Pietarinen, Ahti-Veikko (2011). "Why is the Normativity of Logic Based on Rules?" in Cornelis de Waal and Krzysztof Piotr Chris Skowronski (eds.), The Normative Thought of Charles S. Peirce, Bloomington: Indiana University Press, 150-163. Why is the Normativity of Logic Based on Rules? AHTI-VEIKKO PIETARINEN Abstract According to Peirce, logic is a normative science. What does this actually mean? In a nutshell, rules or laws govern self-controlled action, all communication is in signs, logical thought and habits are self-controlled, and logic is semeiotic. Self-controlled agents have normative ideals in the mind as they converse upon the meaning of intellectual signs and purports. Habits are many-world entities that link situations to actions, and the rules of meaning-constitutive practices and activities provide the logical and strategic structure for habits. This paper argues that the position which takes normativity not to be grounded in the rules governing the meaningconstitutive practices is inconsistent. This argument lies in the core of the proof of pragmaticism. That normativity of logic is grounded in rules governing selfcontrolled action is manifest in the general model-theoretic thinking about logic. Normativity has to do with rule-governed, meaning-constitutive practices and activities, because logic as a normative science is, according to Peirce, one of the “most purely theoretical of purely theoretical sciences” (CP 1.281, c.1902). 1. Introduction: Logic as a Normative Science According to Peirce, normative sciences are the “most purely theoretical of purely theoretical sciences” (CP 1.281, c.1902, A Detailed Classification of the Sciences). At the same time, he takes logic to be a normative science. These two sentences form a highly interesting pair of assertions. Why is logic among the most purely theoretical sciences? What does it actually mean that logic is a normative science? In this paper I will answer these questions by answering to the question of why the normativity of logic is, as a matter of fact, based on rules. The statement that logic is a normative science has been routinely taken to follow from the classification of the sciences that Peirce came up with in 1903, and termed the “perennial classification” by Kent (1988) (cf. Pietarinen 2006a). Namely, normative logic is the ‘third’ normative science that depends upon the second or “mid-normative” science of ethics (a.k.a. practics, anthetics)—or that the second provides grounds or support for the third—and logic and ethics depend upon the first normative science, which Peirce spells esthetics. Moreover, normative sciences as a whole depend upon phenomenology and mathematics, while no normative science depends in these same senses upon metaphysics or the special sciences (idioscopy). To show that normative sciences generally need not draw on the special sciences Peirce first argues that normative sciences have nothing to do with psychology and linguistics, and then goes on to sketch arguments intended to extend the case to other branches of science as well. The first, second and third normative sciences study the three ends of philosophical inquiry. The purpose of logic is to distinguish truth from falsehood. The purpose of ethics is to distinguish good conduct from bad conduct. The purpose of esthetics—a science which Peirce apologies for not having been able to study 150 much of at all—has not so much to do with qualities such as beauty or attraction, let alone “taste” (CP 1.574, 1906, The Basis of Pragmatism), but with what is desirable as such, or with what the aim in any fully deliberate line of conduct or thinking in itself could be, without any special motive or purpose. It is the study of ideals or standards in themselves. Peirce’s view does not seem to differ much from Aristotle’s characterization of aesthetics. In which sense should logic be seen as depending on esthetics? Peirce is not proposing any straightforward answers. Commentators have been puzzled by the few of remarks that he has to offer.95 He vaguely states that “I shall not deny that [logic] depends in some measure, though indirectly for the most part, upon esthetics” (MS 693, 1904, Reason’s Conscience;96 NEM 4:198; cf. CP 2.199, Why Study Logic?). Crucial in interpreting these statements is to first do some reconstructive work on his overall philosophy. For example, the role of logic in his philosophy of pragmaticism is the core issue that needs to be clarified. Such a reconstruction forms the gist of my argument that explains why normative logic is “the most purely theoretical of purely theoretical sciences”. After this clarification, I will observe what the reconstruction implies to the question of the relationship between logic and esthetics. I will proceed to the main argument in a moment. As far as Peirce’s classificationary schemes are concerned, the case that logic depends on ethics is a little more straightforward to back up. 97 He sees the goal of reasoners to perform self-controlled thinking, just as good action requires selfcontrolled conduct. “[A]s the reasoning depends upon the virtue”, he writes in Reason’s Conscience, “so must the theory of the reasoning depend upon the theory of the virtue” (NEM 4:198). In the version of The Basis of Pragmatism published in the Collected Papers he continues that “the control of thinking with a view to its conformity to a standard or ideal is a special case of the control of action to make it conform to a standard” (CP 1.573, 1906, my emphasis). By reasoning Peirce means logic in a wide sense, the “theory of deliberate thinking” (CP 1.573). Since deliberate, inferential thinking is a form of action, logic as self-controlled thought is part of the theory of self-controlled conduct, and so the general theory of reasoning is part of the general theory of logic. The overall point I wish to make is that explaining normativity solely by reference to the role a branch of science plays in the classification scheme is unsatisfactory. I am not saying that there is anything fundamentally out of place in the classification as such, only that it does not serve as an explanation of why individual sciences are so classified in that scheme. Taxonomies and classifications are not scientific explanation. 