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Reflections and replies

Conceptual analysis and the prototype theory of concept formation

A reply to Jovanović
Kenneth Einar Himma

Abstracts

This article critiques Miodrag Jovanović's defense of the prototype theory of concepts as an alternative to metaphysically driven conceptual analysis. It argues that Jovanović's approach confuses the psychological process of concept formation with the semantic theory of conceptual content, failing to provide a new methodology distinct from metaphysical theorizing. The article highlights the distinction between the prototype theory of concept formation (PCF) and the prototype theory of conceptual content (PCC), emphasizing that the latter cannot be deduced from the former. While PCC suggests that concepts have graded membership based on similarity to prototypes, this does not necessarily follow from PCF's empirical observations. The article concludes that prototype methodologies might complement rather than replace traditional conceptual analysis, particularly for concepts with resemblance-based membership criteria.

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1 Introduction

  • 1 Jovanović 2024.

1Miodrag Jovanović recently published an article in this journal defending an approach to analyzing concepts – “the prototype theory of concepts” – that he believes is an alternative to “metaphysically driven conceptual analysis.”1 This essay argues that his defense falls short in three ways. First, one cannot derive a methodology for identifying conceptual content from an empirical theory of how we come to “form” such content; the former is a semantic theory of conceptual content whereas the latter is a psychological theory of the conscious mental states involved in forming concepts. Second, assuming that he has successfully articulated a new methodology for conceptual analysis, it is not an alternative to metaphysical theorizing about a concept; true claims about the content of a concept are necessarily true. Finally, the only way that a prototype methodology seems, without more articulation that it is given, to differ in any significant way from the methods traditionally associated with conceptual analysis is that it must rank those entities that count as members of the relevant kind in terms of their respective resemblances to the corresponding prototype. If this is correct, the two approaches may turn out to be complementary in explicating those concepts that have membership conditions graded in terms of resemblance to some prototype – rather than being rival general approaches.

2 The prototype theories of concept formation and content

  • 2 While one can get a reasonably clear understanding of the prototype theory of concept formation fro (...)

2The methodology that Jovanović defends in his essay is grounded in a psychological theory which purports to explain the conscious mental states that figure into the mental processes of categorizing things – i.e., in an empirical theory of the conscious mental states involved in the psychological processes of concept formation. The prototype theory of concept formation can be summarized as follows:2

  • 3 Prototype theory 2024. Categorization involves the mental actions involved in forming and applying (...)

Prototype theory is a theory of categorization in cognitive science, particularly in psychology and cognitive linguistics, in which there is a graded degree of belonging to a conceptual category, and some members are more central than others…. In this prototype theory, any given concept in any given language has a real world example that best represents this concept.3

  • 4 See Note 2, above.
  • 5 Jovanović refers to this as the “prototype theory of concepts.”
  • 6 As it has been articulated by proponents, PCF and PCC apply to all concepts – and not just concepts (...)

3 There are two different prototype theories, which are consistently conflated in Jovanović’s essay. The first, and original theory, is the prototype theory of concept formation (PCF). According to PCF, we form a concept C by grouping things under C that bear a threshold degree of similarity to things that we converge in believing are paradigmatic, representative, or prototypical of C.4 PCF is hence a theory of the conscious mental processes involved in concept formation. The second is the prototype theory of conceptual content (PCC).5 According to PCC, the content of any concept is defined by membership conditions that are graded in terms of a threshold degree of resemblance to the relevant prototypes.6

  • 7 See Rosch & Mervis 1975.
  • 8 This strikes me as plausible with respect to how we learn new concepts and with respect to how we a (...)

4PCF and PCC are grounded in psychological surveys of competent speakers. For instance, if asked to give an example of something that counts as furniture, subjects more often respond with couch than with wardrobe.7 PCF infers from this and similar surveys that, as a general matter, we form concepts by grouping items that bear some degree of similarity to some item that is regarded as paradigmatic, representative, or prototypical of the kind being conceptualized.8 PCF infers, then, from the study on furniture that subjects regard a couch as being more representative of the concept of furniture than a wardrobe. This modest inference is, of course, unproblematic.

  • 9 General terms, like law, water, blue, proposition, define kinds (of thing). Our concepts describe, (...)

5In contrast, PCC makes a more ambitious inference from these same surveys. In particular, PCC infers that the membership conditions for a concept incorporate a standard that is satisfied by only those items that bear some threshold resemblance to the prototypical items. For instance, PCC infers from the survey on furniture that subjects believe that a couch counts more as furniture than a wardrobe does – which assumes, of course, that both count as furniture. Whether an item counts as a member of some kind described by a concept,9 on PCC, depends on whether it bears a requisite degree of resemblance to a representative example of the reference set that defines the prototype – and it can count as more or less a member of that kind than other of its members. The membership conditions for any concept, then, are graded in terms of degrees of resemblance.

6

7While proponents of PCC seem to deduce PCC from PCF, they never explain how a general semantic theory of conceptual content can be derived from an empirical theory of how beings with the psychological features we have form concepts. Theories of concept formation are empirically psychological in character, while general theories of conceptual content are descriptively semantic in character – and might be metaphysical if formulated to apply to all possible worlds. But, either way, semantic theories of conceptual content are philosophical whereas PCF is psychological.

