THIS paper is an effort to bring together two issues bearing on the moral philosophy of Hume. First, an effort will be made to interpret and clarify the role of general rules in Hume’s account of moral judgment. Second, the proper classification of the moral sentiments according to categories made familiar by studies in the philosophy of mind will be offered. The collective bearing of these two matters on the analysis of Hume’s moral theory will then be explored.

Adam Smith and David Hume agree that first-level general rules of morality may be discovered by induction, and that reflection on these rules may influence human behavior. But Hume thinks a deeper, second level of moral general rules may also be discovered, and used to correct erroneous first-level rules. Thus on Hume's view, some reasoned reflection may be needed in order to feel the proper moral sentiment. Smith holds that, because of human inclination toward (...) selfishness, first-level moral rules should be habitually used to override immediate impulse in the motivation of behavior. This is a valuable habit, but since most people are not able to form such rules for themselves, it is a good idea for them to follow moral rules provided by religion. There is something respectable, according to Smith, in sincerely following flawed moral rules provided by religion. Hume disagrees, holding that it is foolish and blameworthy, indeed dangerous, to follow flawed moral rules provided by religion. (shrink)

In this paper, I examine Hume’s account of an important class of causal belief which he calls “general rules”. I argue that he understands general rules, like all causal beliefs, as lively ideas which are habitually associated with our impressions or memories. However, I argue, he believes that they are unlike any reflectively produced causal beliefs in that they are produced quickly and automatically, such that they occur independently of any other processes of reasoning. Given this, (...) I argue, Hume appears to understand general rules as relatively simple beliefs, expressible only via generic sentences, like “birds lay eggs”. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:"General Rules" in Hume's Treatise THOMAS K. HEARN, JR. IT COULDBE CONFIDENTLYASSERTED in 1925 that Hume was "no longer a living figure." x Stuart Hampshire records that when he began his philosophy studies in 1933, Hume's conclusions were regarded at Oxford as "extravagances of scepticism which no one could seriously accept." 2 That virtually no Anglo-American philosopher would now share such opinions about Hume testifies not only (...) to the general change in the philosophical climate but, in addition, it reflects a transformation which has occurred in the interpretation of Hume's philosophy. In eitecting this transformation.much credit is due to the work of Norman Kemp Smith. Kemp Smith argued that preoccupation with Hume's empiricist heritage and his scepticism had blinded scholars to the fundamentally constructive intent of his philosophy, and, indeed, that only from the perspective of his positive achievement was it possible to grasp the nature and significance of Humean scepticism. This paper, in keeping with the basic orientation of Kemp Smith, sets out a central feature in the attempt to describe and assess Hume's constructive, nonsceptical point of view: Hume attributes to general rules "a mighty influence on our actions and understanding..." (374).4 This paper examines the Treatise to show that this was not just a casual comment. To discuss the "influence" of general rules requires an examination of their character and the various aspects of "action and understanding " in which such rules function. The thesis to be developed can be stated briefly. In Book I Hume introduces two sorts of general rules which must be distinguished carefully. One type of rule describes a propensity of the imagination to extend the scope This research was supported by a grant from the National Foundation on the Arts and Humanities. x Charles W. Hendcl, Studies in the Philosophy of David Hume (New York, 1963), p. 20. (First published in 1925.) For Professor Hendel's later comments on this statement, see pp. xxi ft. "Hume's Place in Philosophy" in David Hume, ed. D. F. Pears (London, 1963), p. 3. a Proper stress is due here to the phrase "basic orientation." There is much about Kemp Smith's understanding of Hume which is mistaken in my view. 9 The page references in parentheses refer to the Svlby-Bigge edition of A Treatise o/ Human Nature (Oxford, 1888). [4o5] 406 HISTORY OF PHILOSOPHY of judgments formed in one set of circumstances to other resembling but non-identical circumstances. The other type of general rule, the discussion of which largely occupies this paper, functions to correct certain natural propensities which result in erroneous belief or action if permitted to operate unchecked. The same pattern, a natural tendency requiring correction by general rules, is exhibited in all three books of the Treatise, and can be said to represent one of the basic ingredients in Hume's account of human nature and experience. It is somewhat surprising that in a book which patiently discusses almost evcxy theme in the Treatise, Kemp Smith's study contains no discussion at all of rules. This is the more puzzling as Kemp Smith clearly