95 See e.g. Barnouw (1995) for attempted clarification of what Peirce might have meant by esthetics, emphasizing how markedly his conception differs from the contemporary study of aesthetics. Pietarinen (2009) is a study of Peirce’s esthetics in the context of pragmaticism. 96 The full title of this manuscript is Reason’s Conscience: A Practical Treatise on the Theory of Discovery; Wherein logic is conceived as Semeiotic. The date 1904 is by Carolyn Eisele. 97 Burks (1943) is the early study concerned with this question. 151 Moreover, Peirce did not intend the classification to be a completed reproduction of the totality of the branches of scientific inquiry, let alone the final word on the complex relationships that may obtain between evolving compartments of science. Rather, he meant it as a blueprint for the future state of the sciences. For one thing, he left open the possibility that the relations between parts, though superficially represented as hierarchies of partial orders or semi-lattices, may involve symmetrical relationships.98 What, then, does it mean that logic is a normative science? To tackle this question I suggest breaking it down to the one of answering why the normativity of logic is based on rules. This is the problem I will analyze next. After that, I will consider the main implications of the solution to that key problem. 2. The Argument for Pragmaticism Let us focus on those intellectual signs that we come across in propositional contexts. Examples are logical constants, such as ‘and’, ‘or’, ‘exists’ or ‘is equivalent to’, for which Peirce shows how they can have objects. They can have objects by virtue of the precepts that guide the actions of the utterers and the interpreters of propositions. But if such signs can have objects, the meanings of our intellectual signs supervene on the contributions signs have to those activities, practices and lines of conducts of the utterers and the interpreters that mediate the ways in which language, cognition and the world stand in a relationship. This compact argument can be made precise. I will use game-theoretic semantics (GTS), which is a nearly exact contemporary rendering of pragmaticism (Hilpinen 1982; Pietarinen 2006b). According to GTS, the truth of a sentence is the existence of a winning strategy in a two-player zero-sum game played on that sentence (Hintikka 1973). But if truth and the existence of a winning strategy are so related, then the contribution a sentence makes to its truth-conditions is its contribution to those semantic games that can be played on sentences. Since semantic games exemplify practices and activities by which we compare sentences to their models, such contributions to truth-conditions are contributions to those practices and activities by which we compare sentences to their models. The argument runs as follows: 1. A is true (resp. false) in (M, w), if and only if the Utterer (resp. the Interpreter) has a winning strategy in a semantic game G(A, M, w).99 Esthetics and logic provide an example of such a mutual dependence. Take contemporary artwork which makes heavy use of multi-modal features, for instance. Such forms of art run the risk of remaining incoherent or hard to comprehend and interpret without the collecting powers of modes of reasoning provided by logic. 99 M is a model, w a possible world, A an assertion, and G a non-cooperative, two-player, zero-sum game of perfect information played on A, in M, and in w. Peirce terms the two parties engaged in such strategic dialogue variously the “utterer-interpreter”, “proponent– opponent”, “defender–attacker”, “speaker–hearer”, “addressor–addressee”, “assertor– critic”, “Graphist–Grapheus”, “Artifex of Nature–Interpreter of Nature”, “symboliser– 98 (cont.) 152 2. The Utterer (the Interpreter) has a winning strategy in G(A, M, w), iff there exists a habit of action associated with A by which we can seek and find certain objects in certain worlds. 3. Logical constants contribute to the habit of action by giving it form in terms of the choices that are possible in a given possible world w. 4. Non-logical constants contribute to the habit of action by giving it points of terminations in w. 5. Thus, A is true in (M, w), iff there exists a habit of action by which we can seek and find certain objects in w, and the sub-expressions of A contribute to the habit by giving it form or points of termination in w. 6. Thus, the sub-expressions of A contribute to the truth-conditions by giving form or points of termination to a habit of action connected with A by which we can seek and find certain objects in world w, and A has truth-conditions only if there exists a habit of action for A by which we can seek and find certain objects in w. 7. If (6), and the truth-conditions of A constitute A’s meaning, the subexpressions of A are meaningful by giving form or points of termination to the habit of action connected with A in w, and A has a meaning by its association with a habit of action by which we can seek and find certain objects in w. 8. The sub-expressions of A are meaningful by giving form or points of termination to the