8An argument is needed to support the inference of PCC from PCF. It should be clear, then, that the general semantic claim that the membership conditions for any concept are graded in terms of similarity to a prototypical exemplar cannot be validly deduced from an empirical psychological theory of concept formation. Although it might be true that we form a concept in terms of degrees of similarity to a favored prototype, it does not follow that the content of the concept is necessarily graded in terms of these similarities. As a matter of formal logic, it is clear PCC cannot be validity deduced from just PCF.

9The logical gap between PCC and PCF can be seen in the following way. It is plausible to hypothesize that most speakers believe the number 2 is “representative” of the set of even numbers. But it is, in contrast, implausible to hypothesize that most speakers believe that the number 2 counts more as an even number than the number 64. There is no question that the membership conditions for even numbers are all-or-nothing. After all, being divisible by 2 is an all-or-nothing property of a number; 2 is no more divisible by 2 than any other number divisible by 2.

  • 10 See Note 2, above.

10Similarly, the fact that speakers are more likely to point to a couch than to a wardrobe as representative of the concept of furniture entails little, by itself, about the membership conditions of that kind.10 In particular, it does not imply that those speakers believe, as a subjective matter of their conscious mental states, a couch counts more as furniture than a wardrobe. Much less does it imply, as an objective matter of semantic content, that the membership conditions for the kind are graded in a manner that entails that a couch counts more as a piece of furniture than a wardrobe.

  • 11 Merriam-Webster, for instance, defines the term furniture as “movable articles used in readying an (...)
  • 12 Merriam-Webster, for instance, defines the term fixture as “something that is fixed or attached (as (...)

11Although it may be true that having a couch is more important than having a wardrobe for making a home habitable, there is nothing obvious in ordinary usage that even remotely suggests a couch counts more as furniture than a wardrobe does. The concept of furniture applies to movable articles that are used to make an interior or exterior space ready for occupancy or use.11 In contrast, the concept of a fixture applies only to articles that are attached, or “fixed,” as a part of the structure or as a permanent appendage.12

  • 13 Most furniture stores sell anything that counts as furniture, including lamps. But there are many s (...)

12 It is true, of course, that if asked to illustrate the concept, we might be more likely to point to a couch than to a lamp; however, that is for reasons that are ultimately epistemic in character. It is plausible to hypothesize that someone who does not understand the meaning of furniture is more likely to understand its meaning if shown a couch than if shown a lamp. But that is, in part, because lamps fall under a number of related concepts, like that of lighting.13

13That said, the issue of how best to illustrate the concept of furniture to someone who does not grasp it is logically distinct from the issue of whether some items that count as furniture count more as furniture than other. I would hypothesize, and this is an empirical hypothesis that requires experimental confirmation, that the reason a couch is viewed as more representative of the concept of furniture than a wardrobe is that fewer people have wardrobes in their homes than have couches. Most homes come with enough closet space to eliminate the need for a cumbersome, albeit more decorous, item of furniture that does the same work as closets while taking up valuable space that adds to their expense.

  • 14 See Note 2, above.

14But the fact that competent speakers are more likely to point to a couch than to a wardrobe as representative of the notion of furniture entails little, by itself, about the membership conditions of that concept.14 In particular, it does not imply that those speakers believe, as a subjective matter of their conscious mental states, that the concept of furniture is graded so that a couch counts more as furniture than a wardrobe. Much less does it imply, as an objective matter of semantic content, that the membership conditions for the concept of furniture are graded so that a couch counts more as a piece of furniture than a wardrobe.

  • 15 Hart 1961.

15It is not implausible, of course, to think that the membership conditions for some categories, which defines their contents, are graded in terms of similarity to some identifiable prototype. The membership conditions for the concept of bald, for instance, seem graded in terms of a resemblance to someone who has no hair on their scalp, either because it has been completely lost or because it has been completely shaved off; it is not inapt, after all, to characterize some people as balder than others. Though there are significant swaths of vagueness pertaining to how much hair one can have and still count as bald any general term will have some area of vagueness or, as Hart puts it, “open texture.”15 This is why PCC might seem facially plausible as a general theory of semantic content.

  • 16 There are also thick evaluative usages of the locution that refer to non-defective and legitimate l (...)

16While it is hence plausible to think that some concepts are graded in terms of resemblance to a prototype, it is clear that not all concepts are. It is not just mathematical concepts like that of an even number that are obviously all-or-nothing. The membership conditions for the concepts of law and legal system, which are the ones, of course, of interest to people working in legal theory, appear to be all-or-nothing. At the very least, there is nothing in our conceptual practices pertaining to those terms that would obviously entail the membership conditions for the descriptive concepts of law and legal system are graded in the way claimed by PCC.16

17Of course, one can compare legal systems in terms of their respective moral qualities. Some legal systems are more just, good, and legitimate than others. But that is because the membership conditions for these concepts appear, like the concept of bald, to be graded in terms of resemblance to a prototype. While there are systems lacking essential features of a legal system that nevertheless still resemble legal systems enough to be described as pre-legal, it is as inapt to claim that the legal system of the U.S. counts more as a legal system than those pre-legal systems as it is to claim that 2 is more of an even number than 3.

18It seems equally inapt from the standpoint of ordinary usage to say that the legal system of the U.S. counts more as a legal system than any other system that also counts as a legal system. I have never heard, for instance, any academic or ordinary speaker say the legal system of the U.S. counts more as a legal system than the legal system of Nazi Germany – though it is obvious the latter is plausibly characterized as uniquely evil. Nor have I heard, although the issues here are more subtle, anyone claim that systems of municipal law count more as legal systems than systems of international law. The canons of ordinary usage seem to assume that the membership conditions for the concepts of law and legal system are all-or-nothing.