recognized that by reflection the understanding supplies principles which are normative for the interpretation of experience.5 Our aim in this study is to discuss what for Hume these principles are, and, as far as possible, how they fit into the Humean account of human nature. A fuller understanding of the nature and function of such reflective principles is required to spare Kemp Smith's interpretation from a seeming inconsistency. This apparent inconsistency arises because Kemp Smith takes the slavery of reason to the passions as the "key" to his understanding of Hume, but then develops the view that for Hume reason/s a passion, in Hume's words, "a wonderful and unintelligible instinct." (179)6 The inconsistency disappears when it is recognized that Kemp Smith's account of Hume requires a more subtle and complex understanding of the role of reason than that suggested by the emphasis on the "slavery of reason" especially in the early parts of the book. This study represents a way of supplying the broader and more const,ructive understanding of reason which... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Hume Studies Volume XXII, Number 1, April 1996, pp. 23-48 Fantastick Associations and Addictive General Rules: A Fundamental Difference between Hutcheson and Hume MICHAEL B. GILL The belief that God created human beings for some moral purpose underlies nearly all the moral philosophy written in Great Britain in the seventeenth and early eighteenth centuries. David Hume attacks this theological conception of human nature on all fronts. It (...) is out of these attacks that Hume develops his own "science of man" based solely on "experience and observation."1 Francis Hutcheson is often taken to be the most important positive influence on Hume. And there can be no doubt that Hume does take on board several crucial Hutchesonian elements. But Hutcheson's moral theory, like that of most of his contemporaries, is grounded in a theological conception of human nature to which Hume is adamantly opposed.2 In this paper I will examine how Hume's disagreements with Hutcheson embody the anti-theological purpose that defines Hume's work as a whole. I will look, in particular, at Hume's and Hutcheson's different positions on the principles of association. I hope to show how Hume's use of these principles in the Treatise advances his larger goal of placing "the science of man" on "a foundation almost entirely new" (T xvi). I will proceed, first, by explaining Hutcheson's conception of human nature and his use of the principles of association; second, by sketching in broad outline how Hume's accounts of the origins of justice and natural virtue undermine crucial components of Hutcheson's conception of human nature; and third, by elucidating in more detail an aspect of Hume's associationism that is particularly revealing of his distance from Hutcheson. Michael B. Gill is at the Department of Philosophy, Purdue University, 1360 Liberal Arts and Education Building, West Lafayette IN 47907 USA. email: [email protected]. 24 Michael B. Gill I. Hutcheson and Association Hutcheson discusses the mind's tendency to associate in all of his writings, but his most extensive treatment of the matter comes in his Essay on the Passions.3 Hutcheson begins the Essay by telling us that something is good if and only if the perception of it "Causes, or Occasions" a pleasurable feeling, and that something is evil if and only if the perception of it causes or occasions a painful feeling (EP 2). Crucially, Hutcheson denies that all of our pleasures and pains are of the same type (EP 1-8).4 He holds, rather, that there are at least five distinct types of pleasures and pains and that each of them grounds a different irreducible type of good and evil. There are, first, the pleasures and pains caused by things we perceive through the external senses of taste, touch, smell, etc.; things that cause such pleasures are called naturally good, while things that cause such pains are called naturally evil. Second, there are the "Pleasant Perceptions, arising from regular, harmonious, uniform Objects" (EP 5); the things that cause these pleasures are called beautiful.5 Third, there are the pleasures and pains we feel upon perceiving the happiness or misery of other human beings; the things that cause these pleasures are called public goods while those that cause the corresponding pains are called public evils. Fourth, there are pleasures and pains, usually called approval and disapproval, that we feel upon perceiving the actions of others; the actions that cause approval are called virtuous or morally good, while those that cause disapproval are called vicious or morally evil. Finally, there are the pleasures and pains we feel upon perceiving others' moral perceptions of our own actions; the pleasure of perceiving others' approval of one's actions is called the feeling of honor, while the pain of perceiving others' disapproval is called the feeling of shame. For Hutcheson, then, natural goodness, beauty, the public good, virtue and honor are all defined by our pleasures and pains. He does not think, however, that these are defined by just any of our actual or occurrent pleasures and pains. He holds, rather, that they are defined by the pleasures and pains we feel under certain privileged... (shrink)

