1 Introduction

The problem of whether philosophical methodology is mainly descriptive or normative in nature has become a central issue in the current metaphilosophical debate. Both in the field of traditional conceptual analysis and in conceptual engineering, which is increasingly influential, positions for and against the possibility of conducting inquiries in a descriptive or normative way are established and defended (for views concerning this issue within the discussion on the nature of conceptual analysis, see, e.g., Weinberg, Nichols, Stich 2001; Williamson 2007; Machery, 2017; Deutsch, 2020a. For a similar discussion regarding the nature of conceptual engineering, see, e.g., Diaz-Leon, 2020; Deutsch, 2020b, 2021; Koch, 2020).

This paper focuses on one of the most popular methods used in analytic philosophy, namely the method of cases. My main aim is to demonstrate that although the use of the method of cases in most philosophical branches could be interpreted as either a descriptive or a normative enterprise, in a theory of reference the most common usage of this method turns out to be exclusively descriptive.

The structure of this paper is as follows. In Sect. 2, I discuss the notions of “target concepts” and “central claim” and their relation to the method of cases. In Sect. 3, I discuss how arguments formulated within the method of cases can be normative or descriptive. I show that the nature of the method of cases is strictly connected with the role of intuitions within this method, and depends on the content of the method’s central claim. In Sect. 4. I discuss the role of intuitions within theory of reference, and argue that the fact that intuitions of extension constitute the data that need to be explained in this theory entails that the instances of the method of cases within the theory of reference are primarily aimed to investigate referential facts via intuitions of extension. In effect the method of cases in theory of reference has to have descriptive and not normative nature. After that I discuss consequences of mentioned assumptions for the structure of paradigmatic instances of the method of cases in theory of reference and theory of knowledge. Namely, I show that the central claim in Gettier cases concerns the applicability of the target concept of a theory of knowledge, i.e., KNOWLEDGE. Therefore, the conclusion concerning Gettier cases can be justified either by intuitions of intension if the method of cases is used in order to shift the meaning of KNOWLEDGE, or by intuitions of extension if the aim is to discover some features of KNOWLEDGE (Sect. 5). In Sect. 6, I show that the main claim in the Gödel case does not state anything about the applicability of its target concept, namely REFERENCE (6.1), but its concern is the structure of the particular instantiation of the target concept, therefore it cannot justify any revision of REFERENCE (6.2). In Sect. 7, I discuss the scope of my results. In particular I argue that Gettier cases and the Gödel case should be seen as representative examples of instances of the method of cases in a theory of knowledge and a theory of reference, respectively, and that conclusions on the nature of Gettier cases might be incorporated into several different branches in philosophy.

2 Target concepts and central claims in the method of cases

Firstly, let me explain what I mean by the “target concept” of any theory that aims to propose a definition (usually formulated as a list of necessary and sufficient conditions) of X and what I mean by a “central claim” in a particular instance of a method of cases. The target concept of a theory of X is simply X. That is, the target concept of a theory of knowledge is KNOWLEDGE. The target concept of a theory of reference is REFERENCE; the target concept of a theory of justice is JUSTICE, and so on. A theory of X could have several purposes regarding X: it may aim to define X, explain X, or construct X. In Sect. 4, I will argue that the limits in revising the concept REFERENCE are caused by the fact that a theory of reference is concerned with different kind of phenomena than theory of knowledge. Putting it a little bit loosely, theory of reference is concerned more with how reference works than with what reference is. On the other hand, for example, a theory of knowledge is focused primarily on what it is to know. More precisely, we can say that while the interest of theory of knowledge are application conditions for KNOWLEDGE, theory of reference is interested not strictly in what application conditions for REFERENCE are, but rather in what grounds those conditionsFootnote 1. In other words, while theory of knowledge is largely happy with establishing the list of necessary and sufficient conditions for someone to know something, the primary goal for theory of reference is to explain why a particular list of conditions is apt for REFERENCE.

However, both these theories in principle propose an analysis of their target concepts by formulating a list of sufficient and necessary conditions for them. Within a theory of reference, we formulate a list of conditions that are fulfilled if and only if an expression e refers to an object o, while within a theory of knowledge we formulate a similar list for a state of affairs in which an agent a knows that p.

Now, few remarks on what I mean by a “central claim”, and how it can be identified in a given instantiation of a method of cases. First of all, in approximation, by “central claim” I mean the most important judgement which seems to be crucial in a given thought experiment. Secondly, the central claim is a verdict regarding given thought experiment which concerns details of a given story, and not some general principles. So when we think about Gettier Cases, the central claim is about Smith’s epistemic state and not epistemic states in generalFootnote 2. Thirdly a central claim should be identified partly by its role in the argument formulated with the help from the method of cases. Such arguments are formulated in order to show a counterexample for a definition of X proposed by a given theory of X. Central claim should be able to form a premise in which it is stated either that a particular state of affairs S is X but does not meet the given definition, or that S does meet the definition but it is not the case of X (for discussion of the logical structure of the method of cases see: Pust 2019). Finally, some examples: a central claim in Gettier Cases has a form “S does not know that p”; in Gödel Case: “the name “Gödel” does not refer to the man who discovered the incompleteness of arithmetic”Footnote 3.

3 Normative and descriptive arguments

The standard view regarding the method of cases states that its conclusion is justified by intuitions about the applicability of the target concept, therefore they enable us to establish some truths about this concept (Bealer, 1998; Cappelen, 2012; Weinberg, 2016). According to such a view, the method of cases is a purely descriptive method, since through it we discover truths about the target concept but do not revise or regulate this concept’s meaning.

However, several authors have argued that the conclusions of the method of cases can be directly justified not by intuitions but by arguments (Williamson, 2007; Cappelen, 2012; Deutsch 2010, 2015; Mizrahi, 2021; Tałasiewicz 2021; Horvath, 2022). These arguments could take different forms depending on their theoretical aim (see e.g. Andow, 2016; Bengson et al., 2022). In (Sękowski, forthcoming) I have argued that if the central claim in the method of cases concerns the applicability of the target concept, i.e., if the central claim states that a scrutinized case does not fall under the target concept, then arguments could be formulated for two reasons. The first reason is to show that the described case has some as yet unnoticed features that are inconsistent with the target concept. For example, imagine that Maggie accepts an H-Name Theory whose target concept is HOG, according to which all animals whose names contain the word “hog” are hogs. Suppose that Maggie also believes that all hogs have hoofs. One could criticize H-Name Theory and show that the name “hedgehog” contains the word “hog”, but hedgehogs are not hogs. Moreover, one could argue in favor of the central claim of such an instance of the method of cases (i.e., “a hedgehog is not a case of a hog”) by pointing out that hedgehogs do not have hoofs, which was not noticed by Maggie.