19This assumption is incorporated in mainstream conceptual theories of law. Hart argues, for instance, that there are two conditions that a system must satisfy to count as a legal system: (1) it must have a rule that governs how law is created and applied by legislative, judicial, and executive officials; and (2) the system must be generally efficacious in guiding behavior. While it is plausible to think that the descriptive concept of a legal system includes additional membership conditions, these two conditions seem all-or-nothing – notwithstanding that the locution generally efficacious has areas of vagueness that allow for borderline cases. As is discussed below, there is no reason to think that the existence of borderline cases of a kind is inconsistent with its membership conditions being all-or-nothing.

20There is an evaluative sense of the term law used to refer to systems and norms that count as law but which are defective qua law in light of its (arguably) conceptual aspiration to do justice. As Dworkin puts this point in connection with the issue of whether the Nazi system was too wicked to count as law:

  • 17 Dworkin 1986. Jonathan Crowe argues that the evaluative usage of law is defined in terms of law’s n (...)

We need not deny that the Nazi system was an example of law … because there is an available sense in which it plainly was law. But we have no difficulty in understanding someone who does say that Nazi law was not really law, or was law in a degenerate sense, or was less than fully law. For he is not then using “law” in that sense; he is not making that sort of preinterpretive judgment but a skeptical interpretive judgment that Nazi law lacked features crucial to flourishing legal systems whose rules and procedures do justify coercion.17

21Dworkin distinguishes two usages of the term law in this important passage – one preinterpretive or descriptive and the other interpretive or evaluative. The evaluative usage is plausibly conceived as graded in terms of resemblance to some system that is a prototype of morally legitimate systems.

  • 18 Merriam-Webster n.d.
  • 19 Dictionary.com n.d.

22Finally, there is nothing in any dictionary definition of law that even remotely suggests that its membership conditions are graded in the way that those of the term bald are graded. Merriam-Webster defines law in terms that assume the membership conditions for a system of law are all-or-nothing: law is, on this definition, “a rule of conduct or action prescribed or formally recognized as binding or enforced by a controlling authority.”18 Dictionary.com defines the term law as “any written or positive rule or collection of rules prescribed under the authority of the state or nation, as by the people in its constitution.”19 There is nothing in these, or any other mainstream dictionary definition of the relevant usage, that even remotely suggests that the membership conditions for law are graded in terms of resemblance to a prototype. Dictionary definitions might not be the last word on matters of word usage. But that both philosophical and dictionary explications of the term converge in rejecting a prototype conception is utterly decisive against the idea that the concept of law has graded membership conditions.

  • 20 It is worth noting that natural kind terms, such as that of a bird, are often given a rigorous defi (...)

23Ultimately, the problem for PCC is that whether the membership conditions of any concept are graded in the appropriate manner depends on how we use the corresponding term – and not on how we come to acquire, form, or develop the concept.20 It may well be true that how we come to acquire, form, or develop a concept logically bears on its content. But even that more modest claim needs an argument because these two claims are not logically equivalent – and, moreover, seem to be logically independent of each other.

24Obviously, there can be difficulties in ascertaining whether an entity p falls under a concept C. For instance, it may not be clear whether a motorcycle counts as a vehicle for purposes of a law that prohibits vehicles in a park. But once it has been authoritatively established that a motorcycle counts as a vehicle on that law, it counts as much as a vehicle as any automobile. A police officer might not ticket a motorcyclist for entering the park if the driver can convince the officer she did not know that her motorcycle counts as such; in that case, she would be arguing that the rule did not provide reasonable notice of what it requires with respect to motorcycles. But, even if she did succeed in convincing the officer, a police officer does not have legal authority to reduce a fine on the strength of such discretionary judgments. Either way, the motorcyclist simply won’t have much success arguing her motorcycle is less of a vehicle than a car – unless she was fortunate enough to have a very gullible – and patient – officer stop her.

25Anticipating this reasoning, Jovanović asserts – without any attempt to make an argument – that “the language of borderline cases is logically incompatible with an ‘all-or-nothing’ view of categories favored by MDCA” [i.e., metaphysically driven conceptual analysis]. He points out, correctly, that the boundaries of the concept of bachelor are unclear with respect to how old a man must be to count as a bachelor; that is because different societies have different legal requirements with respect to the age of majority. But Jovanović then concludes – again, utterly without argument – that borderline cases are inconsistent with MDCA. His rejection of MDCA rests entirely on this crucial, unsupported, and highly counterintuitive claim.

  • 21 Moral considerations of fairness, for instance, dictate that criminal laws be interpreted narrowly (...)

26One would not know this from Jovanović’s discussion, but the idea there can be borderline cases of a concept is utterly uncontentious and has been discussed by theorists, like Hart, Dworkin, and Raz, for years. Indeed, it is well known that the open texture of other general terms used in the law often gives rise to practical difficulties, like how the criminal law can be justifiably applied to imprison or fine offenders.21 Hart, Dworkin, and Raz as well as the younger theorists who followed them have likewise assumed that the existence of borderline instances of law is consistent with the claim that the membership conditions of law are all-or-nothing. Given the impressive pedigree of this claim, one cannot just assume, as Jovanović does, it is false. An argument is needed – and one, moreover, that strikes me as very difficult to make – to justify rejecting the claim that the existence of borderline cases of a kind is consistent with its membership conditions being all-or-nothing.

