Concluding Thought: A Note on Metaphysics, Logic and Epistemology (15)

After attending the 61st PESGB conference in Oxford, where I had talked to delegates about Ruth Barcan Marcus and the educational significance of modal logic, I found myself wanting to press further into a different but related region of contemporary metaphysics, one that has become increasingly important for anyone interested in how educational thought classifies, structures, and organises its world. Barcan Marcus is an excellent place to begin because she helps one see that questions of possibility, necessity, identity, and rational commitment are not remote technical curiosities. They shape how we think about what a learner can do, what a teacher must do, what counts as the same piece of work under different descriptions, what a school is committed to when it adopts a concept, and what follows from a judgement once it has been made. 

But once one starts from there, one quickly encounters a broader development in metaphysics, especially in the work of Kit Fine and some of the philosophers who have responded to him, concerning the relation between modality, essence, explanation, grounding, relevance, and conceptual error, pivoting from his classic account of all this, ' Essence and Modality'. To make that discussion accessible, I've tried to make clear the main technical terms (to the best of my abilities) because although they can sound forbidding when first encountered they are pretty intuitive. Here's a brief recap of the key bits of the machinery. 

Modality is the general philosophical study of possibility and necessity, which Barcan Marcus helped regiment into modern logic. A modal claim is any claim about what can happen, what must be the case, what could have been otherwise, what is impossible, and so on. When a teacher says that a pupil can solve quadratic equations but cannot yet write a sustained essay, or that a class must first learn to listen before it can have an open discussion, those are modal claims. Modal logic is the formal study of such claims. It gives us a more exact way of representing how necessity and possibility work, how they relate to one another, and how they connect with identity, time, and quantification.

Essence is a more specialised idea. It concerns what something is in its nature, what belongs to it not merely by accident or temporary circumstance but because of what it is. If one says that it belongs to the essence of a triangle to have three sides, one means that this is not just a frequent feature of triangles but part of what being a triangle is. Fine’s major contribution was to argue that essence should not simply be reduced to necessity. Something may be necessary without being essential. For example, it may be necessarily true that Socrates is distinct from the Eiffel Tower, but it does not seem to tell us anything important about what Socrates is. Fine’s thought was that questions of essence are finer-grained than questions of mere necessity. They are sensitive to source, to where a truth comes from, to what it is about the thing itself that makes the truth hold.

This leads to hyperintensionality. A distinction is called hyperintensional when it is finer than the ordinary distinction between necessarily equivalent claims. Two statements may be necessarily equivalent, always true together, yet differ in meaning, structure, relevance, or explanatory role. Fine’s argument was that essence is hyperintensional in this sense. It can distinguish between claims that modal logic on its own would treat as equivalent. A more ordinary word for what is at issue here is fine-grainedness, the idea that some conceptual or metaphysical distinctions cut more finely than standard modal or extensional ones.

An extensional approach, by contrast, is one that is concerned only with outcomes or truth-values, not with the route by which those outcomes are reached. If two expressions always pick out the same object, or two sentences are always true under the same conditions, an extensional treatment may regard them as equivalent for present purposes. Intensional approaches take differences in sense or mode of presentation more seriously. Hyperintensional approaches go further still and allow distinctions finer than ordinary intensional semantics usually allows. These issues matter in philosophy of education because educational discourse often depends upon distinctions between outwardly similar but structurally different things, such as understanding and the display of understanding, participation and mere presence, inclusion and co-placement, or authority and control.

Grounding is another key term. To say that one fact grounds another is to say that the second holds in virtue of the first. Grounding is a relation of metaphysical explanation. If a class is unsettled because the pupils do not trust one another, because the room is badly arranged, and because previous lessons have trained them to wait for the teacher’s answer, those lower-level facts may be said to ground the higher-level fact that genuinely open discussion is not yet possible. Grounding is not just causation, nor just correlation. It is explanation in the sense of what makes something the case.

