1993 Abstract for work in JOURNAL OF PHILOSOPHY HOW A FORMAL THEORY CAN BE NORMATIVE The paper distinguishes implementation from interpretation as a possible use of normative formal theory. It identifies the source of normative force as the intention to implement in a particular way, which it deliberately conflates with a contract. Finally, it discusses constructive theories of reasoning which depend on non-deterministic processes. These theories make little sense from an interpretive point of view, and are becoming more common among implementers. 1991 Text of Paper Read At The 2nd Workshop on Human and Machine Cognition HOW A FORMAL THEORY CAN BE NORMATIVE: INTEPRETATION VERSUS IMPLEMENTATION I Even as Davidson advanced the principle of charity as it relates to attribution of mental attitudes, Davidson acknowledged the difficulty of applying formal theory normatively. Davidson noted that applying decision theory requires interpretation. One must first describe the agent. Once described, coherence with axioms of the theory mandates how the agent must additionally be described if the agent is rational. In order for a preference of A over B, with a preference of B over C, to mandate a preference of A over C, the formal symbols ``A > B'' and ``B > C'' must be apropos. That is, the agent's observable behavior, ``I prefer Mozart to Bartok'' must be interpreted as ``A > B''. When, in addition, ``Do you prefer Bartok to Mendelssohn?'' is met with a nod and represented ``B > C'', the would-be wielder of normative theory must still determine what behavior would count as accord or discord with the formal sentence ``A > C''. With extreme charity, vigorous ostensible denial in response to ``Do you prefer Mozart to Mendelssohn?'' might still be written ``A > C''. Davidson was particularly adept at adapting formal language to the situation. He suggested that since an interview with an agent proceeded serially, the preferences thus elicited could be indexed by times: ``A >_@T_1 B'', ``B >_@T_2 C'', ``C >_@T_3 A''. Persistence is not normally required of preferences for rational agents, if X >_@T_1 Y then X >_@T_2 Y, so there would be no inconsistency with the axioms. Liberal description of the agent guaranteed the agent's rationality. Decision theorists who argued for a persistence axiom missed the point. Charity of description could be given in any of a number of ways. Richard Jeffrey's framing objects of value was particularly pernicious. ``Mozart'' in ``I prefer Mozart to Bartok'' was a different object of value from ``Mozart'' in ``I prefer Mendelssohn to Mozart''. The appropriate symbolization was ``AvsB > BvsA'', ``BvsC > CvsB'', ``CvsA > AvsC''. Thus, the language of decision theory can be used to describe the agent's preferences. The description is consistent; it contradicts no combination of preference axioms. The agent is apparently rational. Remarkably, Davidson's charity arose from exigencies of empirical method: he found it unconscionable to call agents irrational while withholding the benefit of indeterminacy. As far as I can tell, his charity did not result from a crisis of conventionalism, or from pursuit of Quine; it happened in the psychology laboratory. One wonders why Kahneman and Tversky are unable to regard their experimental subjects with Davidsonian kindness. Generalizing indeterminacy in the use of decision theory to other theories of rationality is straightforward. Perhaps too much recent philosophy has been devoted to problems of attributing beliefs to an agent, where belief must be consistent in some formal logical language, and that logical language purports to embody a theory of rational belief. Not just decision theory, but any formal normative theory is at similar risk. A theory of rationality, expressed as constraints on sets of symbols, has no normative force because it cannot fix the translation of situations into symbols. Constraints on habits of translation must either refer to situations informally, or expose themselves to interpretation at the (meta-)level at which constraints on translation are formalized. II How can a formal theory of rationality be normative? Formal theory provides meaning postulates for a specialized language in which an agent can be discussed. The more easily discussed the agent in this specialized language, the more easily the agent is taken to be rational. I have elsewhere taken this pessimistic view of normative theory. The view is conventionalist: no theory of rationality has prior privilege. It is not categorical: the agent is not simply rational nor irrational with respect to a theory; instead, the agent is more conveniently discussed in one language, less conveniently in another. This view seeks equilibrium: there is interplay between the choice of language and the application of a chosen language to individuals who are judged by the language. The more powerful a language for prediction, the less easily the language is wielded. The more parameters and syntactic choices in a language that allow indeterminate interpretation, easy wielding, the less predictive the language. The tradeoff of charity against predictive power in application of normative theory can be viewed much like the tradeoff between error and predictive power in curve fitting, or more general scientific theory formation (here I differ from Davidson, who thinks of nomology in science and is less willing