27While there may be additional premises that can be added to PCF that successfully support PCC, this much should be clear: more premises are needed to provide critical support. PCC cannot be validly deduced from just PCF – again – because the former is a philosophical, semantic theory of conceptual content, while the latter is a psychological theory of the conscious mental states that play a role in concept formation. I am skeptical that there are any plausible premises that do the work because PCC strikes me as being obviously inconsistent with our conceptual practices. But this is no part of what I have argued for here. The conclusion of this section is the altogether modest claim that that an argument is needed to deduce, or otherwise infer, PCC from PCF.

3 MDCA: Is there is any other kind?

  • 22 The following discussion borrows heavily from the outstanding van Inwagen et al. 2023. Oddly, for a (...)

28Jovanović argues that PCC defines a conceptual methodology that is not metaphysical in character – which raises the issue of what, exactly, metaphysics is. The term metaphysics has been attributed to Aristotle, though he was not an English speaker and never used the term. Instead, he is translated as having described his work as “first philosophy,” “first science,” “theology” and “wisdom.”22

  • 23 Merriam-Webster defines the prefix meta- as “more comprehensive, transcending,” whereas Dictionary. (...)

29Aristotle’s works were subsequently labeled in English as metaphysical in order to indicate that their topics transcend, or go beyond, physics in the sense that they are concerned with timeless abstract issues, and not the temporal material concerns of the empirical sciences, such as they were at the time.23 As Peter van Inwagen, et. al, explains:

  • 24 van Inwagen et al. 2023.

Aristotle himself did not know the word…. At least one hundred years after Aristotle’s death, an editor of his works … titled those fourteen books “Ta meta ta phusika” – “the after the physicals” or “the ones after the physical ones” – the “physical ones” being the books contained in what we now call Aristotle’s Physics. The title was probably meant to warn students … they should attempt Metaphysics only after they had mastered “the physical ones”, the books about nature or the natural world – that is to say, about change, for change is the defining feature of the natural world.24

30The most probable explanation, then, of the distinction between the physical and the metaphysical, as it was conceived when the term metaphysical was coined, is that the physical is characterized by change, whereas the metaphysical is characterized by changelessness.

  • 25 Leibniz is credited with having introduced the locution “possible worlds” into the philosophical le (...)
  • 26 For an accessible introduction to modal logic, see Chellas 1988.

31 It would be overstating things to claim the meaning of metaphysical is settled. But the idea that metaphysics concerns abstract matters that do not change is now commonly expressed in terms of a focus on explicating necessary truths about these changeless matters. The assumption is that claims concerning matters that do not change are necessarily true, if true, and hence true “in all possible worlds,” as the matter is standardly expressed.25 Indeed, the concept of a possible world has been formalized in systems of modal logic and is regarded as indispensable in metaphysical and mathematical theorizing – so much that graduate students in many top departments in analytic philosophy require a basic course in modal logic, in addition to propositional and quantificational logic.26

  • 27 The semantic machinery of modal logic has also made possible the development of deontic, temporal, (...)
  • 28 True substantive moral claims, like one should not kill, are normatively necessary, if necessarily (...)

32Though it is now commonly accepted that all true metaphysical claims are necessarily true, it is also accepted that not all claims that are necessarily true are metaphysical, as there are at least three kinds of descriptively necessary truths: logically necessary truths;27 metaphysically necessary truths; and nomologically necessary truths.28 The following discussion offers a rough, but largely uncontentious, characterization of these three kinds of descriptively necessary truths.

  • 29 The idea that a claim is logically necessary if and only if it can be deduced from the relevant axi (...)
  • 30 There are, after all, nonstandard propositional, quantificational, modal, and deontic logics. Indee (...)
  • 31 The behavior of the connectives is defined syntactically in terms of its rules of inference and sem (...)

33A claim is logically necessary just in case it can be validly deduced from some favored set of logical axioms, which are assumed to be true in all logically possible worlds, such as the schema that if p, then p.29 Because the axioms of any system of logic do no more than to define the behavior of its connectives and thus make no substantive assertions whatsoever,30 any claim that is logically necessary is true in virtue of its form – and not its content. No matter what proposition is substituted for p in the “if p, then p,” the resulting sentence is necessarily true and thus logically necessary. It is the form of that schema, which is conditioned by the behavior of its connectives,31 that explains its truth – and not its content. Apart from the rules governing the syntax and semantics of the if-then conncective, the schema “if p, then p” has no content until some proposition is substituted for the variable p.

34There are two kinds of descriptive necessity grounded in the content of propositions, rather than their form. The first is the most familiar to laypersons: causal, or, as I will put it, nomological, necessity. Nomological necessity is grounded in the so-called laws of nature, which describe causal regularities that necessarily obtain in this, but not every other, possible world – assuming there are other possible worlds with different causal laws than the ones true in this one. Either way, if these causal claims are necessarily true, then they are true in virtue of their content and not just in virtue of their form. A claim is nomologically necessary, then, just in case it is true but cannot be derived from any set of propositions lacking claims describing these putatively necessary regularities. For instance, the proposition expressed by e = mc2 is nomologically necessary because it can be validly deduced only from a set that includes these causal laws that purport to describe necessary causal regularities.

