be in after that amount of time.

So if the system is in state s now, and we apply the function for time t, we get the state the system will be in t units of time later. This structure encodes the evolution of the system over time. In many cases, the system is deterministic, meaning that from any given state, both the past and the future are uniquely determined. At first sight, this looks purely temporal. It tells us what happens next, not what could happen. But Williamson shows that modality enters when we consider the whole state space. We can define an equivalence relation on states. Two states are equivalent if the system can evolve from one to the other in some amount of time. Each equivalence class is called an orbit. An orbit represents all the states the system passes through along a particular history.

If there is more than one orbit, then from any given state there are other states that the system will never reach, because they belong to a different orbit. Yet these states are still part of the state space. They represent ways the system could have been, given the same underlying structure, but are not part of the actual trajectory. These are counterfactual possibilities.
This is the crucial insight. The mathematics of dynamical systems already involves a space of possibilities. It is not limited to the actual history. If we tried to remove the non actual states and keep only the actual trajectory, we would destroy the mathematical structure that makes the theory work. So the scientific theory implicitly relies on modal notions, even though it is expressed in a non modal language.

Williamson draws analogies with modal logic. The states are like possible worlds in some respects. They are mutually exclusive and exhaustive. But the analogy is not perfect, because states are instantaneous and can repeat over time. They are not simply world time pairs either, because of the possibility of cycles. The point is not to force a perfect identification, but to show that the structures are closely related. He then shows how to translate the dynamical system into a modal temporal language. Propositional variables can be interpreted as sets of states. Modal operators can be understood as ranging over all states in the space. Temporal operators capture the evolution over time. Additional operators can capture topological features. Once this is done, a rich set of principles emerges, including versions of familiar modal laws.

One striking result is that a form of necessitism appears naturally at the propositional level. Because propositions are identified with sets of states, and these sets exist as part of the structure, we can express a principle saying that necessarily, for every proposition, there is a necessarily identical proposition. This mirrors the idea that everything necessarily exists. Williamson notes that this is not forced artificially. It comes out of the natural semantics.

He suggests that this approach opens a broader research programme. Other scientific frameworks may also contain implicit modal structure that can be made explicit using modal logic. In some cases, this will require first order quantification over individuals, for example in agent based systems. The general idea is that modal logic can serve as a tool for uncovering the hidden logical structure of scientific theories.
This argument is typically discussed in epistemology, but its implications for education are profound. Consider what it means to say that a student knows something, or can do something. These are modal claims. They are not simply reports of what has happened. To say that a student understands a concept is to say that they would respond appropriately across a range of relevant situations, that their understanding is not an accident of a particular context. Yet most educational assessments do not test for this kind of modal stability. They test for actual performance under highly constrained conditions.

This creates a structural mismatch between the concept being assessed and the evidence used to assess it. The institution claims to measure ability or understanding, which are inherently modal notions, but relies on actualist evidence, isolated performances. The result is a systematic overextension of inference. From a single or limited set of actualisations, the institution infers a stable capacity. Williamson’s framework shows that this inference is not merely risky but conceptually underdetermined. The evidence does not support the modal claim.

In all dynamical systems the underlying mathematical structure presupposes a space of possibilities (Williamson 2013). A dynamical system consists of a set of states, a set of times, and a family of evolution functions. Given an initial state and a time interval, the system moves to another state. If the system is deterministic, this movement is uniquely determined.
At first glance, this looks like a purely temporal story. We have a sequence of states, one following another. But the full structure of the system includes not just the actual trajectory but the entire state space. By defining an equivalence relation on states, where two states are related if the system can evolve from one to the other, we partition the state space into orbits, each representing a complete possible history of the system. The actual trajectory is just one orbit. Other orbits represent ways the system could have evolved under the same laws but did not.

These non actual states are not optional extras. They are part of the structure that makes the theory intelligible. If one were to remove them and retain only the actual trajectory, one would lose the ability to define the evolution functions, the relations between states, and the overall organisation of the system. In this sense, the theory implicitly relies on modal notions, even though it is expressed in a non modal language.
The analogy with education is immediate and unsettling. The student, our dynamical system, occupies a space of possible states. Each state corresponds to a way of thinking, understanding, performing. The student’s observed performances trace out a trajectory through this space. But that trajectory is only one orbit, one possible history (eg a timed essay about a poem no support). Other orbits, other trajectories, represent ways the student could have developed under different conditions, different sequences of tasks, different forms of support (eg a 3D model of the poem and oral explanation of what the model represents).

