3.1. Describing the Case

Sherrilyn Roush’s ^{Footnote 23} Fairy Godmother case against safety is closer to providing a legitimate counterexample to Williamson. In Roush’s case, S has a fairy godmother who makes all S’s beliefs true at the very moment S forms her belief. In this case, the mental state in question is factive, and to provide a counterexample to Williamson’s conjecture it would be sufficient to describe a scenario in which the subject has a belief but does not have knowledge. Roush’s case, of course, also faces the problem of being analyzable, i.e., being a restricted version of belief. However, if one could find a similar mental state that is not a restricted belief (or some other mental state) and is both primitive and factive and does not entail knowledge, it would suggest a promising case against Williamson. In this section, I endeavour to offer such a state.

Consider a possible world inhabited by a goddess, G. G is a sentient creature whose mind is causally related to the external world in such a way that whenever she is in a certain mental state that entails she has a certain propositional attitude toward P, P (instantly) becomes the case. Call this mental state ‘gelief.’ Gelief is a kind of mental state that works as follows. First, it is a mental state that only those creatures can be in whose minds are causally related to the external world in such a way that their minds can directly cause changes in the world. Second, gelief works in such a way that whenever someone gelieves that P, if P is true nothing happens and P remains true; if P is false, however, it instantaneously becomes the case. In other words, whenever someone gelieves that P, if P is true it remains true and if P is false it becomes true. ^{Footnote 24} For example, if one gelieves that Obama is the president of the United States, nothing happens in this world since it is true now, but if one gelieves that there is a golden mountain under the Pacific Ocean, assuming that there is not one now, then a golden mountain under the Pacific Ocean instantaneously comes about. Add to this story, however, that G’s father has made her falsely believe that whenever she gelieves that P, her father brings about not-P—a kind of parental evil genius problem for G. ^{Footnote 25} So, whenever G gelieves that P, she falsely forms the belief that not-P.

In his discussion of the relation between knowledge and belief, Williamson accepts the following: “if S knows that P, then S believes that P.” He offers a non-disjunctive analysis of ‘believes’ in terms of knowledge that, he admits, validates the above-mentioned proposal that if one knows P then one believes P. ^{Footnote 26} Therefore, he accepts that whenever one knows P, one believes P, and arguably this must be understood in a way that it is true in every possible world, since he offers an analysis of belief in terms of knowledge. So, if G is to know that P, she must also believe P. But, in this case, whenever G gelieves that P, she believes that not-P, and therefore by Williamson’s criterion she does not know that P. Therefore, we may assume that whenever G gelieves that P, she does not know it. But gelief is a factive mental state, since one can have that state only to truths—if P is false, it would become true instantaneously when G gelieves that P.

Our example of the golden mountain under the Pacific Ocean would make the case clearer. ^{Footnote 27} Suppose that, as a matter of fact, before G’s act of gelieving, there is no golden mountain under the Pacific Ocean, so G cannot know that there is one by memory or testimony. In addition, at the time G forms her gelief, she is in a land far from the Pacific Ocean, so she does not have any perceptual access to the golden mountain she brings about by gelieving. So, when she forms the gelief that there is a golden mountain under the Pacific Ocean, she also forms the belief that there is no golden mountain under the Pacific Ocean, since she thinks that her father has made it the case that there is not one there. Therefore, G does not know that there is a golden mountain under the Pacific Ocean.

