2. The problem of deviant realizations

First, let me introduce the problem of deviant realizations, which is the crucial problem for the discussion of the logical structure of the intuitive judgement within the method of cases.

Within the method of cases we can separate the procedure that aims to determine whether the thing which is at issue appears in the current consideration. For example, in the Gettier (Reference Gettier1963) cases the thing that is at issue is knowledge; in the discriminating procedure, we discriminate whether Smith's epistemic state is knowledge or not. As Weinberg (Reference Weinberg, Cappelen, Gendler and Hawthorne2016) states, the verdict within the discriminating procedure can take the form of a conceptual, factual or (meta)linguistic judgement. However, in all of these cases, the essence of this procedure is to determine whether there is a case of X but not of Y, Z …, or the term “X” and not the term “Y” or “Z” … applies to the described case. Therefore, for clarity I will refer to this procedure as the discriminating procedure.

The problem of deviant realizations arises when one aims to determine the logical structure of an argument that uses the discriminating procedure regarding some thought experiment. Since the discussion of this topic revolves around Gettier cases, it is easiest to explain this problem using the example of one of the Gettier cases.

First, let's assume the following convention (after Williamson Reference Williamson2007):

Note that Gettier's aim was to criticize the JTB theory of knowledge, according to which it is necessarily true that knowledge is a justified true belief. This stance could be formalized as:

After considering a few proposals concerning the logical structure of Gettier's argument, Williamson (Reference Williamson2007) finally proposed the following reconstruction:

1. (1) ⬦∃x∃p GC(x,p)

2. (2) □∀x∀p (GC(x,p) ⊃ (JTB(x,p) & ~K(x,p)))

3. (3) ⬦∃x∃p (JTB(x,p) & ~K(x,p),

Hence: (Con) ~□∀x∀p (JTB(x,p) ≡ K(x,p))

in natural language:

1. (1) It's possible for some x to stand to some p as in the Gettier story.

2. (2) Necessarily, if x stands to p as in the Gettier story, then x has a justified true belief that isn't knowledge.

3. (3) It's possible for someone to have a justified true belief that isn't knowledge, hence: (Con) It's not true that a justified true belief is necessarily knowledge.

Williamson himself pointed out the problem with the above formalization, which was later labeled “the problem of deviant realizations”. He notes that very little information is mentioned explicitly in the description of thought experiments. Moreover, in most cases (probably in all of them) it is possible to interpret the described story in such a way that the interpretation would be literally coherent with the explicit description; however, an argument that is based on a thought experiment should not be recognized as conclusive (Williamson Reference Williamson2007: 185).

For instance, consider Gettier's so-called 10-Coins Case,Footnote ^1, Footnote ² and note that there is very little information about Smith. We do not know the color of Smith's hair. We do not know whether Smith is young or old. We assume that he is a man and not a talking beaver, but we don't know this since in the explicit description of this case there's no such information. Of course, information about the color of Smith's hair, his age or species is irrelevant to the verdict on Smith's epistemic state. However, the 10-Coins Case also lacks information which could change the verdict on whether Smith truly and justifiably believes that e (i.e., the man who will get the job has ten coins in his pocket).

Consider the following case:

However, it is clear that the possibility of interpreting the 10-Coins Case in a strange way does not falsify Gettier's argument. If one argued against the Gettier argument by pointing out such a deviant realization as the Mean Boss Case, we would probably just say that such a person simply does not understand Gettier's story.

Note that the problem with deviant realizations is not considered a problem because they refute Gettier's argument. It would not be a problem that there are some bizarre realizations of some thought experiments that are inconsistent with the typical conclusions of these experiments. It is common in philosophy to formulate such cases, and there are well-known counterexamples (for example, on the discussion about the existence of qualia, see Dennett's (Reference Dennett, Alter and Walter2007) RoboMary Case, which is a counterexample for Jacksons’ (Reference Jackson1986) Mary Case. On the discussion about the reference of proper names, consider the way in which Burgess (Reference Burgess2014) argues against Evans’ (Reference Evans1973) conclusions from his Madagascar Case). Putting it somewhat sententiously, the problem with deviant realizations is that we know that they are deviant. In other words, it is clear that deviant realizations do not reflect what an author of a thought experiment intended to communicate (Malmgren Reference Malmgren2011: 276–9; Saint-Germier Reference Saint-Germier2021). The proper reconstruction of the logical structure of thought experiments should not allow the possibility of falsifying some thought experiments by pointing out some of their clearly deviant realizations. This is, in a nutshell, the problem of deviant realizations.

