How to Understand Rule-Constituted Kinds *

The paper distinguishes between two conceptions of kinds defined by constitutive rules, the one suggested by Searle, and the one invoked by Williamson to define assertion. Against recent arguments to the contrary by Maitra, Johnson and others, it argues for the superiority of the latter in the first place as an account of games. On this basis, the paper argues that the alleged disanalogies between real games and language games suggested in the literature in fact don’t exist. The paper relies on Rawls’s distinction between types (“blueprints”, as Rawls called them) of practices and institutions defined by constitutive rules, and those among them that are actually in force , and hence are truly normative; it defends along Rawlsian lines that a plurality of norms apply to actual instances of rule-constituted practices, and uses this Rawlsian line to block the examples that Maitra, Johnson and others provide to sustain their case.


Introduction: The Constitutive vs. Regulative Intuitive Distinction
In introducing his influential distinction between constitutive and regulative rules, 1 Searle (1969,33) admits that he is "fairly confident about the distinction, but do[es] not find it easy to 2 clarify it". He goes on to pretheoretically characterize his target in an intuitive way he had already suggested earlier, illustrating it with compelling examples: I need to distinguish between two different kinds of rules or conventions. Some rules regulate antecedently existing forms of behavior. For example, the rules of polite table behavior regulate eating, but eating exists independently of these rules. Some rules, on the other hand, do not merely regulate but create or define new forms of behavior: the rules of chess, for example, do not merely regulate an antecedently existing activity called playing chess; they, as it were, create the possibility of or define that activity. The activity of playing chess is constituted by action in accordance with these rules. Chess has no existence apart from these rules […] Regulative rules regulate activities whose existence is independent of the rules; constitutive rules constitute (and also regulate) forms of activity whose existence is logically dependent on the rules (Searle 1964, 55) Searle (1965, mentions football instead of chess as illustration of activities defined by constitutive rules -which shows that he doesn't see any relevant difference between these games, against some suggestions (Kaluziński 2018a, §4). As Lorini and Żełaniec (2018, 11) point out, the connection that Searle makes with Kant through the terms he uses is rather dubious; but, more appropriately, he goes on to ascribe it to Rawls (1955) in a footnote. Lorini and Żełaniec also show that the very same intuitive distinction between rules that "regulate antecedently existing forms of behavior" and rules that "do not merely regulate but create or define new forms of behavior", with strikingly similar examples and terminology, had been made in the 1920s by a Polish legal scholar, Czesław Znamierowski; and Adolf Reinach had also articulated it a decade earlier, cf. Reinach (1913), Smith and Żełaniec (2018). 2 Rawls in fact distinguishes between two "concepts" of rules (the summary and the practice concept), but, although I will not argue here for hermeneutic issues in any detail, like Searle he 3 was also making an ontological distinction. 3 This is certainly the case when it comes to Searle and Reinach (Smith and Żełaniec 2018). On the view that Searle (and Rawls and others before him) want to promote, games are a distinctive sort of entity: rule-constituted kinds, or types; illocutionary types like assertions or promises are further examples of the same sort, as Midgley (1959), Austin (1962) and Alston (1964) had also contended.
Following earlier discussions, here I will use 'formalism' to refer to "the view that games (and sports to the extent that sports are games of physical skill) can be defined primarily by reference to the idea of constitutive rules and goals or obstacles designated by the rules themselves, which are unintelligible apart from them", Simon (2000, 2). 4 Formalism is thus the view that some rules in games -and illocutionary types if the language games simile stands -are constitutive and not merely regulative; i.e., that they provide the essence, nature or "real" definition of such kinds.
Formalism thus contends that practices are "natural kinds", in the contemporary sense: they have "real definitions". 5 Here 'natural' is not used in opposition to 'social', but rather to refer to properties and kinds in Lewis's (1983) "sparse" (as opposed to "abundant") sense. In fact, the account I'll suggest for illocutionary types like assertion and games takes them to be "social constructs", definable by social rules. 6 "Natural" properties and kinds are those that play substantive explanatory roles, and hence have a "hidden nature" which only reveals itself after theorizing. This might be philosophical, armchair-like, "a priori" -as Reinach (1913) wanted.
But it must be substantive -hence prima facie exposed to Moorean "open-question"-like objections -7 and unifiable with empirical theorizing.
Anti-formalism, in contrast, rejects that games have a rule-constituted essence. This might be predicated on the Wittgensteinian aversion to definitions that Suits (1978, 21) disparages. 8 This is not compelling, however; kinds might not have definitions in terms of intrinsic properties, but they might have perfectly fitting and explanatory relational ones (Bach 2016). A more plausible version of anti-formalism doesn't deny that games and speech acts have definitions, but claims 4 instead that the ones they have are (as in the case of 'jade') not deeply explanatory; perhaps they only have cluster or historical definitions that essentially appeal to their manifest, superficial or criterial properties, like those that have been claimed for biological and social kinds, and those that should be ascribed to literary genres or institutions like Analytic Philosophy (García-Carpintero 2011, 2021b. I'll come back in §3 to this, offering a rapprochement of sorts.