35The second kind of content-based descriptive necessity is metaphysical necessity. A claim is metaphysically necessary just in case it follows from the union of some class of favored logical axioms and a class of claims assumed to be true no matter which laws describing causal regularities in this world are true but does not follow from just the class of favored logical axioms. The claim that nothing can be red and green all over counts as metaphysically necessary if, as seems clear, it is true regardless of what the laws of nature had turned out to be. But this claim cannot be validly deduced from a set consisting of favored logical axioms and laws describing causal regularities in this world. It can be validly deduced only from a set that includes necessary truths not entailed by those two other sets of claims. Like nomologically necessity, metaphysical necessity is explained, at least in part, by the content of a statement.

  • 32 Our conceptual practices are grounded, of course, in our semantic conventions for using words, whic (...)

36There are two kinds of metaphysically necessary truths: conceptual and nonconceptual. A metaphysically necessary truth counts as conceptual if and only if it is true in virtue of how we use the constituent words: the claim all bachelors are unmarried counts as conceptual because it is true in virtue of the way we use the terms – i.e., our conceptual practices.32 A metaphysically necessary truth counts as nonconceptual, in contrast, if it is true but not simply in virtue of how we use the terms: the claim that nothing can be red and green all over counts as nonconceptual because it is true no matter what the laws of nature turned out to be but does not follow from just a set consisting of favored logical axioms and claims which exhaustively describe our conceptual practices. The descriptive necessity of each of these claims is explained, in part, by its content.

  • 33 See, e.g., Lewis 2000; Plantinga 1979.
  • 34 One exception, discussed in depth by Jovanović, has to do with how old a male must be to count as a (...)
  • 35 Our semantic conventions for using any term can change and are therefore contingent. But that does (...)

37Whatever methodology can be extracted from PCC, it is not an alternative to MDCA – at least not if its claims about conceptual content are only contingently true, which entails that they do not count as metaphysical. It is uncontentious both that true conceptual claims are necessarily true and that the relevant modality is metaphysical necessity,33 rather than logical or nomological necessity. If it is a necessary condition for a man to count as a bachelor that he is unmarried, then it is as much a necessary truth that there are no married bachelors as it is that there are no square circles. Both of these claims are necessarily true, then, because their denials, given the transparent meanings of the terms, express contradictions – and contradictions are false, as a matter of logical necessity. It is true, of course, that there are borderline cases pertaining to whether it is a sufficient condition for someone to count as a bachelor that he is unmarried.34 But this much has been settled: our conventions for using bachelor preclude, in principle, its application to married people.35

  • 36 Try getting a government grant for that research project.
  • 37 Those conventions can change, of course. But, until they do, it is a conceptually necessary truth t (...)

38Here is one way to grasp that true conceptual claims are necessarily true – regardless of the methodology for explicating such claims. It is clear the strategy for justifying metaphysical claims differs in crucial ways from that of justifying non-metaphysical claims. Consider the metaphysical claim that there cannot be a married bachelor and the empirical claim that some bachelors are taller than 7 feet. To justify this last claim, we need to go out into the world to observe whether there are bachelors taller than 7 feet because whether that claim is true depends on contingent facts about how tall people are now; there was, after all, a time in our history when no one was taller than 7 feet. In contrast, it would be silly to conduct an empirical survey to ascertain whether there are any married bachelors.36 That can be settled by inspecting the obvious core content of our conventions for using the term bachelor. This content clearly entails that it is necessarily true that there are no married bachelors and that what explains the necessary truth of this claim is its content, and not its form.37

39But if every bachelor is unmarried is necessarily true, then it counts, contra Jovanović, as metaphysical in character – regardless of whether one gets this from a prototype methodology. The proponent of a prototype methodology must hence confront the following dilemma. If instantiating the so-called prototype features of a concept is not a necessary condition to count as an instance of the corresponding kind, then theoretical inferences about these features are both contingent and empirical, and not metaphysical; for this reason, they tell us nothing about the nature of the relevant kind and are hence not conceptual. If, on the other hand, instantiating these prototype features is a necessary condition to count as an instance of that kind, it is conceptually, and thus metaphysically, impossible for a thing to count as an instance of that kind without instantiating those features. In that case, theoretical inferences about these prototypes count as conceptual, but they do so because they are necessarily true and hence metaphysical, rather than logical or nomological, in character.

  • 38 Whether they are, in fact, unjust depends on theoretical moral matters, such as whether the truths (...)

40Conceptual claims about law are also necessarily true. For instance, it is clearly a necessary truth, given the way we use the words, both that every legal system includes some norms and that every law is a norm. As we have seen, the epistemic justification of such claims is quite different from the epistemic justification of wholly empirical claims, such as that some laws are considered unjust.38 There is no need to conduct an empirical survey to justify the claim that every normative system that counts as law includes norms or that every proposition that counts as a law expresses a norm. These are simply transparent implications of our conceptual practices. In clear and distinct contrast, we need to conduct empirical surveys to justify believing that some laws are considered unjust because that cannot be validly deduced from just claims describing our conceptual practices – though there is enough empirical evidence in the form of televised protests to justify that obvious claim.

41It doesn’t matter whether the membership conditions for law are graded in the way claimed by PCC: those membership conditions express necessary truths. It is a conceptually necessary truth that a legal system includes some norms and that every proposition that counts as a law expresses, or purports to express, a norm. Though it might be true that every general term, including law, has an area of vagueness, or open texture, that does not change the fact that true claims about the nature of law are necessarily true in virtue of content – notwithstanding that the truth-value of such claims supervenes on a set of semantic conventions that can change and are hence contingent. And, as we have seen, Jovanović has given no reason to think that borderline cases implicating these areas of open texture are inconsistent with MDCA – which is the claim that his rejection of MDCA wholly rests upon.