An examination of the role played by general rules in Hume's positive (nonskeptical) epistemology. General rules for Hume are roughly just general beliefs. The difference between justified and unjustified belief is a matter of the influence of good versus bad general rules, the good general rules being the "extensive" and "constant" ones.

This chapter concerns Hume's account in Book I of the Treatise of Human Nature (1739) of the operation of ‘general rules’. It considers their relation to conceptions of regularity, probability, circumstance, and experience that obtained in early modern logic and natural philosophy, taking occasion to reflect upon the significance of Hume's claim, in the Enquiry Concerning Human Understanding, that natural philosophy and moral philosophy are ‘derived from the same principles’. It concludes by suggesting that a number of Hume's (...) essays are structured as reflections and refinements upon commonly-held general rules. (shrink)

This paper advances an interpretation of what Hume called ‘the general rules’: natural principles of belief-formation that nevertheless can be augmented via reflection. According to Hume, reflection is, in part, what separates the wise from the vulgar. In this paper, I argue that for Hume being wise must therefore be, to some degree, voluntary. Hume faced a significant problem in attempting to reconcile his epistemic normativity, i.e. his claims about what we ought to believe, with his largely involuntarist (...) theory of the mind. Reflection on the General Rules, and an interpretation of that reflection as voluntary, helps explain not only Hume's theory of belief, but also how he hoped to reconcile epistemic normativity with naturalism about the mental. (shrink)

Throughout the nineteenth and early twentieth centuries, judges and lawmakers sought to erase the visibility of unmarried women. In the public law arena, for example, legislators conflated women and wives for the purpose of the franchise, arguing that women did not need the vote because their husbands voted for them. In the private law arena, doctrines intended to guarantee support to unmarried women functioned by constructing single women's legal identities in relation to marriage, thereby suggesting that marriage could provide for (...) all women's material needs. This essay argues that understanding the history of single women's legal rights is critical to understanding the legal construction of marriage as the dominant institution for regulating all women's private relationships to men and public relationships to the state. Denying single women's existence allowed the law to ignore the potential threat they posed to a marriage-centric socio-legal order. Legal and political changes in the early decades of the twentieth century, however, made it increasingly difficult for the law to deny the existence of unmarried women. As single women gained social prominence, nonlegal writers in the 1930s and 1940s produced a new genre of prescriptive and descriptive literature for and about women living outside of marriage. Unlike earlier legal texts, these works embraced single women as a permanent and visible part of society. Like their legal predecessors, however, these modern authors sought to minimize the threat posed by single women to the institution of marriage, pointing to single women as proof of marriage's modern, consensual, democratic nature. (shrink)

Phonological rules create alternations in the phonetic realizations of related words. These rules must be learned by infants in order to identify the phonological inventory, the morphological structure, and the lexicon of a language. Recent work proposes a computational model for the learning of one kind of phonological alternation, allophony . This paper extends the model to account for learning of a broader set of phonological alternations and the formalization of these alternations as general rules. In (...) Experiment 1, we apply the original model to new data in Dutch and demonstrate its limitations in learning nonallophonic rules. In Experiment 2, we extend the model to allow it to learn general rules for alternations that apply to a class of segments. In Experiment 3, the model is further extended to allow for generalization by context; we argue that this generalization must be constrained by linguistic principles. (shrink)