The second reason is to argue that we should not consider a particular case as falling under the target concept because the target concept should fulfill some expectations towards it that have not yet been taken into account and which are not satisfied by the scrutinized case. Consider a situation in which Maggie believes that H-Name Theory is a correct theory of hogs, but she does not believe that all hogs have hoofs. One could similarly criticize H-Name Theory by showing hedgehogs as a counterexample to this theory but argue for the claim that “a hedgehog is not a case of a hog” by pointing out some expectations towards the concept HOG. One could then show that it is reasonable to accept a theory of hogs which is compatible with biological systematics, according to which hogs belong to the even-toed ungulates order, therefore we should expect from the concept HOG that all entities falling under this concept should have hoofs. Maggie could be unaware of this feature, but she could agree that such an expectation towards the concept HOG seems reasonable.

The difference between these two kinds of arguments can be nicely explained with reference to two philosophical methods discussed in the literature. The first one is actually a group of methods that refer to the Carnapian notion of explication (Carnap, 1950). Through explication one aims to construct a new, improved version of a pre-theoretic term in order to better satisfy certain standards important from the perspective of the ongoing investigation. This method is cultivated by, e.g., Craig (1990) in his theory of knowledge. Craig introduces a useful distinction between two kinds of intuitions and argues that instead of intuitions of extension, i.e., concerning whether an agent knows that p in concrete situations, a proper theory of knowledge should be coherent with our intuitions of intensions, i.e., those intuitions that inform us about general features of knowledge, so e.g., what role knowledge plays in science or (as is more important to Craig) in everyday life. More recently, this method has been defended by conceptual engineers, who argue that the meaning of a concept could be regulated or revised in order to fulfill our expectations (social, scientific, aesthetic etc.) towards that concept (see Bengson et al., 2022: 59; Nado, 2021; for examples of using the method of argument within conceptual engineering in practice, see, e.g., Haslanger, 1999; 2000; 2012; for an example of how this method can be applied to Gettier cases see Sękowski forthcoming). If within this method some arguments justify the conclusion in the method of cases, i.e., if they appear while analyzing counterexamples for some theory, then they play a normative role. The reason for this is that they are arguments for the claim concerning how the target concept should be understood rather than what the real meaning of this concept is.

The second method, that reflects the descriptive account towards the investigation of concepts is “reflective equilibrium”, which refers to the method proposed by Rawls (1971). This method aims to build a theory that is coherent with the most relevant judgements about particular cases and beliefs about general principles. Leaving the latter aside, when we consider judgements about particular cases and we find someone whose judgement is different than ours, we could argue that such a person is wrong because she does not take into account all the relevant factors of the scrutinized case. In such a situation, we do not aim to revise or regulate the concept; instead, we try to elicit spontaneous judgement about a particular case. However, we could argue that some judgement is a correct reaction to a particular case by stressing that maybe someone has overlooked some relevant details of the story.

The crucial difference between these two kinds of arguments is therefore that we assume that the target concept is already established in arguments that are aimed at eliciting spontaneous judgements regarding its application in certain situations. Intuitions of extension of the target concept, following Craig’s terminology, therefore play a major role here, and they serve as a criterion for a proper theory. In such a case the target concept’s application conditions are to be discovered. They are already determined by people’s intuitions regarding application of a target concept. Hence arguments of this kind are descriptive in their nature.

On the other hand, in case of arguments that focus on our expectations towards the target concept (these expectations express our intuitions of intension) we do not assume that the concept has any objective application conditions that are to be discovered. They aim to justify claims regarding meaning of a concept, and thereby what its application conditions should be. The aim of this kind of arguments is to show how the target concept should be understood, even if it is incoherent with the concept constituted by our pre-theoretical judgements about the application of this concept in particular cases. This is why e.g. Craig or Haslanger say that normative investigations aim to revise the meaning of scrutinized concepts. The revision concerns a concept that might be constituted by our judgements regarding applications of a target concept.

It is crucial, that according to this view, normativity does not mean that one necessary aims to change a practice of using a given concept to be as it should be. Although some conceptual engineers have ambitions to go further in their normative activity and involve implementation of the proposed way of understanding the target concept, a revision is understood here as changing or regulating a pre-theoretic concept that is constituted by our intuitions regarding application of a target concept in certain cases. In what follows, when I will talk about concept revision, revision of concept’s meaning or changing it, it should be understood in a weaker sense just described.

In sum, when the method of cases is used in order to change the meaning of a concept, the intuitions of extension can be abandoned by pointing to some other challenges that are assumed to be met by the proper theory that is being proposed. These challenges express some intuitions of intension about a target concept. For an illustration, consider Haslanger’s project of engineering the concept WOMAN (2000). She argues that even if we intuit that “woman” refers to x, sometimes we have to abandon such an intuition because one of her main aims is to construct the concept WOMAN in such a way that it would enable the promotion of social justice, while intuitions of intension dictate that the concept WOMAN should have such a social feature. Defending the concept WOMAN that is coherent with all our intuitions of extension prevents us, however, from achieving that goal.

Hence, pace the traditional view, the method of cases could be interpreted not only as descriptive, i.e., aimed at discovering truths about a concept by testing intuitions of extension, but also as normative, i.e., aimed at revising a concept in accordance with intuitions of intension. Note that both these arguments justify the claim concerning the applicability of the target concept, since the conclusion in both situations is “this is/is not a case of X”. So, both arguments that are formulated in order to describe facts about concepts with established meaning and arguments that aim to revise concepts could be formulated in order to argue for the applicability of the target concept. In other words, these two possible interpretations of the method of cases become available if the central claim in a particular instance of the method of cases concerns the applicability of its target concept.

