1. The alleged non-compositionality of knowledge (first approximation)

Knowing entails believing, knowing entails truth, and true belief is insufficient for knowing; Williamson accepts all of this. So, we might think that there must be an “additional part” which conjoined with belief and truth would amount to knowledge. Let us call this “remaining part” of knowledge F. A key idea that forms part of Williamson's view is the rejection of the existence of such a third component, F, if it is conceived as a non-redundant factor in a possible definition of knowledge. We can put it in other words: if (*) is a correct definition of knowledge,

then Q is a redundant condition, in the sense that Q – by itself – entails the truth of P. Traditional approaches to defining knowledge have proposed characterizations that fit the template (*). Furthermore, according to Williamson, such traditional approaches have looked for a Q that is a non-redundant factor (so that neither of the other two factors – P is true and S believes that P – is entailed by Q). But, Williamson takes that tradition to be doomed to failure. In that sense, knowing could not be analysed by discomposing it into different independent components.

Williamson's main negative thesis on the prospects of defining knowledge has to do with this idea. Things are somewhat more complicated, however, which makes the task of identifying that negative thesis a hard one. Some other theses of his, closely related to the previous remarks, are also relevant to this discussion. For instance, suppose that (*) is a correct definition, where Q is a redundant factor (Williamson does not reject this possibility). Even in this case, Williamson claims, the concept expressed by ‘knows that P’ (the concept of knowing that P) will not be identical to the conjunctive concept expressed by ‘believes that P, P is true and Q’. This other negative result is a consequence of his theory about mental concepts and states (cf. section 4 below). In fact, Williamson defends not just one, but several interrelated negative theses that, when combined, form a general pessimistic picture of our chances of finding an appropriate characterization of knowledge. Since I am going to examine some of these theses I first need to identify them.

2. Alternative versions of Williamson's negative thesis

Williamson relies on a standard distinction between concepts, on the one hand, and states or conditions, on the other.Footnote ¹ He illustrates the contrast by means of a classical example. The concept gold – i.e., the concept expressed by ‘gold’ – and the concept the element with atomic number 79 are two different concepts of the same state, or condition: being gold. And, of course, the metaphysical state, being gold, is not identical to either of those two concepts, or to any other concept of it that may exist. (Cf. Williamson Reference Williamson2000: 29.) Now, the concept knows (or the concept knows that P, for a given proposition P) is not identical to the metaphysical state of knowing (or to the metaphysical state of knowing that P), which it is a concept of. It is an open possibility that some other concept – different from the concept knows – is also a concept of the same state, a concept of the state of knowing.

Suppose a given definition has the following form: S knows that P if and only if F. Let us introduce some terminology. The definition is reductive just in case all the concepts in the definiens (the concepts constituting the concept expressed by ‘F’) are more basic than the concept knows that P. It is a conjunctive definition just in case the concept F is a conjunctive concept, with the form: C₁ and C₂ and … C_n (for n > 1). It is a traditional-conjunctive definition just in case it is a non-circular conjunctive definition and one of the conjuncts, C_i, is P is true. We can now formulate some negative hypotheses about the chances of defining knowledge, or the chances of defining the concept of knowledge (i.e., the concept knows). As we will see, Williamson holds all of them, save one.

• Undefinability: No informative and non-circular definition will provide correct necessary and sufficient conditions for knowledge. (This is the negative claim that Williamson does not hold.)

• Unreductibility: No reductive definition will provide correct necessary and sufficient conditions for knowledge.

• Unanalysability of the State: No traditional-conjunctive definition will provide correct necessary and sufficient conditions for knowledge; i.e., there will be no necessarily true and non-circular definition of knowledge of the form “S knows that P if and only if C₁ and C₂ and … C_n”, where one of the conjuncts, C_i, is P is true.Footnote ²

• Unanalysability of the Concept: No traditional-conjunctive definition where definiendum and definiens are the same concept will provide correct necessary and sufficient conditions for knowledge; i.e., there will be no necessarily true and non-circular definition of knowledge of the form “S knows that P if and only if C₁ and C₂ and … C_n”, where one of the conjuncts, C_i, is P is true, and such that S knows that P and C₁ and C₂ and … C_n are the same concept.

In subsequent sections, I will comment on each of these negative hypotheses. For reasons that will become clear later, I think that Unanalysability of the State is the most important of them, and the best candidate to be considered as Williamson's main negative thesis on the prospects of defining knowledge. In any case, my discussion will mostly focus on Unanalysability of the State. Before entering into that discussion, however, it is convenient to dedicate the next section to some methodological remarks.

