5.1. Intuitions of extension in application and revision G-Grounds

To determine whether G-Grounds could be justified by intuitions of extension, we have to determine whether any premise in such arguments expresses the possible content of intuitions of extension. On the example of the Disconnect G-Ground (see §4), in this section I will argue that there is no possible candidate for a premise that could express an intuition of extension.

The content of an intuition of extension could be a proposition which states whether or not a particular epistemic state falls under the ‘knowledge’ concept. What is crucial is that the content of an intuition of extension is about knowledge ascription and not about knowledge itself.

Now let us check whether in my reconstruction of the Disconnect G-Ground there is a premise that could be the content of an intuition of extension. The argument has three premises: (G1), (G2) and (G3) (see §2).

Neither (G1) nor (G2) is about knowledge ascription. Neither of them is about whether some entity falls under some concept. While intuitions of extension reflect how we categorize entities, (G1) and (G2) are about the relations between some facts in the world. (G1) states that there is a causal relation between Smith's belief and both (i) and (ii). (G1) is therefore about the causes of Smith's belief. (G2) states that between Smith's belief and both (i*) and (ii*) there is another relation, namely a relation which holds between true beliefs and their truthmakers. Hence, (G1) and (G2) do not express any intuitions of extension.

Since (G1) and (G2) cannot be the content of an intuition of extension, let us think about a proposed enthymematic premise (G3).

(G3) clearly is an example of the content of an intuition of intension. It is not about ascribing knowledge to particular subject, as this would make it an intuition of extension; it is rather a proposition about some general property of knowledge, as is characteristic of intuitions of intension. This property is a non-accidental connection between what makes some belief true and how this belief is acquired. Since (G3) is not about ascribing knowledge to someone, it could not be the content of any intuition of extension.

However, it is possible that (G3) is not the only enthymematic premise candidate that could make the Disconnect G-Ground work. There could be another enthymematic premise candidate that could be the content of some possible intuition of extension.

Consider an obvious candidate:

• (G3*) Smith does not know that ‘the man who has 10 coins in his pocket will get the job’.

There is, however, no connection between (G3*) and the two other premises. Conclusion (J1) results directly from (G3*), hence that argument does not need either of the other two explicitly expressed premises to be conclusive. Moreover, the content of this premise is just the same as the content of the conclusion. If we accept that (G3*) is the enthymematic premise of the Disconnect G-Ground, this argument turns out to be circular.

Consider then another possibility:

• (G3**) If Smith knows that ‘the man who has 10 coins in his pocket will get the job’, then the facts that led Smith to acquire the belief that ‘the man who has 10 coins in his pocket will get the job’ are truthmakers for the proposition that ‘the man who has 10 coins in his pocket will get the job’.

Note that the content of (G3**) is not the same as conclusion (J1). It is also not the case that conclusion (J1) follows directly from (G3**) without the other premises. Therefore, upon the acceptance of premise (G3**), there is no danger of a vicious circle, nor can this solution be accused of not taking into account the other premises of the Disconnect G-Ground.

Even though (G3**), (G1) and (G2) entail (J1), (G3**) cannot be seen as premise that is justified by an intuition of extension. This is because the content of (G3**) is not actually the content of an intuition of extension. Intuitions of extension are about the epistemic state of an agent in a particular situation; in contrast, intuitions of intension concern properties of knowledge itself. If a proposition states a condition for knowledge, then such a proposition is about some property of knowledge, and thereby such a proposition expresses an intuition of intension. The proposition expressed by (G3**) is a conditional proposition and is about the same property of knowledge as (G3). It is not about whether Smith has knowledge or not: it is about the conditions under which it is concluded whether or not Smith has knowledge. Hence, (G3**) is the content of a special case of an intuition of intension.