The performative system, however, tends to treat the observed trajectory as if it were exhaustive. It collapses the state space into the path that has been sampled. The student’s modal structure, their capacity to reach other states, to move along alternative trajectories, is inferred from this limited evidence. In effect, the institution is attempting to reconstruct the entire state space from a single orbit. Williamson’s analysis shows why this is untenable.

To make this precise, consider the notion of equivalence classes or orbits. In the dynamical system, states are grouped according to the histories they belong to. Two states are in the same orbit if there is a sequence of evolutions that connects them. In educational terms, one might think of an orbit as a coherent developmental pathway, a sequence of states that a student can move through given certain conditions. The key point is that there may be multiple such orbits, multiple pathways through the space of learning (eg timed essay, 3-D modelling, oral analysis etc).

A student who appears to be on a low attaining trajectory in a traditional assessment regime may in fact be situated on an orbit that is not well captured by that regime. For example, a student may struggle with timed written tasks but demonstrate sophisticated reasoning in oral discussion or collaborative problem solving. These performances belong to different regions of the state space and may be connected by transitions that are not available in the standard assessment pathway. The institution, by focusing on a single orbit, fails to recognise the existence of others.

This is where the concept of counterfactual possibility becomes crucial. The states that are not visited in the actual trajectory are not irrelevant. They represent ways the student could have been, given the same underlying capacities and the same general structure of learning. These are not merely hypothetical in a weak sense. They are structurally embedded possibilities. The failure to actualise them may be due to the design of the learning environment, the choice of tasks, the forms of representation, the timing, the social configuration, rather than to any intrinsic limitation of the student.
Performativity systems systematically ignore these counterfactual possibilities. They operate as if the actual trajectory reveals the full extent of the student’s capacity. This is a conceptual error. It treats the absence of evidence for a state not just as evidence of its absence but of its impossibility. Williamson’s framework makes clear that the absence of a state in the actual trajectory does not entail that it is not part of the state space, nor that it is unreachable under different conditions.

The implications for the concept of potential are particularly stark. In performative discourse, potential is often invoked to account for discrepancies between current performance and expected ability. A student may be said to have high potential but low attainment, or vice versa. But this notion of potential is rarely grounded in a clear account of the underlying modal structure. It functions more as a heuristic or a gesture than as a precise concept.

Within a Williamsonian framework, potential must be understood in terms of reachability within the state space. A student’s potential is not a hidden quantity but a feature of the transitions that are available from their current state. It depends on the structure of the space, the accessibility relations, the stability of states under variation, and the conditions that enable or block movement. Potential is therefore not simply located in the student. It is distributed across the learner, the task, the representation, and the institutional environment.This leads to a radical rethinking of assessment. If the aim is to make modal claims about students, to say what they can do, then the assessment system must be designed to sample the relevant modal space. It must create conditions under which different states can be actualised and observed. It must test for stability across variations, not just performance in a single context. This is a far more demanding requirement than current systems typically meet.

Without such sampling, the institution is forced to rely on extrapolation. It takes a small number of observed states and projects them across the space of possibilities. This projection is then codified in grades, levels, and categories, which are treated as if they directly represent the student’s ability. The result is a reified system in which the model, the representation of the student’s capacity, becomes more real than the underlying modal structure it is supposed to describe.
So far my argument shows that performative systems rest on a deep confusion between actual performance and modal capacity. Now I want to show how that confusion is not accidental but structurally produced, stabilised, and defended by the institutional architecture of schooling. The point is not simply that schools make mistakes about students, but that the very way in which evidence is generated, processed, and circulated makes those mistakes almost inevitable unless the underlying epistemology is challenged.

In most contemporary systems, evidence of learning is tightly coupled to specific formats, most notably timed written work, individualised outputs, and standardised tasks. These formats define a very particular region of the state space as visible and legitimate. To perform well in such formats requires not only subject understanding but a specific configuration of temporal control, linguistic fluency, self regulation under pressure, familiarity with the genre, and alignment with the expectations encoded in marking schemes. 

Take a student who occupies a state in which understanding is present but these other conditions are not yet stabilised may fail to produce the required output. From the perspective of dynamical systems, what we are observing is not the absence of a state, but the failure of a transition. The student is not in the state of producing a polished written response under timed conditions, but this does not entail that they are not in a nearby state of understanding, nor that such a state is unreachable. It may simply be that the pathway from understanding to that particular formal expression is blocked under the given conditions. The performative system, however, tends to treat the observed state as definitive. It collapses the distinction between being in a state and being able to reach a state under altered conditions.