3. The evidence against traditional definitions of knowledge

Unreductibility, Unanalysability of the State and Unanalysability of the Concept are supported by Williamson's claims in different ways. On the one hand, he thinks that we have inductive evidence against the three theses: all reductive and traditional-conjunctive definitions of knowledge proposed to date have counterexamples, according to Williamson. In this article, I will not go into the discussion of this particular claim. For the sake of the argument, I grant this history of failures of previous traditional attempts to analyse knowledge. This alleged experience certainly provides support for the three negative theses.

On the other hand, Williamson advances a theory about the mental nature of some concepts, the mental nature of some states, and the links between the two issues. I will refer to his theory as WTM (for Williamson's Theory of the Mental). Unanalysability of the Concept is entailed by WTM. Unanalysability of the State is not strictly a consequence of WTM, but if we accept WTM it would be very reasonable – in Williamson's view, at least – to accept Unanalysability of the State (cf. Williamson Reference Williamson2000: 30; I will return to this point in section 4).

Williamson develops his proposals using different argumentative strategies that have not always proved to be sufficiently clear. So much so that Pritchard (Reference Pritchard2012: note 1), for instance, has interpreted Williamson as attacking the task of searching for an adequate (informative and non-circular) definition of knowledge. That is not Williamson's intention at all, since – as we will see in section 8 – Williamson himself offers and defends his own definition; in other words, Williamson rejects Undefinability.

Not so wide of the mark, Cassam (Reference Cassam, Greenough and Pritchard2009) partially misidentified the kind of evidence Williamson offers in favour of some of his negative theses. Apparently, Cassam focuses on a claim that he calls the Unanalysability Hypothesis (UH): the concept knows cannot be analysed into more basic concepts (cf. Williamson Reference Williamson2000: 33; Cassam Reference Cassam, Greenough and Pritchard2009: 12). At first sight, UH would amount to – what I have called – Unreductibility. However, when Cassam examines the issue, the argument of Williamson that he discusses most is not evidence for Unreductibility, but rather for something closer to Unanalysability of the Concept. Cassam calls it the Distinct Concepts Argument. This argument takes as premises some theses from WTM, in particular the crucial claim that knows is a mental concept, and concludes that every standard analysis of the concept knows is incorrect.Footnote ³ Cassam suggests that the Distinct Concepts Argument is independent of the inductive argument also put forward by Williamson in support of the same conclusion; and he rejects the former argument, mainly on the basis of a number of objections to some of its premises. I mostly agree with those objections (cf. section 5 below). However, I do not think they are as strong as Cassam seems to assume, precisely because the Distinct Concepts Argument is not a completely independent argument.

Williamson clarifies the dialectics in his reply to Cassam (cf. Williamson Reference Williamson, Greenough and Pritchard2009a: 291–2). The claim that knows is a mental concept – which, in light of Cassam's criticisms, might seem to have some stipulative flavour – is not supported in isolation with independence of the inductive evidence for the conclusion of the Distinct Concepts Argument. On the contrary:

In fact, it is not just this hypothesis (that the concept of knowledge is mental) that would be abductively supported by such a history of previous failures. Some other parts of WTM are in the same position. So, in general terms, the overall web of relations of evidential support should be understood as follows. The (alleged) history of failures of traditional analysis inductively supports negative hypotheses such as Unanalysability of the State and Unanalysability of the Concept. These hypotheses, in their turn, abductively support WTM, since WTM is a general theory that entails Unanalysability of the Concept and that would make it reasonable to accept Unanalysability of the State. WTM is advanced, then, as the best explanation of such negative hypotheses.

Nevertheless, this scheme also entails that the support for Unanalysability of the State and Unanalysability of the Concept is not merely inductive (Cassam is right about this). WTM results from some generalizations and provides a certain systematicity in a range of phenomena that it would account for, including – presumably – phenomena other than the history of failures of the traditional analysis of knowledge. In that sense, if Williamson is right, WTM would confer additional support on Unanalysability of the State and Unanalysability of the Concept, additional to the merely inductive support coming from the “experience” (the “experience” consisting of the alleged history of failures). Indeed, that is so even if eventually the evidence for WTM comes from that same “experience” and some other related phenomena that it would explain.