to believe that natural laws can simply be chosen). Offer little charity, that is, make preferences atemporal and objects of value largely indistinguishable, and the agent's behavior can be modeled in the language by rejecting some observations as error. Offer more charity, that is, allow parameters to proliferate, like a high-degree polynomial through a small data set, and indeterminacy weakens all prediction. A preference is recommended because it is predicted by the best theory about the agent's preferences, according to our conventions regarding best theories, not because coherence with the axioms could not otherwise be attained. Predictive power is all that remains of normative theory's compulsion. The right to compel derives from the fact that a language matches pre-theoretic intuitions about rationality, given the de facto habits of translation of a community of language users. III There is another way in which a formal theory can be compulsory. Formal theory can be implemented; behavior that arises out of implemented theory is thus guided and compelled by the theory. It is one thing to come upon an agent with a formal theory with no interpretation fixed, with no right to fix an interpretation; it is an entirely other thing to adopt a formal theory, fix an interpretation by right, and thereby implement the theory. In some situations, to apply theory, an interpretation must be adduced. In others, to apply theory, an interpretation can be declared. Situations in which this declaration has force are situations in which the theory has normative force: commitment to an interpretation binds the agent, fetters the agent to norm. Consider the formal symbol system of chess, and the concept of a forced move in a chess position. Coming upon two gods in an ancient Mediterranean sky, or upon two opposing generals in desert sands, or two gaming undergraduates moving tokens about a lunch table, one might wonder whether an interpretation of their behavior as chess-playing in a forcing position would mandate further behavior: whether the forced move is exhibited. Taking Athens, or the 101st Airborne Division, or the black lacquer button to be a bishop, a move might be forced which corresponds to behavior that the players do not exhibit. One cannot say that they are not chess-players because the imposed interpretation renders their behavior inconsistent with the rules of chess. One must seek a better interpretation. This is a situation that demands charity. Evidence for an interpretation and inclination toward the interpretation might be superb. But interpreters must be prepared to doubt the evidence: giving a hearing to the hypothesis that they are playing chess, the hypothesis must temporarily be placed at the center of the web of belief. Consider instead the gods or the generals or the undergraduates who consciously decide to play chess with their Greeks, brigades, and buttons. They seek to abide by the rules of chess; they intend to play chess. It is their right to agree on an interpretation, even if by that interpretation, following the rules of the game would be trivial, or by their interpretation, following the rules would seem taxing. What matters is that it is the implementer's right to declare an interpretation of the symbols. After declaration, the interpretation and the rules of the formal system are binding. Implementers, in fact, have not just the privilege but also the responsibility of fixing the intended interpretation, at least in their own minds. Forming the intention to instantiate symbols of a formal system is a contract, wherefrom normative force derives. This contract cannot be declared in a formal language, lest there be regress. This contract is frequently made with oneself, or made among oneselves. Nevertheless, it binds. As an interpreter, one cannot use a logic to prescribe another's beliefs. The best an interpreter can do is provide analysis, the best scientific analysis, respecting all the conventions of science, to determine theory, interpretation, and prediction at once. As an implementer, instead, one can use a logic to form the belief that P, once one decides what is to count as the belief that P. An implementer, decided in how the system should be implemented, must alter behavior to abide by that system. Analyst and subject can communicate, agree on interpretation bilaterally. But failure of the bilateral interpretation sometimes provokes search for a new interpretation, unilaterally if necessary. Some bilateral agreements on interpretation bind. In such cases, the parties to the agreement become implementers. In both interpretation and implementation, there can be unintended interpretations according to which there is conformance with theory. The chess players may intend to violate the rules as declared, but there could be another way of seeing things, according to which they follow the rules. When theory is wielded interpretively, that accident makes them chess players, like it or not; none has the right to declare a privileged interpretation. Accidental, unintended implementations however are less satisfying. Setting out to implement a formal theory of a brain with a trillion Chinese operating hydraulic pumps, and failing, it is meager consolation to know that one of the trillion Chinese implements the theory of the brain by himself. The doctrine of privileged access stands in poor stead