4 How does a prototype methodology differ from MDCA?

42Although the lines of conflict between PCC and traditional assumptions about conceptual content grounding the traditional methodology for conceptual analysis are fairly clear, little has been said by way of developing a distinct prototype methodology that can be deployed to illustrate how these concepts are graded in terms of comparative resemblance to a prototype and provides guidelines for grading them in a conceptual analysis. For his part, Jovanović says little about how a prototype methodology differs from the more traditional methodology – which has been applied consistently by conceptual jurisprudes with some variation for at least the last 70 years. Apart from saying these resemblance gradings must be addressed in articulating a prototype theory of a concept’s content, he says nothing that indicates what a prototype analysis of a concept or a prototype methodology would look like in practice.

43At the outset, I should point out that my remarks in this section are a more speculative than those in the rest of this essay. There is, as far as I have found in my research, little to no published research that articulates, even roughly, the methodology for analysing concepts with membership conditions that are graded in terms of some threshold level of resemblance to some prototype. For what it is worth, I have not seen even one published paper that provides a substantive prototype analysis of any concept, including those of furniture and law. Unfortunately, there are none that are cited in Jovanović’s paper.

44The problem here is that it is not clear how the content of a prototype analysis of a concept would differ from the content of a traditional metaphysical analysis. It is unclear, for instance, how the role played by obvious claims about the prototype would differ from the role played by truisms in MDCA. After all, the truism that law consists of norms seems to pick out a prototype feature of law – namely that the law consists of norms. Similarly, whether it is a prototype feature of law that some norms prohibiting violence are enforced by a sanction depends on whether it is a conceptual truth that some legal norms prohibiting violence are enforced by a sanction.

  • 39 The mode of a set of values strikes me as the closest statistical measure of typicality, rather tha (...)

45 Further, the very concept of a prototype feature of law needs development. It appears clear, for instance, that the concepts of representativeness and typicality, which underwrite PCC and its methodology, can come apart. Consider, for instance, a society where white men outnumber black men by 20 to 1. On the one hand, the typical bachelor in that society is white because typical has a statistical character39 in the sense that it picks out properties instantiated by the vast majority of bachelors in that society and the vast majority of bachelors in that society are white. On the other, it is implausible to think that a white man is representative of the class of bachelors in that society – at least on any intuitive analysis of the notion of representativeness.

  • 40 See Note 2, above.

46 There are, as discussed above,40 similarly worrisome ambiguities with respect to the notion of concept formation that grounds PCF and PCC. On the one hand, the locution concept formation might be concerned with how we collectively manufacture concepts; on the other hand, it might be concerned with how a speaker comes to learn a new concept. There is, as seen above, a logical gap between PCF and PCC – and that is true on any plausible interpretation of the term formation.

  • 41 It is not absurd to think that if the social processes of creating a new concept (or picking it out (...)

47That said, the magnitude of the gap depends on what is meant by the term formation. There is a bigger logical gap between PCC and the claim that a person learns new concepts by grasping prototypes than there is between PCC and the claim that we manufacture new concepts by positing prototypes.41 Although an argument is needed to fill both gaps, more argument is needed to fill the bigger gap than the latter; the latter, after all, bears more directly on the content of the concepts.

48Assuming all this can be satisfactorily worked out, there remains a deeper question. If there are concepts that with membership conditions that are graded in terms of a threshold resemblance to some prototype, then the only difference between a traditional methodology for analyzing those concepts and a prototype methodology is that the latter must expose and quantify those gradations of resemblance – which the traditional methodology is, admittedly, not equipped to do. But, if as argued here, comparative concepts, like just and good, have a minimum threshold for membership, then the membership conditions for even those concepts are all-or-nothing. Although two members of the reference set would still count equally as members of that set, they can be compared in terms of which has more of the relevant property.

49This suggests that the two approaches may be complementary in the following respect. The traditional methodology can be deployed to explicate the all-or-nothing existence conditions of the concept and a prototype methodology can be used to identify and quantify the relevant resemblance relations. While special training in statistics would be needed to quantify the resemblance relations, the analysis interpreting the relevant data would still be philosophical in character. For this reason, an analysis of the all-or-nothing existence conditions would result in necessary truths and count as metaphysical. In contrast, the values of the resemblance relations might change over time without altering their all-or-nothing existence conditions. What is considered representative of the concept of furniture at one time need not be considered representative of it at another. But either way, these internal resemblance relations can change without altering the all-or-nothing existence conditions of the concept of furniture.

50These tentative suggestions should not be construed as a criticism of either PCF or PCC. It is arguable, as discussed above, that some comparative concepts, like good or bald, can be graded in terms of resemblance to some prototype. Further, even if the concepts of bachelor and law are, as I think is clear, all-or-nothing, there might be prototypes of those concepts that deepen our grasp of features of our conceptual practices that are contingent because the views of competent speakers evolve with respect to which features are prototypical in ways that do not impact the all-or-nothing existence conditions.

  • 42 This difference would make a substantive difference in the content of a normative theory of moral l (...)

51Accordingly, though tentative, these suggestions raise matters that need to be addressed by proponents of a prototype methodology. In particular, proponents need to explain how to identify and quantify the relevant resemblance relationships. Additionally, proponents need to explain what significance we can derive from the fact, to return to a familiar example, that subjects view a couch as being more representative of furniture than a wardrobe. In the case of law, it is crucial to explain what difference it makes to the normative theory of legitimacy whether law is necessarily coercive or whether it is just typically coercive.42 It seems to me there is a great deal of work that must be done just to get PCC and a corresponding methodology off the ground.