The purpose of this brief note is to prove a limitative theorem for a generalization of the deduction theorem. I discuss the relationship between the deduction theorem and rules of inference. Often when the deduction theorem is claimed to fail, particularly in the case of normal modal logics, it is the result of a confusion over what the deduction theorem is trying to show. The classic deduction theorem is trying to show that all so-called ‘derivable rules’ can be (...) encoded into the object language using the material conditional. The deduction theorem can be generalized in the sense that one can attempt to encode all types of rules into the object language. When a rule is encoded in this way I say that it is reflected in the object language. What I show, however, is that certain logics which reflect a certain kind of rule must be trivial. Therefore, my generalization of the deduction theorem does fail where the classic deduction theorem didn’t. (shrink)

This paper studies a ranking rule of the following type axiomatically: each voter places k candidates into n categories with ranks from n to 1 attached to these categories, the candidate(s) with the highest aggregate score is (are) the winner(s). We show that it is characterized by a monotonicity condition and a multi-stage cancellation property.

The structure of derivations in natural deduction is analyzed through isomorphism with a suitable sequent calculus, with twelve hidden convertibilities revealed in usual natural deduction. A general formulation of conjunction and implication elimination rules is given, analogous to disjunction elimination. Normalization through permutative conversions now applies in all cases. Derivations in normal form have all major premisses of elimination rules as assumptions. Conversion in any order terminates.Through the condition that in a cut-free derivation of the sequent Γ⇒C, (...) no inactive weakening or contraction formulas remain in Γ, a correspondence with the formal derivability relation of natural deduction is obtained: All formulas of Γ become open assumptions in natural deduction, through an inductively defined translation. Weakenings are interpreted as vacuous discharges, and contractions as multiple discharges. In the other direction, non-normal derivations translate into derivations with cuts having the cut formula principal either in both premisses or in the right premiss only. (shrink)

This paper studies axiomatic characterizations of the constrained equal awards rule for bankruptcy problems. We show that many results apply in a much more general context than for which they are originally formulated. In particular, we generalize several axiomatic characterizations based on symmetry, sustainability, and consistency to the domain of bankruptcy problems with nontransferable utility.

The comparison between biological and social macroevolution is a very important (though insufficiently studied) subject whose analysis renders new significant possibilities to comprehend the processes, trends, mechanisms, and peculiarities of each of the two types of macroevolution. Of course, there are a few rather important (and very understandable) differences between them; however, it appears possible to identify a number of fundamental similarities. One may single out at least three fundamental sets of factors determining those similarities. First of all, those similarities (...) stem from the fact that in both cases we are dealing with very complex non-equilibrium (but rather stable) systems whose principles of functioning and evolution are described by the General Systems' Theory, as well as by a number of cybernetic principles and laws. -/- Secondly, in both cases we do not deal with isolated systems; in both cases we deal with a complex interaction between systems of organic systems and external environment, whereas the reaction of systems to external challenges can be described in terms of certain general principles (that, however, express themselves rather differently within the biological reality, on the one hand, and within the social reality, on the other). -/- Thirdly, it is necessary to mention a direct ‘genetic’ link between the two types of macroevolution and their mutual influence. -/- It is important to emphasize that the very similarity of the principles and regularities of the two types of macroevolution does not imply their identity. Rather significant similarities are frequently accompanied by enormous differences. For example, genomes of the chimpanzees and the humans are very similar – with differences constituting just a few per cent; however, there are enormous differences with respect to intellectual and social differences of the chimpanzees and the humans hidden behind the apparently ‘insignificant’ difference between the two genomes. Thus, in certain respects it appears reasonable to consider the biological and social macroevolution as a single macroevolutionary process. This implies the necessity to comprehend the general laws and regularities that describe this process, though their manifestations may display significant variations depending on properties of a concrete evolving entity (biological, or social one). An important notion that may contribute to the improvement of the operationalization level as regards the comparison between the two types of macroevolution is the one that we suggested some time ago – the social aromorphosis (that was developed as a counterpart to the notion of biological aromorphosis well established within Russian evolutionary biology). We regard social aromorphosis as a rare qualitative macrochange that increases in a very significant way complexity, adaptability, and mutual influence of the social systems, that opens new possibilities for social macrodevelopment. In our paper we discuss a number of regularities that describe biological and social macroevolution and that employ the notions of social and biological aromorphosis such as ones of the module evolution (or the evolutionary ‘block assemblage’), ‘payment for arogenic progress’ etc. (shrink)