As I will show in the following sections, the problem of deviant realization can be solved by appealing to the procedure that precedes the discriminating procedure. In this prior procedure it is determined which states of affairs are genuine realizations of the given thought experiment. What is important, it could be done thanks to semantic intuition that takes into account contextual clues given both by the author of the experiment and by the context in which the description of the thought experiment is given.

3. Counterfactuals and actual deviant realizations – Williamson's account

In the following section, I will analyze Williamson's answer to this problem and its critique in more detail. I will show that close examination of both Williamson's account and its criticism highlights the fact that the discriminating procedure within the method of cases is preceded by another procedure.

In order to formulate a reconstruction of Gettier's argument which is immune to the problem of deviant realizations, Williamson weakened (2). According to him, while evaluating Gettier's thought experiment, we do make a claim about whether someone would have a justified true belief that p and would know that p. Hence, Williamson proposes changing (2) to a counterfactual claim (2*), according to which if someone were to stand to some p as in the Gettier story, then anyone who stood to any proposition in the same way would have justified the true belief that p but would not know that p:

• (2*) ∃x∃p GC(x,p) □→ ∀x∀p (GC(x,p) ⊃ (JTB(x,p) & ~K(x,p)))

Williamson insists that the logical structure of Gettier's argument enriched with (2*) is immune to the problem of deviant realizations. According to Williamson, counterfactual claims limit us to only the nearest possible worlds. To make (2*) true, it is enough that Smith's justified true belief is not knowledge in our actual world and in the nearest ones. It is then unnecessary to prove that Smith has a justified true belief that isn't knowledge in all possible realizations of the 10-Coins Case (Williamson Reference Williamson2007: 185–6).

However, Williamson's proposal was criticized on exactly this ground. Although according to (2*) we don't make a claim about the epistemic state of every subject in every possible world that stands to e as Smith did in Gettier's story, there is still a possibility that there could be a deviant realization of Gettier's story in the actual world. Consider the following “Uncle Case”. Suppose I actually do have an Uncle Ted who has indeed applied for a job, who had 10 coins in his pocket, who was unaware of this, and so on (i.e., he was in the same situation as Gettier described). However, Uncle Ted has also had a conversation with his friend Sue about the mean boss's habit of lying to applicants, and he recalled that conversation just in the moment of inferring e from d. Such a case would be a deviant realization of the 10-Coins Case that would refute Gettier's argument if we accept (2*) as a genuine formalization of Gettier's intuition. Williamson's second proposition is therefore not immune to the problem he intended to solve (see: Ichikawa and Jarvis Reference Ichikawa and Jarvis2009; Malmgren Reference Malmgren2011).

In response to this criticism (see Williamson Reference Williamson2007: 201Footnote ³; Malmgren Reference Malmgren2011: 279–80), Williamson claims that if there indeed were an actual situation in which my uncle stood to e as Smith did in the 10-Coins Case, and my uncle did indeed not have a true and justified belief that e, then the 10-Coins Case would need to be revised. In such a case, it would turn out that the realization in which Uncle Ted appears is not deviant at all. This would mean that Gettier and other philosophers were simply wrong when they considered that Gettier's thought experiment was in fact conclusive as a refutation of the JTB theory of knowledge.

Consider what the mistake would be in such a case. For simplicity, suppose that the description of the Uncle Case was known but no one revised the 10-Coins Case until the situation described in the Uncle Case actually happenedFootnote ⁴.

The mistake would not concern attributing knowledge to Uncle Ted or to Smith; therefore, it would not appear in the discriminating procedure. The mistake would concern the fact that one considered Uncle Ted's story to be a deviant realization of the 10-Coins Case; in effect, one counts it as a deviant counterexample, but it is actually genuine. As I have mentioned, before perceiving Uncle Ted's position, nobody would suspect that it is possible that someone could stand to e as in the Gettier story but not have justified belief that e. However, the actual existence of Uncle Ted and his unjustified belief that e would be proof that there is a possibility to stand to e as Smith did in the 10-Coins Case but not justifiably believe that e. It would thereby mean that the Uncle Case is not a deviant realization of the 10-Coins Case; instead, it is a genuine counterexample to Gettier's argument.