52There is much to be learned from Jovanović’s paper, but there is much that needs further elaboration and argument. Though I am admittedly skeptical that there are cogent answers to some of the questions raised in this paper, I am not hostile to the project. What doubts I have are tentative – and consistent with thinking that there is much going on in debates about methodology, including a prototype methodology and experimental jurisprudence, that is worth exploring. All I take myself to have accomplished in this paper is to call attention to some of the issues that need more argument than they have gotten at this point in this newly developing debate.

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Bibliography

Chellas, B. F. (1980). Modal Logic: An Introduction. Cambridge University Press. https://doi.org/10.1017/CBO9780511621192

Corcoran, J. (2006). C. I. Lewis: History and Philosophy of Logic. Transactions of the Charles S. Peirce Society, 42(1), 1–9.

Crowe, J. (2022). Chapter 3: Defects and failures in legal artifacts. https://www.elgaronline.com/edcollchap/book/9781800885929/book-part-9781800885929-8.xml

Merriam-Webster. (n.d.). Law. In Merriam-Webster.com dictionary. Retrieved from  https://www.merriam-webster.com/dictionary/law

Dworkin, R. (1986). Law’s Empire. Belknap Press of Harvard Univ. Press.

Hart, H. L. A. (1961). The Concept of Law. Oxford University Press.

Jovanović, M. (2024). Prototype theory of concepts and analytical account of law. Revus. Journal for Constitutional Theory and Philosophy of Law, 54, https://doi.org/10.4000/13ew1

Dictionary.com. (n.d.). Law. In Dictionary.com. Retrieved April 17, 2025, from https://www.dictionary.com/browse/law

Lewis, D. K. (2000). On the Plurality of Worlds. Blackwell.

Perry, J. R. (2016). Semantics, possible worlds. In Routledge Encyclopedia of Philosophy (1st ed.). Routledge. https://doi.org/10.4324/9780415249126-U039-1

Plantinga, A. (1979). The Nature of Necessity. Clarendon Press.

Prototype theory. (2024). In Wikipedia. https://en.wikipedia.org/w/index.php?title=Prototype_theory&oldid=1258536884

Rosch, E., & Mervis, C. B. (1975). Family resemblances: Studies in the internal structure of categories. Cognitive Psychology, 7(4), 573–605. https://doi.org/10.1016/0010-0285(75)90024-9

van Inwagen, P., Sullivan, M., & Bernstein, S. (2023). Metaphysics. In E. N. Zalta & U. Nodelman (Eds.), The Stanford Encyclopedia of Philosophy (Summer 2023). Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/sum2023/entries/metaphysics/

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Notes

1 Jovanović 2024.

2 While one can get a reasonably clear understanding of the prototype theory of concept formation from the discussion in Jovanović’s essay, he never provides a canonical formulation. There are two problems with this. First, the locution concept formation is ambiguous: it can be interpreted as concerned with how we learn new concepts; or concerned with how we adopt new concepts through our linguistic practices. Second, as discussed below, it is not clear how to derive a semantic theory of conceptual content from the theory of concept formation or what a prototype methodology would look like in practice.

3 Prototype theory 2024. Categorization involves the mental actions involved in forming and applying concepts. Psychological theories are, after all, concerned with what goes on in the mind in the form of mental processes that are conscious whereas neurophysiological theories are concerned with what goes on in the brain in the form of mental processes that are unconscious; there are, of course, parallels between the two and the latter is plausibly thought to cause the former. Freudian psychiatry is concerned with what is paradoxically called the subconscious mind.

4 See Note 2, above.

5 Jovanović refers to this as the “prototype theory of concepts.”

6 As it has been articulated by proponents, PCF and PCC apply to all concepts – and not just concepts that are explicitly comparative in character, like bald or good. This strikes me as a mistake, as will be discussed in more detail below.

7 See Rosch & Mervis 1975.

8 This strikes me as plausible with respect to how we learn new concepts and with respect to how we adopt or create them. See Note 2, above.

9 General terms, like law, water, blue, proposition, define kinds (of thing). Our concepts describe, or pick out, kinds.

10 See Note 2, above.

11 Merriam-Webster, for instance, defines the term furniture as “movable articles used in readying an area (such as a room or patio) for occupancy or use.” Dictionary definitions are not, of course, philosophically authoritative – at least not comprehensively so; however, they are authoritative as to our semantic conventions for using words because they are grounded in scientifically rigorous lexical surveys of those conventions – which, it bears emphasizing, cover only easy application cases.

12 Merriam-Webster, for instance, defines the term fixture as “something that is fixed or attached (as to a building) as a permanent appendage or as a structural part.”

13 Most furniture stores sell anything that counts as furniture, including lamps. But there are many stores that sell only lighting – which is why the concept of furniture is not as effectively imparted by pointing to lamps than to other items, like couches and wardrobes.

14 See Note 2, above.

15 Hart 1961.

16 There are also thick evaluative usages of the locution that refer to non-defective and legitimate legal systems. See, e.g., Crowe 2022.

17 Dworkin 1986. Jonathan Crowe argues that the evaluative usage of law is defined in terms of law’s non-defectiveness conditions while the descriptive usage is defined in terms of law’s existence conditions. Crowe 2022.