Semantic generalists and semantic particularists disagree over the role of rules or principles in linguistic competence and in the determination of linguistic meaning, and hence over the importance of the notions of a rule or of a principle in philosophical accounts of language. In this paper, I have argued that the particularist’s case against generalism is far from decisive and that by moderating the claims she makes on behalf of her thesis the generalist can accommodate many of the considerations (...) that the particularist cites in support of her position. (shrink)

The widely discussed "discursive dilemma" shows that majority voting in a group of individuals on logically connected propositions may produce irrational collective judgments. We generalize majority voting by considering quota rules, which accept each proposition if and only if the number of individuals accepting it exceeds a given threshold, where different thresholds may be used for different propositions. After characterizing quota rules, we prove necessary and sufficient conditions on the required thresholds for various collective rationality requirements. We also (...) consider sequential quota rules, which ensure collective rationality by adjudicating propositions sequentially and letting earlier judgments constrain later ones. Sequential rules may be path-dependent and strategically manipulable. We characterize path-independence and prove its essential equivalence to strategy-proofness. Our results shed light on the rationality of simple-, super-, and sub-majoritarian decision-making. (shrink)

Bilateral proof systems, which provide rules for both affirming and denying sentences, have been prominent in the development of proof-theoretic semantics for classical logic in recent years. However, such systems provide a substantial amount of freedom in the formulation of the rules, and, as a result, a number of different sets of rules have been put forward as definitive of the meanings of the classical connectives. In this paper, I argue that a single general schema for (...) bilateral proof rules has a reasonable claim to inferentially articulating the core meaning of all of the classical connectives. I propose this schema in the context of a bilateral sequent calculus in which each connective is given exactly two rules: a rule for affirmation and a rule for denial. Positive and negative rules for all of the classical connectives are given by a single rule schema, harmony between these positive and negative rules is established at the schematic level by a pair of elimination theorems, and the truth-conditions for all of the classical connectives are read off at once from the schema itself. (shrink)

As it is well known, in the forties of the past century, Curry proved that in any logic S closed under Modus Ponens, uniform substitution of propositional variables and the Contraction Law, the naïve Comprehension axiom trivializes S in the sense that all propositions are derivable in S plus CA. Not less known is the fact that, ever since Curry published his proof, theses and rules weaker than W have been shown to cause the same effect as W causes. (...) Among these, the Contraction rule or the Modus Ponens axiom, for example, are to be noted. But, moreover, as Brady has proved, even the Generalized Modus Ponens axiom or the Generalized Contraction rule give rise to “Curry’s Paradox” under the same circumstances as W does. In some previous work by us, “weak relevant model structures” are defined on “weak relevant matrices” by generalizing Brady’s model structure MCL built upon Meyer’s Crystal matrix CL. We have proved that wr-ms only verify logics with the “depth relevance condition”. The aim of this paper is to show how to falsify gMPa and gRW in certain wr-ms. In particular, it will be shown that gMPa is falisfied in any wr-ms and gRW in any wr-ms verifying Routley and Meyer’s basic positive logic B+. (shrink)

RÉSUMÉLe «clair» et le «distinct» comptent parmi les concepts les plus importants de la théorie cartésienne de la connaissance. Il n'est pas étonnant dès lors qu'il se soit trouvé quelques divergences quant à la façon dont ces concepts doivent être compris. Mais jusqu'à tout récemment, les chercheurs ne se sont guère attardés sur ces divergences, alors pourtant que certaines d'entre elles sont fort remarquables. Ainsi certaines interprétations de la théorie soutiennent que le fait de contraindre la volonté est la marque (...) des idées claires et distinctes, tandis que cela est rejeté par d'autres. Certaines encore soutiennent que le clair et le distinct sont susceptibles de degrés, tandis que d'autres ne sont pas d'accord. Mon objectif dans cet article est d'esquisser une théorie générale capable de rendre compte, dans ces cas comme dans un certain nombre d'autres, de cette variété d'interprétations du clair et du distinct qui est enracinée dans le corpus cartésien même. J'appelle cette théorie «générale» dans la mesure où les diverses interprétations évoquées sont par rapport à elle comme des espèces par rapport à un genre. Ma reconstruction de la théorie générale trouve son appui textuel dans l'ensemble du corpus cartésien. Le gros de mes efforts, cependant, consiste à retracer la théorie dans un texte qui fut l'un des premiers écrits de Descartes : les Régies pour la direction de l'esprit. (shrink)