Now, my main contribution in this article is to argue for this conditional claim: if WTM supports Unanalysability of the State, it does so at an excessive cost. WTM only supports this negative hypothesis insofar as it also supports some other hypotheses that seem highly implausible. Therefore, the preferable available options are to reject WTM, or to reject the claim that WTM supports Unanalysability of the State. A corollary of this result is that the only adequate evidence for Unanalysability of the State provided by Williamson is the merely inductive evidence (which is controversial, but which – for the sake of argument – I am granting here). When we enter into the details of the discussion, another corollary will emerge: Williamson's definition of knowledge seems to fail.

4. Williamson's theory of mental concepts and states

I have anticipated some theses that belong to WTM, regarding the distinction between the concept of knowledge and the state of knowing (section 2 above).Footnote ⁵ The concept of knowledge is a concept of the state of knowing. And, as any other state, the state of knowing can be the state of different concepts (some of them not identical to the concept of knowledge).

Besides this, WTM includes a number of particular claims as well as general theses. In the former group, we find claims such as these:

1. (1) The concept knows is mental.

2. (2) The state of knowing is mental.

3. (3) The concept is true is not mental (at least, not when the true proposition is an ordinary contingent proposition about the external environment; henceforth, I will drop the mention to this restriction, which should be understood).

4. (4) The state, or the condition, of being true is not mental.

5. (5) The concept believes truly is not mental.

6. (6) The state of believing truly is not mental.

When we ask ourselves how claims about the mental character of some concepts relate to claims about the mental character of some states, WTM offers us an explicit answer:

1. (7) A state is mental if and only if there could be a mental concept of that state (cf. Williamson Reference Williamson2000: 28).

Thesis (7) suggests that it is our acceptance that the concept knows is mental that allows us to accept that the corresponding state is also mental, not the other way around. It is true that Williamson defends (2) not on the basis of (1) and (7), but by pointing out – among other considerations – that the state of knowing would be a sort of paradigm of a mental state; for instance, he says “Our initial presumption should be that knowing is a mental state” (Williamson Reference Williamson2000: 22). Nevertheless, if an objector who accepts (7) but rejects (2) challenged Williamson to argue for (2), her challenge would amount to a request for the identification of a mental concept that was a concept of (corresponding to) the state of knowing. Williamson would offer – I imagine – the concept knows as the obvious example. So, I think that Williamson would extend to the concept knows his considerations about our pre-theoretical presumptions and its status as a paradigmatic mental concept. In any case, in the framework of WTM, (1) and (7) entails (2); and, of course, (1) is not entailed by (2) and (7).

In addition to (7), these other general theses also belong to WTM:

1. (8) If concept C is a conjunction of concepts C₁,…, and C_n, and one of these concepts, C_i, is not mental, then C is not mental. This is so even if C_i is a redundant factor (so that at least some other conjunct, C_j, entails C_i).

2. (9) States S₁ and S₂ are identical if and only if necessarily: (everything is in S₁ if and only if it is in S₂).

3. (10) The concepts is C and is C and such that T are different concepts, even if they are logically equivalent (for instance, when T is a logical truth).

Thesis (8) plays a crucial role in the derivation of several important claims entailed or supported by WTM. Thus, thesis (5), the concept believes truly is not mental, follows from (3), the concept is true is not mental, and (8), under the further assumption that believes truly that P is the same concept as the conjunctive concept (believes that P) and (P is true). (I have no objection to this last assumption.)

Now, we arrive at Unanalysability of the Concept, which follows from (1), (3) and (8): since knows is a mental concept, by (1), it cannot be identical, by (8), to a conjunctive concept one of whose conjuncts is the concept of truth, which is not mental, by (3).Footnote ⁶

What about Unanalysability of the State? It does not follow strictly from WTM. However, according to Williamson, once we accept Unanalysability of the Concept we should also accept Unanalysability of the State. He expresses the idea in this fragment:

In the same vein, Williamson declares: “If the concept believes truly is non-mental, its imagined necessary coextensiveness with a mental concept would be a bizarre metaphysical coincidence” (Williamson Reference Williamson2000: 29). As I take it, when he describes such a possibility as a bizarre metaphysical coincidence, Williamson is highlighting the same general point: the theory, WTM, does not entail the impossibility of that necessary coextensiveness, but it would make much reasonable to reject it. In that sense, WTM would support both claims: given that knows is a mental concept, there is no other non-mental conjunctive concept necessarily coextensive with it; and given that believes truly is a non-mental concept, there is no other mental concept necessarily coextensive with it. The first of these two claims entails precisely Unanalysability of the State. In the framework of WTM, the second claim entails – in virtue of (7) – Williamson's thesis (6): the state of believing truly is non-mental.