(G3**) expresses a singular and not a general proposition, which may suggest that it concerns a particular case in which we assess whether a given entity has knowledge. However, the difference between intuitions of intension and intuitions of extension does not apply to whether the content of an intuition is a particular or a general proposition. Intuitions of intension can be about specific particulars, nevertheless they remain intuitions of intension. An intuition of extension determines whether a given subject has knowledge or not. The content of an intuition of intension states in what case we can talk about knowledge. The content of an intuition of intension, however, can be both singular and general; it can therefore be both a proposition with the following content:

1. (I1) For each X, if X is an animal, then X is a dog,

as well as a proposition:

1. (I2) If Saba is an animal, then Saba is a dog.

On the other hand, the only proposition that can have analogous content in the case of intuitions of extension is the following:

1. (E1) Saba is a dog.

In fact, it may turn out that some intuitions of intension could be acquired as a result of considering intuitions of extension. For example, I could acquire (I2) as a result of considering (E1), which is a related biological intuition of extension of the form ‘Saba is a dog’, and other similar intuitions of extension like ‘Marshall is a dog’, ‘Marshall is an animal’, ‘Danny is a dog’, ‘Danny is an animal’ etc. However, this does not have to be the case. I could have intuition (I2) without considering whether Saba is a dog, but, for example, I could infer it from the general proposition (I1). Regardless of whether I accept (G3**) because I inferred it from a singular proposition (like (E1)) or from a general proposition (like I1), the content of (G3**) is the content of an intuition of intension but not of an intuition of extension.

In sum, the content of (G1) or (G2) or (G3) does not correspond to the content of an intuition of extension. Moreover I have also checked whether there are any plausible enthymematic premise candidates in the scrutinized G-Ground other than (G3), and I have shown that plausible candidates either lead to a vicious circle (as (G3*)) or expresses intuition of intension (as (G3**)). In view of the above considerations, intuitions of extension cannot justify any premise of the Disconnect G-Ground.

This result concerns both application and revision G-Grounds. Regardless of whether the Disconnect G-Ground is formulated in order to prove something about Smith's epistemic state or about knowledge in general, the premises of this argument remain the same. If none of the premises of such a G-Ground could be justified by an intuition of extension, it does not matter which interpretation of this argument we adopt. Hence, an intuition of extension cannot serve an evidential role in the case of application or revision G-Grounds.

5.2. Intuitions of intension in application G-Grounds

In this section, I show that intuitions of intension could justify the premises in application G-Grounds; however, they cannot be a good source of evidence because they are dependent on philosophically irrelevant factors. This conclusion is coherent with the Negative Xphi's critique and shows that application G-Grounds are unreliable sources of evidence.

Note that (G3) could be the content of an intuition of intension as it expresses a certain property of knowledge. As I already mentioned in the last section, this property can be expressed as a ‘non-accidental connection between what makes it true and how it was acquired’.

While considering application G-Grounds, in order to assess whether the epistemic state of the agent in a given scenario falls under the concept of knowledge, we must first adopt a specific concept of knowledge. In order to assess whether the Disconnect G-Ground is valid, it is only necessary to check whether or not the property expressed by (G3) is included in some specific concept of knowledge (hereafter, I will refer to the adopted concept of knowledge as K).

Consider now in virtue of what we could accept K, and how (G3) could be justified. The first possibility is that K is someone's private psychological concept. So, if a property described in (G3) is included in K, we can justify (G3) by the intuitiveness of (G3). However, such a justification could be accepted only by a person possessing K. In this case, the justification of (G3) is its intuitiveness, while (G3) is the content of an intuition of intension.

On the other hand, if K is a concept adopted under some convention, then why we adopt the given convention should be justified since it could be adopted for many debatable reasons. Such a choice can be made without any justification – just like the starting point for the analysis of the concept of knowledge; however, in that case the strength of a G-Ground would be negligible. Whether a G-Ground is valid would depend only on an arbitrarily chosen convention. If K is adopted without any justification just as a starting point for consideration, it would be bizarre to use such a concept in application G-Grounds. It is hard to imagine any reason why we would check whether a particular situation meets the arbitrarily adopted concept K, and then, in virtue of that, conclude that the given situation is a case of knowledge. More plausible is that someone adopts some concept for some reasons. Even if a concept used in the analysis of ‘knowledge’ is adopted under a convention, we could argue in favour of such a convention. One might indicate that we should adopt K because it is simple or is consistent with some other theory. If, however, we argue why we should adopt some concept of knowledge, and then on that basis we argue that Smith does not know that p, this would no longer be an application G-Ground: it would be a revision G-Ground, since revision G-Grounds differ from application G-Grounds in that the former are arguments for adopting some properties of the analysed concept of knowledge, but unlike application G-Grounds they are not arguments for ascribing a particular epistemic state to someone.