In this paper, missing attribute values in incomplete data sets have three possible interpretations: lost values, attribute-concept values and ‘do not care’ conditions. For rule induction, we use characteristic sets and generalized maximal consistent blocks. Therefore, we apply six different approaches for data mining. As follows from our previous experiments, where we used an error rate evaluated by ten-fold cross validation as the main criterion of quality, no approach is universally the best. Thus, we decided to compare our six approaches (...) using complexity of rule sets induced from incomplete data sets. We show that the smallest rule sets are induced from incomplete data sets with attribute-concept values, while the most complicated rule sets are induced from data sets with lost values. The choice between interpretations of missing attribute values is more important than the choice between characteristic sets and generalized maximal consistent blocks. (shrink)

What is the likelihood of controlling technology by means of the law? In traditional societies, the law was deeply embedded in, and dependent on, culture (the totality of human creations for making sense of and living in the world). Industrialization required a complete restructuring of both technology and society, thus engulfing all traditions in a flood of new situations for which there were no precedents. This necessitated a growing reliance on reason at the expense of culture, thereby creating a rational (...) and technical order that evolved with less and less reference to sense (i.e. experience and culture). It is within this context that recent legal transformations must be understood as participating in an order of non-sense. This bodes ill for protecting and helping to ensure a livable, sustainable human future. (shrink)

In this paper I explore what the P4C philosophical novel can contribute to deciding how we should use ethical rules in moral education. As I see it the philosophical novel urges us to regard ethical rule-following with some suspicion. Instead we are directed to appreciate the particular contexts and circumstances of ethical thinking, saying, and doing. But if we don’t teach ethics by the rules, then what is the alternative pedagogy? One possibility is to cultivate ethical expertise by (...) analogy to an epistemic skill model of practical activity, as some moral particularists have urged. Employing a skill model has significant implications for teaching ethics in a wide range of institutional settings where general rules and principles typically prevail. (shrink)

We present a general framework for representing belief-revision rules and use it to characterize Bayes's rule as a classical example and Jeffrey's rule as a non-classical one. In Jeffrey's rule, the input to a belief revision is not simply the information that some event has occurred, as in Bayes's rule, but a new assignment of probabilities to some events. Despite their differences, Bayes's and Jeffrey's rules can be characterized in terms of the same axioms: "responsiveness", which requires (...) that revised beliefs incorporate what has been learnt, and "conservativeness", which requires that beliefs on which the learnt input is "silent" do not change. To illustrate the use of non-Bayesian belief revision in economic theory, we sketch a simple decision-theoretic application. (shrink)

Wittgenstein famously remarks that ‘the meaning of a word is its use’ (PI §43). Whether or not one views this as gesturing at a ‘theory’ of meaning, or instead as aiming primarily at dissuading us from certain misconceptions of language that are a source of puzzlement, it is clear that Wittgenstein held that for certain purposes the meaning of an expression could profitably be characterised as its use. Throughout his later writings, however, Wittgenstein’s appeal to the notion of use pulls (...) in two directions. In several places, Wittgenstein seems to connect the notion of an expression’s meaning with that of use in the sense of usage or practice. More specifically, he suggests that for an expression to possess meaning is for there to be a practice of employing it according to certain rules. ‘That’, he tells us, ‘is why there exists a correspondence between the concepts “rule” and “meaning”’ (OC §62; cf. PG 68; PO 51; RFM VI §28; VW 103). Indeed, Wittgenstein goes so far as to say, ‘The rule-governed nature of our languages permeates our life’ (RC §303). Call the view that the meaning of an expression is determined by a general principle governing its use, rulism. (shrink)