To sum up, WTM entails Unanalysability of the Concept, and makes it reasonable – for Williamson, at least – to accept Unanalysability of the State, as well as to accept (and for the same kind of reason: to discard what would otherwise appear to be a bizarre metaphysical coincidence) that the state of believing truly is non-mental.Footnote ⁷

5. Concepts and conceptual necessity

Now, it is time for replies. I present in this section a few critical comments. My main criticism comes in sections 6, 7 and 8.

First, theses like (8) and (10) seem to have a certain stipulative flavour, and Williamson does little to dispel this impression. In particular, thesis (8) does not appear as clearly more natural or pre-theoretically intuitive than the following thesis (8*), which one might propose:

1. (8*) If it is metaphysically necessary that (if the concept C has an instance, then the non-mental concept D has an instance), then C is not mental.

Of course, Williamson must reject (8*) since it would entail – assuming that ‘knows’ is factive and the concept is true is non-mental – that the concept knows is non-mental.

Second, sometimes Williamson attacks opponents who certainly do not represent most contemporary attempts to define knowledge. For instance, occasionally he leads the discussion as if the opponent to Unanalysability of the State should be committed to rejecting Unreductibility, or to rejecting Unanalysability of the Concept. This is not so (Cassam Reference Cassam, Greenough and Pritchard2009: 17 makes a similar point).

In fact, even if we look for a definition of knowledge in which the modality of the link between definiens and definiendum is conceptual, that does not entail that definiens and definiendum are the same concept, as demanded by the negation of Unanalysability of the Concept. We can accept that a given analysis ‘G if and only if R’ is conceptually true, while being agnostic as to whether the concept G is or is not identical to the concept R (cf. also Cassam Reference Cassam, Greenough and Pritchard2009: 18–19). Therefore, we should not assume that Unanalysability of the Concept is equivalent to this other claim:

The plausibility of Unanalysability of the Concept will depend – among other things – on specificities and details of our preferred theory of concepts; Williamson commits himself to some of those specificities about identity conditions for concepts when he includes in his WTM theses like (8) and (10). The issue is obviously related to, but independent of, our preferred view of conceptual necessity, which is the subject matter of Unanalysability* of the Concept. In general, I think that a significant portion of contemporary epistemologists searching for an interesting definition of knowledge typically commit themselves to the denial of Unanalysability of the State.Footnote ⁸ Some of them would also reject Unanalysability* of the Concept. However, Unanalysability of the Concept is a different matter; it is of comparatively limited interest to epistemologists (philosophers of language and philosophers of mind may be more interested in it). Finally, I think that Williamson's criticism to Unreductibility has a modest scope, since the search for a reductive definition of knowledge (in the sense specified in section 2) is a relatively old-fashioned project (and it was already so in 2000, when Williamson published his book). Putting it in other words: how many influential epistemologists make (now, or in 2000) explicit claims committing themselves with definitions of knowing where all the concepts in the definiens would supposedly be more basic than the concept knows that P?

6. A metaphysical anthropological hypothesis

Let us recall: for Williamson, knows is a mental concept and believes truly is a non-mental concept. Why is this so? The basic idea, underlying this discriminatory treatment, seems to be this: the concept believes truly is a kind of hybrid composite concept, which stipulatively combines a mental concept (believes) and a non-mental concept (true). The state corresponding to the concept (the state of believing truly) is “reached” or referred to by the concept in just such a composite way.Footnote ⁹ Thesis (8) in WTM states the (alleged) intuition that composite concepts of this sort cannot be mental. Unlike believes truly, the concept knows would be – for Williamson – simple or primitive; it cannot be factored into different independent components, one of which is non-mental (in section 1 above, I already advanced this idea). The concept knows refers to, or “reaches”, its corresponding state in a simple, non-hybrid way, we may say.

Note that it would be complicated to argue for the non-mental character of the concept believes truly – thesis (5) in WTM – on the basis of the non-mental character of the state of believing truly, i.e. on the basis of Williamson's thesis (6) (pace Reed Reference Reed2005: 138). Granting (7), it would be an open possibility that even if the concept believes truly was non-mental, some other concept of the same state could be mental. Williamson rejects this possibility as a bizarre metaphysical coincidence (cf. the previous section). However, his rejection assumes that the concept believes truly is non-mental. Its being non-mental, therefore, would be accounted for – in Williamson's view – by the fact that I have emphasized: it is a hybrid, non-simple combination of a mental concept and a non-mental concept.