Thus, within application G-Grounds a certain premise may be justified by an intuition of intension. In the case of the Disconnect G-Ground, this premise is (G3). However, (G3) is justified only if its intuitiveness corresponds to the properties of the psychological concept of knowledge that the person evaluating the G-Ground possesses. These intuitions however vary with philosophically insignificant factors such as culture (see, e.g., Nisbett et al. Reference Nisbett, Peng, Choi and Norenzayan2001; Hofer Reference Hofer and Khine2008), gender (see, e.g., Baxter Magolda Reference Baxter Magolda2001; Karabenick and Moosa Reference Karabenick and Moosa2005) or even childhood experiences (see Bartsch Reference Bartsch2002), which means that they are not a good source of evidence according to the Negative Xphi critique.

The following conclusions can be drawn from this section: intuitions of intension may justify some of the premises of application G-Grounds, but such intuitions are a poor source of evidence. These results support the Negative Xphi critique, but only in the case of application G-Grounds. To determine whether Negative Xphi's critique is sound or whether adopting (D2) makes it possible to defend the reliability of Gettier's argumentation, we also have to explore the role of intuitions of intension in revision G-Grounds.

5.3. Intuitions of intension in revision G-Grounds

Finally, we are able to consider the last option. The previous section shows that (G3) could be the content of an intuition of intension. Moreover, we know that the conclusion of application and revision G-Grounds is the same: it is (J1). This means that intuitions of intension could be a source of evidence for one premise in a revision G-Ground, and therefore Deutsch is wrong about the role of intuitions in Gettier cases since there are some kinds of intuitions that support G-Grounds. However, in the next section I will argue that some kinds of intuition could be a good source of evidence in the case of revision G-Grounds. This would mean that although Deutsch is wrong about (D2), adopting (D1) makes it possible to defend Method of Cases against the Negative Xphi's critique.

Let me stress that the defence of reliability of Gettier's argument, presented below is an interpretation of Gettier's argument. I do not claim that this is its only possible interpretation. I do not claim also that Gettier himself, if asked, would agree that I correctly described his method. I insist however that this interpretation is plausible, and that it might be useful if one wants to defend the reliability of the Method of Cases.

The justification for the view that some intuitions of intension are a good source of evidence in Gettier's argument requires granting philosophers the specific status of ‘experts’. However, it is crucial that I am not saying that philosophers have some competences that are better developed in philosophers due to their philosophical training, as other proponents of the so-called expertise defence postulate (see e.g. Kauppinen Reference Kauppinen2007; Williamson Reference Williamson, Sytsma and Buckwalter2016). I am also not saying that philosophers make more accurate verdicts about some cases.

In order to grasp the kind of expertise I'm referring to, we have to look closer at the role of intuitions of intension in concept-revision arguments. According to the view I am defending, while using a concept-revision argument we could appeal to our intuitions of intension that expresses our expectations towards this concept. For example, if I have an expectation towards the concept C that C should be such-and-such, I could express an intuition of intension that C is such-and-such. Note that it is not argued in such a case that C is such-and-such. It is argued that C should be such-and-such. Therefore, such an argument is normative and not descriptive in its nature.Footnote ⁵ Moreover, note that our expectations concerning C could be more or less accurate in particular contexts. For example an expectation towards a philosophical concept of knowledge that knowledge should capture only funny beliefs is less accurate from the philosophical perspective than an expectation that knowledge should be certain. Similarly, an expectation that during playing hide-and-seek all children ought to learn something important about teamwork is less accurate from the perspective of children engaged in the game, than, for example, an expectation that the game should be as exciting as possible. On the other hand, from the perspective of parents, the former expectation towards the rules of hide-and-seek game might be more accurate, just as the expectation regarding the funny beliefs might be accurate from a perspective of someone who, let's say, construes an unusual world in a science fiction novel.