Note that, by Williamson’s standards, gelief must be counted as an FMSO. It behaves syntactically like verbs and is semantically unanalyzable. ^{Footnote 28} In addition, it satisfies the three conditions mentioned above for being an FMSO. First, its subject term denotes something animate—it must be a term for some sentient creature whose mind is such-and-such—and takes as object a proposition referred to by a that-clause. Second, it is factive. And third, ‘S gelieves that P’ attributes to S an attitude toward a proposition, since one must grasp the proposition that P to gelieve that P. In addition, Williamson argues that factive attitudes, like knowledge, are similar enough to paradigmatic cases of mental states and dissimilar enough to non-examples of mental states: “[t]o call knowing a mental state is to assimilate it, in a certain respect, to paradigmatic mental states such as believing, desiring and being in pain. It is also to contrast it with various non-examples of mental states [such as believing truly].” ^{Footnote 29} So, knowing is a mental state since it is sufficiently similar to, say, believing, and sufficiently dissimilar to things that are not mental states, such as believing truly. Now, whatever one can offer in favour of the similarity between knowledge and paradigmatic cases of mental states, and dissimilarity with their non-examples, one can also offer in favour of the similarity and dissimilarity of gelieving and paradigmatic cases of mental states and paradigmatic non-examples, respectively. In sum, I suggest that gelief can be considered as a primitive factive mental state, in exactly the same way Williamson introduces knowledge as a primitive factive mental state. Therefore, gelief is a primitive factive mental state that does not entail knowledge, and so can be regarded as a counterexample to Williamson’s claim.

Now, one can see the difference between Roush’s case and mine. In Roush’s example, the subject S has a fairy godmother who makes all S’s beliefs the case at the very time she forms them. In my example, quite to the contrary, the mental state in question is not belief. In addition, in my example what brings about the content of G’s gelief is the causal relation of G’s mind to the world, not a fairy godmother’s intervention, which is essential to my argument for the unanalyzability of gelief below. ^{Footnote 30}

Before proceeding to Section 3.2, Objections and Replies, there are two immediate worries that need to be addressed. First, one might argue that G can gradually become aware by inductive inference that whenever she gelieves that P, P rather than not-P becomes the case, and therefore gain knowledge that gelief is factive. That is, after gelieving propositions several times and observing that, whenever she forms that attitude, the proposition she gelieves and not its negation comes about, she would correct her false belief. After that time, whenever she gelieves that P she believes that P as well, and therefore there would not be any problem in her knowing that P. But gaining such knowledge based on inductive evidence takes time, and before that evidence has accumulated she does not have any knowledge or belief as to the factivity of the mental state. ^{Footnote 31} Note that all we need to refute the conjecture is to show that there is at least one case such that one is in a factive mental state and does not have knowledge. So the evidence accumulation does not touch the example.

The second worry is about the factivity of gelief. One might argue that I have, in explaining the notion of ‘gelief,’ said that, whenever one gelieves that P, ‘P would become the case.’ That is, one might continue, when P is false before gelieving, it is ‘after’ forming that mental state that P comes about and there is a time gap between the mental state gelief and P’s becoming true. If this is true, gelief would not be factive after all, since there is a time t in which one gelieves that P, but P is still false, and this is contrary to the definition of factive mental states, i.e., mental states that one has necessarily to truths. It is important to note that the term ‘instantaneously’ here is essential, since, as described, there doesn’t need to be any time gap between gelieving that P and P’s coming about. That is, it is an assumption of the case that exactly at the time of gelieving, P becomes the case. Put another way, there is no need to assume a time gap between forming a gelief and the respective proposition coming about, so there is no problem with the factivity of gelief. Exactly at the same time that one gelieves that P, P becomes true and so one can only have that mental state to truths. ^{Footnote 32}

3.2. Objections and Replies

The first objection might be that gelief is not a different mental state than belief. That is, the objector might complain that every characteristic satisfied by belief is also satisfied by gelief. According to the objector, then, it is possible for there to be more than one concept of a single mental state, and gelief and belief are two concepts for one and the same mental state. ^{Footnote 33} If true, this shows that in fact we have been unsuccessful in finding a new primitive mental state, and gelief is in fact belief, restricted to satisfy the factivity condition. In other words, this counterexample falls victim to exactly what made the previously mentioned examples ineffective, i.e., using an actual non-factive mental state and restricting it to make it factive.

The objection, however, fails. Williamson offers an identity condition for mental states as follows: “states S₁ and S₂ are identical if and only if necessarily everything is in S₁ if and only if it is in S₂.” ^{Footnote 34} That is, if one can be in a state S₁ and at the same time not be in state S₂, they are not one and the same mental state. To show that belief and gelief are not one and the same mental state, therefore, one must show that belief and gelief don’t satisfy this condition. That is, one must show that, first, there are propositions one can believe but cannot gelieve, and second, there are propositions that one can gelieve but cannot believe. In other words, given Williamson’s criterion, once one has shown this, one has shown that belief and gelief are different mental states.