The truth of formalism would thus vindicate the constitutive-regulative distinction that Searle was "fairly confident about", in this way: if formalism is true, then the intuitive distinction that Reinach, Rawls, Searle et al. gestured at is instantiated by actually enacted practices that impose their constitutive obligations on rational beings. Such a vindication of the intuitive distinction will play a central role in my arguments below. The distinction that formalism aims thus to vindicate is intuitive, pre-theoretical. We need philosophical theory to properly articulate it, and, as it happens, there are two very different ways of theoretically understanding constitutive rules, and hence formalism. 9 My argument will crucially rely on the claim that only one really vindicates the intuitive constitutive/regulative distinction.
After years in which expressivist, psychologistic views of speech acts promoted by Grice (1957) and Strawson (1964) dominated the philosophical scene, Williamson (1996) reinstated to a prominent position the rule-constitution view, discussing in particular the case of assertion.
However, as Maitra (2011, 282), McCamon (2014, and Johnson (2018, 55) complain (echoing earlier objections by Ziff (1960) and Rosenberg (1974)), Williamson's understanding of rule-constitution crucially differs from what they take to operate in the case of games, on the basis of Searle's discussion. Under Searle's influence, Jankovic (2018, 376, fn. 11) explains that "[i]t is a rule of chess that a pawn moves a certain way, and one is not playing chess if one is not acting in accord with this rule"; similarly, Ludwig (2017, 102) offers a "deflationary" definition of constitutive rules (deflationary in that it uses only psychological, non-normative notions), on which they are "rules the intentional following of which is constitutive of the type of activity that they govern". On these views, when what I'll call the "defining condition" invoked in the rule fails to obtain -the pawn (intentionally) moves in ways not permitted by the rule -we have an Austinian misfire (Austin 1962, 167): the activity is no longer a chess game. This is explicitly not so on Williamson's view: it would make the language-games view clearly wrongheaded.
Williamson takes knowing p to figure in the defining condition for a "flat-out" assertion of p; but he explicitly allows for the (intentional) violation of such a norm to be an Austinian abuse (Austin 1962, 168) -a case in which one does assert, albeit making a mistake in doing so.
The Jankovic-Ludwig understanding of rule-constitution is clearly suggested by Searle, if not endorsed; for reasons given below, I'll call it Descriptive Formalism, FD. It was promoted for games by Suits (1967;1978, 39, 52), and assumed in their criticisms by anti-formalists on sports like D'Agostino (1981, 7), Lehman (1981, 41), and Morgan (1987, 1). In this paper I have three main goals. First, I want to show that Williamson's is just another version of formalism, as characterized above; I'll call it Normative Formalism, FN. It is one that D'Agostino, Lehman and Morgan had actually considered, describing it as "Platonist". They use this label not because FN characterizes abstract entities, which is common to the two views; but rather because it primarily characterizes an ideal for games -what a good game should be. FN thus characterizes norm kinds in Wolterstorff's (1980, 56) sense, see below. 10 The only difference between the two lies in that, while FD assumes a non-normative defining condition, defining conditions are instead normative on FN: the relevant rule-constituted types are hence normative kinds.
It seems clear to me that early theorists like Rawls (1955) and Black (1962, 123-5) had FN in mind rather than FD; I'll indicate why below, §4. My second goal is to show that, essentially for their reasons, FN is a much more plausible view than the one advocated by Midgley and Suits and suggested by Searle, FD. FN has better chances of vindicating the intuitive distinction between constitutive and regulative rules than FD; besides, unlike FD, FN is not refuted, but in fact upheld by the (in my view entirely compelling) anti-formalist critical considerations, rehearsed below.
6 My third goal is to explain how FN can account for Austinian misfires -the existence of which is, to my knowledge, the only prima facie compelling motivation for FD to be found in the current literature. The next section aims to accomplish the two first goals; §3 tackles the third.