here. When analyst and subject are one, there could still be an interpretive aspect: self-interpretation is not necessarily fixed interpretation. Upon acknowledging belief in P, belief in Q, and disbelief in P & Q, the self-analyst might balk and reinterpret. We customarily suppose we are in a privileged position to know whether we believe P. Are we so sure of privileged access to believing if P then defeasibly Q? The rules of the formal system governing defeasible rules can be altered fancifully; any suredness of self-knowledge of defeasible rules will quickly disappear as the semantics of the rules grows arcane. There are many people in this world who just do not know whether they can be said to be playing three-dimensional chess. IV Distinguishing implementation from interpretation is important not only because these days, with artificial intelligence, formal systems are implemented on computer systems. There is, too, a particular kind of formal system for rational belief which forces this distinction. These systems are more concerned with construction than with coherence. They confer warrant as the result of process, and outcome of process is non-deterministic. There may be many different computations that constitute a fair hearing, and they do not all reach the same conclusion. A dialectical approach to knowledge is an example of such a process. A probabilistic test for determining whether an integer is prime is another. For these constructive conceptions of rational belief, interpretation is ridiculous. Dialectic is a process that produces warranted belief by adjudicating a disputation. Arguments and counterarguments are produced until some termination condition obtains. Search for arguments and the order in which arguments are advanced are non-deterministic. One disputation might result in a judgement pro; repeating the disputation, the verdict might be reversed. Primality testing is a celebrated example of a randomized algorithm. Under certain randomization conditions, a number that cannot be factored after several tries is probably prime: the probability rises exponentially as factorizations are tried. One test for primality might result in rational belief that a number is prime; a subsequent test can reverse the verdict. In each case, belief is rational because it is constructed via a process, not because the belief coheres with other beliefs. Moreover, the outcome of the process could have been otherwise. Like elections and lotteries, the accident of making is what does the making. The difference between coherence theories of rationality and process theories, as regards charity, is not merely following rules over time versus cohering with rules at a time. Declaring how dynamic rules are to be interpreted is much the same as declaring how static rules are to be interpreted. Proclaim that button-takes-button is at one time ``knight takes knight'', then button-taking-button is at a later time ``rook takes pawn''. This is as easily proclaimed as `five buttons on the table must include one that is not a ``knight'''. The difference, as regards charity, actually lies in the non-determinism of process. When there is non-determinism, there can be charity even when the interpretation is fixed. Many bad decisions are defended by referring to the process by which they were made: charitable interpretation is blind to whether the process used in the defense of the decision is the same process used in construction of the decision. It is too easily claimed that there was a chance set-up with a bad outcome, when perhaps, there was no chance set-up at all, or not the chance set-up that is claimed. Claim too easily, after the fact, that a hearing was fair. Losing advocates advanced no arguments because, though they were given the opportunity, there was some probability that their search procedures would find none of the effective arguments that could have been constructed. Apparently, this low-probability outcome was realized. Claim too easily, after the fact, that a primality test was fair: selection of would-be divisors failed to find an actual divisor because there was some probability that this could happen. Interpretation permits the lynch mob, post hoc rationality, bad random number generators. It is easy to interpret an unusual outcome as the result of bad luck in a process, but warranted nevertheless by that process. Not so easy, though, is actually conducting the trial, holding the debate, or performing the test. The die actually have to be thrown. The advocates must really be given time. The parties to the process must subject themselves to the non-determinism. The judge can still be biased, the die throw bogus, the defense mute. But, at least if there really is non-determinism, the outcomes of chance events cannot simply be faked, the chance set-ups presumed to exist by charitable interpretation. What is needed is some constraint on the post hoc interpretation of chance set-ups. V Anyone who has implemented a formal system knows its normative force, or more precisely, the normative force of the contract to implement as intended. Anyone who has attempted to impose a formal theory of rationality knows indeterminacy. Charity threatens anti-intellectualism among formalists. Why invent beautiful formalism if complex constraint can dissipate in insipid interpretation? Because: we want to construct attitudes, not just have them.