The C account of assertion: a negative result

According to what Williamson labels ‘the C account of assertion’, there is one and only one rule that is constitutive of assertion. This rule, the so-called ‘C Rule’, states that one must assert p only if p has property C. This paper argues that the C account of assertion is incompatible with any live proposal for C in the literature.


Introduction
Let's start with two observations. First, we assert things all the time. For instance, we frequently ask questions that are subsequently answered by our interlocutors. When they do so, they assert these answers. Second, speakers are not allowed to assert whatever they like. Rather, assertion is governed by rules. For instance, when we assert that Seattle is the capital of Spain, we are violating a rule of assertion.
Unsurprisingly, then, two important philosophical questions about assertion concern its nature and normativity. Williamson (1996Williamson ( , 2000 has famously offered an account of assertion that promises to answer both of these questions at the same time. The key idea here is that assertion is governed by rules that are constitutive of assertion in much the same way in which the rules of games are constitutive of games. In particular, Williamson proposes the following appealingly simple account of assertion, B Christoph Kelp christoph.kelp@glasgow.ac.uk Mona Simion simionm@cardiff.ac.uk 1 Philosophy, University of Glasgow, 67-69 Oakfield Ave., Glasgow G12 8LP, UK 2 Philosophy, Cardiff University, John Percival Building, Colum Drive, Cardiff CF10 3EU, UK the so called 'C account of assertion' (CAA), according to which assertion is the only speech act governed by a unique constitutive rule of the following form: C Rule One must: assert p only if p has property C.
If correct, CAA offers an account of the nature of assertion: assertion is by its very nature the speech act that is governed by C Rule. In addition, CAA will also shed light on the normativity of this rule of assertion: the normativity is the normativity of a constitutive rule.
Of course, C Rule leaves open the question of the identity of the key property C. Williamson himself identifies C with knowledge. That is to say, he accepts: K Rule One must: assert p only if one knows p.
While Williamson's proposal is one of the most prominent ones, perhaps the most popular one at present, there are a number of live alternatives in the literature, including the justification rule (J Rule, e.g. Douven 2006;Lackey 2007;Kvanvig 2011), the truth rule (T Rule, e.g . Weiner 2005;Whiting 2013) and the belief rule (B Rule, e.g. Bach 2008;Hindriks 2007), which identify C, respectively, with justification, truth and belief.
This paper aims to show that CAA is false: C Rule is not the unique constitutive rule governing assertion. Or, to be more precise, C Rule is not the unique constitutive rule for a wide range of candidates for the identity of C, including all of the live proposals just mentioned. 1 To this effect, we will first defend a necessary condition on what it takes to count as engaging in an activity that is governed by constitutive norms. Then we will argue that, on CAA, assertion does not satisfy this condition and that this means that there is reason to think that CAA is false.

Constitutive rules and conditions of engagement
Williamson distinguishes two questions that one can ask about activities that are governed by constitutive rules. The first is what the rules governing the activity actually are, the second concerns the non-circular necessary and sufficient conditions that people must satisfy to engage in the activity. While Williamson's main concern is with the first of these two questions and, in particular, with mounting a case for K Rule, he does make two points about the second question. First, "constitutive rules do not lay down necessary conditions for performing the constituted act." (Williamson 2000, p. 240) That is to say, one can break a constitutive rule and still continue to engage in 1 We'd like to emphasise that we are not arguing that none of the aforementioned ways of fleshing out C Rule is a rule of assertion. On the contrary, everything we say here is compatible with the thesis that assertion is governed by any of these rules. [That's why we don't engage the literature on the identity of property C at issue in C Rule. For the record, however, we both agree with Williamson that C is knowledge and have defended the corresponding K Rule elsewhere (e.g. Kelp 2013, Forthcoming;Kelp and Simion 2017;Simion 2016a, b)]. The question we take up in this paper concerns specifically the issue of constitutivity and, in particular, whether C Rule is the only constitutive rule governing assertion. It may be worth noting that this issue, unlike the issue of the identity of property C, is not widely discussed in the literature. Notable exceptions are Cappelen (2011), Hindriks (2007, Pagin (2016) and Maitra (2011). We'll return to Maitra's discussion below as her argument is similar to our own. Cappelen, Hindriks and Pagin approach the issue from a different angle, which is why we will set them aside here. the constituted activity. In the case of draughts, for instance, one can cheat without thereby ceasing to play draughts. Williamson even grants that one may break constitutive rules often. Second, "some sensitivity to the difference-in both oneself and others-between conforming to the rule and breaking it presumably is a necessary condition of playing the game, speaking the language, or performing the speech act." (Williamson 2000, p. 240) In the case of draughts, for instance, if one is completely insensitive to the fact that players who move pieces diagonally conform with the rules and players who move them vertically don't, then one won't be playing draughts, even if one happens to move pieces only diagonally. For present purposes, we will grant Williamson both of these claims. 2 That said, it is worth noting that while Williamson does take the above condition to be a necessary condition for engaging in an activity that is governed by constitutive rules, he does not claim that it is also sufficient. It is thus compatible with what Williamson has to say about the conditions for engaging in activities that are governed by constitutive rules that there are further necessary conditions, besides the one he himself countenances. We will argue for one such condition below.