Two Varieties of Formalism
On Searle's (1969, 34) intuitive characterization of the distinction, regulative rules "regulate a pre-existing activity, an activity whose existence is logically independent of the rules", while constitutive rules "create the possibility of new forms of behavior" (ibid., 35). As I'll presently show, the distinction is only apt if made relative to a specific practice. To vindicate it we should thus find a specific existing practice to which it applies. (1) below is meant to illustrate the regulative, (2) the constitutive, for the same actual game, chess. I use imperative versions as primary, for reasons that will become clear momentarily, but also the more malleable declarative modal formulation I take them to illocutionarily entail (fn. 1): (1) Press the clock with the same hand with which you made your move! \ One must (press the clock with the same hand with which one made one's move) 11 (2) Castle only if the castling king is not in check! \ One must (castle only if the castling king is not in check) Constitutive rules, Searle says, "often have the form: X counts as Y in context C" (35); in a more recent piece he still sticks to this grammatical elucidation: "[i]t is […] natural to think of these rules as having characteristically different syntactic forms. The regulative typically takes the form of an imperative, "Drive on the right!", for example; the constitutive rules, not so obviously but I think nonetheless apparently, take the form "X counts as Y" or "X counts as Y in context C", Searle (2018, 52). (Note the hedges, 'often', 'typically'.) (2) thus becomes (3):

7
(3) x counts as castling in chess only if the castling king is not in check when x is performed This strongly suggests the distinctive tenet of FD, to wit, that the only 'must' in constitutive rules is not really prescriptive, but definitional; it is that of logical or conceptual necessity. Kinds defined by constitutive rules don't differ on this view from 'water', on the standard Kripke-Putnam line. We thus obtain the following application to our case of FD: (4) x isdf castling in chess only if the castling king is not in check when x is performed This is of course only a partial definition; other conditions should be added to obtain a full one: see rule 3.8 in the FIDE Laws of Chess. 12 In accordance with Jankovic's and Ludwig's accounts, when the rule is (intentionally) broken and the defining condition in (4) fails to obtain, the activity doesn't occur -the performance is an Austinian misfire, not an abuse. Williamson (1996) offers an account of assertion in terms of constitutive rules, taking games as models. He hypothesizes (for abductive inquiry) that a single CR-shaped norm defines it, in which C stands for a suitable property of the expressed proposition: (CR) One must (assert p only if p has C) However, in explicitly drawn contrast to FD, Williamson insists that the 'must' in (CR) is genuinely prescriptive: "Constitutive rules do not lay down necessary conditions for performing the constituted act. When one breaks a rule of a game, one does not thereby cease to be playing that game" (1996,240). Assuming FD, philosophers hence object that this view does not really assimilate speech acts to games (Johnson 2018, 55); norms like (CR) don't have the proper Searlian form to be constitutive norms (Maitra 2011, 282). 13 In my experience, Maitra's is the crucial consideration that moves defenders of FD: if a norm is expressed in the imperative, that already makes it "regulative"; for a rule to be constitutive, it must be in the "count as" form.
However, as has been pointed out in the literature, this syntactical characterization of the distinction is misguided, and it would thwart any vindication of the constitutive-regulative 8 distinction. The "count as" account is a misguided attempt at capturing the correct point that constitutive rules provide real definitions for rule-constituted kinds. First, as Lewis (1979, 344) indicates and (2) illustrates, straightforward imperatives might well be constitutive rules in the pretheoretical sense (Ransdell 1971, 390-2;Glüer & Pagin 1999, 220;Morin 2011, 190).
Second, little ingenuity is required to turn any imperative into explicit definitional locutions (Black 1962, 123-4;D'Agostino 1981, 12;Glüer & Pagin 1999, 217;Goldberg 2015, 22): 14 Rules of the FN kind only differ from those of the FD sort in having truly normative, deontic conditions in their definiens, i.e., in their defining conditions. They thus allow for Austinian abuses, in addition to misfires; or better require them, as Williamson points out: "The rule unconditionally forbids this combination: one asserts p when p lacks C. The combination is possible, otherwise it would be pointless to forbid it" (ibid., 254). But this is consistent with having the status of truly providing the constitutive nature of kinds, and hence with their character of constitutive norms, "creating the possibility of" new behavior. This is thus still formalism: it espouses the distinction between constitutive and regulative norms, and grants that the former provide the nature or essence of distinctive kinds. 15 It is the version disparagingly qualified as Platonist by the earlier critics who pointed out the obvious failures of FD (D'Agostino 1981, 9;Morgan 1987, 2), as said because it primarily characterizes an ideal for games -what a good game should be. Games are on this view norm kinds in Wolterstorff's (1980, 56) sense, kinds "such that it is possible for them to have properly formed and also possible for them to have improperly formed examples"; their defining conditions are normative 9 in the kind (ibid., 57): no properly formed example can lack it. 16 On the FN variety of formalism, the partial definition for castling in (4) should be replaced by (7): x isdf castling in chess only if it is not allowed if the castling king is under check 17 What are those "obvious" failures of FD? It has the unacceptable consequence that cheaters, tactical breakers of constitutive rules, or inept players are not playing the relevant games (D'Agostino (1981, 9); Lehman (1981, 42); Williamson (1996, 240); Rescorla (2009, 101); Kreider (2011, 56); Ridge (2017, 7); Fricker (2017, 407)). Lehman mentions the case of a very prominent baseball player, the pitcher Gaylord Perry, who is in the baseball Hall of Fame even though it is generally accepted that throughout his career he threw spitballs -pitches that are illegal according to the rules of baseball, thrown after applying some foreign substance to the ball, causing it to do unpredictable things. The FD account would entail that Perry never pitched in the relevant games, and nor, in consequence, did his teammates either.