This collapse is reinforced by the way in which evidence is aggregated. Individual performances are combined into scores, scores into grades, grades into levels, and levels into profiles. At each stage, the complexity of the underlying modal structure is reduced. The aggregation process is designed to produce comparability and manageability, to allow students to be ranked, grouped, and tracked. But it also strips away the information needed to make nuanced modal judgements. The resulting categories appear stable and objective, but they are in fact highly compressed representations of a much richer space.

These categories are then fed back into the system as if they were properties of the students. They inform teaching decisions, grouping arrangements, resource allocation, and expectations. A student labelled as low ability may be given less challenging work, fewer opportunities to engage with complex tasks, and lower expectations for performance. This, in turn, shapes the trajectory of their learning, restricting the range of states they are likely to occupy. The model becomes performative in a literal sense. It does not merely describe the student. It helps to produce the very pattern it purports to capture.

This feedback loop can be analysed in modal terms. The initial classification is a hypothesis about the student’s modal space, based on limited evidence. The institutional response then alters the accessibility relations within that space, making certain states more or less reachable. Over time, the student’s actual trajectory may come to align with the initial classification, not because it was accurate, but because it has been enacted. The orbit has been, in effect, selected and stabilised by the institution.

Williamson’s framework allows us to see that this is not simply a social or psychological phenomenon, though it is that as well. It is a misalignment between the structure of the claims being made and the structure of the evidence used to support them. The institution makes modal claims, about ability, potential, trajectory, but grounds them in actualist evidence. It then treats these claims as if they were directly observed facts, and acts on them in ways that reshape the underlying space.

For a claim about a student’s ability to be safe, it must hold across relevant nearby cases. But the institution rarely tests this. It does not systematically vary the conditions under which the student is asked to perform. It does not ask whether the student would succeed under slightly different tasks, representations, or temporal structures. Instead, it assumes that performance in the given context is indicative of performance in all relevant contexts. 

To disrupt this pattern, one must intervene at the level of evidence production. This is where the idea of varied enactment becomes not just pedagogically desirable but epistemologically necessary. If we are to make responsible modal claims, we need to observe the student across a range of conditions. This means designing tasks that vary in representation, modality, social configuration, and temporal structure. It means creating opportunities for oral reasoning, collaborative work, iterative development, and a fecundity of alternative forms of expression. It means allowing for rehearsal, feedback, and revision, so that fragile states can be stabilised and transitions can be observed.

The aim is not to generate more data in the sense of more numbers, but to generate richer evidence about the structure of the student’s modal space. For example, a student who struggles with written explanations in mathematics may demonstrate clear conceptual understanding when asked to explain verbally, to use diagrams, or to work through problems collaboratively. Observing these performances allows the teacher to distinguish between different kinds of limitation, a lack of conceptual understanding versus a difficulty in expressing that understanding in a particular form.

This richer evidence base changes the nature of judgement. Instead of assigning a student to a category based on a small number of performances, the teacher can construct a more nuanced account of the student’s modal profile. This account might include which states are currently accessible, which transitions are stable, which are fragile, and which appear to be blocked. It might also include hypotheses about how these transitions could be opened, through changes in task design, representation, or support.

At the institutional level, however, this poses significant challenges. The structures of accountability and reporting are not designed to accommodate such nuanced accounts. They require clear, comparable, and standardised measures. There is therefore a tension between the epistemological demands of modal reasoning and the practical demands of institutional management. This tension cannot be resolved simply by exhorting teachers to be more reflective or more flexible. It requires a rethinking of how institutions represent and use information about learning.

One possible direction is to separate, at least partially, the functions of assessment. On the one hand, there is a need for summative judgements, for decisions about progression, certification, and accountability. On the other hand, there is a need for formative understanding, for insight into the student’s modal space that can inform teaching and learning. These functions are often conflated, with the same assessments serving both purposes. This conflation exacerbates the problems identified here, because it encourages the use of narrow, standardised measures for purposes that require rich, context sensitive information.

A more modal sensitive approach would involve developing forms of assessment that are explicitly designed to explore the student’s state space. These might include tasks that require transfer across contexts, that vary representations, that involve collaboration, that allow for iteration. The results of such tasks would not be reduced to a single score but would be used to build a profile of the student’s capacities across conditions. This profile would then inform teaching, rather than being used directly for high stakes decisions.