Finally, we'd like to point out that while the issues the two questions touch upon are indeed different, they are not unrelated. To see this consider once more Williamson's proposed condition according to which engaging in an activity governed by a constitutive rule requires some sensitivity to the difference between conforming to a constitutive rule and breaking it. Now consider arbitrary activity, A, and rule, r , such that r is (putatively) constitutive of A. From Williamson's condition it follows that engaging in A requires some sensitivity to the difference between conforming to r and breaking it. This means that, for any A such that it can be shown that one can engage in A even though one is not at all sensitive to the difference between conforming with r and breaking r , r is not constitutive of A after all. In this way, then, the correct answer to the question of what the necessary and sufficient conditions on engaging in activities governed by constitutive rules are may have implications for the correct answer to the question as to what the constitutive rules governing a certain activity are. The issues the two questions raise, whilst different, are thus related.
In what follows, we will consider two arguments that exploit a parallel relation between conditions for engaging in an activity governed by constitutive rules to make a case against CAA. While, as we will argue momentarily, the first one remains ultimately unsuccessful, the second will do the job.

Maitra's argument
The first argument we will consider is due to Maitra (2011), who adduces an argument that can at least be reconstructed as proceeding along the lines sketched above. Here is the crucial condition on engaging in activities that are constituted by rules she proposes: Maitra's Condition If r is a constitutive rule of some activity A, then one cannot violate r flagrantly without ceasing to engage in A. Crucially, according to Maitra, a violation is flagrant "if it is intentional and sufficiently marked" (2011, p. 282).
With Maitra's Condition in play, we can run an argument parallel to the one featuring Williamson's proposed condition above to establish a relation between Maitra's Condition and the issue of which constitutive rules, if any, govern a given activity. Again, consider arbitrary activity, A, and rule, r , such that r is (putatively) constitutive of A. From Maitra's Condition it follows that engaging in A requires not violating r flagrantly. This means that, for any A such that it can be shown that one can engage in A and violate r flagrantly, r is not a constitutive rule governing A. Crucially, it is clearly possible to make assertions that flagrantly violate C Rule, for instance, when one asserts a blatant falsehood that one doesn't believe and doesn't have any reason to believe. In this way, we have an argument from Maitra's Condition to the falsity of the thesis that C Rule is constitutive of assertion. A fortiori, C Rule cannot be the only constitutive rule governing assertion. CAA is bound to be false.
While it will come as no surprise that we are sympathetic to the general strategy of the above argument, we don't think that Maitra's Condition really is a necessary condition for engaging in activities constituted by rules. That is to say, we don't think that engaging in activities that are constituted by rules really does not admit of flagrant violations of these constitutive rules. To see why, consider the case of English once more. It is clear that one may flagrantly violate a constitutive rule of English, without thereby ceasing to speak English. For instance, were we to say "Maitra's argument just don't work", we would have flagrantly violated the rule that requires us to add 's'/'es' to present tense verbs in the third person singular. While we'd be speaking bad English, we would not thereby cease to speak English altogether. Similarly, by intentionally committing an obvious foul, a football player may flagrantly violate the constitutive rule of football that prohibits fouls. However, he doesn't thereby stop playing football. (In fact, the game may not even be stopped as the referee may call an advantage for the fouled team.) Since there is reason to think that Maitra's Condition is not a necessary condition on engaging in activities constituted by rules, the above argument will not go through.