Chess is usually mentioned as a game that, unlike football or basketball, doesn't allow for any rule violations, and hence fits the FD account well (Kaluziński 2018a, §4). But this is far from being the case. Article 7 of the FIDE Laws, on "irregularities" (7.1 b) reads: "If during a game it is found that the chessboard has been placed contrary to Article 2.1, the game continues but the position reached must be transferred to a correctly placed chessboard"; FD has the consequence that this would not have been a chess match in the first place. According to 7.4 b, a player loses the game (which therefore is supposed to have taken place!) after three violations of the rules.
Even more outrightly, article 11B of the USRC says that if "it is found that an illegal move was made prior to each player's last ten moves, the illegal move shall stand and the game shall continue"; the same applies, according to 11A, if an illegal move during the last ten moves is found, but "the position cannot be reinstated" to how it was immediately before. Moreover, the rules for castling in both sets of regulations fit (7) instead of (4); what the rules say is that the move is "illegal" or "prevented" in such conditions. Conte (1988, 253) acknowledges this, providing examples of constitutive rules that fit (7), which he calls 'deontic'; but (assuming I guess the misguided syntactic characterization of the constitutive-regulative distinction) he distinguishes rules like the one defining 'checkmate', which he calls 'ontic' or 'adeontic', for which he just provides a descriptive condition fitting (4): "A checkmate is made when the king is attacked in such a way that no move will leave it unattacked". But in fact article 1.2 of the FIDE Laws has legal move instead of move; which is better than Conte's proposal, on account of the possibility of checkmates that remain overlooked through 10 or more moves, see the previously mentioned article 11B of the USRC rules. The normative characterization is also better suited to acknowledge the point made by Suits' spoilsport: "Checkmate is the condition when you have immobilized my king. But you have not immobilized my king. Behold; I am moving it about in the air!" (Suits 1978, 59). 18 Supporters of FD might try to pursue Pearson's (1973) strategy, redefining cheating as occurring "when one has contracted to participate in one sort of activity, and then deliberately engages in another sort of activity" (ibid., 116). But I fail to see the need to engage in such "conceptual engineering", and I don't know how far it can sensibly be taken: I don't see any reason to believe that cheaters like Gaylord Perry deliberately want to engage in another sort of activity. One can try instead a form of "legal positivism/realism", claiming that a move in a game is illegal if and only if a referee decrees it so. 19 But this is just another unmotivated form of engineering. For one thing, it leaves out games played without a referee (Kaluziński 2018, 119).
And it assumes a questionable view of what referees do, as Russell (1999)  force. This explains why referees make mistakes in their rule-regulated decisions, validating illegal moves, and may have their illegal decisions overturned by overruling committees. It also explains why changes are made to provide referees with better technological means to enforce the rules. Thus, even if we acknowledge the rule-regulated decisions of referees, we still have cases of games in which the rules are broken: an illegal move occurred, overlooked and thus validated by the referee; or a legal move was wrongly counted as illegal by the referee. Pollock's (1982, ch. 10) discussion is close to mine in two crucial respects. First, like me, he considers FD and FN as just two different varieties of formalism, as understood above (Pollock 1982, 211-12), the former simply being the "orthodox" one assumed by early critics of the language-game analogy like Ziff (1960) and Rosenberg (1974). Second, like me (see below, §3), he distinguishes merely "abstract" rule-constituted kinds from those that are in force, and he takes the explanation of what it is for them to be in force ('participation' in the practice, in his terms) to be of the utmost importance (ibid., 211). Now, Pollock rejects the orthodox view as predicated on "a simplistic account of the constitutive rules of an institution" (ibid., 212), on the basis of the considerations about cheating, inept playing and intentional violations just discussed.
However, like Conte (1988) he still feels compelled -I take it -by some remnants of the "orthodox view" FD to distinguish two different sorts of equally constitutive rules: those that are truly "definitional" and cannot be broken, and those that can (ibid., 212-3).
Kretchmar (2015) and Kaluziński (2018aKaluziński ( , 2018b) make similar suggestions. 20 Thus, among the constitutive rules that Kaluziński takes to define a game, he distinguishes between two groups, in terms of their centrality: "There is a 'hard core' of the game, which is a very small number of rules that cannot be violated and a much larger set of rules that could be violated without any serious consequences. Violation of the rules of the former type, i.e. those rules that form the hard core of the game, entails termination of the game" (Kaluziński 2018b, 116;cp. Kretchmar 2015, 18). He goes on to provide examples of the former: "It appears to me that it is essential in such a game as football that there be a goal and that we be trying to put the ball into it by using our legs 12 or head; in the case of basketball we are trying to put the ball into the basket by using our hands" (ibid.). However, if he means by this to offer the actual rules of soccer regarding the use of the hands as an illustration of "hard core" rules, it is manifest that they are in fact violated; just remember the "Hand of God" at the 1986 World Cup. Pollock had a similar example, which is subject to the same objection: "What would it mean, for example to talk about breaking the rule that carrying the football across the goal line counts as making a touchdown …?" But another famous soccer case in a World Cup final, England's 1966 "ghost goal", refutes the example, for what corresponds to touchdowns there (goals). Kaluziński (2018a, §4) in fact offers a more nuanced view, on which central rules have only "game-termination potential"; by violating them "we risk" game termination. But there is no significant difference in this respect between the rules that he counts as "central" and those he counts as "peripheral"; aimlessly kicking the ball around when it reaches you clearly has "gametermination potential". There is only the difference of degree that my own account of misfires in the next section (i.e., "game-termination") provides. But all of them have "game-termination potential", in that all allow for generating misfires, if systematically, intentionally and manifestly violated the way spoilsports do, for reasons I provide in §3. Note also that "central" and "peripheral" rules must be equally constitutive, for the very good reason that otherwise we don't get a true definition of the game, as Kaluziński acknowledges, §4; cp. also Pollock ibid., I agree that there is a difference in the significance of the rules, as Searle (1969, 34) also points out; I also agree that it matters, in that this is what explains why games likes soccer and chess intuitively keep their identity throughout changes in their defining rules. But this has nothing to do with the "true constitutivity" of inviolability; I will explain it in §3.