Therefore, in order to check whether Gettier's argument is conclusive, meaning that a justified true belief is not necessarily knowledge, we have to employ two procedures. Firstly, we have to determine which realizations of the 10-Coins Case are genuine, since deviant realizations of this case cannot either disprove or confirm the conclusion of Gettier's argument. As soon as we know which realizations are genuine, we can employ a discriminating procedure by which we can investigate the genuine realizations of the 10-Coins Case and check whether some genuine Smith has a justified true belief which is not knowledge. Hence, there are at least two procedures which have to be employed during investigation of the 10-Coins Case; since all thought experiments can be interpreted in a strange way, this fact applies to all thought experiments. The first procedure requires the proper interpretation of a given thought experiment, which is why I call it the interpretative procedure, and during this procedure all deviant realizations are ruled out. The second procedure is the discriminating procedure, in which we are already operating on the set of genuine interpretations of a given case. In the next section, I will show that the faculty which enables us to employ the interpretative procedure is semantic intuition, and explain how ruling out deviant realizations within this procedure is done.

4. The interpretative procedure and semantic intuitions

In order to show that semantic intuition enables us to determine which realizations are or are not deviant, I have to explain in more detail what it means that something is a deviant realization of a case.

Note that deviant realizations – just like genuine realizations – are some states of affairs. They could be either possible or impossible (if a thought experiment is fallacious). They could be fictional (as in the proposition formulated by Ichikawa and Jarvis Reference Ichikawa and Jarvis2009), counterfactual (as in Williamson's proposal) or factual (as the Uncle Case shows). However, it is quite clear that deviant realizations are just states of affairs, which in the 10-Coins Case must contain Smith, Jones, the president of some company, and at least 20 coins (10 in Smith's pocket and 10 in Jones’).

Now, note that a certain state of affairs is described in every thought experiment. The 10-Coins Case is nothing more than a long description of some state of affairs which contains Smith, Jones, etc. One can describe a pencil using the description “green pencil”. One can also describe some state of affairs with a longer description, such as “Mary surprises John with a present”. Gettier also described a certain state of affairs with a much longer description which starts with the words “Smith and Jones have applied for a certain job …”. Some elements of this state of affairs are explicitly stated (such as the number of coins in Smith's pocket), and some are not (such as Smith's haircut). But, after all, the formulation of the 10-Coins Case, just as any other thought experiment, is nothing more than a long description of a state of affairs.

Now that this is clear, let me propose a definition of a deviant realization:

In the above definition, I distinguish between the case and the description of the case, since it could be controversial if what is crucial for a thought experiment is a formulation of that thought experiment or a state of affairs which is the subject of that experiment. However, the main point is that a certain state of affairs is a deviant realization of a certain thought experiment if that state of affairs is not a denotation of a description which is used in the formulation of that thought experiment.

Now, let us consider semantic intuition, which is typically understood as a spontaneous faculty which enables us to determine the denotation of some utterances (see, e.g., Machery et al. Reference Machery, Mallon, Nichols and Stich2004). A paradigmatic example of the usage of semantic intuition in philosophy is the Gödel Case proposed by Kripke (Reference Kripke1980). In this thought experiment, semantic intuition is the faculty by which we determine the denotation (reference) of the name “Gödel”. Even if one argued, as, e.g., Deutsch (Reference Deutsch2015) did, that arguments instead of intuitions justify our judgement that “the man who killed the discoverer of the incompleteness of arithmetic” is not a denotation of the name “Gödel”, semantic intuition still allows us to determine the denotation of that name. Semantic intuition might not be a justificatory source for Kripke's claim, but it is still a faculty which enables us to determine the denotation of the name “Gödel”. This is why, even for Deutsch, semantic intuition could be a causal source for Kripke's argument.

The same might be said about definite descriptions and their denotations. In order to determine the denotation of a given description, we appeal to semantic intuitions. Hence, semantic intuitions are responsible for recognizing which states of affairs are denotations of some descriptions and which are not, and thereby which states of affairs are deviant realizations of some thought experiments and which are genuine ones.

5. The context dependency of descriptions of thought experiments

It could still be unclear how semantic intuitions fulfill their role in the interpretative procedure. In the following section, I will argue that the problem of deviant realizations is strictly connected with the context dependency of the interpretative procedure. Therefore, I will introduce an explanation of how semantic intuitions are contextually sensitive that is based on two approaches to the contextual dependency problem: one which refers to Levinson's idea of default interpretation, and a second one which is a semantic approach to the problem of the context-dependency of quantifier phrases.