The status of ‘experts’ that I ascribe to philosophers bases on the fact that their intuitions of intension regarding philosophical concepts are more accurate in the context of philosophical debate. This follows from their both explicit and tacit knowledge about the purpose of the particular debate and arguments formulated within this debate in the past. This kind of expertise comes from philosophers’ immersion in a particular kind of activity, and it is the same kind of expertise as children from my neighbourhood have regarding the rules of their games, musicians have regarding the concepts or properties of musical activity, or mathematicians have regarding mathematical concepts. All of these groups create a part of reality and since their expectations towards this part of reality partly constitute it, they are specific kinds of experts regarding it.

Now, consider the 10-coin case. We may argue that Smith does not know that e because his epistemic state does not meet our expectation towards the concept of knowledge, according to which if someone knows that p there must be a non-accidental connection between what makes p true and how belief that p was acquired. This expectation was actually mentioned by Gettier in his argument (see Deutsch's presentation of the Disconnect G-Ground in §2). It seems plausible that he expressed this stance since it is intuitive that knowledge should meet the mentioned expectation. Gettier was well informed about, for example, aims of philosophical analysis of knowledge, doubts raised in the past etc, and his expectations are formed partly on the basis of this awareness. The argument was formulated within an epistemological dispute, and therefore Gettier's expectation expressed by his intuition of intension, forms a reliable source of evidence.

It is important to note that philosophical concepts, even if homonymous with everyday concepts, could be slightly different from them because they serve specific purposes defined by philosophers during analyses. An example of such a purpose may be to fit concept ‘A’ into the established theoretical framework containing ‘A’. For example, concept of knowledge should be compatible with concept of justification established within some theory. Such expectations towards the consistency of theoretical framework are negligible for most people but they are crucial for both philosophers and scientists. There are however also some expectations which are not shared by philosophers and scientists, but specific for philosophers and were formed during the history of, for example, epistemology. For instance, according to Craig (Reference Craig1990: 6) how philosophical concept of knowledge differs from the folk one is that the former should face a sceptical challenge in some way just because of philosophers’ expectations, while the latter does not. Nowadays, it is important that such a concept should be immune to Gettier cases. Since Gettier (Reference Gettier1963) wrote his famous paper and others wrote some answers to it, it is also clear that philosophers require that knowledge cannot be true just by accident.

Hence, unlike the folk use of the concept of knowledge, the philosophical use must consider the tasks that have been imposed on the concept of knowledge over the course of the history of philosophical inquiry. To understand which concept is at issue in the Method of Cases, and therefore to properly interpret thought experiments, it is crucial to understand the theoretical context in which a particular thought experiment is investigated (see Cohnitz and Häggqvist Reference Cohnitz, Häggqvist, Stuart, Fehige and Brown2016; Sękowski Reference Sękowski2022). Therefore, since philosophical concept of knowledge emerges from the philosophical practice, people familiar with that practice acquire linguistic competence to use the term ‘knowledge’ that is in line with the expectations that epistemology imposes on it.

Note that the difference between philosophical and everyday concepts was described above as “slight”. Although there is a lot of such epistemological platitudes which are insignificant or even strange for lay people, a possible and plausible expectation is that the concept of knowledge ought to be, for example, coherent to some extent with the ordinary usage of the word ‘knowledge’. It is nicely expressed by one recent philosophical strand focused on the method of conceptual analyses: the so-called Canberra Plan represented by, for example, Chalmers, Jackson or Lewis (see Braddon-Mitchell and Nola Reference Braddon-Mitchell and Nola2009). According to the proponents of the Canberra Plan, the philosophical investigation should start with some platitudes, and then try to find out which entities satisfy most of these platitudes. It is assumed that, especially in the case of technical terms, not all folk beliefs ought to be included in the list that should be satisfied by the final definition of some term (see: Kornblith Reference Kornblith, Cappelen, Gendler and Hawthorne2016). However, since a theoretical concept, such as the philosophical concept of ‘knowledge’, has to be defined partly with regard to the set of the most obvious platitudes about knowledge which are shared by philosophers, scientists and lay people, the philosophical concept of knowledge should not concern something entirely different from the folk concept of knowledge. The philosophical concept of knowledge cannot refer to some colour or a kind of cutlery as this would be extremely incompatible with philosophical expectations towards ‘knowledge’, which in this case coincide with common usage of the term ‘knowledge’.