Pollock and Kaluziński are right that some flagrant violations of the rules will not be Austinian abuses, but misfires -no longer game-playing: "If some football player started passing the ball to his or her teammates, and not with his or her foot but with his/her hands, he or she would, of 13 course, terminate playing football, i.e. it would just not be a football match anymore" (Kaluziński 2018a, §4). Searlian formalists provide similar examples: "If, for example, a player came onto the field wielding a racquet, she is not playing soccer, even if the context is casual", Johnson (2018, 54); "Derek refuses to leave the batter's box. He admits that he has already earned three strikes, but insists that the game would be more enjoyable for the spectators if he were allowed an extra strike […] if Derek is sufficiently recalcitrant about being allowed the fourth strike, […] he has stopped playing baseball altogether", Maitra (2011, 281). Agents in all these cases act like Suits's spoilsport: they ruin the game, causing "game-termination".

Maitra (2011, 281) offers
Derek's case as one of what she calls "flagrant" violations of constitutive rules, which she considers misfire-inducing; but she accepts inept or otherwise unintentional violations as mere abuses. This suggests that she is thinking along the lines of Ludwig's (2017, 102) "minimal" characterization of constitutive rules, quoted above: "rules the intentional following of which is constitutive of the type of activity that they govern". 22 As I have contended above, such a view entails unmotivated conceptual engineering, as (flagrant) tactical rule-violations illustrate. 23 I thus conclude that FD is wrong as an account of the intuitive constitutive-regulative distinction. It is unmotivated, because Searle's syntactic criterion to trace the distinction, which is what appears to support it, is utterly inadequate; and it would induce unmotivated conceptual engineering, by counting as misfires many cases that intuitively are not. 24 FN offers much better prospects of vindicating the intuitive constitutive-regulative distinction. However, I grant that there are misfires in games, of the kind illustrated above. How does FN account for them? This is the topic of the final section.

Blueprints for Rule-Constituted Types, Kinds in Force, and Misfires
In this section I'll rely on Rawls's (1955, 26 fn.) distinction between blueprint kinds defined by constitutive rules, and those that are in force (Glüer & Pagin 1999, 221) in order to introduce a crucial missing piece of the account of rule-constituted kinds so far. There must be some account of why the rule-constituted kind has come to be in force or accepted. This will allow us to appreciate an ambiguity in 'game' (a form of polysemy, actually, over and above the familiar type/token one). It will offer a rapprochement between formalism and anti-formalism: in a (primary) sense, games are defined by constitutive rules. In another sense, games are defined by causal-historical relations. Last but not least, it will also help us to account for misfires.
Many kinds defined by constitutive norms are not in force, and hence are not really normative: they don't give anybody a reason to act. 25 Think of variations we can concoct on the rules that define actual games, and the "possible" games they define (I use scare quotes because, as abstract kinds, they are actual). They define putative, candidate kinds; but, if they are not in force, nobody is obligated by them. They don't give anybody a reason to act, and, in that way, they are not normative. 26 What would make such putative rule-constituted kinds "actual" in a given community, practices whose constitutive norms players are bound by?
What this requires is the collective acceptance that Searle (1995) discusses in more recent work, or something corresponding to Hart's (1961, 51-61) rules of recognition for legal codes.