It is crucial that semantic intuition, especially regarding descriptions, is not only limited to the ability to assess whether a given state of affairs meets the conditions explicitly stated in the formulation of a thought experiment. Semantic intuitions’ outputs are context dependent. Probably the most important contextual issue which has to be considered when interpreting thought experiments is the purpose for which the case was formulated. Note that deviant realizations do not contradict the descriptions in Gettier's story. Nevertheless, they are not its denotations since we know that Gettier's reason for formulating the 10-Coins Case was to show that some justified true beliefs are not cases of knowledge. Therefore, it is obvious that plausible denotations of the 10-Coins Case are states of affairs which contain Smith, who has a justified true belief about the man who will get the job, and not an unjustified true belief as, e.g., in the Mean Boss Case. Note that this is the case even though the description of the Mean Boss Case does not contradict anything that is stated explicitly in Gettier's story.

This relation is similar to the one that occurs in the following situation. Suppose that Tom is getting ready for a walk with his dog. He is in a hurry, so while putting the dog on the leash he's asking his wife to pass him the blue shoes. Then, suppose that his wife hands him the blue shoes of their six-month-old son. It is clear that Tom's son's blue shoes are not what he meant when asking his wife for blue shoes, despite the fact that his son's blue shoes are also a pair of blue shoes. Since the fact that what Tom was talking about was his shoes is about the denotation of the description “the blue shoes”, it is plausible that we know what the denotation of this description is because of our semantic intuition. Similarly, semantic intuition allows us to determine whether a given interpretation of a thought experiment scenario is deviant or not, since we know the context of formulating thought experiments quite well.

Now, we can consider an important issue: what is the mechanism that underlies semantic intuitions? At first, it is worth noting that it is reasonable that such a mechanism could vary depending on what the content of some intuition is. For example, both intuitions about the denotation of proper names and descriptions are semantic intuitions, since both of them concern denotations of some utterances. However, it is possible that a different set of information is processed when determining a denotation in a case of proper names than in a case of descriptions. For example, according to the Kripkean tradition, when establishing the denotation of proper names, some causal-historical features have to be taken into account, but such information is irrelevant in the case of descriptions.

In the theory of context dependence, as in the whole of semantics, there is an important distinction between two kinds of problems regarding context dependence and, respectively, two kinds of explanations. In the literature, this distinction is drawn between a theory of languages and a theory of language (Lewis Reference Lewis and Gunderson1975), between semantics and metasemantics (Kaplan Reference Kaplan, Almog, Perry and Wettstein1989: 573), or between foundational semantics and descriptive semantics (Stalnaker Reference Stalnaker, Hale and Wright1997; Stanley and Gendler Szabó Reference Stanley and Gendler Szabó2000). This distinction is discussed by Stanley and Gendler Szabó in detail in the context of the problem of contextual dependency regarding the domain of incomplete descriptions. So, I will use their terminology, and I will refer to their explanation of this issue.

Stanley and Gendler Szabó explicate the descriptive and foundational problems of context dependence as follows:

In short, in a descriptive theory of the context dependence of descriptions, one has to propose the general idea of what is a proper interpretation of descriptions relative to the context in which they are uttered. Foundational theory provides an explanation: how it is done. In what follows, I will discuss Saint-Germier's (Reference Saint-Germier2021) foundational explanation of the contextual dependence of descriptions of thought experiments, and Stanley and Gendler Szabó's (Reference Stanley and Gendler Szabó2000) descriptive theory of the contextual dependence of incomplete descriptions. I will argue that each of these theories could explain different aspects of the problem of deviant realizations, and I will discuss the consequences of these theories for that problem.

6. Comparison to other accounts

As I have shown the problem of deviant realizations can be solved by appealing to the interpretative procedure that precedes the verdict on whether the thing that is at issue appears in a given state of affairs. As I have shown in section 3, Williamsonian reconstruction of the logical form of the method of cases has to be enriched with the account focused on the interpretative procedure in order to solve that problem. Below I will compare my solution also to other existing approaches in the literature.