At the same time, the institution would need to maintain an awareness of the provisional nature of these profiles. They are models, not realities. They are constructed from evidence that is always partial. They should therefore be open to revision in light of new observations. This requires a cultural shift, from seeing assessment as producing definitive judgements to seeing it as generating hypotheses about the student’s modal structure.

This shift also has implications for how teachers collaborate. If the aim is to understand the student’s modal space, then no single teacher, observing the student in a single subject and context, has access to the full picture. Different subjects, tasks, and interactions reveal different regions of the state space. Collaborative discussion among teachers can therefore be a powerful way of integrating these partial views. Instead of simply sharing grades or levels, teachers can share observations about how the student performs under different conditions, building a more comprehensive understanding.
However, this collaboration must be structured in a way that resists reification. There is a risk that collective judgements simply reproduce and reinforce existing categories. To avoid this, discussions need to focus on variation and anomaly, on cases where the student’s performance does not fit the expected pattern, and on exploring alternative explanations. This is analogous to the role of anomalies in scientific practice, where unexpected results prompt a re-examination of the underlying model.

Finally, one must consider the broader implications for educational purpose. If learning is understood as movement within a space of possibilities, then education is not simply about achieving predefined outcomes. It is about expanding that space, opening new pathways, enabling students to access regions of understanding and capability that would otherwise remain closed. This does not mean abandoning standards or rigour. It means recognising that standards themselves are located within a space of possibilities, and that the task of education is to bring students into relation with that space in a way that is both demanding and enabling.
In this sense, Williamson’s work offers the basis for a different conception of educational practice, one that is more attuned to the structure of learning as a modal phenomenon. The challenge is to translate this conception into institutional forms that can sustain it without collapsing back into the very patterns it seeks to disrupt.

What should now be visible is that the problem is not simply that current educational systems are too narrow, too test driven, or too performative in a sociological sense. It is that they are operating with an impoverished metaphysics of learning. They assume, often tacitly, that the real is exhausted by the actual, that what is observed in standardised conditions can stand in for what a learner is and can become. Williamson’s work, read carefully and extended into this domain, shows that this assumption is untenable. It misdescribes the structure of the phenomena it seeks to govern.

The force of the destabilisation lies precisely in the fact that it does not rely on appeals to individuality, creativity, or the ineffability of the learner, though those themes may have their place. It proceeds instead by tightening the logical screws. To ascribe ability, understanding, or knowledge is to make a modal claim. It is to say something about what would happen across a range of relevantly similar situations. But if the evidential basis for that claim is restricted to a small number of actual performances under highly specific conditions, then the claim outruns the evidence. The institution is, in effect, projecting a modal structure onto the learner that it has not adequately sampled. This projection is then stabilised through institutional practice. Categories are assigned, expectations set, pathways determined, and over time the learner’s trajectory comes to align with the initial classification. What appears, at the end, as an accurate description of ability may in fact be the sedimented result of a series of modal closures, points at which alternative pathways were not explored, transitions not opened, possibilities not enacted. The performative system, in this sense, is not measuring learning. It is actively shaping the space in which learning can occur.

To see this clearly is to recognise that reform at the level of technique, more varied assessment, more formative feedback, more personalised learning, while valuable, will be insufficient if the underlying epistemology remains unchanged. What is required is a shift in how educational systems understand the relationship between evidence and claim, between performance and capacity, between actuality and possibility. Williamson’s framework provides the conceptual resources for such a shift, but it also imposes constraints. It demands more disciplined reasoning, more careful attention to the structure of the evidence, and a more explicit articulation of the conditions under which modal claims are justified.

One way to bring this into focus is to return to that notion of safety mentioned above. If we say that a student understands a concept, we are committed to the claim that they would continue to demonstrate that understanding across relevant variations. But what counts as relevant variation is itself a substantive question. It cannot be settled by fiat or by convenience. It requires an understanding of the domain, of what it means to grasp a concept, of how that grasp is manifested in different forms. In mathematics, this might involve moving between symbolic, graphical, and verbal representations. In literature, it might involve interpreting texts across genres, contexts, and creative modes of response. In science, it might involve applying concepts to novel situations, designing experiments, explaining phenomena.

The implication is that assessment must be designed to probe these variations. Not exhaustively, which would be impossible, but sufficiently to provide a basis for modal inference. This is where the idea of varied enactment, developed earlier, acquires its full significance. It is not simply a matter of pedagogical richness (although it is that too!). It is a condition for epistemic adequacy. Without it, the institution cannot make the claims it purports to make.