As García-Carpintero (2019) explains, this might come to a convention or agreement; more in general, it is effected by social norms (cf. Bicchieri 2006ch.1, Southwood 2019. 27 There will be some related teleology, some "coordination problems" (Lewis 1969) or goals more in general that are to be achieved by enforcing the norms (Graham 2019). 28 For the case of games, this has been discussed under the topic of the game "ethos", "the purpose of the activity, which can guide both the selection of rules and behavior outside the rules" (Nguyen 15 2017, 11) -which anti-formalists of different denominations (D'Agostino 1981, Lehman 1981, Morgan 1987§5, 2004 invoke in offering an alternative account, and formalists upholding FD have also aimed to accommodate (Kretchmar 2001(Kretchmar , 2015. FN offers the resources to incorporate the insights behind the appeal to the ethos of games without abandoning the intuitive distinction between constitutive and regulative rules -in fact vindicating it. For these purposes, I'll rely on Suits's deservedly influential account of games, on which their constitutive rules are enforced to enable players to perform a "voluntary attempt to overcome unnecessary obstacles" (Suits 1978, 55). 29 As Russell (1999)  context that allows for the realization of those obstacles and the related excellences (the "lusory means") that are available to overcome them" (Russell 1999, 35). Suits assumes FD, but there is no reason why advocates of FN cannot adopt his otherwise compelling view. On the resulting account, games (and speech acts when modeled on them) are social artifacts of a constitutively normative kind (Thomasson 2014), serving the goals that explain why they are in force. 30 As Simon (2000) notes, a version of formalism that incorporates this functional account has the resources to explain why the rules of games are modified on the basis of reasons. Although on the present proposal this, in a primary sense of 'game', involves replacing one for another (Williamson 1996, 239), the resulting view also has the resources to explain our sense of continuity, on the basis of something more than sheer causal-historical relations. After the introduction of VAR technology to improve on the means to make sure that soccer games fit their previous constitutive rules, distinctive "lusory means" they provide (in contrast with those of other sports, like basketball, handball, or rugby) are still preserved. It is along these lines that I envisage a proper elaboration of Searle's (1969, 34) idea (shared by others, as indicated above) that some constitutive rules have a more "central" role than others: these are the ones that account for their specific, distinctive "lusory means", preserved across modifications such as those introduced in soccer over the years.
This offers a rapprochement of sorts between formalism and anti-formalism, the latter understood as the view that games have only relational essences. Soccer understood as a historical entity (including perhaps a stage when it was brought to England by Germanic settlers in the fifth to seventh centuries and continuing till the VAR-improved game of nowadays) is such a historical kind. However, on the present proposal, to properly characterize it we must think of each of its stages as a game defined by a specific set of constitutive rules; to that extent, anti-formalism is rejected. 'Game' turns out to be polysemous. It primarily refers to institutions defined by constitutive rules that have come to be enforced along the lines just outlined; but it can also refer to historically related classes of such institutions, sharing a distinctive cluster of their constitutive rules -distinctive when it comes to the "lusory means" they afford. There is in addition the more standard type/token polysemy applying to both sorts of kinds. If the games analogy works, the same polysemy affects 'language', 'word' and so on. 31 There has been ample discussion in the sports literature on the nature of the social norms that, along the suggested lines, explain why rules definings rule-constituted kinds are in force, whether they are moral, prudential, or conventional (Simon 2000, Morgan 2004, Russell 2004, Ciomaga 2013. 32 In his own discussion of this issue, Rawls (1955, 24) had famously advocated rule-utilitarianism, to provide a justification for why the constitutive norms for punishment and promising are in place. But perhaps the sort of contractualism advanced by Pearson (1973) does a good job instead in the case of sports; and perhaps, as some authors have argued, we should just be pluralists. For present purposes we don't need to go any further into this. 33 As a matter of fact, on the present proposal we must be normative pluralists, committed to norms with different sources. As Williamson (1996, 240) points out, the normativity of constitutive rules is sui generis and pro tanto; in any particular case, it might well be all things considered undone by norms with other sources, prudential, moral, or what have you. Antiformalists will wonder, why do we need constitutive norms to account for the normative features of games, when in any case we need to assume in the full account norms with other sources (the "ethos" of games)? 34 My reply (which of course I cannot properly develop here) would be what I take to be Rawls's (1955, 16, 26): in any particular case, those other normative sources might recommend actions that breach the rule, and might well overrule it, all things considered; but there is no question that the action is prima facie wrong. 35 The previous discussion concerns the issue what makes norms defining a normative kind (a "possible" game) to be in force (in a community). Assuming such an account, there is still a related issue about tokens of that type. 36 Given that rules defining a norm-constituted kind are in force in a community, we still need to explain what makes it the case that an instance of it occurs, so that the relevant agents become thereby beholden to its defining norms -see Suits' (1978, 58-9) distinction between games as institutions (kinds) and their putative instances, which he uses to account for triflers and spoilsports along the lines suggested below. Additional norms apply here, including "preparatory" or "conceptual" norms (Williamson 1996, 238, 245). Agents must have the proper intentions (Glüer & Pagin 1999, 212), they must not be under duress, serious deception, and so on. I agree with Kreider (2011, 61) that the (intentional) commitment to being answerable to the constitutive rules is both necessary and sufficient for game-playing. 37 My suggestion is that spoilsports, if rational, fail to have the required commitments. 38 I appeal here to a plausible cognitive rational requirement on intentions, to the effect that one's beliefs constrain the intentions one might have, if rational. A plausible version should allow that the basketball player who shoots from behind halfcourt just before time expires does it rationally. On a view I like, one rationally intends to F in doing G just in case one believes that G makes it more probable than it otherwise would be for F to come about (Sinhababu 2013, 681). 39 For rational players of games to become beholden to the constitutive rules of the game they play, what they do must make it more probable than it would otherwise be to achieve the goals explaining the enforcement of such rules, the function of the game. Cheaters (and Suits's "triflers" who do not aim to win, like trainers who aim to motivate their trainees by allowing them to win) lack those goals: they don't mean to prove their excellence by truly overcoming the obstacles imposed by the rules. Like professional players, they have ulterior motives; unlike theirs, cheaters' and triflers' ulterior motives are incompatible with the aim of properly achieving the values of the game. But such ulterior motives are still compatible with rationally having the intention of being answerable to the norms and with being committed to obeying them. Their behavior doesn't depart from that of the most straightforwardly honest players, who may nonetheless break the rules, and fail to win. This is obviously the case when it comes to tactical breakers of rules, no matter how flagrant, and inept but nonetheless committed players. But it clearly fails in the case of spoilsports: their behavior is incompatible with their rationally intending to be committed to abiding by the norms that define the game, so as to achieve the ends that this is supposed to serve. This is ultimately why -I suggest -their performances are misfires. 40 Far from this being only accounted for by FD -which we have very good reasons to reject anyway -it is easily explained by a general constraint on rational action, assuming FN.