First, consider how the identity between belief and gelief can fail in the left-right direction, i.e., that there are propositions one can believe but cannot gelieve. That there are beliefs that are not geliefs can be shown by the goddess’s believing necessarily false propositions. Suppose that, as a matter of fact, Goldbach’s conjecture (GC) is true. In that case, ‘GC is false’ is a necessarily false proposition and a belief in it would be a false belief. We can reasonably allow that in G’s world there is a common belief that GC is false, and that G believes that GC is false. ^{Footnote 35} But, not surprisingly, she cannot gelieve that proposition, since it is a necessarily false proposition and no one, including G, can gelieve something that is necessarily false. Therefore, there is a proposition that one can believe but cannot gelieve; so, according to Williamson’s identity condition of mental states, there are beliefs that are not geliefs. ^{Footnote 36} Note that assuming that one cannot gelieve necessarily false propositions is not as odd as it may seem at first. There are restrictions on the range of propositions toward which one can have other factive mental states, and assuming such a restriction in the case of gelief would not be strange. For example, one cannot know false propositions, and one cannot perceive unobservable ones. Allowing that there is a restriction in the case of gelief is no different. ^{Footnote 37} In addition, mental states like intention are arguably very special mental states that one cannot have toward necessarily false propositions or (false) propositions about the past. So, it is reasonable to assume that one cannot gelieve necessarily false propositions or (false) propositions about the past, or propositions such that gelieving them would make gelieving such propositions possible—such as the proposition that I can gelieve necessarily false propositions or (false) propositions about the past. There is no disanalogy here between intention and gelief, unless otherwise proved. ^{Footnote 38} It is important to bear in mind that, as it is possible for S to falsely believe that S knows a false proposition, it is possible for S to falsely believe that S gelieves a necessarily false proposition or a false proposition about the past.

As for the right-left implication, i.e., that there are geliefs that are not beliefs, one must show that there is at least one proposition that one can gelieve but cannot believe. Consider the proposition that G cannot believe anything. Call this proposition P. It is obvious that G cannot both gelieve and believe P at the same time. Instantaneously, when she gelieves that P, she would not be able to believe anything, including P. The case would be more evident if we can find a single proposition that G cannot at the same time both gelieve and believe. Self-referential propositions would be helpful here. Consider the proposition that G cannot believe this proposition, where ‘this proposition’ refers to the very proposition denoted by the that-clause. ^{Footnote 39} In this case, insofar as G gelieves this proposition, she cannot believe it. This shows that there are geliefs that are not beliefs. I conclude that gelief and belief are not identical mental states.

This objection, of course, might be repeated for other mental states like desire, fear, and hope. For any such mental state, however, the very same argument shows that gelief is not identical to it. For example, G may desire that GC is false, but G cannot gelieve that GC is false. Also, she cannot at the same time gelieve that she cannot desire anything and desire not to be able to desire anything. This argument, of course, can be repeated for other mental states, such as fear and hope, and the conclusion would be that they are not one and the same mental state as gelief.

The issue becomes more complicated, though, when we consider mental states like intention, that one cannot have to necessarily false propositions. For instance, one cannot intend that 2 + 2 = 3 or, if we allow that GC is true, that GC is false. So, the argument above that there are beliefs that are not geliefs cannot be applied to the case of intention, since, although one cannot gelieve that GC is false, one cannot intend that proposition either. Put another way, the argument we offered to falsify the left-right direction of the identity between belief and gelief is unavailable in the case of intention, or other mental states similar to it, if there are any. So, the objector might conclude, there are intentions that are geliefs, and therefore they are not different mental states after all.