In sum, three claims follow from the above considerations:

(CLAIM)

If the central claim in the method of cases concerns the applicability of its target concept, then this claim could be justified either by arguments regarding the target concept’s application or by arguments that aim to change the target concept’s meaning.

(DESC)

If the central claim in the method of cases is justified by arguments that aim to discover what the target concept is, then this method is part of a descriptive enterprise.

(NORM)

If the central claim in the method of cases is justified by arguments that aim to change the target concept’s meaning, then this method is part of a normative enterprise.

Recently Andow (2020) proposed a normative interpretation of the method of cases which is slightly different from that one described above. According to him, at least some instances of this method might be interpreted as arguments for how we should think about a target concept. What’s more, these arguments are justified by intuitions regarding the application of a target concept in certain cases. At the first glance it seems therefore that Andow takes intuition of extension to play an evidential role in normatively understood method of cases. It appears to be incoherent with a characteristic of normative argumentations proposed above, since I’ve argued that a distinguished feature of such methods is that intuitions of intension provide reasons to abandon intuitions of extension.

However I think that there is a way to interpret Andow’s stance as similar to the one focused on intuitions of intension. Andow claims that in normatively understood method of cases an evidential role is played by intuitive judgements about cases. As I mentioned in a previous section, intuitive judgements about cases might be justified by either intuitions of extension or intuitions of intension depending on the aim of the argument. An intuitive judgement about a case might be justified straightforwardly by intuition of extension that concerns application of a target concept, or it might be justified by intuition of intension that refers to some general features of a target concept, and thereby justifies a judgement about application. If we look closer at Andow’s examples of arguments constructed within normatively understood method of cases, we will see that in each of them some reasons are given in order to justify the judgement about a given case. Moreover, as Andow stresses out, intuitions about cases might serve as evidence for some more general constrains that arise from more general dispositions of some group of people. It is plausible that these more general dispositions are formed by general beliefs about a target concept, what makes them pretty similar to intuitions of intension. In such a case, a justificatory chain aimed at justifying normative conclusions of an instance of the method of cases, does not end at intuitions of extension, but it has a more fundamental chain link, namely intuitions of intension in a form of general beliefs about a target concept.

Although it might be unintended by Andow, both interpretations of his stance, the one that places evidential role in intuitions of intension, and the one that places it in intuitions of extension, are open. Therefore in the next section I will refer to both of them.

4 The role of intuitions in theory of reference

Now, I will move on to the analysis of the role that is played by intuitions within theory of reference. Below I will show that this role determines the fact that the instances of the method of cases that are focused on the concept REFERENCE (hereafter: semantic MoCs) cannot be interpreted as normative.

My main claim is that since intuitions of extension play different role in theory of reference than in most other theories, semantic MoC cannot be interpreted as normative while most other kinds of MoC can. Let me remind the reader that intuitions of extension are intuitions which are expressed by our judgements about which objects belong to the extension of some expression (see: Craig, 1990: 1).

Theories of reference are concerned with intuitions of extension in a peculiar way. The reason for this is that intuitions of extension concern the relation between expressions and the objects they refer to. This relation is in turn the extension of the target concept of a theory of reference, namely REFERENCE. Note that in most theories the phenomena that they are interested in are distinct from the intuitions of extension. For example, in theory of knowledge, the phenomena that is under consideration is knowledge, and not our intuitions about the application of KNOWLEDGE, although some intuitions about it might (but not have to!) constitute a set of data for epistemological theory. However, intuitions of extension do constitute the phenomenon to be explained in theory of reference, that is, some linguistic facts (Nado & Johnson, 2016). As Cohnitz and Haukioja have argued (2013, 2015) this is why intuitions of extension play a constitutive and not an evidential role in theory of reference, and why this theory should be understood as aimed at explaining and systematizing them. In other words, a theory of reference aims to capture all intuitions of extension in order to explain them rather than to formulate such a theory that would mainly satisfy the intuitions of extension concerning the target concept.

This property of theories of reference has already been noticed, but so far it hasn’t been stressed explicitly in the context of normativity or descriptivity. Philosophers who have pointed out this feature of theories of reference have argued that their data are linguistic intuitions, i.e., intuitions about the reference of particular expressions and not metalinguistic intuitions, i.e., intuitions about semantic terms such as “reference” (Martí, 2009; Nado & Johnson, 2016). In other words, data for any theory of reference are intuitions of extension of ordinary expressions and not intuitions about what reference is.

Now think about epistemological MoCs. In a descriptive interpretation, epistemological intuitions of extension constitute the relevant data for the theory of knowledge. However, there is also a possible normative interpretation in which our intuitions about what knowledge is, i.e., epistemological intuitions of intension, are crucial, hence epistemological intuitions of extension, i.e., intuitions about which epistemic state falls under some concept of knowledge, could be abandoned if they are incoherent with the previous ones. But this is not the case for a theory of reference because its relevant data are, as I mentioned, first and foremost intuitions of extensions of ordinary expressions.

Moreover, although intuitions of extensions can concern the word “reference”, these are not the most important intuitions that should be captured by a theory of reference. This is another important difference between most semantic MoCs and, e.g., epistemological MoCs, since if any intuitions of extension constitute data for a theory of knowledge, they are those concerning the extension of “knowledge” (a word corresponding to the target concept of a theory of knowledge). On the other hand, all intuitions of extension are relevant for a theory of reference, and those concerning the extension of “reference” are less rather than more important. The first reason for this is that intuitions of extension in a theory of reference are not used in order to define the concept to which they refer but in order to explain the mechanism behind the phenomenon of referring. Secondly, “reference” is a technical term, and since a theory of reference is concerned with the relation between expressions and their referents, it is simply more useful to focus on usage and referential intuitions of ordinary and easy-to-understand expressions such as “the man drinking a martini”, “horse” or “Aristotle”.

The main thing, however, is that a theory of reference uses intuitions of extension as its data in a unique way because it aims to capture the actual referential intuitions and to explain the phenomenon that occurs when referring to things using words. In order to answer the crucial question for this theory, it is required to assume that we have to at least implicitly or procedurally understand what reference is. The reason for this is that the aim of a theory of reference is explanatory rather than defining. It is focused on explaining the phenomenon of reference that is indicated by a known practice; it is not focused on constructing the concept of reference with regards to some assumed principles.