Closely related is ontological dependence. This concerns what depends for its being or identity on what. A singleton set containing Socrates depends on Socrates in a way that Socrates does not depend on the set. A classroom discussion depends on the pupils, the teacher, and their relations in a way that no one pupil depends on that discussion for existing. Fine often uses this notion to explain why some facts seem relevant to what a thing is while others do not. It is one thing to mention something merely associated with an object, another to mention something on which its nature actually depends.

Another important distinction is between ordinary modality and metaphysical necessity. Ordinary modality concerns the kinds of possibilities and necessities that arise in everyday practical life. A teacher says that a pupil can work independently in a quiet room, or that a lesson cannot move on until the key concept is understood, or that a school could not yet implement a certain reform. These are not usually claims about the deepest nature of reality. They are context-sensitive, circumstance-sensitive, and often change over time. Metaphysical necessity is a stronger and more austere notion. It concerns what must be the case in virtue of the nature of things themselves. Barbara Vetter’s work asks how these two levels relate. Her question is especially relevant to education, which is saturated with ordinary modal language but often lacks any clear account of the stronger modal and metaphysical assumptions built into its practices.

Another term that recurs in what follows is generated entity or generated form. This refers to something that is real, but real in virtue of a structured set of relations rather than as a basic thing in its own right. A lesson, a seminar discussion, a curriculum sequence, or an assessment event can be understood in this way. They are not mere heaps of items, but nor are they independent substances. They are generated by relations among learners, teachers, materials, norms, spaces, and times. This idea becomes particularly useful when thinking about assessment, participation, disability, and classroom interaction, because it helps distinguish an educational good from the particular form in which it happens to be displayed.

The term heuristic is also central. A heuristic is a quick, usually useful, but fallible cognitive shortcut. It helps us reach judgements efficiently, but it can also mislead us. Williamson argues that some of the intuitions supporting Fine’s examples may arise from a relevance heuristic. We see certain details in a sentence as extraneous to answering the question “What is this thing?” and we then judge the whole statement to be false or inessential. His warning is that philosophers may then overfit their theories to these intuitions, building increasingly complicated metaphysical frameworks to save what are really error-prone data points. 

Overfitting, borrowed from statistics and the sciences, names the mistake of making a theory more and more elaborate so that it fits selected cases perfectly while losing touch with the underlying structure.This is one reason the discussion matters so much for philosophy of education. Educational theory is full of concepts that appear rich and indispensable, inclusion, voice, agency, wellbeing, resilience, decolonisation, hope, belonging, empowerment, and so on. Fine’s approach encourages us to ask whether these concepts pick out genuine structures, generated forms, or relations of dependence. Williamson’s pressure then asks whether our confidence in these concepts is well-grounded or whether we are simply following a relevance filter that gathers together whatever feels morally and politically pertinent. 

Where Fine had pushed us to ask what is essential to a thing, Rosen presses the prior question, which candidate essences are even legitimate in the first place? This means that philosophy of education cannot simply move from a valued concept, inclusion, hope, agency, decolonisation, discussion, resilience, belonging etc etc, and ask what its essence is. It must first ask whether the thing in question is ontologically disciplined enough to bear an essence at all. Rosen’s problem of “essentialist existence” is therefore crucial for education, because the field constantly introduces entities, profiles, cultures, ecosystems, learner types, capabilities, identities, pathways, without first asking whether these are real educational kinds, generated entities, loose bundles, or merely heuristic labels. In that sense, Rosen gives the whole discussion a gatekeeping function. He helps us see that many educational debates may go wrong before they even begin, because they presuppose the legitimacy of the very thing whose essence they then dispute. Rosen also matters because of the role he gives to explicit definition, implicit definition, conservativity, and generated individuals. 

These are extremely fertile for educational analysis. An explicitly defined educational kind is one whose structure can be relatively clearly stated. An implicitly defined one is recognised more through the role it plays in a wider structure. Conservativity is the thought that a higher-level item should not magically generate new content not already grounded in the more basic things on which it depends. This lets us ask whether a category like “inclusive school culture” or “student voice” is genuinely conservative over identifiable practices and relations, or whether it is being used as if it introduced a substantial educational reality where really there is only rhetorical aggregation. Rosen therefore gives us the pressure to ask, not just whether a concept is good or politically resonant, but whether it has ontological seriousness.