Even so, we want to insist that there are limits to how persistently and systematically one can break the constitutive rules of an activity and still engage in the constituted activity. To see why, suppose you are playing a game of draughts with a friend. It may be that your friend cheats, perhaps even often. But now suppose you are attempting to play a game of draughts with a friend only to find that he persistently and systematically moves the pieces horizontally and vertically rather than diagonally. In this case, your friend is not really playing draughts. Alternatively, suppose you have promised a friend to help him bake Jamie Oliver's famous chocolate cake for a birthday party. It may of course be that your friend deviates from Oliver's recipe, perhaps even significantly. But now suppose that you discover that what he is actually producing is a blend of kiwis, kidneys and marmite, which he subsequently pours into martini glasses. In this case, your friend is not really baking Jamie Oliver's chocolate cake. Similarly, if, in an attempt to play tennis, your friend starts throwing punches until he has knocked his opponent to the ground, he is not really playing tennis. Finally, suppose you wanted to strike up a conversation in English with him. It may be that he breaks the rules of English and perhaps he does so frequently. But now consider a case in which he persistently and systematically utters only strings of the phoneme 'ka'. When you ask him how he is doing he responds: 'Kakaka', when you ask him whether he has gone mad his answer is: 'Kaka kakaka ka', and so on. If he persists in this behaviour too systematically, he is not speaking English.
We take these considerations to motivate the following condition on engaging in activities that are constituted by constitutive rules: Engagement Condition If some activity A is constituted by a set of constitutive rules, R, then one cannot violate too many members of R too systematically without ceasing to engage in A. 3 Two comments by way of clarification: First, we may want to allow for variation in what counts as violating too many members of a set of constitutive rules and what counts as violating them too systematically. To see this, compare the draughts case with the English case. In the draughts case, your friend is not playing even though he violates only one rule, albeit with near maximum systematicity. (Note that maximum systematicity is not required. If your friend were to move the pieces vertically and horizontally nearly all of the time, he'd still not be playing.) In contrast, in the English case, your friend violates many rules with a very high degree of systematicity. Here, we may want to allow that systematically violating a single rule does not mean that one ceases to speak English. If your friend were to systematically fail to add 's'/'es' to present tense verbs in the third person singular, we would want to allow that he still speaks English.
Second, Engagement Condition is plausible even when your friend breaks the rules non-deliberately or otherwise blamelessly, when he tries to follow the rules or when he thinks he is following the rules. To see this, consider the draughts case once more. Suppose your friend is misinformed about the rules of draughts, say because he was told that pieces move horizontally and vertically. When, in this case, he systematically moves the pieces in these ways, he will systematically break the rules of draughts whilst doing so non-deliberately and blamelessly, whilst trying to follow them and thinking that he is following them. Even so, he is not playing draughts. 4 If Engagement Condition is plausible, then so is the following: Engagement Condition' If activity, A, is constituted by only a single constitutive rule, r , and if one violates r with near maximum systematicity, then one does not engage in A. Consider, for instance, a card game, call it 'Ace of Spades' in which the only constitutive rule is that one must continue to turn over cards from a standard deck until one turns over the ace of spades. If you violate this rule with near maximum systematicity, say because you regularly stop turning over cards when and only when you turn over the three of hearts, you are not playing Ace of Spades.
It is easy to see that we can run an argument parallel to the one sketched above to establish a relation between Engagement Condition' and the issue of which constitutive rules, if any, govern a given activity. Again, consider arbitrary activity, A, and rule, r , such that r is (putatively) constitutive of A. From Engagement Condition', it follows that engaging in A requires not breaking r with near maximum systematicity. This means that, for any A such that it can be shown that one can engage in A and break r with near maximum systematicity, r is not a constitutive rule governing A.
In the next two sections, we will make a case that it is possible to violate C Rule with near maximum systematicity for a wide range of proposals concerning the identity of C at issue in C Rule, including all the live ones in the literature mentioned in the 4 But what if one is very good at cheating and systematically breaks the constitutive rules of an activity surreptitiously such that others would treat one as continuing to engage in the relevant activity. Doesn't that look like a counterexample to Engagement Condition? (Thanks to an anonymous referee for raising this issue.) We'd like to make three points by way of response: First, all that Engagement Condition requires is that one doesn't violate too many constitutive rules too systematically. It may thus be that what this amounts to is that one violates nearly all constitutive rules nearly all the time. It's compatible with Engagement Condition that one violates very many constitutive rules very systematically.