habit of action connected with A in w, and A has a meaning by its association with a habit of action by which we can seek and find certain objects in w. This argument establishes that intellectual signs have a meaning by virtue of the habit of action by which we compare signs with their models and the world. Signs are here assumed to be sentential expressions that have propositional content. In the simplest and perhaps most typical case, they are declarative assertions of subject-predicate sentences. The logical structure of these sentences is constituted by logical and non-logical constants. The domain of the applicability of GTS can be extended to cover other classes of sentential expressions as well. Elsewhere, we have argued that this reconstruction of the key features of Peirce’s pragmaticism in terms of the framework of GTS serves as a conclusive argument for Peirce’s middle proof of pragmaticism (Pietarinen & Snellman 2006; Pietarinen 2011b). His “proof” is therefore not merely a “seductive persuasion” for the truth of pragmaticism as he himself tended to state but a logical demonstration of its validity. Now we are ready to proceed to the argument according to which this demonstration also serves to establish the fundamental connection between pragmaticism and logic as a normative science. thinker”, “scribe–user”, “affirmer–denier”, “ego–non-ego”, “quasi-utterer–quasiinterpreter”, “delineator–interpreter”, “concurrent–antagonist”, “compeller–resister”, “agent–patient”, “putter forth–auditor”, “writer–reader”, “Me–Against-Me”, and “interlocutor–receiver”. These pairs are feigned in our “make believe”, yet they must have the qualities of “intelligent agents” (MS 280: 29; MS 3). 153 3. Meaning is Rule Governed Habits are many-world entities which inhabit not only our actual world. Think of the habit of greeting a friend: we act according to this habit if, and only if, in any situation in which we may meet a friend we normally and typically greet him. Habits connect possible situations and scenarios with acting according to, or being guided by, the habit. More precisely, what corresponds to such a habit is a mapping from possible worlds or situations to actions. The range of those mappings is defined by the acts that are permitted (or determined) by the habits in whatever kind of world or situation.100 Semantic games work by way of two kinds of rules: defining rules and strategic rules. A rule is defining if, and only if, an action is a move in a game and the action is permitted by the rule. A rule is strategic if, and only if, an action maximises the expected payoff and is permitted by the rule.101 Which habits qualify for the ‘language games of seeking and finding’ (cf. item 5 above) is given gametheoretically and is based on the characteristics of the defining rules, because defining rules constitute the actions that are correct or legitimate as soon as the model and its domains have been given. Likewise, since the defining rules constitute both the various plays of the game (game histories) as well as the rules for winning the plays of the game, they also constitute which strategic rules and plans of actions are correct as soon as the model and its domain is given (since every value of a strategic rule is also a value of a defining rule). Since the defining rules give the winning conditions as well as all the available choices for all the possible continuations of the game, and strategic rules give the right choices in every situation that has more than one available choice, rules provide the logical and strategic structure to the habit of action by which we seek and find objects and possible continuations of events within classes of models that are evoked in our logical (semeiotic) inquiries. Consequently, our intellectual signs and purports have a logical role in these strategic activities according to the game-theoretic rules. Our individual acts are By a mapping we mean generalizations of an ordinary concept of a function to accommodate, for example, non-deterministic and intensional forms of mappings. By model theory we mean its wide sense that takes into account possible-worlds semantics and intensional concepts. Ordinary notions of a function or a model theory do not cover such extensions. The broader conception of model theory comes close to what Peirce’s intention was in regarding formal semantics/pragmatics as the logical theory of semeiotics (see Pietarinen 2006b, 2006c). 101 This vague definition of strategic rules may well need to be qualified in several ways. But nothing in the argument depends on the details of those qualifications. Recent literature in game theory is rife with suggestions about the ways in which ‘the maximization of expected utilities’ could or should be replaced with goals and ends that make less-thanideal assumptions concerning, for instance, the rationality of the players (Gintis 2009; Rubinstein 1998). 