It must, however, be clear that, for my argument to work, it is enough to block the right-left implication. That is, the only reason I argued against the left-right implication was to make the non-identity of belief and gelief more evident. In other words, to show that gelief is analyzable, one needs to show that it is synonymous with a complex expression such that it is a known mental state, say intention, plus some other condition. But showing that there are some intentions that are also geliefs is not sufficient, or even necessary, for showing this. What one must show is that every gelief is intention plus something else, not that there are some intentions that are some kind of gelief. So, simply showing that there is a gelief that is not intention, i.e., showing that there is a proposition one can gelieve but not intend, is enough to refute the objection. But, as a matter of fact, the very same argument used above for showing that there is a gelief that is not a belief can show that there is a gelief that is not intention, i.e., gelieving the proposition that G cannot intend P, for whatever proposition G is in principle in a position to grasp. Therefore, whether there is a proposition one can intend but cannot gelieve is unnecessary for my argument. So, gelief is not intention either and the objection fails.

By this line of argument, however, another trick of the objector would be blocked, i.e., introducing a new mental state belief* (desire*, fear*, etc.) by restricting belief (desire, fear, etc.) to those beliefs (desires, fears, etc.) whose object is a contingently true proposition about the present or future, and so make it a mental state that works like intention. G can gelieve and at the same time cannot believe* (desire*, fear*, etc.) the proposition that G cannot believe* (desire*, fear*, etc.) anything.

Note that the trick used here to show that gelief is not identical to any other mental state is unavailable to Reed. Above, I noted that a charitable reconstruction of his example is that he introduces a new primitive factive mental state, but fails to do so because he gives us no argument to support the claim that gnowledge is not a combination of belief and some restriction. The reason that I can use the argument offered here, and Reed cannot, is the direct causal relation of the goddess’s mind to the external world, so it is impossible for her to gelieve and believe (desire, intend, etc.) a certain proposition, and this shows that gelief is different from all other mental states. But I am aware of no proposition that one can gnow but cannot believe, desire, etc. Perhaps Reed has an argument in mind to show this; I have no idea what it would be.

All these arguments are designed to show that gelief is analyzable and therefore falls victim of the very same objection I made to the counterexamples offered in the literature. That is, all these objections were endeavours to show that gelief is another mental state, such as belief or intention, that is restricted to make it factive. The arguments discussed above, if successful, show that gelief cannot be analyzed in terms of actually known mental states. But the objector might argue that, even if one accepts that gelief is not identical to actually known non-factive mental states such as belief and desire, one can after all offer an analysis of gelief. Put another way, one can find an expression that is synonymous with gelief, and this shows that it is analyzable after all, albeit not in terms of other actually known mental states: ‘a propositional attitude the content of which comes about (is made true) due to the formation of the attitude’ is a case in point. ^{Footnote 40}

Williamson offers some arguments in favour of the unanalyzability of knowledge that, to my mind, can be used against the analyzability of gelief as well. The argument, which I, following Cassim Cassam, ^{Footnote 41} call the ‘distinct concept argument’ (DCA), runs as follows. Williamson maintains that knowledge is a mental concept. He offers no definition of a mental concept, but as Cassam ^{Footnote 42} suggests, a concept can be counted as mental if it makes a reference to a subject, or, conversely, it is not mental if it “makes no reference to a subject.” ^{Footnote 43} This is, as Cassam stressed, far from being a definition, but it shows why he considers knows but not true as a mental concept. Now, according to Williamson, the criterion for a conjunctive concept to be mental is as follows: “if the concept C is the conjunction of concepts C₁, …, C _n , then C is mental if and only if every C _i is mental.” ^{Footnote 44} On this account, believes truly as well as has a justified true belief are not mental concepts, since true “makes no reference to a subject,” and therefore it is not a mental concept. But, Williamson continues, every traditional analysis of knowledge must contain the conjunct true, and therefore “[g]iven that the concept knows is mental, every analysis of it of the standard kind is therefore incorrect as a claim of concept identity, for the analyzing concept is distinct from the concept to be analyzed.” ^{Footnote 45}

The very same argument, I suggest, can be reproduced to defend the unanalyzability of the concept gelief. Since gelieves like knows makes reference to a subject, it must be considered as a mental concept by Williamson’s own lights. Every suggested analysis of gelieves, however, must contain the conjunct that the mental state makes the proposition true, i.e., like every analysis of knows, it must contain true as a non-redundant conjunct and this very non-mental conjunct makes the concept non-mental. So, to draw on Williamson’s own words, “every analysis of [the concept gelieves] … is therefore incorrect as a claim of concept identity, for the analyzing concept is distinct from the concept to be analyzed.” ^{Footnote 46}