Second, very often, it will be well nigh impossible to break nearly all constitutive rules of an activity nearly all the time in a surreptitious manner. Consider the baking case once more. It's hard to see how one could be so surreptitious about mixing kiwis, kidneys and marmite in such a way as to make others think that one is following Jamie Oliver's recipe for chocolate cake.
Third, even when one does actually manage to surreptitiously break too many of the constitutive rules of an activity too systematically, we'd say that one is really fooling others into thinking that one is engaging in the activity, whereas, as a matter of fact, one isn't. Moreover, we'd say that the reason why they continue to treat one as engaging in the activity is (at least in part) that they mistakenly believe that one is conforming with (enough of the) rules. This seems plausible to us in all of the cases described above. When one moves one's draughts pieces only horizontally and vertically/mixes kiwis, kidneys and marmite/throws punches/only utters strings of the phoneme 'ka', one is not playing draughts/baking Jamie Oliver's chocolate cake/playing tennis/speaking English. If, in addition, one somehow manages to be so surreptitious about this that one gets others to think that one is playing draughts/baking Jamie Oliver's chocolate cake/playing tennis/speaking English, then one is simply fooling them into thinking that one is engaging in these activities even though one is not. In any case, this interpretation of what's happening in these cases strikes us as much more plausible than one according to which one does actually engage in them.
introduction. It is now easy to see that if this can be done, CAA cannot be combined with any of the proposals in the target range.

Some cases involving assertions
In what follows, we'd like to consider a couple of cases. Here is the first: Case 1 S 1 has been in causal contact with physical objects long enough for his thoughts to have the same contents as the thoughts of inhabitants of Earth. S 1 is a member of a very small set of unfortunate individuals who, shortly after the contents of their thoughts were fixed, came under the spell of an evil demon, who sees to it that nearly all their beliefs are false.
Consider the following thesis about Case 1: Possible Assertion 1 It is possible for S 1 to assert a wide range of propositions.
(For instance, S 1 may assert that it is raining outside, that there is coffee in his mug, etc. even though S 1 is merely deceived into believing this and, as a matter of fact, it's not raining outside, there is no coffee in his mug, etc.) We take Possible Assertion 1 to be eminently plausible. However, for those in doubt, there is independent reason to think that it is true. After all, S 1 's relevant speech acts may have a number of hallmark features of assertions, including the following: they present their contents as true, they furnish others with a prima facie 5 entitlement to believe their contents, and we will hold S 1 accountable for the truth of their contents. 6 Let us assume, as we may, that S 1 happens to be both an exceptionally sincere and rather chatty person. Of course, since nearly all of S 1 's beliefs are false, this gives us: Systematic Falsity S 1 makes assertions that, with near maximum systematicity, are false.
With these points about the first case in play, we'd now like to move on to the second case. Here goes: Case 2 S 2 is a compulsive liar: S 2 is strongly disposed-perhaps even hard-wiredto assert p only when he believes p to be false.

Now consider the following thesis about Case 2:
Possible Assertion 2 It is possible for S 2 to assert a wide range propositions. (For instance, S 1 may assert that it is raining outside, that there is coffee in his mug, etc., even though he is lying about this: S 1 really believes that it isn't raining outside, that there is no coffee in his mug, etc.) 7 We also take Possible Assertion 2 to be eminently plausible. Those in doubt may note that the considerations adduced in support of Possible Assertion 1 will work here just as well. Let us assume, as we may, that S 2 happens to be not only rather chatty but also an exceptionally reliable cognitive agent who lives in an exceptionally hospitable epistemic environment with the result that nearly all of his beliefs qualify as knowledge. We then get: Systematic Counter-Knowledge S 1 makes assertions that, with near maximum systematicity, are false and run counter to what S 2 knows.

The negative result
We now have motivated a couple of conditions on engaging in activities that are constituted by rules-to wit, Engagement Condition and Engagement Condition'-and a few theses about a couple of cases involving assertions-to wit, Possible Assertion 1 and 2 as well as Systematic Falsity and Systematic Counter-Knowledge. This is all we need for our argument against CAA.