100 154 made in accordance with the habits, or are being guided by them if, and only if, they are made in accordance with, or are guided by, the rules of the game. Now suppose, for the sake of argument, that the meaning of our intellectual signs is not based on rules in the manner just described. This would require showing that the normativity of these semantic games is not based on rules, since strategic rules determine what the right choices are in every non-terminal contingency, no matter how improbable they are.102 However, the assertion that the normativity of games is not based on rules is inconsistent. The reductio goes as follows. If the normativity of games is not based on the rules of the game, it is based on what our actions in fact are in those plays of the game that are actually played. However, our actions are those that we in fact do. But if that is the case, then only one world, namely this current, actual world of ours, is relevant to the formation of habits that constitute the meaning of our intellectual signs. If only one world is relevant to the formation of habits that constitute the meaning of our signs, in applying the sign or expression to something we affect or change the ways in which situations are mapped to actions. And as argued, these mappings correspond to habits. But if so, then all action constitutes meaning, and hence language could not be misused and all sentences would be true: all communication would be impossible. Since there is communication (and for the sake of sanity and non-solipsism we must take this for granted), this conclusion is absurd. The above argument thus establishes the following three conclusions. First, the actual world is not the sufficient ‘thing’ for the formation of meaning-constitutive habits. Second, it is inconsistent and hence not true to take the meaning of our intellectual signs not to be based on rules. Third, it is not true that the normativity of semantic games, the habits of which constitute the meaning of our intellectual signs, is not governed by rules. I have argued in this section that logic, in its wide sense,103 is the general theory of the meaning of intellectual signs, in other words pragmaticism, and in section 2 I associated that theory with the theory of semantic games. We can thus see the reason why the normativity of logic is, and has to be, based on rules.104 This is really how strategies are conceived both in Peirce’s sense and in contemporary game theory. Knock-down evidence comes from Peirce’s 1893 marginal addition to his revision of How to Make Our Ideas Clear, where he writes, next to his definition of the identity of a habit as leading us to action under any possible (even zero-probability) circumstance: “No matter if contrary to all experience” (CP 5.400). 103 On Peirce’s notion of logic conceived in its broad and narrow senses, as well as their relations to normative sciences, see Bergman (2007). 104 It might help one to savor this conclusion by thinking of rules as very complex entities: in addition to being non-deterministic and intensional functions and mappings, they can come in the forms of conditionals, subjunctives and counterfactuals, among others. Or rules can have antecedents whose falsity calls for demonstration by abductive reasoning. It is by no means the case that rules in question are static, indefeasible entities or canons that restrict or constrain our actions. Instead of rules, one might think of habits as laws, including statistical laws, but this is problematic since such terminology suggests a 102 (cont.) 155 4. Habits, Ethics and Ideals That normativity is based on rules of the game-theoretic kind is something Peirce struggled to establish. His terminology of course differs from ours, but the motivations and goals are the same, and they are best expounded in the contemporary frameworks provided by logical semantics, pragmatics, and the theory of games, all of which can be taken to pertain to normative sciences.105 One of the most acute struggles to articulate these frameworks takes place in the unpublished MS 280 The Basis of Pragmaticism from 1905: A critical analysis of the nature of a sign would show that the action requires a source of concepts to be conveyed, and therefore in some sense a mind from which the ideas and [concepts,] propositions, and arguments are conveyed to the mind of the interpreter; and the two minds must be capable of coming to an understanding and of observing it when it is reached. This supposes a power of deliberate self-controlled thinking. Now nothing can be controlled that cannot be observed while it is in action. It is therefore requisite that both minds but especially that of the Graphist-mind should have a power of self-observation. Moreover, control supposes a capacity in that which is to be controlled of acting in accordance with definite tendencies of a tolerably stable nature, which implies a reality in this governing principle. But these habits, so to call them, must be capable of being modified according to some ideal in the mind of the controlling agent; and this controlling agent is to be the very same as the agent controlled; the control extending even to the modes of control themselves, since we suppose that the interpreter[-mind] under the guidance of the Graphist-mind discusses the rationale of logic itself. Taking all these factors into account, in a way that can here only be suggested, we should come to the same conclusion that common-sense would have jumped to at the outset; namely, that the Graphist-mind and interpreter-mind must have all the characters of personal intellects endowed with possessed of moral natures. But let us not to be forgotten that the Graphist, whom we now speak of as a person, is such a person that the truth and being of the things that are objects of thought, consist in his assent to their being. (MS 280: 30-33, 1905, emphases and paragraph skip added) This is what it all comes down to. The relationship between pragmaticism and semantic games is, in a nutshell, as follows. “The two minds” are the two players of the game, the Graphist (the Utterer) and the Interpreter (the Grapheus). The two minds undertake to show the material truth or the falsity of the given assertion. naturalistic interpretation of habits which is alien to Peirce’s own argument about their identity. 105 Admittedly, there is considerable disagreement among game theorists on whether what the study is to be conceived as a normative, descriptive or prescriptive science (see Osborne & Rubinstein 1994; Pietarinen 2003). 