At the same time, the argument cautions against a naive expansion of evidence. Simply adding more tasks, more formats, more data points, does not automatically solve the problem. The issue is not quantity but structure. The variations introduced must be relevant to the capacities being assessed. They must be designed to test the stability of performance across conditions that matter for the domain. Otherwise, one risks generating noise rather than insight, or worse, reinforcing existing patterns under the guise of diversity.

There is also a temporal dimension that must be foregrounded. Learning unfolds over time, and the stability of a capacity is not something that can be established in a single moment. A student may demonstrate understanding in one instance and fail in another, not because the capacity is absent, but because it is in the process of being formed. Williamson’s framework, with its emphasis on nearby possibilities, suggests that we should be attentive to trajectories, to how performance changes under repeated engagement, feedback, and revision. 

This again sits uneasily with performative systems that privilege snapshot judgements and fixed categories.
Institutionally, this points toward the need for forms of organisation that can accommodate temporal and modal complexity. This may involve rethinking reporting systems, moving away from single grades toward richer profiles that capture patterns of performance across conditions and over time. It may involve creating space for professional judgement that is informed by but not reducible to numerical data. It may involve developing collaborative practices among teachers that focus on interpreting evidence in modal terms, rather than simply aggregating scores.

Such changes run against the grain of current policy environments, which often demand clarity, comparability, and accountability. There is a risk that any move toward greater complexity will be resisted as impractical or opaque. Yet the alternative is to continue operating with a system that produces clear but misleading representations of learning, representations that are then used to make consequential decisions about students’ futures.

At this point, it is worth returning to the more abstract level at which Williamson’s argument operates. One of its central claims is that modality is not an add on to our understanding of the world but is embedded in the very structures we use to describe it. The example of dynamical systems shows that even when we think we are dealing purely with actual processes, the underlying mathematics presupposes a space of possibilities. To remove that space is to undermine the theory itself. The parallel in education is that the space of learning possibilities is not something we can ignore or treat as secondary. It is constitutive of what learning is. A student’s development cannot be fully understood by tracing a single path of performances. It requires an account of the space in which those performances are situated, the states that are reachable, the transitions that are available, the conditions that enable or block movement. To ignore this is not merely to simplify. It is to misrepresent the phenomenon.

There is, finally, an ethical dimension to this argument. When institutions treat students as if they were exhausted by their observed performances, they risk closing down possibilities that have not yet been realised. This is not simply a matter of fairness or equity, though it is that as well. It is a matter of truth. The institution is acting on a false picture of the student’s capacities. Its lying. (I don't think intention has anything to do with lying by the way but am not going to argue that here.) By contrast, an approach that takes seriously the modal structure of learning is one that remains open to the emergence of new capacities, that recognises the provisional nature of its judgements, and that seeks to create conditions under which a wider range of possibilities can be actualised.

This does not guarantee success. There will still be limits, constraints, failures. Not all possibilities can be realised, and not all transitions can be opened. But the point is that these limits should be discovered through engagement with the structure of the learning space, not imposed prematurely through the reification of narrow evidence.

In conclusion, Williamson’s work offers a way of rethinking the relationship between actuality and possibility that has direct and far reaching implications for education. By showing that our best theories already rely on modal structures, it undermines the assumption that actual performance can serve as a sufficient basis for judgement. By emphasising the need for stability across nearby possibilities, it highlights the inadequacy of assessments that sample only a narrow range of conditions. And by insisting on the distinction between model and reality, it warns against the reification of institutional representations.

To take these insights seriously is to embark on a demanding but necessary reorientation of educational theory and practice. It requires a more sophisticated understanding of evidence, a more nuanced approach to assessment, a more reflexive use of models, and a more expansive conception of what it means to learn. It also requires courage, because it challenges entrenched systems and familiar ways of thinking. But if the aim of education is, in part, to enable students to realise their possibilities, then it is difficult to see how we can proceed without confronting the modal structure of learning head on.

References

Ball, Stephen J. 2003. “The Teacher’s Soul and the Terrors of Performativity.” Journal of Education Policy 18 (2): 215–228.

Biesta, Gert. 2010. Good Education in an Age of Measurement: Ethics, Politics, Democracy. Boulder: Paradigm.

Williamson, Timothy. 2000. Knowledge and Its Limits. Oxford: Oxford University Press.

Williamson, Timothy. 2013. Modal Logic as Metaphysics. Oxford: Oxford University Press.