To begin with, recall that, according to CAA, the following is the unique constitutive rule of assertion: C Rule One must: assert p only if p has property C.

Now consider the following condition:
Factivity p has C only if p is true.
Engagement Condition' and Systematic Falsity (alternatively: Systematic Counter-Knowledge) serve to show that CAA is incompatible with any version of C Rule such that C that satisfies Factivity. Here is how: Suppose that CAA is true and that C satisfies Factivity. By Systematic Falsity (alternatively: Systematic Counter-Knowledge), S 1 (S 2 ) makes assertions that, with near maximum systematicity, are false. Since C 7 An anonymous referee suggested to us that one might take this case to be an instance of the kind of case described in fn.4, i.e. as one in which S 2 is fooling others into thinking that he is making assertions, when in fact he isn't. Ultimately, we don't think this move will work. To see why not, we'd like to return to the cases in which it is plausible that the relevant agent fools us into thinking that they are engaging in some activity with constitutive rules. In particular, we'd like to ask you to imagine that we find out that we have been fooled and how. Suppose, for instance, that we discover that our interlocutor only ever uttered strings of the phoneme 'ka', that we mistook this for English and how this could have come to pass. There can be no question that we would now take it that our interlocutor never spoke English in the first place. And the same goes, mutatis mutandis, for the draughts, chocolate cake and tennis cases. What comes to light is the unsurprising fact that our beliefs that these agents were engaging in the relevant activities does not survive unveiling the deception. Now consider the case of S 2 . If we had indeed been deceived into believing that S 2 made assertions, once we find out about what was going on, our beliefs that he did should not survive. However, that's not what we find. On the contrary, it's very plausible that we'd still take S 2 to have made a variety of assertions even after we discover that S 2 is a compulsive liar and why this is so. By the same token, there is reason to think that the case of S 2 is not one in which we are merely fooled into thinking that he is making assertions.
satisfies Factivity, S 1 (S 2 ) violates C Rule with near maximum systematicity. It follows that S 1 (S 2 ) makes assertions that, with near maximum systematicity, violate C Rule.
But now recall the relation between Engagement Condition' and the issue of which constitutive rules, if any, govern a given activity. In particular, recall that for any activity, A, such that it can be shown that one can engage in A and break r with near maximum systematicity, r is not a constitutive rule governing A. Since S 1 (S 2 ) makes assertions that, with near maximum systematicity, violate C Rule, it follows that C Rule cannot be a constitutive rule of assertion for any C that satisfies Factivity. By the same token, CAA will be false on any version of the view on which C Rule satisfies Factivity. This, in turn, means that CAA cannot be combined with either K Rule or T Rule as, on both of these proposals, C satisfies Factivity. Since Williamson's own preferred version of CAA combines CAA with K Rule, it follows that that version of CAA is in trouble.
Given that CAA is incompatible with factive C, we might think that we'd be better off combining CAA with a property C that is non-factive such as justification or belief. Unfortunately, however, the negative result generalises beyond factive C. Consider the following two conditions: Knowledge-Condition If one knows that p, then p has C.
Consistency. If p has C, then notp does not have C.

Engagement Condition' and Systematic Counter-Knowledge serve to show that CAA is incompatible with any C that satisfies Knowledge-Condition and Consistency.
Here is how: Suppose that CAA is true and that C satisfies Knowledge-Condition and Consistency. By Systematic Counter-Knowledge, S 2 makes assertions that, with near maximum systematicity, run counter to what S 2 knows. That is to say, with near maximum systematicity, when S 2 asserts p he knows notp. Since C satisfies Knowledge-Condition, notp has C. 8 Since C satisfies Consistency, p does not have C. In consequence, S 2 violates C Rule with near maximum systematicity. It follows that S 2 makes assertions that with near maximum systematicity, violate C Rule.
And, of course, we can now run an argument parallel to the one that established that CAA cannot be combined with any version of CAA such that C satisfies Factivity to show that CAA cannot be combined with any version of CAA such that C satisfies both Knowledge-Condition and Consistency. Since justification satisfies both, it follows that another main candidate for fleshing out CAA cannot be made to work either.