Where Rosen asks which essences are legitimate, Litland asks whether real definition itself might be more basic than essence. Instead of first saying what belongs to the essence of x, one asks how x is really defined, and then treats essence as what follows from all the real definitions of x. The central gain here is his idea of an essential manifold. A thing may have several legitimate definitions, not one unique canonical one, and what is essential is what survives across that manifold. This has obvious importance for education, because so many central educational terms function exactly like this. 

Many educational things are often not captured by one strict explicit definition. But that does not mean they are empty. Litland gives us a way of saying that a concept may have multiple admissible definitional routes, and the philosophical task is to ask what, if anything, remains invariant across them. That is a crucial resource against both inflation and scepticism. Against inflation, Litland reminds us that not every associated feature belongs to the essence. Against scepticism, he reminds us that lack of a single definition does not yet mean there is no structure. The question is whether there is a disciplined manifold. He gives us a way of distinguishing a family of related but structured definitions from a mere heap of politically attractive associations. He also contributes something methodologically important through his attention to immediate and full real definition, definitional unity, and the inferential role of concepts. 

Even if one does not accept the full formal apparatus, the educational lesson is clear. A term should not be treated as deep merely because it attracts many resonant descriptions. We should ask whether its various uses hang together, whether they preserve a common structure, and whether the concept is being held together by genuine definitional unity or only by institutional and moral prestige. That is exactly the potential problem we later saw with some educational buzzwords.

A final term worth clarifying is incompossibility. Two things are incompossible when each may be possible on its own but the two cannot both be fully realised together. This notion becomes useful in education when we consider whether two desirable projects, for example decolonisation and demasculinisation, or certain forms of anti racism and certain forms of class analysis, can always be jointly instantiated in one coherent educational arrangement. The point is not merely that they may be difficult to combine politically, but that there may be deeper structural tensions between the forms of authority, explanation, or educational ordering they require.

This discussion grew out of the conviction, strengthened at the Oxford conference, that philosophy of education has often either ignored these developments in modality and metaphysics or used them in an unsteady way. The introduction of Barcan Marcus to delegates was one attempt to show that formal and modal thought has genuine educational value. Why? Because educational thought is already full of modal judgements, claims about necessity, possibility, dependence, identity, relevance, explanation, and classification. It constantly moves between what things are, what they can become, what counts as the same, what is essential to a practice, what is merely circumstantial, what follows from an educational commitment, and what is ruled out by it. Without some disciplined account of these matters, the field too easily oscillates between rhetorical inflation and bureaucratic flattening.

Fine gives us an apparatus for asking what educational things are, what they depend upon, and what forms of modality are in play. Vetter broadens the field by reconnecting metaphysical modality with ordinary practical modal judgement. Williamson introduces methodological pressure by warning that some of our most compelling conceptual distinctions may be generated by heuristics rather than by genuine metaphysical structure. Taken together, I think these debates provide a much richer and more demanding frame for educational thought than the field usually allows itself. They may help us think more clearly about curriculum, discussion, disability, assessment, authority, inclusion, and many of the buzzwords that now dominate educational discourse. They may also help us see where some of those buzzwords are genuine conceptual achievements and where they are, perhaps, emperors without clothes.

So, to conclude, my path began with Barcan Marcus, who shows that modality is not an abstract technical corner of philosophical logic but a way of articulating commitment, identity, and consequence in thought and practice. Once that door is opened, Fine’s work presses us further, inviting us to distinguish between necessity and essence, to recognise that what something must be and what it is in its nature may come apart, and to treat questions of structure, dependence, and explanation as central rather than optional. It allows us to ask not just whether a learner can perform a task, but what it is for that performance to count as understanding, not just whether a classroom appears orderly, but what generates genuine participation, not just whether a curriculum includes certain elements, but what its organising form consists in.

Vetter’s intervention complicates this picture in a productive way. She reminds us that most educational judgements are not made at the level of austere metaphysical necessity but within ordinary modal discourse, claims about what can be done here, what must be done now, what is possible for this pupil under these conditions. Her work forces a connection between these everyday modalities and the more rarefied metaphysical ones. That connection is not straightforward, but the very difficulty is instructive. It reveals that educational thought moves constantly between levels of modality without noticing, and that greater clarity about those levels could sharpen both theory and practice.