There are two worries about this argument that need to be addressed. First, one might worry that DCA is fallacious, or at any rate doesn’t work. It is beyond the domain of this paper to argue in favour of DCA; I presuppose for the sake of argument that it works and this is what Williamson and I share. However, it is noteworthy that Williamson himself defends this argument, and so he must accept it in the case of gelief, unless proved otherwise, and it is his burden to do that. Second, one might reasonably argue that there is a linguistic and explanatory practice of attributing knowledge to subjects to which Williamson can appeal in order to defend the premise that the concept of knowledge is a concept of a mental state. There is no such linguistic and explanatory practice to which I can appeal in order to defend that the concept of gelief is a mental concept. The only reason Williamson offers in favour of the mentality of the concept knowledge, however, is that it makes reference to a subject, and one can say that gelief makes that reference as well. However, the objector can reply that such a reference in the case of knowledge is well established, contrary to the case of gelief. My reply is that we can arguably assume an extension of English in which there is such a linguistic practice in case of gelief as well as knowledge, or that there is such a language in the goddess world in question. So, there would be no problem about gelief being a mental concept. Put another way, in the extended English, or the goddess world’s English, ‘gelief’ is rather like ‘knowledge’: people use it to refer to a subject and this linguistic practice makes it a legitimate candidate for a mental concept. I conclude that gelief is a primitive factive mental state that is not semantically analyzable.

The last objection would be that I have not shown that there really is such a mental state. To show that Williamson’s conjecture is false, then, I must find a real mental state that does not entail knowledge. Seemingly, the objection is that the mental state in question is not actual. But it is important to bear in mind that Williamson’s conjecture that knowledge is the most general factive stative attitude is a necessary claim. That is, he is to be understood as saying that there is no possible world in which there is a factive mental state that does not entail knowledge. If it was not a necessary claim, it would not be of any philosophical interest. Rather, it would be simply an inductive claim about the actual world and therefore couldn’t account for the importance of knowledge, nor comprise the “modest positive account of [knowledge]” that Williamson takes it to be. In addition, when summarizing his account of FMSOs in three principles (as mentioned above), he offers an argument for the conclusion that the two latter principles “characterize the concept of knowing uniquely, up to logical equivalence, in terms of the concept of an FMSO.” ^{Footnote 47} Showing the mere possibility of a factive mental state that does not entail knowledge, then, is enough to refute the claim.

A more promising line of argument would be that I did not show the possibility of the case. That is, the objection is that I merely stipulated that there is a mental state such as gelief, and did not show its possibility. In response, I suggest that it is conceivable that there is a mental state such as gelief, and its conceivability can be considered as an evidence in favour of its possibility. It is important to bear in mind that I do not claim that this conceivability entails the possibility in question, rather it is simply evidence for that conclusion. Put another way, unless we have strong reason to doubt the possibility of a conceivable situation, and unless that possibility were defeated, it is reasonable to assume its possibility, and the burden of proof here is on the side of the opponent to find such a defeater. That is, since we can imagine such a scenario, our intuition is that it is possible; it is, then, the objector who is in charge of offering an argument against its possibility. Of course, it is a controversial matter whether conceivability is a sign of possibility; if the objector is on the other side of the debate, he can consider my argument in this paper as a conditional: if conceivability—in the absence of any reason to believe otherwise—is evidence for possibility, then gelief is a counterexample to Williamson’s conjecture.

Finally, note that the objection against Reed—that he simply stipulated the conclusion—does not work against my proposal, since I merely put forward that there is a mental state with such-and-such a property, and then argued in favour of its primitiveness and endeavoured to show that it satisfies whatever features it needs to be a counterexample to Williamson’s conjecture. I didn’t assume that it is a primitive factive mental state in the first place, and therefore I didn’t beg the question against Williamson. Therefore, if the arguments are sound, it is indeed a counterexample to the conjecture in question.