I am going to present a specific metaphysical-anthropological hypothesis. We have no evidence for its truth. However, its mere possibility poses a serious problem for Williamson's view. The whole pack of Williamson's theses that I have laid out lead us to think that if the hypothesis is possible, then the state of believing truly is mental.

This is the hypothesis:

Williamson's thesis (5) indicates that the concept believes truly is non-mental. MAH says nothing about such a concept. It concerns a different concept, which is a concept of (that corresponds to or refers to) the same state. Unlike believes truly, the concept X is “simple-primitive” in the same sense in which – for Williamson – knows is “simple-primitive”. The concept X refers to, or “reaches”, its corresponding state in a simple, primitive, non-hybrid way.

Now, MAH seems clearly to be a possible hypothesis (more on this below and in the next section). But, Williamson's theorizing about concepts and states entails that if MAH is possible, then the concepts postulated by it really exist – not just as a mere possibility. In particular, according to Williamson the state of believing truly exists; and, if MAH is possible, then there could be a concept X, with the traits indicated in MAH, of that state. Meanwhile, if we grant that knows is a mental concept, we have no good reasons to deny that X is also a mental concept. An important consequence is the following: by (7), the state of believing truly is a mental state, because there could be a mental concept of it, e.g., the concept X.Footnote ¹¹

Note that, in the present discussion, it would be question-begging to say something along the lines of the following reasoning:

Why would it be question-begging? At present, we are looking for (not merely inductive) evidence supporting Unanalysability of the State. More specifically, we are asking ourselves how WTM and in particular the thesis that knows is mental – thesis (1) in WTM – would support Unanalysability of the State. Therefore, we cannot assume Unanalysability of the State. In other words, it is dialectically illegitimate to assume that the concept knows does not admit of an analysis with the form: S knows that P if and only if (S believes that P) and (P is true) and Q. But (**) only works as a justification for the alleged non-mental character of the concept X if it is assumed that knows, unlike X, does not admit of such an analysis.

We can expand this point. My main claim in this work is that WTM only supports Unanalysability of the State if it also supports ruling out as impossible certain metaphysical hypotheses – MAH is one such example – that clearly seem to be possible. There are two ways for this claim to be true: (a) WTM does not support Unanalysability of the State; or (b) WTM supports ruling out as impossible hypotheses such as MAH which seem to be possible. Now, MAH involves a certain notion of simplicity-primitiveness and establishes that there could be a concept X (which refers to the state of believing truly) that is simple-primitive, as knows is. I have not said much about what exactly this notion of simplicity-primitiveness amounts to, precisely because the burden of clarifying it would rest with Williamson, if doubts about its intelligibility were raised. I am using ‘simple-primitive’ to refer to what Williamson must say to justify the claim that knows is mental and believing truly is non-mental. This simplicity-primitiveness is somehow related to the idea that the concept “does not admit of an analysis that factors it into different independent components, one of which is non-mental”. Whatever the exact connection between them, I am invoking the notion of simplicity-primitiveness under this assumption: saying that the concept knows refers to its state in a simple-primitive way does not entail by definition that knows does not admit of a traditional-conjunctive analysis. In other words, I am assuming that the simplicity-primitiveness of knows does not entail by definition Unanalysability of the State (of Knowing). Analogously, I am assuming – against (**) – that the simplicity-primitiveness of X does not entail by definition Unanalysability of the State of X, which is a false thesis, as (**) correctly says.Footnote ¹² If the assumption is right, then (**) is wrong. X can have the simplicity-primitiveness of knows, and consequently it should be classified as mental; (b) holds. What happens if I am wrong regarding that assumption? If the alleged simplicity-primitiveness of X entails by definition Unanalysability of the State of X, then MAH is impossible; (b) does not hold. But then, (a) holds. The fact that knows is a mental concept – thesis (1) in WTM – entails by definition the very thesis Unanalysability of the State (of Knowing). There is no interesting support for Unanalysability of the State coming from WTM, and particularly none coming from thesis (1).