Williamson’s challenge then introduces a necessary discipline. He does not deny that there are real distinctions to be made. What he questions is our confidence in the intuitions that seem to support them. His appeal to heuristics and to the danger of overfitting shows how easily philosophers can mistake a pattern in their own judgements for a structure in the world. The relevance filter, the tendency to treat some elements as central and others as peripheral without sufficient justification, turns out to be especially powerful in a field like education where concepts are saturated with moral and political significance. It helps explain why certain terms gather prestige and apparent depth while remaining conceptually unstable.

Fine shows that Williamson’s semantic assumptions are contestable, that the route from linguistic form to metaphysical conclusion is not secure, and that even if some examples are less stable than once thought, the broader conceptual framework of essence, grounding, and ontological dependence has earned its place through its explanatory and organisational power. Perhaps most importantly, Fine’s distinction between the weak, intermediate, and stronger theses offers a way of continuing inquiry without either premature reification or premature dismissal. We may not yet be in a position to assert that a given educational concept has a fixed essence. But we may still be justified in treating questions about its nature, its grounds, and its structure as real and substantive.

When these threads are brought back into philosophy of education, several consequences follow. First, the field can no longer treat its central concepts as self-evident. Terms such as reason, inclusion, agency, belonging, decolonisation, hope, or wellbeing must be examined for what kind of entities or structures they are supposed to pick out. Are they unified properties, families of related goods, generated forms, or heuristic bundles? 

Second, the field gains a more precise vocabulary for doing that work. The notions of grounding, dependence, modality, and hyperintensional distinction allow for a more careful mapping of educational phenomena than the usual oscillation between empirical description and normative assertion. 

Third, Williamson’s epistemic pressure makes it clear that not all such concepts will survive this scrutiny intact. Some will turn out to be overfitted, sustained by relevance heuristics, rhetorical accumulation, and institutional reinforcement rather than by genuine ontological unity. Recognising this is clarifying. It allows educational thought to redistribute what had been bundled together, to separate distinct goods, to identify real tensions and incompossibilities, and to avoid pseudo-debates conducted under the illusion of a shared concept.

Fourth, Fine’s insistence on usefulness reminds us that metaphysical concepts are not judged only by their resistance to sceptical challenge but by what they enable us to do. In education, this means asking whether a conceptual framework helps us understand practices more clearly, articulate differences more precisely, and formulate problems in ways that can guide action. If the apparatus of essence and grounding allows us to distinguish, for example, between the appearance and the reality of inclusion, between the display and the possession of understanding, or between different forms of participation, then it has earned its place even if some of its initial motivations require revision.

Where this leaves philosophy of education is in a more demanding but also more promising position. It can no longer rely on the unexamined authority of its key terms, nor can it dismiss metaphysical work as irrelevant. It must instead navigate between two risks. On one side lies inflation, the tendency to treat every morally attractive concept as a deep educational reality. On the other lies deflation, the temptation to reduce all such concepts to loose heuristics or policy conveniences. 

The Fine Williamson exchange shows that neither extreme is satisfactory. What is required is a practice of conceptual discipline that is sensitive both to the possibility of real structure and to the ease with which we project structure where none exists. If that practice is taken seriously, then philosophy of education becomes at once more technical and more grounded. More technical because it must engage with distinctions about modality, essence, and dependence that are often left implicit. More grounded because those distinctions are brought to bear on the everyday realities of classrooms, curricula, institutions, and learners. 

The result is a change in posture. Educational concepts are no longer taken at face value, nor are they dismissed as mere rhetoric. They are treated as candidates for analysis, to be tested, refined, sometimes dismantled, and sometimes reconstructed using the philosophical apparatus examined here that tends to be ignored by much contemporary philosophy of education. In that sense, the discussion opens a way of working, one in which philosophy of education becomes more attentive to what its concepts are, what they do, and whether they deserve the authority they so often claim.