18 Merriam-Webster n.d.

19 Dictionary.com n.d.

20 It is worth noting that natural kind terms, such as that of a bird, are often given a rigorous definition by scientists. Although it might be true that people are more likely to think of a robin as a prototypical representation of a bird than a penguin, both count equally, as far scientists – and hence the proper usage of the term – are concerned, as birds.

21 Moral considerations of fairness, for instance, dictate that criminal laws be interpreted narrowly in accordance with the obvious plain meanings of the terms to ensure that defendants had reasonable notice of what behaviors are punished by law.

22 The following discussion borrows heavily from the outstanding van Inwagen et al. 2023. Oddly, for all the attention to conceptual issues in philosophy of mind, language, metaethics, and, of course, metaphysics, there isn’t much of a contemporary literature concerned with the concept of the metaphysical. It might be true that, as far as that concept of metaphysics resembles that of obscenity in the sense that it is enough to say, as the latter matter was described by Supreme Court Justice Potter Stewart, “we know it when we see it”. However, it would be helpful to have a more rigorous analysis of the term metaphysical than we have. I hope the following discussion, though obviously incomplete, is helpful in this regard.

23 Merriam-Webster defines the prefix meta- as “more comprehensive, transcending,” whereas Dictionary.com defines it as “designating another subject that analyzes the original one but at a more abstract, higher level.”

24 van Inwagen et al. 2023.

25 Leibniz is credited with having introduced the locution “possible worlds” into the philosophical lexicon.

26 For an accessible introduction to modal logic, see Chellas 1988.

27 The semantic machinery of modal logic has also made possible the development of deontic, temporal, conditional, and other logics of interest. See, e.g., Perry, 1998. Intriguingly, notwithstanding its many applications in mathematics, the concepts of logical necessity and possibility were invented and formalized by Clarence I. Lewis, a philosopher, while Saul Kripke, another philosopher, is credited with the invention of possible worlds semantics. See, e.g., Corcoran 2006. This speaks to the importance of modal logic to metaphysical theorizing. Metaphysicians realized they needed a more precise framework for discussing possible and impossible states of affairs given these abstract changeless matters.

28 True substantive moral claims, like one should not kill, are normatively necessary, if necessarily true.

29 The idea that a claim is logically necessary if and only if it can be deduced from the relevant axioms is the syntactical formulation of the notion, while the idea that a claim is logically necessary if and only if it is true in all possible worlds is the semantic formulation of the notion. Every system of logic has a syntax which stipulates the axioms and rules of deduction and a semantics which stipulates the conditions under which statements in the system are true.

30 There are, after all, nonstandard propositional, quantificational, modal, and deontic logics. Indeed, there are systems of fuzzy logic that attempt to assess justification in terms of degrees, which does not map onto PCC.

31 The behavior of the connectives is defined syntactically in terms of its rules of inference and semantically in terms of its truth conditions.

32 Our conceptual practices are grounded, of course, in our semantic conventions for using words, which defines their ordinary meanings or definitions. However, these conventions are sometimes conditioned in hard cases by philosophical assumptions about the nature of the corresponding kind that illustrate why we have adopted the term. As seen above, the conventions for using the term bachelor are arguably qualified by the philosophical assumption that it is part of the very nature of bachelorhood that one must be institutionally eligible for marriage to count as a bachelor. The point of coining the term bachelor is, after all, to distinguish men who are legally marriageable from men who are not. But this assumption is no part of the ordinary meaning of the term as it is reported in mainstream dictionaries. Our semantic conventions generally cover only easy cases.

33 See, e.g., Lewis 2000; Plantinga 1979.

34 One exception, discussed in depth by Jovanović, has to do with how old a male must be to count as a man and hence as a bachelor. The answer to that, as discussed above, depends on the content of municipal law, as the age of majority and the age at which a male is permitted to enter a marital contract is typically established by the law. Religious law governing marriage in the U.S. recognizes only those marriages that are legally sanctioned by the state.

35 Our semantic conventions for using any term can change and are therefore contingent. But that does not imply that conceptual claims, or claims about the nature of a kind, are contingent.

36 Try getting a government grant for that research project.

37 Those conventions can change, of course. But, until they do, it is a conceptually necessary truth that there are no married bachelors and that every bachelor is unmarried.

38 Whether they are, in fact, unjust depends on theoretical moral matters, such as whether the truths or morality are objective or socially constructed.

39 The mode of a set of values strikes me as the closest statistical measure of typicality, rather than the mean or median of those values. Perhaps there is some combination of these three values that together might provide a more accurate description of what is typical among a statistical sample.

40 See Note 2, above.

41 It is not absurd to think that if the social processes of creating a new concept (or picking it out with a new word) involves assessing the extent to which an entity resembles a prototype, then the membership conditions for that concept are graded in terms of some threshold resemblance. While the logical gap is smaller here, the problem is that it is more plausible to think that individuals learn new concepts by comparing them to prototypes that that we collectively adopt or manufacture new concepts by grading the membership conditions.

42 This difference would make a substantive difference in the content of a normative theory of moral legitimacy. Would it matter, for instance, if coercion were a necessary but not a prototypical feature of law? Would the corresponding moral theory have to also be graded; and if so, how would that be done?

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Kenneth Einar Himma, “Conceptual analysis and the prototype theory of concept formation”Revus [Online], 54 | 2024, Online since 17 April 2025, connection on 15 May 2025. URL: http://journals.openedition.org/revus/10991; DOI: https://doi.org/10.4000/13rpo

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