Therefore a normative understanding of the method of cases according to which normative constrains are given by intuitions of intension that can justify abandoning some intuitions of extension regarding a target concept cannot be applied to the theory of reference. Intuitions of extension cannot be abandoned because they constitute a data for any theory of reference. Abandoning them would be excluding some part of the phenomenon from the analysis in which we want to explain this phenomenon in its entirety.

What about Andow’s picture, according to which normative constrains are given by intuitions of extension? It is also not apt for theory of reference. Note that the crucial difference between descriptive and normative interpretation of the method of cases according to Andow is that in the former intuitions of extension serve as evidence because they inform us about the structure of an existing instantiation of a target concept, and therefore the content of these intuitions has to be highly related with the structure of that instantiation. On the other hand in the method of cases conducted within a normative mode, intuitions of extension are not related with the structure of an existing instantiation of a target concept. This is the case because the reason why intuitions of extension serve as evidence in normative method of cases is that they can reveal constraints that we impose on a target concept. These constraints are however independent from the structure of the concept or its instantiation (they are related to e.g. political, moral or prudential considerations). However, since intuitions of extension constitute a phenomenon that needs to be explained by theory of reference, they have to be related with the structure of really existing phenomena: referential facts. These facts are, as mentioned, constituted by intuitions of extension.

In sum, the method of cases in theory of reference is descriptive in its nature. This result has some implications for the structure of typical instantiations of the method of cases. Below I will turn to the analysis of paradigmatic examples of the method of cases in theory of knowledge and in theory of reference. I will show how general assumptions regarding the role of intuitions in these theories reflect in their structure, and explain in more detail why paradigmatic examples of the method of cases in theory of knowledge might be interpreted as either a descriptive or a normative enterprise, while in theory of reference they cannot be interpreted as normative.

5 The core of Gettier cases

Let me start with the method of cases in theory of knowledge. As I stated before, an instance of the method of cases might be interpreted as either a descriptive or a normative enterprise, if the central claim in the method of cases concerns applicability of the target concept (see CLAIM, DESC and NORM in Sect. 3). In the following section, I will demonstrate that the central claim in Gettier cases does concern the applicability of their target concept (KNOWLEDGE). I will show that this result entails that Gettier cases, which are instances of the method of cases, can be considered as a normative as well as a descriptive enterprise.

Consider the structure of Gettier cases. They are instances of the method of cases that concern the concept of knowledge (epistemological MoCs). In epistemological MoCs, the main aim is to argue against a theory of knowledge according to which for any epistemic state x, x is knowledge if and only if x meets the list of conditions CK, by showing a case in which either x meets CK but x is not a case of knowledge, or x does not meet CK but x is a case of knowledge. For example, the main aim of Gettier cases is to present a case in which an agent’s epistemic state concerning p meets all conditions for knowing something required by the JTB theory of knowledge, but she does not know that p. In Gettier cases, the crucial question is then whether an agent in a scrutinized case does know something or not. It is reasonable then to agree that the general forms of possible relevant answers to the crucial question in Gettier cases are: {yes, a does know that p; no, a does not know that p}.

Now, consider the difference between these two possible answers. What distinguishes the positive answer from the negative one is whether knowledge could be ascribed to the agent depicted in the described story. In other words, these answers could be interpreted as stating whether a’s epistemic state is a case of knowledge or not. More precisely, we can say that if the two mentioned answers are all possible relevant answers to the crucial question in Gettier cases, then the general form of the central claim in Gettier cases can be formulated as “x is/is not a case of KNOWLEDGE”. In effect we can establish that possible answers in Gettier cases concern the applicability of the concept of KNOWLEDGE, since when we consider whether x is a case of knowledge, we are doing nothing other than establishing whether the concept KNOWLEDGE applies to that particular case. As established in Sect. 3 (see: CLAIM, DESC and NORM), if the central claim of the instance of the method of cases concerns the applicability of its target concept then this instance can be interpreted as either descriptive or normative enterprise depending on the kind of argument that will be formulated in order to justify the verdict about a certain case. In effect, Gettier cases can be interpreted in these two ways.

6 The core of the Gödel case

Let’s turn to an instance of semantic MoC, namely the Gödel case formulated by Kripke (1980). Below, I will show that in the Gödel case the situation is slightly but significantly different than in Gettier cases. Namely, I will show that the Gödel case does not concern the applicability of the target concept (Sect. 6.1.) but it concern details of the particular instantiation of the target concept and, in effect, the Gödel case can be considered only as an instance of the method of cases that is used descriptively and not normatively (Sect. 6.2.).

6.1 The core of the Gödel case – a negative answer

First, let me show that the central claims in the Gödel case do not concern the applicability of its target concept.

Within a semantic MoC, one argues against some particular theory of reference according to which an expression e refers to an object o if and only if all conditions from the list CR are met. The best-known example of a semantic MoC is the Gödel case, in which Kripke describes a situation in which for the relation between the expression “Gödel” and the man who discovered the incompleteness of arithmetic (hereafter, the Discoverer), all conditions required by the descriptivist theory of reference are met, but in which the expression “Gödel” does not refer to the Discoverer.

Again, consider the set of possible answers to the crucial question in the Gödel case. Since in reacting to the Gödel case we determine whether the man who discovered the incompleteness of arithmetic is the referent of the name “Gödel”, then the answers to the crucial question in such cases concern whether a particular object is a referent of a particular expression. In effect, we know that the set with all possible relevant answers to the crucial questions in the Gödel case is: {yes, o is a referent of e; no, o is not a referent of e}.