The generalized Bayes’ rule (GBR) can be used to conduct ‘quasi-Bayesian’ analyses when prior beliefs are represented by imprecise probability models. We describe a procedure for deriving coherent imprecise probability models when the event space consists of a finite set of mutually exclusive and exhaustive events. The procedure is based on Walley’s theory of upper and lower prevision and employs simple linear programming models. We then describe how these models can be updated using Cozman’s linear programming formulation of the GBR. (...) Examples are provided to demonstrate how the GBR can be applied in practice. These examples also illustrate the effects of prior imprecision and prior-data conflict on the precision of the posterior probability distribution. (shrink)

This article deals with a set-theoretic interpretation of the Talmudic rules of General and Specific, known as Klal and Prat (KP), Prat and Klal (PK), Klal and Prat and Klal (KPK) and Prat and Klal and Prat (PKP).

Prawitz conjectured that the proof-theoretically valid logic is intuitionistic logic. Recent work on proof-theoretic validity has disproven this. In fact, it has been shown that proof-theoretic validity is not even closed under substitution. In this paper, we make a minor modification to the definition of proof-theoretic validity found in Prawitz’s 1973paper ‘Towards a foundation of a general proof theory’ and refined by Schroeder-Heister in ‘Validity concepts in proof-theoretic semantics’ (2006). We will call the new notion generalized proof-theoretic validity and (...) show that the logic of generalized proof-theoretic validity is intuitionistic logic. (shrink)

Probability theory, epistemically interpreted, provides an excellent, if not the best available account of inductive reasoning. This is so because there are general and definite rules for the change of subjective probabilities through information or experience; induction and belief change are one and same topic, after all. The most basic of these rules is simply to conditionalize with respect to the information received; and there are similar and more general rules. 1 Hence, a fundamental reason (...) for the epistemological success of probability theory is that there at all exists a well-behaved concept of conditional probability. Still, people have, and have reasons for, various concerns over probability theory. One of these is my starting point: Intuitively, we have the notion of plain belief; we believe propositions2 to be true (or to be false or neither). Probability theory, however, offers no formal counterpart to this notion. Believing A is not the same as having probability 1 for A, because probability 1 is incorrigible3; but plain belief is clearly corrigible. And believing A is not the same as giving A a probability larger than some 1 - c, because believing A and believing B is usually taken to be equivalent to believing A & B.4 Thus, it seems that the formal representation of plain belief has to take a non-probabilistic route. Indeed, representing plain belief seems easy enough: simply represent an epistemic state by the set of all propositions believed true in it or, since I make the common assumption that plain belief is deductively closed, by the conjunction of all propositions believed true in it. But this does not yet provide a theory of induction, i.e. an answer to the question how epistemic states so represented are changed tbrough information or experience. There is a convincing partial answer: if the new information is compatible with the old epistemic state, then the new epistemic state is simply represented by the conjunction of the new information and the old beliefs. This answer is partial because it does not cover the quite common case where the new information is incompatible with the old beliefs. It is, however, important to complete the answer and to cover this case, too; otherwise, we would not represent plain belief as conigible. The crucial problem is that there is no good completion. When epistemic states are represented simply by the conjunction of all propositions believed true in it, the answer cannot be completed; and though there is a lot of fruitful work, no other representation of epistemic states has been proposed, as far as I know, which provides a complete solution to this problem. In this paper, I want to suggest such a solution. In [4], I have more fully argued that this is the only solution, if certain plausible desiderata are to be satisfied. Here, in section 2, I will be content with formally defining and intuitively explaining my proposal. I will compare my proposal with probability theory in section 3. It will turn out that the theory I am proposing is structurally homomorphic to probability theory in important respects and that it is thus equally easily implementable, but moreover computationally simpler. Section 4 contains a very brief comparison with various kinds of logics, in particular conditional logic, with Shackle's functions of potential surprise and related theories, and with the Dempster - Shafer theory of belief functions. (shrink)