The role of appealing to intuitions of intensions could be then as such, that it justifies a concept-revision argument, which is convincing if the expectation that is expressed by intuition justifying the argument is shared or at least looks plausible. There remains a question, however. What if two philosophers do not share the same intuition of intension or share two incompatible intuitions of intension?

It is a common situation in philosophical practice. Suppose that A would argue that the proper theory of concept of ‘X’ is so-and-so, because of i1, which is A's intuition of intension about X. However, B argues that A's theory of X should be refuted because of i2, which is another intuition of intension about X. The plausible prediction, coherent with Deutsch's picture of philosophical methodology, is that A and B would probably look for an argument which could help to decide which one is right. This is Deutsch's solution to the ‘relocation-problem’, according to which at some level all arguments rest on intuitions (2015: 122–7). He argues that even if G-Ground, or any other philosophical argument seems to rest on some intuition, we should be aware that there is always some possible argument which could justify that intuition. As mentioned, the explicit formulation of Gettier's argument contains a phrase which refers to the possible intuition of intension that justify Disconnect G-Ground and therefore we are able to claim that this argument serves as evidence in Gettier argument. However, as I mentioned in §3, Gettier's argument lacks any clue of some possible argument which could justify the intuition of intension that is a premise in Disconnect G-Ground. Therefore, even if an intuition of intension expressed by (G3) could be justified by some argument, it does not change the fact that (G3) is accepted, and it makes the Disconnect G-Ground sound, because it is intuitive.

Let me return to the example of A and B discussing the theory of X. It is now clear that the argument which might tip the scales in B's favour also would rest on some intuition of intension. Note that in such a case both A and B should abandon a hitherto accepted definition of ‘X’ and accept another. It is because B's argument based on intuitions of intension must be a concept-revision argument which, naturally, leads to conceptual revision. Of course, later, someone else – C, who is immersed in epistemological discourse, could propose another concept-revision argument based on intuition of intension i3. If A and B share i3, then the definition of X would be revised again. This illustrates how philosophers could approximate a definition of ‘X’ which meets all their relevant expectations.

Variety of philosophers’ intuitions of intension is not a problem when it comes to revision-concept arguments then. The reliability of intuitions of intension in a case of justifying concept-revision arguments does not come from stability of these intuitions, but from the facts that they express expectations of someone who takes part in a particular practice of negotiation of the target concept's meaning, and that this person is immersed in this practice. Epistemic intuitions of intension do vary across epistemologists. However, if a philosopher is a mindful and minimally competent participant of a particular dispute on a given epistemological concept, and if she is aware of at least the most influential expectations imposed on the scrutinized concept in the past within this dispute, then her intuitions of intension towards the meaning of the target concept are reliable, in a sense that they might be reasonably considered and discussed within this dispute.

In sum, even if we agree with Deutsch that the evidence for (J1) is arguments instead of intuitions, these arguments are supported by their own intuitiveness. This conclusion contradicts Deutsch's thesis (D1). However, in the case of revision G-Grounds, intuitions of intension could be a good source of evidence. This is the case if these are intuitions of intension of a speaker immersed in the context of a particular philosophical dispute. However, this conclusion contradicts one of Deutsch's views, and it also opens a way to defend the Method of Cases against the Negative Xphi's critique. Although intuitions of intension do serve an evidential role in the Gettier cases, they could be reliable.