Let’s have a look at these answers and consider the difference between them. Suppose that two people, Gogo and Didi, react to the Gödel case differently. Gogo claims that the name “Gödel” does not refer to the Discoverer, while Didi argues that it does refer to that person. Now, note that Gogo and Didi do not disagree on whether there is an instance of reference or not in the scrutinized case. In other words, they do not disagree on whether the name “Gödel” does refer at all. Gogo and Didi differ in their opinion on what the referent of “Gödel” is. This is why the Gödel case is structurally different from Gettier cases. In Gettier cases, we are determining whether some epistemic state is a case of knowledge or not. Therefore, we can interpret Gettier cases as stating whether the relation between a subject and a certain proposition is knowledge, as it is defined by the JTB theory of knowledge. If it is not, then that theory should be abandoned. However, such an interpretation of the Gödel case is misleading. The difference in possible answers to the crucial question does not concern whether the relation between some particular object and the name “Gödel” is reference, as “reference” is understood by descriptivism. This difference concerns whether that particular object is the referent of the name “Gödel” or not. In the Gödel case, we simply do not take into account the possibility that the relation between the name and the possible referents is not reference. The fact that we are dealing with the referential relation in the Gödel case is already assumed.

One could argue that the answer “no, o is not the referent of e” expresses judgment that the relation between o and e is not reference, and therefore it concerns the applicability of the concept REFERENCE. However, there is a difference between saying that the relation between o and e is not reference because (a) reference holds between e and a different object, and stating that this relation is not reference because (b) e does not refer. Interpreting judgements like “no, o is not the referent of e” as being about the applicability of REFERENCE does not capture this difference. However, this difference is important since the crucial claim in the Gödel case is stated not on the grounds of the fact that a certain name does not refer but on the grounds of realizing which object is the referent of that name. Let me recall that when we were analyzing Gettier cases, we used a question regarding whether the general form of the central claim in the method of cases could be formulated as “x is a case of knowledge” as a criterion for whether it concerns the applicability of KNOWLEDGE. Since the crucial claim in the Gödel case concerns not whether some expressions refer but what their referents are, then it cannot be formulated as “x is a case of REFERENCE”. Hence, we can conclude that in the Gödel case, the central claim does not concern the applicability of its target concept.

6.2 The core of the Gödel case – a positive answer

The conclusion of the previous section is a negative stance. It says what the central claim in the Gödel case is not about. However, we can ask what the subject of this claim is. Again look at the crucial question in the Gödel case. It could be formulated as “What is the referent of e?”. As I have already shown, in this question we are not asking whether there is an instance of reference in a situation. It is assumed in the Gödel case that in a given case we are dealing with some instantiation of the relation of reference. The case description in the Gödel case also explicitly states which object is a relata of the instantiation of this relation in a given case. The possible answers to the crucial question differ in what the referent of e is. In order to ask, however, what the referent of e is, we have to establish that the relation of reference already holds between e and some other object. In the Gödel case, it is stated that the particular exemplar of reference that is under scrutiny is instantiated partly by the name “Gödel”. The central claim in the Gödel case concerns which object together with the name Gödel instantiates the relation of reference, or more generally the concept REFERENCE. In effect, since all possible relevant answers to the crucial question in the instance of semantic MoC concern what is the referent of e then the central claim in semantic MoCs can be formulated as “x is/is not an object that instantiates REFERENCE together with e”. This enables us to conclude that in semantic MoCs, the central claim concerns the structure of a particular instantiation of the target concept.

Let me remind that Gettier cases can play a descriptive role if they are used in order to show some facts about knowledge by appealing to our intuitions of extension of KNOWLEDGE. If Gettier cases aim to revise the concept of knowledge, we can abandon our intuitions of extension in order to justify the revision of the concept KNOWLEDGE by some expectations towards that concept which are expressed by our intuitions of intension. In such cases, Gettier cases play a normative role.

Since the central claim in the Gödel case does not concern the applicability of its target concept, the conclusion about Gettier cases cannot be straightforwardly generalized to the Gödel case. In order to determine what role the Gödel case (and structurally similar cases) could play, we have to investigate the content of its central claim and determine whether instances of the method of cases concerning the structure of the particular instantiation of their target concept can play both a normative and a descriptive role.

As stated before, the standard interpretation of a MoC states that it plays a descriptive role. Such an interpretation of semantic MoCs is quite natural. According to this view, when determining what instantiates REFERENCE in the Gödel case, we either appeal to our intuition of extension, which is our source of knowledge about the reference of particular expressions, or we try to find these elements in the case that are compatible (or not) with the already known set of information about REFERENCE in order to justify that a particular object does or does not instantiate a particular referential relation. For example, we know that if e refers to o, then people would normally say “e” when pointing at o. If in a scrutinized case some people were to use the name “Tom” when pointing at a particular man, it could be justification for the claim that “Tom” refers to that man.

On the other hand, it is quite hard to explain how cases like the Gödel case could play a normative role if my explication of the core of the Gödel case is a proper one. Let me recall that if a MoC plays a normative role, its aim is to revise the meaning of its target concept. In Gettier cases it is possible to revise the concept KNOWLEDGE in such a way that this concept can be incompatible with our intuitions of extension (intuitions about which objects satisfy the target concept). At the same time, this revision would be justified by the fact that it captures our intuitions of intension (which express our expectations toward the target concept). Trivially, this cannot be done in the case of the Gödel case because, as mentioned above, in the Gödel case it is assumed that the relation in the scrutinized case is a case of reference. If a verdict in a MoC is inconsistent with the intuition of extension, then it is inconsistent with the assumptions of that particular MoC and, what’s more important, with more general assumptions about the role of intuitions of extension in theory of reference, according to which these intuitions constitute the data to be explained by a proper theory of reference.

One could argue, however, that in cases like the Gödel case we can revise REFERENCE by formulating arguments that at the same time rest on our expectations towards that concept and could justify its revision even if it is incompatible with our intuitions of extension of the expression at issue in the case. In other words, according to this line of reasoning, we could argue that in the Gödel case we should say that the name “Gödel” refers to Discoverer because REFERENCE should capture some of our expectations towards REFERENCE even if we intuit that the reference of “Gödel” is some other man (this is in line with the one of Andow’s stance’s interpretations discussed in Sect. 4). In particular, studies on theory of reference might be motivated by the relation between some other word-world relation than reference and some theoretical endeavor that is also distinct from theory of reference (e.g. development of truth-conditional semantic theories, understanding episodes in the history of science, clarifying communicative mishaps in everyday language, etc.) One could argue that in such cases, we might dismiss certain referential intuitions. Someone’s judgement that “Gödel” refers to the Discoverer might be formed on the basis of some word-world relationship, but not the one crucial for our theorizing given the theoretical purposes to which REFERENCE is scrutinized.