156 What “capable of coming to an understanding and of observing it” means is that the payoffs, determined at the terminal histories of each play of the game, are known, and commonly known to be known, by the players. Common knowledge of payoffs is a standard assumption in game theory in so far as the class of complete information games is concerned. The “power of deliberate self-controlled thinking” and the “power of self-observation” refer to strategic thinking and planning. As any game theorist is quick to confirm, our plans need to be able to accommodate and undergo changes that reflect the expectations we formulate about the actions of our fellow contestants. Peirce’s self-control, expressed here in terms of the “definite tendencies of a tolerably stable nature”, refers to the fact that the existence of certain winning strategies, or habits of acting for a purpose, is eventually guaranteed. Such stable tendencies and acting for a purpose are the essence of reaching the equilibrium points. They can be likened to the ways solution concepts behave for a wide variety of games. A number of solution concepts have been proposed in game theory. A central issue has been how to choose among them. One candidate I would like to suggest as the solution concept of a Peircean stripe of game theoretic action is Reinhard Selten’s trembling-hand perfect equilibrium (Selten 1975). According to it, players may sometimes, though very rarely, play unintended moves and thus slightly deviate from optimal strategies. Trembling hands are also closely related to evolutionary stability. We can in fact add evolutionary superstructure to our semantic games, thus taking a step closer to (i) Peirce’s own understanding of various levels of self-control as not assuming full rationality (Pietarinen 2005a), (ii) that faculty of logical reasoning (logica utens) which according to Peirce is based on “instinctive” reasoning (see De Waal’s chapter in this book and Pietarinen 2005b), and (iii) evolutionary stable strategies which unlike classical game theory do not assume full rationality and hence not full but fallible and self-corrective self-control. Evolutionary stable strategies in fact come close to revealing the mechanisms that would explain what Peirce’s evolutionary cosmology struggles to be. Equally interesting is the latter paragraph of the quotation, in which Peirce reveals that the two minds “must have all the characters of personal intellects possessed of moral natures”. He is not saying that they are morally acting personal intellects. On another occasion he makes the well-known allusion to ‘sops thrown to Cerberus’ in order to make his view that a sign “determines an effect upon a person” (SS 80-81, 1908, Letter to Welby; Pietarinen 2006b) better understood. Those “agents” who “discuss the rationale of logic itself” are theoretical constructs which nevertheless need to possess the same characteristics as personal intellects do. In explaining the fundaments of the philosophy of his later diagrammatic logic, “the dyadics”, Peirce repeatedly tells that these minds, in other words the participants in the logical dialogue taking place in thought, are “intelligent agents” (MS 3, c.1903, On Dyadics: the Simplest Possible Mathematics). In other words, our theories of logic must be able to incorporate the theory of the characteristics of intelligent agents into the concept of the logical agenthood. Or, alternatively, since GTS is a theory of logical semantics, they must be able to 157 incorporate those characteristics into the concept of the player of a semantic game.106 This I take to be the impact of Peirce’s assertion that logic as a normative science is among the “most purely theoretical of purely theoretical sciences”. The agents, endowed with the characteristics equal to personal intellects and capable of discussing “the rationale of logic itself” as they according to Peirce are prescribed to do, are the key theoretical constructs indispensable in what pragmaticism ultimately is calculated to achieve.107 I believe what was just said explains what it means that logic depends on ethics, or that ethics provides grounds or support for logic. But what is more, contained is the previous remarks are also intriguing hints as to the senses in which logic could be taken to hinge on esthetics. Peirce’s well-known remark concerning ideals read as follows: “If conduct is to be thoroughly deliberate, the ideal must be a habit of feeling which has grown up under the influence of a course of self-criticism and of hetero-criticism” (CP 1.574, 1906).108 From this, he goes on to define esthetics, pretty non-standardly, as “the theory of the deliberate formation of such habits of feeling” (CP 1.574).109 Recall that in the long quotation from MS 280 above, Peirce states that “habits [of action], so to call them, must be capable of being The notion of agenthood that could be gleaned from the structure and dynamics of games is a prominent topic in the game and decision-theoretic literature. 