Conclusion
In this paper I have first argued that the truly normative view of constitutive rules promoted by Williamson (1996) is still a version of formalism, the view that the intuitive distinction between constitutive and regulative rules tracks a really instantiated important ontological category -that of the social construct. It applies to language games exactly in the same way as it does to games; and it does a much better job in explaining this than the Searle-inspired view that many philosophers currently take for granted. Williamson's paper, however, overlooks a crucial aspect of such social constructs, to wit, that they must be in force. I have indicated how the kinds, and then their instances, come to be so in the case of games, and how we can explain on this basis the existence of misfires for rule-constituted kinds, from the perspective of such a truly normative version of formalism. This disposes of the only compelling argument in support of the Searlian version of formalism -cases in which the defining rules are broken in ways intuitively incompatible with the rule-constituted kind being instantiated.  41 In addition to Rawls (1955), which inspired it, the account I have offered is also intimated in the three pages that Black (1962) devotes to these matters: "To say that chess is constituted by the rules of chess is to say that a man who failed to heed the rules would not count as playing the game" (ibid., 123), he says, and he goes on to point out that heeding the rules is compatible with not observing them. I thus take it that "heeding" the rules is being answerable to them: spoilsports fail to "heed" the rules, unlike cheaters, triflers or inept players. Black worries that the constitutive rules account might be "superficial" (ibid., 124), because any set of rules might be used to define a rule-constituted kind -a mere blueprint, on my account. He sensibly goes on to suggest that we might deal with this by taking further into consideration the "external aims" or "interests" that explain why people enforce rules (ibid., 124-5) -i.e., their being in force. D'Agostino (1981) notes Black's more nuanced version of formalism, but objects that it is "ad hoc and unmotivated by anything more systematic than his quite correct intuitions about games" (ibid., 17). I hope that the previous pages have done enough to answer this criticism. and Wojtek Żełaniec for helpful discussion, and to Michael Maudsley for his grammatical revision.
1 I'll use 'rule' and 'norm' interchangeably. As I use these terms, rules are just what "flat-out" imperatives -typically conditional ones: do Q! (if P) -signify, to echo Williamson's (1996, 246) usage for the case of assertion: the specific force that is indicated in default, literal uses of imperative phrases, cf. García-Carpintero (2021a). "Flat-out" directives are those uttered by someone presumed to have the required authority to make a command, as when I say 'Eat!' to my daughter, and in contrast with 'Take it!' said to give advice, 'Come in' to give permission or 'Keep well!' to express good will. Against recent theorizing (Hanks 2015), I think of what the schematic P and Q stand for above as force-neutral contents, which I take to be just properties of verifying conditions or situations (Richard 2013). Kaufman (2012) argues that a directive that p is synonymous with an assertion that the addressee should/must make it the case that p. On standard Kratzerian contextualist modal semantics, the obligation is conditional on implicit or explicit features that select accessible worlds and order them. This is implausible (Charlow 2018, 82;Roberts 2018, 331); but I do take directives to entail on illocutionary grounds Kaufman's assertoric counterparts (Charlow 2014), and I'll avail myself of this throughout the paper. There are important distinctions to be made among rules or prescriptions in this wide sense (objective vs subjective, general vs particular, cp. Brennan et al. 2013; see below, §3. 2 Conte (1988, 251-2) provides a fuller history of the distinction.
3 In brief, my reasons are these. Rules in the "practice" sense define practices, says Rawls (1955,25). This is a "technical" notion for a normative category, "any form of activity specified by a system of rules which defines offices, roles, moves, penalties, defenses, and so on, and which gives the activity its structure", like "games and rituals, trials and parliaments", ibid., 3.