However, such a strategy, if truly understood normatively, is inconsistent with the fact that the central claim in semantic MoC concerns the details of a particular instantiation of REFERENCE. According to it, we are pointing at the relation of reference that is already instantiated and then we are establishing which object is one of its relata. Of course, we can formulate arguments for the central claims of the Gödel case that would look similar to those justified by intuitions of intensions in normative instances of an epistemological MoC. They would not be normative in a strict sense, but abductive. Note that in the Gödel case we are firstly assuming that a particular concrete instance of relation holds in some case, and then our verdict concerns that particular relation. In such cases, these arguments should be considered as inferences to the best explanations. Therefore, they are purely descriptive. An example of such an argument was formulated by Kripke himself (1980, 85n, 87) and discussed by Deutsch (2010). Deutsch argues that arguments rather than intuitions justify the conclusion in the Gödel case. In particular, according to one of Kripke’s arguments, we should say that the Discoverer is the referent of “Gödel” because otherwise it would be impossible to be “mistaken in uttering a sentence of the form ‘N is the F’, when ‘the F’ denotes, and is a definite description one associates with ‘N’, a proper name” (Deutsch, 2010: 454). However, as Deutsch paraphrases Kripke: “one can be mistaken in uttering ‘Peano is the discoverer of the axioms’, even if one associates ‘the discoverer of the axioms’ with ‘Peano’”(Deutsch, 2010: 454). In this argument, Kripke correctly pointed out the consequences of asserting that Discoverer is not the referent of “Gödel”. He also aptly indicated the fact that justifies the claim that there are counterexamples to these consequences. However, these counterexamples are justified by the fact that “Peano” does not refer to the discoverer of the Peano axioms. This argument is then actually descriptive, as it is justified by factual evidence, namely the referential facts of some expressions.

Moreover, note that, as I mentioned in Sect. 3, a particular instance of the method of cases is normative not in virtue of the fact that some intuitions of extension are abandoned within this method because of our general expectations towards a given theory, but in virtue of the fact that intuition of extension about the target concept are abandoned because of such expectations. In a situation in which someone’s verdict on the Gödel Case is dismissed in virtue of its incoherence with our expectation towards the theory of reference, that verdict expresses someone’s intuitions of extension of GÖDEL, while the target concept for theory of reference is REFERENCE and not GÖDEL. Therefore, in a case in which our theoretical expectations towards theory of reference justify our decision of dismissing our intuitions about the referent in the Gödel Case, the crucial intuition of extension, that is the intuition that reference does obtain in the Gödel Case, is not abandoned. Moreover, note that even intuitions about GÖDEL in such a case, if judged as wrong are still in the set of data that a theory of reference has to explain. The intuitions of extension of REFERENCE constitute the set of linguistic facts that are the subject for the theory of reference. Some of these linguistic facts might be about mistakes, but nevertheless they are the data to be explained by a theory of reference. Therefore, even intuitions of extension of GÖDEL in the discussed situation, are not abandoned in the same way as it can be done in instances of the method of cases in other branches of philosophy.Footnote 4

But still, one could insist that these conclusions are based on a contingent fact that the reaction to the Gödel case was “Gödel refers, but to whom?”, since this reaction might, without any theoretical cost, takes form: “Gödel might refer to S1, S2 or no one – which is right?”, or since Gödel case might be presented as a story that occurs in two worlds: one in which there is no person who satisfies descriptive conditions to be a referent of “Gödel”, but there is a person who satisfies causal-theory conditions, and one in which the opposite situation occurs (in fact, one of Kripke’s other thought experiments, the Jonah case shares that structure)Footnote 5. In such cases, the question on whether “Gödel” or “Jonah” does refer is legitimate, and the answer might be negative.

However, let me stress out clearly that my claim is that the main reason why semantic MoC cannot be interpreted as normative, stems from the role of intuitions within theory of reference that is determined by some widely-shared assumptions regarding theory of reference. There are two crucial consequences of this fact. Firstly, the way in which Gödel case has to be interpreted is determined not only by its logical structure, but also by the assumptions on the role of intuitions within theory of reference. Secondly, when I say that semantic MoC cannot be interpreted as normative, it is a little bit weaker “cannot” than “it is metaphysically/logically impossible” or so. My claim is that semantic MoC cannot be interpreted as normative, because if they will be, it would make them so distant from the theory of reference in a form that has been conducted for decades, that it would be strange to say that it is still the same kind of inquiry.

That being said, lets investigate how the reaction according to which “Gödel” fails to refer should be understood if the interpretation has to be in line with the role of intuitions in theory of reference discussed in Sect. 3. As stated in Sect. 3, the verdict on an instance of MoC might be justified by either intuitions of intension in order to revise the meaning of the target concept or by intuitions of extension in order to show some facts about that concept. Theory of reference aims to capture referential fact that can be reached only thorough (fallible) intuitions of extension. Theory of reference tries therefore to capture or explain intuitions of extension. Hence, if we have an instance of the method of cases in which we are considering what is the referent of a given expression, even if one seriously considers the possibility that no one can be a referent of that expression, it should be understood as an operation in which we are looking for some referential fact, and not in which we are considering whether any referential fact really occurs.

Note that a judgement according to which “Gödel” refers to no one is significantly different from the judgement according to which a henhouse refers to no one (not the word “henhouse”, but henhouse the building). In fact, when we are saying that henhouse refers to no one, we have in mind that henhouse cannot refer to anything because it is a building, while between buildings and other objects the relation of reference does not occur. When we are saying that the name “Gödel” refers to no one, we are saying that it might refer to some object, but it fails to do so.

This difference is crucial since it shows that when some semantic MoC is in use, we try to establish what is the reference of a certain expression, even if it refers to some nothing. This intuition is reflected e.g. in a number of stances towards the reference of empty names. Think about Meinongian theory according to which empty names do refer to some non-existing objects (see e.g. Meinong, 1904), about Frege who says that we should establish some kind of referent for such names thorough some special stipulation (e.g. that the referent for such names should be a number “0”) (see Frege, 1892), or about Braun (1993) who argues that in order to prevent the direct reference theory we should represent the referent of empty names by an empty slot in a Russellian proposition. All of these stances share the belief, that when names, as expressions that might refer, fail to refer, they still are in some relation with REFERENCE, in which beings that cannot refer (like buildings, animals or colors) cannot be.