107 Peirce’s late proof involves the establishment of habits as logical interpretants by exclusion of other propositional attitudes such as conceptions, desires and expectations (MS 318; Pietarinen & Snellman 2006). The logical interpretant “can only be a Habit”, he writes to Giovanni Papini in 1907, “which consists in a conditional future; namely that, with a given motive, a man, under given circumstances, would rationally behave in a certain way” (Letter to Papini, p. 7, 10 April 1907). In a little treatise Logic and the Basis of Ethics (1949: 75) Arthur Prior, who was paying special attention to Scottish moral philosophers and seeking to ground the normative aspect of logic in ethics and at the same time avoiding lapses into psychologism, goes on to assimilate habits with desires. Prior was much influenced by Peirce’s writings since early in his career, but his notion of a habit is more narrowly conceived than Peirce’s. I believe the key reason for this is Prior’s universalistic presupposition concerning the theory of logic. It was quite commonplace thing to have in the wake of Russell, Quine, and the formalistic restructuring of symbolic logic. And the book was written just prior to the emergence of model-theoretic approaches. 108 The notion of control (both in the sense of “self-control” and “hetero-control”) is a metalogical principle in operation in Peirce’s logic. Game-theoretically, control presupposes that the agents know their own types as well as the other players’ types, including knowledge and common knowledge of the payoff distributions in the game. In the nomenclature of game theory these standard epistemological assumptions refer to the class of games that have complete information. MS 280 refers to the agents’ capabilities of “coming to an understanding and of observing it”, which from the game-theoretic point of view interestingly expresses one side of the principle of complete information: players’ knowledge of their own types. 109 This definition was written around the same time, in 1905, as the manuscript 280 from which the key quotation is taken. 106 158 modified according to some ideal in the mind of the controlling agent”. Now such habits are rules for thinking about, and thus rules for proper conduct concerning, the meaning of signs. Habits are modified or changed with reference to the purpose or ideal that an agent has in mind. But an ideal is also a controlled habit, a habit that has to do with feeling and not only with thinking or action. Therefore, in the senses given both in his 1905 definition of esthetics and in the central passages from MS 280 written in the same year, Peirce is implanting the ‘first’ of the normative science into the very core of logic. For these reasons, he is justified in regarding logic as the general theory of the meaning of all intellectual signs, thoughts, generalities, concepts and purports. 5. The Normativity of Esthetics and Its Implications to Logical Theory Since esthetics for Peirce has to do with controlled habits and not merely qualities of feelings, it should not be regarded only as the most fundamental of the normative sciences. Also, the question of why the normativity of esthetics is based on rules falls, mutatis mutandis, from the argument for the normativity of logic. The only issue that needs to be separately considered is whether habits of feelings are manyworld entities just as are habits of thinking and action. It turns out that, analogously to habits of thinking and action being many-world entities, to confine the formation and application of habits of feeling to the actual world is liable to lead to an inconsistent position in semeiotic, that is, aesthetic relativism. In comparison to the habits of reasoning and action it is, however, a considerably mightier question to address what kinds of rules or laws there are that give habits of feelings their form or their points of termination. Suffice it to remark here that this question should be discussed in connection with phenomenology (phaneroscopy), the first compartment of philosophy immediately preceding the normative science of esthetics. Second, if we are to regard habits as having to do with game-theoretic actions of ‘seeking and finding’, then the question boils down to what is it that in fact constitutes the universes of discourses concerning our habitual activities of feeling. My suggestion as to this latter question goes along the following lines. (i) For logic and its habits of reasoning and self-controlled thinking, the universes of the model consist of objects and possible states of affairs. Objects can be of very varied kinds and refer to “special kinds of universes”, such as times, fictions, limits, collections, continuities or different kinds of modalities (MS 1632, Logic Notebook 639, 1909). (ii) For practics and its habits of acting and self-controlled conduct, the domains of discourse are characterized by those parts of the world which we actually inhabit.110 (iii) For esthetics and its habits of feeling and controlled ideas, it is the Phaneron, “the total content of any one consciousness” and “the sum of all we 110 And so in metaethical terms Peirce would agree with cognitivism, that ethical statements have propositional content and that they can be evaluated by virtue of that content. A necessary qualification is that his understanding of propositional content (the content of dicisigns) is somewhat broader than what normally is accepted in contemporary philosophy of language. 