Practices are actually instantiated kinds: "Blue-prints for a practice do not make a practice. That there is a practice entails that there are instances of people having been engaged and now being engaged in it", ibid., 26. Commitment to real, actually instantiated normative kinds fits Rawls's moral realism at the time (Russell 2004, 144).
4 Similar characterizations can be found in the literature: according to formalism, "games are a product of their constitutive rules … these rules jointly create and define the game" (Kretchmar 2015, 11); "the essential nature of a game is its rule-set and … proper play involves obeying the rules" (Nguyen 2017, 9). Discussing the specific case of sports, Devine & Lopez Frias (2020, §2.1) characterize instead formalism as the view that a game is "constituted solely by written rules … just the set of written rules that govern it", my emphasis. But this only identifies a straw man who, in Rawls' terms above, fn. 3, identifies games with blueprints for games. It doesn't even fit the arch-formalist Suits (1978, 54-5), for a central element in his characterization is that players have the "lusory attitude"; this is his very influential rendering of what anti-formalists call the "ethos" of games -in my own account below, §3, the practical grounds for the enforcement, or acceptance, of specific kinds defined by constitutive rules.
5 Recent discussion of these issues mostly stems from the deservedly influential work of Kit norms on the "summary" conception -which, as said, is just his term for regulative rules. But given that other colleagues somehow agree with the referee, I replaced them with the one in the text, suggested by Iñigo Valero, cf. also Reiland 2020, 145. It has the problem that it is actually FIDE rule 6.2.3. I think it can be considered regulative, because intuitively the same game would be played if a bluetooth device activated the clock when the player makes the move; and it doesn't apply to internet chess, which again intuitively is the same game. It may well be a borderline case of the regulative vs. constitutive distinction, which I grant is indeterminate as many other nonetheless real ones, e.g. male vs. female. If the reader has doubts, however, please substitute instead the strategic advice cases, or (closer to Searle's examples) a politeness rule of chess, say, Shake your opponent's hand before the match! 12 As a matter of fact, as Searle (1969, 36) points out, only the whole set of rules will do, see below; a proper definition could be obtained from them by Ramseyfication (Lewis 1970).
32 13 Hindriks (2009, 272), Hindriks & Guala (2014, 472), Guala & Hindriks (2015, 188-9), Guala (2016, 58-9), Marsili (2019, §2), McCamon (2014, 138), and Reiland (2020, 142, fn. 9) all assume the linguistic characterization of the distinction in their discussions -to which I am otherwise sympathetic, see fn. 41. Our disagreement is this: they assume a (flawed) theoretical account of the constitutive vs. regulative distinction (Searle's "count as" account of constitutive rules); hence, by rejecting it as one should, they also wrongly reject the significance of the distinction. I assume instead a pretheoretical account in terms of exemplars and an intuitive gloss, and then I offer a different theoretical proposal, FN, which (I claim) vindicates it. The full package I offer -kinds defined by constitutive rules, enforced by social norms -is similar to theirs, so in that respect we are fundamentally in agreement. But our disagreement is not merely terminological. First, their inferential path is methodologically flawed; leaving aside Searle's misguided characterization, the constitutive-regulative distinction is intuitively in good standing.
Second, on my account kinds constituted by rules are straightforwardly normative.
14 Searle begrudgingly admits as much: casting the rule in the "X counts as Y in context C" mold "is not intended as a formal criterion for distinguishing constitutive and regulative rules.
Any regulative rule could be twisted into this form, e.g., 'Non-wearing of ties at dinner counts as wrong officer behavior'." But he goes on to argue in support of the "counts-as" characterization, that "here the noun phrase following 'counts as' is used as a term of appraisal not of specification. Where the rule naturally can be phrased in this form and where the Y term is a specification, the rule is likely to be constitutive" (Searle 1969, 36). (Note again the hedges 'naturally' and 'likely'.) But the noun phrase 'an assertion that p' is a "specification" in (5) and (6); for (I take it) the "specification" sense of the "count as" locution is just its use to state a definition. And it is easy to turn (1) into a partial definition of a rule-constituted activity, in the way Searle envisages here for rules of etiquette -which he (wrongly, in my view, see fn. 27) expresses metaphysical possibility; but some are such that they cannot be broken without revealing the agent to be a spoilsport, and hence creating an Austinian misfire, cf. fn. 35. 21 If we just appeal to the sort of unspecific rule that Kaluziński (2018b, 116) proffers for the case of soccer in the quotation above, we will not be able to distinguish, say, American Football, rugby and Australian footy, which must be different games defined by constitutive rules if the regulative-constitutive distinction is to be vindicated. 22 Maitra (2018, 72) offers some elaboration: "an intentional and sufficiently marked failure to conform to a constitutive rule" is a sufficient condition for flagrance. She declines to provide necessary conditions; but she insists that "flagrant failures to conform to a constitutive rule governing an act are incompatible with performing that act" (ibid).