Finally, it is easy to see that the CAA cannot be combined with B Rule. In fact, Engagement Condition' and Systematic Counter-Knowledge again serve to make this point. To see how, suppose CAA is true and that C is belief by the speaker. By Systematic Counter-Knowledge, S 2 makes assertions that, with near maximum systematicity, run counter to what S 2 knows. That is to say, with near maximum systematicity, when S 2 asserts p he knows notp. But now recall that, ex hypothesi, nearly all of S 2 's beliefs qualify as knowledge. As a result, when S 2 knows that notp, he nearly never believes that p. It follows that with near maximum systematicity, S 2 asserts that p only when he does not believe that p. In consequence, S 2 violates C Rule with near maximum systematicity. Hence, S 2 makes assertions that, with near maximum systematicity violate C Rule. This means that CAA cannot be combined with B Rule either, again for reasons parallel to the ones given above.
It comes to light that CAA is false on all the live proposals for the crucial C Rule in the literature. This means that unless we have been heading down the wrong track in the debate on the identity of C entirely, there is reason to believe that CAA is false. There is no unique constitutive rule of assertion. 9

Objections and replies
Isn't it the case that even if an individual can violate a certain rule governing an activity with near maximum systematicity without thereby ceasing to engage in the activity, the same could not be true of the entire population? For instance, while an individual can systematically move draughts pieces vertically and horizontally without compromising the practice of engaging in the activity of the population, if the entire population started behaving in this way, wouldn't that just mean that the practice of playing draughts is discontinued? Isn't, mutatis mutandis, the same true of the practice of making assertions? And, finally, isn't that the important fact about constitutive rules that vindicates CAA? By way of response, even if we grant that this is one important fact about constitutive rules and one that tallies nicely with CAA, it is certainly not the only important fact about constitutive rules there is to capture. In particular, what the objector develops here is at the very best an important fact about constitutive rules in the sense that it captures a necessary condition on engaging in activities with constitutive rules. It is entirely compatible with this that there are other important facts about constitutive rules, including that Engagement Condition and Engagement Condition' are also necessary conditions on engaging in activities constituted by constitutive rules. As a result, these points do very little to block the above argument against CAA.
But perhaps the thought is not that these considerations rescue CAA but rather that what Williamson is best understood as advancing is not a thesis about the constitutive rules of assertion, but a thesis about the constitutive rules of the practice of making assertions. 10 Moreover, so understood, an argument similar to the above serves to confirm this very thesis. After all, if the practice of assertion were to be constituted by C Rule and C Rule only, we would expect that if an entire population of speakers were to systematically violate C Rule, the practice of assertion would at some point no longer be continued, for reasons similar to the above. And since this is just what we would find, the thesis about the practice of assertion is at any rate confirmed.
As a first observation, we'd like to point out that even if the objector were right in that the practice of making assertions is constituted by C Rule and C Rule only, abandoning CAA as a thesis concerning the constitutive rule of assertion comes at a considerable cost. After all, recall that two attractive features of CAA so understood were that it serves to shed light on the nature and the normativity of assertion. If it is granted that C Rule is not the unique constitutive rule of assertion, the accounts of both nature and normativity of assertion will be lost, even if C Rule is constitutive of the practice of making assertions.
Second, we are not even convinced that CAA is correct when understood as a thesis about the practice of making assertions. Let's grant the objector (i) that practices of engaging in activities can be constituted by rules and (ii) that an important necessary condition on operating such a practice is: Engagement Condition* If a population's practice, P, of engaging in an activity, A, is constituted by a set of constitutive rules, R, and if too many members of the population violate too many members of R too systematically, then the population does not operate P.
If Engagement Condition* is plausible, then so is: Engagement Condition**. If a population's practice, P, of engaging in a rule governed activity, A, is constituted by only a single constitutive rule, r , and if nearly all members of the population violate r with near maximum systematicity, then the population does not operate P.
CAA understood as a thesis about the practice of making assertions and Engagement Condition** do indeed entail: No Practice If too many members of a population of speakers violate C Rule with near maximum systematicity, then the population does not operate a practice of making assertions.