Ichikawa and Jarvis (Reference Ichikawa and Jarvis2009) proposed that we should treat facts about the protagonists from Gettier's case as claims about what is true in the fiction described by Gettier with reference to the Lewisian theory of truth in fiction. According to them, we have to accept the proposition g that “every element from the set of propositions true in the fiction created by Gettier is true”. Now, as Ichikawa and Jarvis note, some propositions from this set are inconsistent with deviant realizations (among these propositions, there is, e.g., one, that states that the president of the company does not lie to Smith). What is important, the fiction is somehow demonstratively given by Gettier case's description, and therefore the truth-value of propositions about Gettier cases are independent of anyone's interpretation. According to Ichikawa and Jarvis, the proper reconstruction of Gettier's argument is then the following:

Another proposal was formulated by Malmgren (Reference Malmgren2011) who suggested that crucial in evaluating Gettier's thought experiment is the claim concerning the metaphysical possibility of a non-deviant realization of Gettier's story in which Smith justifiably and truly believes that e but does not know that e. However, the possibility of one non-deviant realization of Gettier's story is sufficient to contradict the thesis of JTB theory of knowledge. Therefore, a possibility of deviant interpretations does not harm Gettier's argument. The logical structure of Gettier's argument is then according to Malmgren as follows:

Both of these accounts were criticized. For example, Malmgren pointed out that (2IJ) could be satisfied by someone who has justified true belief that is not knowledge outside Gettier's fiction, even if one would fill the set of propositions true-in-fiction in a deviant way (let me call the situation in which it is the case: Outsider Case). In such a case, it would be possible to accept Gettier's argument even if one interprets his thought experiment in a deviant, and therefore wrong, way. Against Malmgren's account it was raised among others that it is possible that (1M) is true and accepted by someone, even if that person does not believe that Smith from Gettier case has justified true belief that is not knowledge. Suppose for example, that Ann believes that knowledge differs from justified true beliefs because she was convinced by some other argument than Gettier's, e.g., by the lottery case, but at the same time she does not think that Smith from Gettier's does not know that e. In such a case (1M) would be true, even if Ann would think about deviant realization of Gettier cases, or simply does not share Gettier's intuition (see, e.g., Gardiner 2015: 712) (I will refer to this possibility as Ann Case).

Let me remind you that one of the most important arguments against Williamson's view was that the predicate GC in the content of the intuitive judgement could refer to some actual deviant realization of the case's description, as Uncle Case shows. Now, let consider what Williamson's, Ichikawa and Jarvis’ and Malmgren's views have in common. All of these accounts aim to solve the problem of deviant realizations by appealing to the content of a judgement within the discriminating procedure, and arguing that a certain formulation of that content would exclude deviant realization. However, as counterexamples formulated against all of the mentioned accounts show (Uncle Case for Williamson's account; Outsider Case for Ichikawa and Jarvis’; and Ann Case for Malmgren's) all of these accounts fail if considered as attempts to solve the problem of deviant realization. They could be a plausible account of the so-called content problem, i.e., the problem of what is the content of the intuitive judgement in the method of cases. All of them fail however if faced with the possibility of deviant interpretation of the given case description.

The strategy proposed in this paper has to be added to each of the mentioned accounts in order to make them truly deviant realizations-proof. If we think that the intuitive judgement in Gettier cases is a counterfactual claim (as in Williamson's approach), we have first to determine which set of situations Gettier intended to refer to. After that, we can start the investigation of what would have been the case if things were as Gettier intended to describe. Similarly, if we think, following Ichikawa and Jarvis, that in Gettier cases we are making judgements about the fiction, we have to establish what kind of fiction Gettier wanted to demonstrate to us. Finally, if we think, after Malmgren, that the judgement about Gettier cases is a judgement about a particular metaphysical possibility, we have to establish which possibility Gettier intended to describe.

This task can be achieved if we accept the account proposed in this paper according to which discriminating procedure is preceded by another, interpretative procedure in which it is determined which states of affairs are genuine realizations of a given case on the basis of analysis of contextual clues regarding the meaning of the substantive terms. This strategy was partly anticipated by Grundmann and Horvath (Reference Grundmann and Horvath2014) and Saint-Germier (Reference Saint-Germier2021). Showing that deviant realizations of Gettier cases could be excluded by reformulation of their description by the former and establishing the idea according to which the deviant-proof reformulation of the Gettier case corresponds with the default interpretation of Gettier cases by the latter, puts the discussion concerning the problem of deviant realizations on the right track. My solution, in contrast to Grundmann and Horvath's and Saint-Germier's, sets aside the content problem (according to both of these accounts the content of the intuitive judgement in Gettier case is a strict conditional), and proposes more detailed explanation of how thought experiments are interpreted. What is most important in the account proposed, and what was missed by all of the previous ones, is that the solution of the problem of deviant realization is independent from the solution of the content problem, and what is more, the essence of that solution is that deviant realizations are ruled out by the previous stage at which semantic intuitions help us to interpret the substantial terms in the case description in a way coherent with both the author's intentions and the theoretical context of the formulation of the case.