159 have in mind in any way whatever, regardless of its cognitive value”(EP 2:362, The Basis of Pragmaticism in Phaneroscopy), as Peirce remarks in that annus mirabilis of his, 1905. Therefore, the universe of our habitual activities of feeling in a certain way in certain kinds of aesthetic or artistic situations is constituted by the totality of the content of a mind. It is noteworthy that phaneroscopy is the locus in which Peirce’s logical theory of Existential Graphs is really set in motion. The sheet of assertion (MS 298, 1905, Phaneroscopy) upon which logical graphs are scribed contains all the conceivable mind-like qualities that the interpreter may come across. The sheet of assertion “represents the state of mind of the interpreter” (MS 280: 22). The question of what it is that the agents seek and find in the Phaneron is thus related to the question of what the rules are that govern the interpretations of those simple qualities scribed upon the sheets of assertion. And such simple qualities, denoted as certain bounded regions of space differing in quality from other regions of the space, constitute the meaning of the diagrammatic correlates to predicate and relation terms. Such simple qualities are thus the building blocks of logical propositions (expressed in the graphical language of iconic logic) and hence contribute to the habits of action by providing them with points of termination. The rules or laws that govern the interpretation of these simple qualities are, however, quite different from the rules or laws that govern the interpretation of logical propositions. The former are analogous to the interpretation of non-logical constants of our vocabularies (Pietarinen 2011a). Thus, such rules have to do with the processes of constructing the models to which propositions are compared in the first place, and not with the semantic processes of interpreting the assertions in the models. In that sense they precede the rules governing the interpretation of propositional signs. * * * I would like to emphasize in conclusion one distinctive feature of such Peircean model-construction game activities: they are cooperative rather than competitive. The sheet of assertion represents “everything that is well understood to be taken for granted between the two parties”, and Peirce goes on to insist that “the two must come to an agreement of convention” (MS 280)—otherwise all communication is impossible.111 111 Recall David Lewis’s (1969) argument how the establishment of conventions appears to follow certain simple cooperative signalling games. Like Lewis, Peirce presupposes the common ground between communicants and analyses its constitution in terms of an infinitary construction of common knowledge (MS 614; Pietarinen 2006b). However, despite its name, Peirce would regard Lewis’s modal realism an unacceptable form of nominalism because of its commitment to actuality and indexicality only. Modal realism does not take real unactualised possibilities seriously. 160 These activities seem to concern actual communicative practices and discourse rather than non-cooperative games that mediate the semantics of propositions. The former, it seems, have to do with the issues which we may in Peirce’s terms consider to fall within the realm of speculative rhetoric.112 However, there is an important result that needs to be taken into consideration as to the presumption that the classes of games that describe the two kinds of activities are different. For one thing, it needs to be asked whether “the two parties” engaged, on the one hand, in cooperative model-building communicative activities and, on the other, in non-cooperative meaning-constitutive activities, are fundamentally different entities. We might indeed be led to think, sight unseen, that in the former, model-building activities, they are the actual participants in actual conversational situations, and in the latter they are the theoretical agents that are real but which subsist, as Peirce remarks, in our “make believe”.113 However, the contrary is, at the end, the case. For one thing, Peirce’s writings do not support the distinction between agents of these two kinds of activities pertaining to altogether different categories (Pietarinen 2007b). Cooperative modelbuilding resorts to same theoretical constructs of the make-believe agents as the strictly competitive semantic activities do. Secondly, we can bring forth a technical result supporting this unanimity: what the two minds practice are not fundamentally separate activities after all.114 The two kinds of games, the semantic and model-construction games, are two sides of the same conceptual coin. Cooperation and competition can peacefully coexist. The fundamental correlation or intermingling of cooperation and competition has some significant implications. Let me mention one, namely that any hard and fast division between Peirce’s second division of normative logic, logic proper (critic), and the third division, that of speculative rhetoric, is liable to be an illusion and be in the name only. And this was, I believe, also Peirce’s aim to be able to establish. Nowadays we can bring the same argument to bear on the much-debated distinctions and interfaces between the study of semantics and the study of pragmatics. I have argued in Pietarinen (2007a) that from the game-theoretic point of view, the semantics/pragmatics distinction is an epistemological one and has to do with the players’ knowledge of the content of their strategies. If we need not be concerned with that kind of knowledge as we normally do not, the distinction Liszka’s and Redondo’s chapters in the present book characterize speculative rhetoric. “In our make believe, two parties are feigned to be concerned in all scribing of graphs; the one called the Graphist, the other the interpreter” (MS 280). 114 To prove this connection, we show the following. From the winning strategies of the model-construction games we can construe a model set that guarantees the existence of witness individuals and witness predicates in the semantic game correlated with a sentence A. There exists a habit of choosing these witness individuals and predicates if, and only if, there exists a winning strategy in the semantic game correlated with A. Conversely, if there exists a winning strategy in the semantic game correlated with A, we can construe a model set from which we get a model for A by playing through all the positions allowed by the model set in question. 