What's not so clear to us is that No Practice is really correct. To see why not, consider: Case 3 φ is a population of agents such that (i) all its members only ever say what they believe to be false, (ii) this is common knowledge and, consequently, (iii) whenever a member of the population says that p, members of the audience will infer and thereupon come to believe that notp. 11 It seems to us that the following is plausible about Case 3: 11 An anonymous referee wondered why we shouldn't say that when a member of the population says ' p' what he really asserts is that notp. After all, if the connection between what we say and what we thereby assert is conventional it seems possible that the community has the convention of assertion that notp by saying ' p'. While we would agree that it is possible that some such community could have the convention of asserting notp by saying ' p', we also believe that it is not necessary. That is to say, we believe that it is also possible for such a community to have the familiar convention of asserting p by saying ' p'. Crucially, this is all we need to get the argument off the ground. After all, the constitutivity claim under consideration is necessarily true if true at all. As a result, all we need to mount a case against it is one possible case in which it doesn't hold.
In fact, there is at least some reason to think that, in the above case, the convention is the familiar one of asserting p by saying ' p'. After all, it is explicitly stated that hearers form beliefs based on these assertions by inferring notp. This is just what we'd expect if by saying ' p' one asserts p here. If, on the other hand, Possible Assertion 3 It is possible for the members of φ to assert a wide range propositions.
Let us assume, as we may, that the members of φ happen to be not only very chatty but also otherwise exceptionally reliable cognitive agents who live in an exceptionally hospitable epistemic environment with the result that nearly all of their beliefs qualify as knowledge. We then get: Systematic Counter-Knowledge* The members of φ make assertions that, with near maximum systematicity, are false and run counter to what they know.
It is easy to see that arguments parallel to the ones given in Sect. 6, with Engagement Condition** in place of Engagement Condition' and Systematic Counter-Knowledge* in place of Systematic Counter-Knowledge, will serve to show that No Practice is false on all live ways of fleshing out C Rule. If so, pace our objector, CAA understood as a thesis about the practice of making assertions is disconfirmed also.
Here is one final objection we'd like to consider. Doesn't Williamson offer an account of constitutive rules according to which constitutive rules are essential to the constituted act in the sense that it "necessarily, the rule governs every performance of the act" (Williamson 2000, p. 239)? And doesn't C Rule come out to be a constitutive rule on this account?
By way of response, note that while Williamson does claim that the above is a necessary condition on constitutive rules, he once again does not claim that it is also sufficient. Note, furthermore, that Williamson will do well not to strengthen this necessary condition into a sufficient condition. After all, moral and practical norms also govern every performance of a given act with necessity. However, we take it that it would be rather implausible to say that moral and practical norms qualify as constitutive rules of say, moves in draughts, utterances in English or assertions. 12 Williamson's necessity claim is thus only plausible if taken to be a necessary condition on constitutive rules. As a result, it is compatible with further necessary conditions on constitutive rules as well as necessary conditions on what it takes to engage in acts constituted by constitutive rules. In particular, it is compatible with Engagement Condition and Engagement Condition'. Since we have seen that these conditions are independently plausible, the prospects of blocking the argument by appeal to the necessity claim are also dim.
Footnote 11 continued the case were one in which members of the community really asserted that notp by saying ' p', we would expect hearers not to form their beliefs by inference. Rather, we'd expect them to respond to the assertions by forming the relevant belief (that not-p) non-inferentially. Finally, we are of course free to describe the case such that the members of the community draw the relevant inferences. 12 In fact, it seems to us that one very plausible way of distinguishing between constitutive rules and other norms that govern acts necessarily, such as moral and practical norms, is that constitutive rules come with conditions on what it takes to engage in the constituted act like the one Williamson mentions and the one we defended above. While constitutive rules are like moral and practical norms in that they are not contingent, they differ from the latter in that one cannot engage in a constituted act unless, for instance, one is sensitive to what counts as conforming to the constitutive rule and breaking it. In contrast, in the case of moral and practical norms, such insensitivity does not prevent one from engaging in the constituted act.

Conclusion
In this paper we have argued that it is possible to systematically break C Rule nearly all the time and yet continue to count as making assertions, for a range of ways of unpacking C, including all the major proposals in the literature. What's more, even the practice of making assertions can continue to exist even when nearly all practitioners systematically break C Rule nearly all of the time. These arguments provide excellent reason to think that neither the speech act nor the practice of assertion is constituted by C Rule and C Rule only, at least not so long as C is fleshed out along anything like the lines that recent literature has suggested. That, however, means that there is excellent reason to believe that CAA is false.