Let me make some further consequences of accepting that X is a mental concept explicit (besides the fact that believing truly would be a mental state). Granting that believes truly is a non-mental concept, its necessary coextensiveness with a mental concept is not – pace Williamson – a bizarre metaphysical coincidence; in other words, it is not unreasonable to think that there is a mental concept that is necessarily coextensive with believes truly. On the contrary: it would be a bizarre metaphysical coincidence if there were no such mental concept; because that non-existence would require that MAH were impossible, and that would indeed be a metaphysical impossibility that was extremely hard to explain.

Analogously, the necessary coextensiveness of knows with a non-mental concept would not be a bizarre metaphysical coincidence; i.e., it would not be unreasonable to think that there was a non-mental concept that was necessarily coextensive with knows. Therefore, pace Williamson, it is not unreasonable to reject Unanalysability of the State. If WTM supports Unanalysability of the State, it does so at an excessive cost: it also supports MAH being impossible.

8. Some corollaries about general factive mental states

In Chapter 2 of his book, Williamson presents and defends an alternative definition of knowledge. Knowing, according to that definition, would be the most general factive mental state; i.e., the factive mental state metaphysically implied by all factive mental states.

Believing truly is a factive state, and it is more general than knowing. Williamson does not see it as a counterexample to his definition, since he thinks that believing truly is non-mental. However, in the light of our previous results, the concept X would be a mental concept. So, by (7), believing truly would be a mental state. In that sense, apparently Williamson's proposal would fail.

Things are not so easy, however, since Williamson is somewhat unclear as to exactly what the status of his characterization of knowledge is. Sosa (Reference Sosa, Greenough and Pritchard2009) claims that the state of safely believing is a counter-example to Williamson's definition. In response, Williamson writes:

There are at least two problems with this response to Sosa (besides the problem anticipated by Sosa himself). First, the counterexample concerns the state, not a concept. Even if ‘safely believes p’, like ‘believes truly’, is semantically analysable, there is the possibility, according to (7), that some other concept that refers to the same state is semantically unanalysable. Second, suppose we accept that by (stipulative) definition, FMSOs are semantically unanalysable.Footnote ¹⁶ Then, we cannot unproblematically assume that ‘knows’ is an FMSO. Otherwise, we would obtain the apparently substantive thesis Unanalysability* of the Concept, or something very close to it, from a stipulative definition and an unproblematic assumption.

Regardless of these problems, I take it that Williamson's exact definition of knowing involves the notion of factive mental state operators, and it would take approximately the following form:

(W) implies at least the following two substantive hypotheses: the state of knowing is mental; and it is the most general factive mental state. If by definition FMSOs are semantically unanalysable, then (W) also implies this other substantive hypothesis: ‘knows’ is semantically unanalysable. Of course, Williamson is perfectly clear in defending this last hypothesis. The lack of clarity I refer to concerns whether or not he wanted that hypothesis to be implied by his characterization of knowledge. Taking into account his later comments – Williamson (Reference Williamson, Greenough and Pritchard2000a: 285; Reference Williamson, Greenough and Pritchard2000c: 364) – the answer is positive.

Let me now examine more carefully whether or not the state of believing truly is a counterexample to (W). If semantic unanalysability is not built into the definition of ‘FMSO’ as a necessary condition, then there is no reason to reject the claim that ‘X’ is an FMSO. From the discussion in previous sections, I take it that ‘X’ expresses a mental concept (if ‘knows’ expresses a mental concept). Therefore, (W) would fail, because believing truly is a counterexample.

However, let us accept that the notion of FMSO definitionally entails semantic unanalysability. Then, there are two issues. First, it is controversial that ‘knows’ is indeed an FMSO; if it is not, then (W) fails. Even if ‘knows’ is an FMSO, it is an open question whether or not ‘X’ is semantically unanalysable. Williamson says: “An artificial verb stipulated to mean the same as ‘believe truly’ would not be an FMSO” (Williamson Reference Williamson2000: 36). However, ‘X’ is not an artificial verb stipulated to mean the same as ‘believe truly’ (cf. our section 7, in special note 14). Certainly, ‘X’ admits of a traditional-conjunctive analysis; Unanalysability of the State of X is a false hypothesis. But we cannot infer from this that the analysis in question is purely semantic; we cannot assume that ‘X’ and ‘believes truly’ are synonyms. If ‘X’ is semantically unanalysable, again there is no reason to reject the claim that ‘X’ is an FMSO. So, (W) would fail. If ‘X’ is semantically analysable, then we have not found a counterexample to (W).Footnote ^19, Footnote ²⁰