In the case of Jonah, it is worth noting that the observation I’m referring to, is also seen in an operationalization in empirical studies on semantic intuitions. Participants in such studies are not usually asked whether the relation of reference occurs (even in other, less technical, words), but rather whether someone who uses the name “Jonah” or similar is talking about a real person or about a fictional character (see the meta-analysis of studies on semantic intuitions: van Dongen et al., 2021). It strengthens the claim that when we are talking about an expression that might refer, but fails to do so, we state something different than when we say that some object simply does not refer. Note that, in contrast, when we say that Smith does not know in Gettier case, although Smith might know something, we are not saying, that Smith still have some strange or different kind of knowledge. Instead, it is simply stated that knowledge does not occurs in Gettier case but some different epistemic state does (e.g. belief). In effect, even if we think that the reaction to Gödel case might be that “Gödel” refers to nothing, it is assumed that the relation of reference occurs in this situation, and therefore we are looking for some evidence about objectively existing facts via our intuitions of extension.

This consideration enables us to state that since the central claim in Gödel case concerns the structure of the particular instantiation of the target concept then this claim could be justified by arguments regarding the facts about the target concept’s instantiation. In effect, the Gödel case can be interpreted as a descriptive and not as a normative enterprise.

7 The scope of the argument

In this section, I discuss how far my results generalize beyond (1) Gettier cases, as examples of an epistemological MoC, (2) the Gödel case as an example of a semantic MoC, and (3) other branches of philosophy.

Regarding Gettier cases, it is quite unproblematic to show that conclusions about them generalize to other instances of an epistemological MoC. The reconstruction of Gettier cases that is proposed in Sect. 4 is in line with the common view concerning the structure of the method of cases, and I am not aware of anyone who would argue that the structure of some instances of an epistemological MoC in particular would significantly differ. It should be noted that although there are at least several types of the method of cases among instances of an epistemological MoC, they differ not in their core but in the way in which the agent’s beliefs should not be considered as cases of knowledge (see Blouw et al. 2017).

However, one could argue that it is possible to formulate some arguments that would have different structure than the Gettier case. For instance, there might be a case in which it is stated that Alice knows something, but it is asked what is the content of that knowledge. Another example would be a case in which there are two subjects: Alice and Bob. Each has a justified true belief that p. One got lucky, the other didn’t, and the crucial question would be “by whom the proposition that p is known?”Footnote 6. However, let me remind the reader that my main claim is that the method of cases cannot be interpreted as normative in theory of reference, while in theory of knowledge there might be instances of normative as well as descriptive method of cases. So, the fact that in theory of knowledge, there might be some cases that share the structure with those that cannot be interpreted as normative, does not change the fact that at least some of epistemological MoCs are open to the two interpretations, while it is not true about semantic MoCs. Moreover, note that there are no similar examples from the literature to the two mentioned (or at least I am not aware of any such examples) while Gettier cases and the like are typical for theory of knowledge. My suspicion is that it is due to the very fact that the crucial data for theory of knowledge is not constituted by our intuitions of extension, but by some facts about knowledge, and therefore theory of knowledge is not so interested in explaining intuitions about the extension of “knowledge”.

So, given that the structure of the method of cases in a particular theory is a consequence of the role that intuitions play in this theory, the fact that mentioned cases although possible do not appear in epistemological literature makes my stance about the nature of the method of cases in theory of knowledge rather stronger than weaker.

Let’s now turn to the theory of reference. One might argue that analyzing the Gödel case as a paradigmatic example of a semantic MoC is misleading because there are other instances of the MoC within theories of reference that have different structures. Let me stress that it is probably possible to formulate an instance of a semantic MoC that shares the same structure as Gettier cases and therefore enables us to argue in favor of changing the meaning of REFERENCE. However, my claim is that the Gödel case is a typical example of a semantic MoC, and it is characteristic for theories of reference. Even if it is possible to construe a normative semantic MoC, and even if there are such instances of the MoC, it is important to note that paradigmatic semantic MoCs share the same structure as the Gödel case but not as Gettier cases. Thereby, REFERENCE seems to be treated in a theory of reference as much more stable concept than, e.g., KNOWLEDGE in a theory of knowledge.

The main argument for this claim is that the Gödel case is simply taken as a paradigmatic example of the MoC. Most of the literature about the reliability of semantic MoCs concerns the Gödel case (Machery et al. 2004; Marti 2009; Nado & Johnson, 2016). Although it was argued that the Gödel case plays a minimal role in Kripke’s arguments against descriptivism (Devitt, 2011), and it might be the case that the focus on Gödel case is caused simply by the fact that Machery et al. (2004) who started the discussion on the method of cases within semantics used it in their study. However, this does not change the fact that many other Kripke’s examples, like Feynman case, Cicero case or Peano and Dedekind case which play more important role in his agenda (see Nado & Johnson, 2016) share the structure with Gödel case, and that Gödel case was cited as a paradigmatic MoC even before Machery et al.’s study (e.g. Bealer, 1996). Moreover, meta-analyses of the empirical research on semantic intuitions shows that the Gödel case or very similar cases that share its structureFootnote 7 are used as examples of semantic MoC (see Machery, 2017; van Dongen et al., 2021).

However, as mentioned, it is possible that there are other semantic MoCs. Let me discuss one case that – at least prima facie – looks like a plausible semantic MoC that has the same structure as Gettier cases. As I will show, even in such a case the descriptive interpretation is much more plausible than the normative one.