112 113 161 simply is not there. Separating pragmatics from semantics is not something that general theories of meaning such as pragmaticism need to be concerned with. In this very concrete sense the divide between semantics and pragmatics is artificial and has little philosophical support. It also means that Charles Morris’s suggestion that the studies of semantics and pragmatics be grouped with critic and speculative rhetoric, respectively, is not correct. University of Helsinki [email protected] Acknowledgments Supported by the University of Helsinki Excellence in Research Grant (Peirce’s Pragmatistic Philosphy and Its Applications, 2006-2008, project 2104027, Principal Investigator A.-V. Pietarinen). My thanks to the organizers and participants of Charles S. Peirce’s Normative Thought: International Conference in Philosophy held in Opole, Poland in June 2007. Mats Bergman, Vincent Colapietro, Nathan Houser, Dan Nesher, Mateusz W. Oleksy, Helmut Pape and Sami Pihlström merit an individual mention for their comments and criticism concerning earlier versions. Lauri Snellman deserves special credit for participating in the formulation and contesting of the key arguments of Sections 3 and 4. This paper is dedicated to the memory of Mateusz W. Oleksy, with who I exchanged thoughts on our papers during that conference. REFERENCES Bergman, Mats (2007). ―Is logic in the broad sense normative?‖, manuscript. Barnouw, Jeffrey (1995). ―The place of Peirce‘s ‗Esthetic‘ in his thought and in the tradition of esthetics‖. In: Herman Parret (ed.), Peirce and Value Theory: On Peircean Ethics and Aesthetics, Amsterdam: John Benjamins, 155-178. Burks, Arthur W. (1943). ―Peirce‘s conception of logic as a normative science‖, The Philosophical Review 52, 187-193. Gintis, Herbert (2009). The Bounds of Reason: Game Theory and the Unification of the Behavioral Sciences. Princeton: Princeton University Press. Hilpinen, Risto (1982). ―On C. S. Peirce‘s theory of the proposition: Peirce as a precursor of game-theoretical semantics‖. The Monist 65, 182-188. Hintikka, Jaakko (1973). ―Language-games for quantifiers‖. In: Jaakko Hintikka, Logic, Language-Games and Information. London: Oxford University Press, 53-83. Kent, Beverley (1988). Charles S. Peirce: Logic and the Classification of the Sciences. Kingston: McGill-Queen. Lewis, David (1969). Convention: A Philosophical Study. Cambridge, Mass.: Harvard University Press. Osborne, Martin J. and Rubinstein, Ariel (1994). A Course in Game Theory. Cambridge, Mass.: MIT Press. Peirce, Charles S. (1931-58). (CP) Collected Papers of Charles Sanders Peirce. 8 vols., ed. by Charles Hartshorne, Paul Weiss, and Arthur W. Burks. Cambridge, Mass.: Harvard University Press. ———. (1967). (MS) Manuscripts in the Houghton Library of Harvard University, as identified by Richard Robin, Annotated Catalogue of the Papers of Charles S. Peirce 162 (Amherst: University of Massachusetts Press, 1967), and in The Peirce Papers: A supplementary catalogue, Transactions of the C. S. Peirce Society 7 (1971), 37-57. ———. (1976). (NEM) The New Elements of Mathematics, Edited by Carolyn Eisele, The Hague: Mouton Publishers. ———. (1977). (SS) Semiotic and Significs: The Correspondence Between Charles S. Peirce and Victoria Lady Welby. Edited by Charles S. Hardwick and J. Cook, Bloomington: Indiana University Press. ———. (1998). (EP) The Essential Peirce 2. Peirce Edition Project, Bloomington: Indiana University Press. Pietarinen, Ahti-Veikko (2003). ―Games as formal tools versus games as explanations in logic and science‖, Foundations of Science 8, 317-364. ——— (2005a). ―Evolutionary game-theoretic semantics and its foundational status‖, in N. Gontier, J. P. Van Bendegem and D. Aerts, (eds), Evolutionary Epistemology, Language and Culture: A Nonadaptationist Systems-theoretical Approach, Dordrecht: Springer, 429-452. ——— (2005b). ―Cultivating habits of reason: Peirce and the logica utens vs. logic docens distinction‖, History of Philosophy Quarterly 22, 357-372. ——— (2006a). ―Interdisciplinarity and Peirce‘s classification of the sciences: a centennial reassessment‖, Perspectives on Science 14, 127-152. ——— (2006b). Signs of Logic: Peircean Themes on the Philosophy of Language, Games, and Communication (Synthese Library 329). Dordrecht: Springer. ——— (2006c). ―Peirce‘s contributions to possible-worlds semantics‖, Studia Logica 82, 345-369. ——— (ed.) (2007a). ‖The semantics/pragmatics distinction from the game-theoretic point of view‖, in Pietarinen, Ahti-Veikko (ed.),Game Theory and Linguistic Meaning (Current Research in the Semantics/Pragmatics Interface 18), Oxford: Elsevier, 229-242. ——— (2007b). ―To Peirce Hintikka‘s thoughts‖, The Epistemology and Methodology of Jaakko Hintikka, The Carlsberg Academy, to appear. ——— (2008). ―Esthetic interpretants: Pragmatism, semiotics, and the meaning of art‖, Chinese Semiotic Studies: Journal of the International Institute for Semiotic Studies. Nanjing: Nanjing Normal University Press, 223-229. ——— (2011a). ―Peirce and the logic of image‖, to appear in Semiotica. ——— (2011b). ―Moving pictures of thought II: Graphs, games, and pragmaticism‘s proof‖, to appear in Semiotica. Pietarinen, Ahti-Veikko and Lauri Snellman (2006). ‖On Peirce‘s late proof of pragmaticism‖. In: Tuomo Aho and Ahti-Veikko Pietarinen (eds), Truth and Games, Helsinki: Acta Philosophica Fennica, 275-288. Prior, Arthur N. (1949). Logic and the Basis of Ethics, Oxford: Clarendon Press. Rubintein, Ariel (1998). Modeling Bounded Rationality. Cambridge, Mass.: MIT Press. Selten, Reinhard (1975). ―A reexamination of the perfectness concept for equilibrium points in extensive games‖, International Journal of Game Theory 4, 25-55. 163
© Copyright 2024