Crittenden (1991) argues that fictional names are counterexamples to the causal theory since they appear in perfectly acceptable sentences which are not in any evident way causally related to a referent. One might be tempted to say that Crittenden’s argument is an instance of a semantic MoC in which the crucial claim concerns the applicability of the target concept, since his conclusion about fictional names is that they do refer, pace causal theories of reference. However, such a view is misleading. As Cohnitz and Häggqvist suggest (2017), although it is common to equate thought experiments with the method of cases, we should distinguish, for example, between thought experiments that are alethic refuters (they constitute the actual method of cases) and those that are puzzle cases. The former aim to refute a theory by showing a counterexample to it, while the latter aim to provoke theoretical analysis. An example of a puzzle case is the trolley case (see Thompson 1985), in which we are explaining our intuitive judgements rather than using them in order to refute some theory.

Now, although Crittenden states that fictional names constitute counterexamples to causal theory, it is much more plausible that they constitute a puzzle for it rather than refute it.

Of course, one could interpret fictional names as constituting similar genuine counterexamples as Gettier cases do; however, both the structure of Crittenden’s argument and the actual reactions to it suggest that fictional names should be analyzed as constituting puzzle cases rather than alethic refuters. Note that although Crittenden’s argument is not based on a thought experiment in a strict sense (he only says that fictional names constitute a counterexamples to the causal theory of reference), he could present his argument via thought experiment by pointing to the possible situation in which someone uses the name “Sherlock Holmes”, stating that this name has no causal relation with its referent, and concluding that this is incompatible with causal theory of reference. However, the fact that Crittenden in his argument states a general problem that causal theory of reference has to face, and does not consider a particular case about which we are asked to make a verdict, make the puzzle and not alethic-refuter interpretation of his argument more plausible.

One could still interpret fictional names as alethic refuters. However, there are more reasons to think that this is not a correct interpretation. In particular, note that it is not the case that one of the conditions in the definition of reference in causal theory is “n refers to o if and only if n is not a fictional name”. Instead, one of the consequences of a condition in a form like “n refers to o if and only if there is a causal connection between o and the usage of n” is that fictional names could be a counterexample since they seem to have no evident causal relation to their referents. However, this is a case in which our intuitions of extension of fictional names call for an explanation but do not refute anything. This is clearly visible in reactions towards such arguments. Thomasson (1993) argues how fictional characters could become a subject of the initial baptism (following Kripke’s terminology). Kripke himself (2013) discusses the ontology of fictional objects in order to show how we can refer to fictional characters. The case of fictional names does not constitute an instance of the method of cases since they are not straightforward counterexamples to any claims of a causal theory of reference. They constitute a puzzle case that provokes causal theorists to investigate their explanation of peculiar usages of sentences with fictional names.

In the light of the above considerations, Gettier cases and the Gödel case should be seen as representative examples of the method of cases from a theory of knowledge and a theory of reference, respectively. And even if one doubts it and points at some examples that do not share the structure with these thought experiments, the main conclusions regarding the role of intuitions and the assumptions regarding the applicability of the target concept in Gödel case and Gettier case do apply to other thought experiments from theory of reference and theory of knowledge. Now let us consider how far results about an epistemological MoC generalize beyond epistemology. I have to disclose that I’m quite skeptical of whether all instances of the MoC share their structure with their epistemological counterpart. Nevertheless, there are some reasons to suspect that a lot of the target-concept-oriented MoCs from different branches of philosophy share the structure of their central claims. In most of them, the structure of these claims is visible to the naked eye.

Consider ethics, a theory of justice: when Plato in Republic argues against the theory according to which “justice is the truth and giving back what a man has taken from another”, the central claim of his argument is that giving back weapons to the mad friend is not just (see Plato Republic 331 C). An example from philosophy of mind is Block’s argument against functionalism, according to which “each type of mental state is a state consisting of a disposition to act in certain ways and to have certain mental states, given certain sensory inputs and certain mental states” (Block 1978: 262). He describes a situation in which the whole Chinese nation simulates brain activity, so the whole system meets the conditions that, according to functionalism, are necessary and sufficient for x to ascribe mental states to x. However, as he claims – and this claim is a central claim in his argument – this system obviously does not have mental states. A nice example from the philosophy of action can be found in Hursthouse’s critique (1991) of the Davidsonian theory of action, according to which “intentional actions are actions done because the agent has a certain desire/belief pair that explains the action by rationalizing it” (Hursthouse, 1991: 57). She argues against this theory by describing irrational actions such as kicking doors in anger and by stating that although these actions are not explained by any reason, they surely are cases of intentional actions. Now, note that the last claim is the key claim for her argument, and again it shares the same structure as the central claims in an epistemological MoC.

It seems plausible then that the argument formulated for a theory of knowledge applies to target-concept-oriented instances of the MoC in many branches of philosophy. Apart from the above-mentioned theories of justice, mental states, and intentional action, many other theories could be added to this group: for example, the theories of truth, love, beauty, duty, introspection, wisdom and so on. Nevertheless, as we have seen, this group does not include the theory of reference.

8 Conclusion

In this paper I analyzed the limits of normative interpretation of the method of cases. I explained how the answer to the question on whether instances of the method of cases in a particular branch of philosophy might be interpreted as normative or descriptive depends on the role of intuition within that branch. I have shown that in epistemological MoC, and in many other branches of philosophy the method of cases might be interpreted in two ways. In effect, the results of the method of cases within these branches of philosophy can either stem from the investigation of intuitions of extension concerning the target concept (if conducted within descriptive mode) or disregard these intuitions but arise from normative considerations (if conducted within normative mode). I have shown that this feature is reflected in the structure of particular instances of the method of cases.

However, what’s even more important, as it turns out, the theory of reference is an exception among philosophical theories. It cannot abandon intuitions of extension because they constitute its subject of investigation in its matter. A theory of reference is based on our intuition about the reference of some expressions, but, contrary to other theories, if their usage of the method of cases is interpreted in descriptive way, within a theory of reference we do not use them in order to check whether we are dealing with the reference in particular cases. Rather, a theory of reference assumes that it is uncontroversial what reference is. On this ground, a theory of reference aims to capture ordinary intuitions of extension and proposes a mechanism that explains them and therefore the structure of semantic MoC are significantly different from e.g. epistemological ones. In effect the nature of the method of cases within the theory of reference turns out to be purely descriptive, which as well is reflected in the structure of particular instances of this method in theory of reference. These claims reveal the take-home message: the concept REFERENCE is much more stable than most other concepts examined in philosophical considerations.