Deductive Cogency holds that the set of propositions towards which one has, or is prepared to have, a given type of propositional attitude should be consistent and closed under logical consequence. While there are many propositional attitudes that are not subject to this requirement, e.g. hoping and imagining, it is at least prima facie plausible that Deductive Cogency applies to the doxastic attitude involved in propositional knowledge, viz. belief. However, this thought is undermined by the well-known preface paradox, (...) leading a number of philosophers to conclude that Deductive Cogency has at best a very limited role to play in our epistemic lives. I argue here that Deductive Cogency is still an important epistemic requirement, albeit not as a requirement on belief. Instead, building on a distinction between belief and acceptance introduced by Jonathan Cohen and recent developments in the epistemology of understanding, I propose that Deductive Cogency applies to the attitude of treating propositions as given in the context of attempting to understand a given phenomenon. I then argue that this simultaneously accounts for the plausibility of the considerations in favor of Deductive Cogency and avoids the problematic consequences of the preface paradox. (shrink)

In attempt to provide an answer to the question of origin of deductive proofs, I argue that Aristotle’s philosophy of math is more accurate opposed to a Platonic philosophy of math, given the evidence of how mathematics began. Aristotle says that mathematical knowledge is a posteriori, known through induction; but once knowledge has become unqualified it can grow into deduction. Two pieces of recent scholarship on Greek mathematics propose new ways of thinking about how mathematics began in the Greek (...) culture. Both claimed there was a close relationship between the culture and mathematicians; mathematics was understood through imaginative processes, experiencing the proofs in tangible ways, and establishing a consistent unified form of argumentation. These pieces of evidence provide the context in which Aristotle worked and their contributions lend support to the argument that mathematical premises as inductively available is a better way of understanding the origins of deductive practices, opposed to the Platonic tradition. (shrink)

It is often assumed that Fichte's aim in Part I of the System of Ethics is to provide a deduction of the moral law, the very thing that Kant – after years of unsuccessful attempts – deemed impossible. On this familiar reading, what Kant eventually viewed as an underivable 'fact' (Factum), the authority of the moral law, is what Fichte traces to its highest ground in what he calls the principle of the 'I'. However, scholars have largely overlooked a passage (...) in the System of Ethics where Fichte explicitly invokes Kant's doctrine of the fact of reason with approval, claiming that consciousness of the moral law grounds our belief in freedom (GA I/5:65). On the reading I defend, Fichte's invocation of the Factum is consistent with the structure of Part I when we distinguish (a) the feeling of moral compulsion from (b) the moral law itself. (shrink)

The paper provides an argument for the thesis that an agent’s degrees of disbelief should obey the ranking calculus. This Consistency Argument is based on the Consistency Theorem. The latter says that an agent’s belief set is and will always be consistent and deductively closed iff her degrees of entrenchment satisfy the ranking axioms and are updated according to the ranktheoretic update rules.

It is argued that the goal of Hilbert's program was to prove the model-theoretical consistency of different axiom systems. This Hilbert proposed to do by proving the deductive consistency of the relevant systems. In the extended independence-friendly logic there is a complete proof method for the contradictory negations of independence-friendly sentences, so the existence of a single proposition that is not disprovable from arithmetic axioms can be shown formally in the extended independence-friendly logic. It can also be (...) proved by means of independence-friendly logic that proof-theoretical consistency of a sentence S implies the existence of a model in which S is not false. Hence the consistency of the axioms of arithmetic in the sense of being not-false in a model can be proved. (shrink)

All existing impossibility theorems on judgment aggregation require individual and collective judgment sets to be consistent and complete, arguably a demanding rationality requirement. They do not carry over to aggregation functions mapping profiles of consistent individual judgment sets to consistent collective ones. We prove that, whenever the agenda of propositions under consideration exhibits mild interconnections, any such aggregation function that is "neutral" between the acceptance and rejection of each proposition is dictatorial. We relate this theorem to the literature.

The present PhD thesis is concerned with the question whether good reasoning requires that the subject has some cognitive grip on the relation between premises and conclusion. One consideration in favor of such a requirement goes as follows: In order for my belief-formation to be an instance of reasoning, and not merely a causally related sequence of beliefs, the process must be guided by my endorsement of a rule of reasoning. Therefore I must have justified beliefs about the relation between (...) my premises and my conclusion. -/- The rationality of a belief often depends on whether it is rightly connected to other beliefs, or more generally to other mental states —the states capable of providing a reason to holding the belief in question. For instance, some rational beliefs are connected to other beliefs by being inferred from them. It is often accepted that the connection implies that the subject in some sense ‘takes the mental states in question to be reason-providing’. But views on how exactly this is to be understood differ widely. They range from interpretations according to which ‘taking a mental state to be reason-providing’ imposes a mere causal sustaining relation between belief and reason-providing state to interpretations according to which one ‘takes a mental state to be reason-providing’ only if one believes that the state is reason-providing. The most common worry about the latter view is that it faces a vicious regress. In this thesis a different but in some respects similar interpretation of ‘taking something as reason-providing’ is given. It is argued to consist of a disposition to react in certain ways to information that challenges the reason-providing capacity of the allegedly reason-providing state. For instance, that one has inferred A from B partly consists in being disposed to suspend judgment about A if one obtains a reason to believe that B does not render A probable. The account is defended against regress-objections and the suspicion of explanatory circularity. (shrink)

Few of Kant’s doctrines are as difficult to understand as that of self-affection. Its brief career in the published literature consists principally in its unheralded introduction in the Transcendental Aesthetic and unexpected re-appearance at a key moment in the Deduction chapter in the B edition of the first Critique. Kant’s commentators, confronted with the difficulty of this doctrine, have naturally resorted to various strategies of clarification, ranging from distinguishing between empirical and transcendental self-affection, divorcing self-affection from the claims of self-knowledge (...) with which Kant explicitly connects it, and, perhaps least justified of all, ignoring the doctrine altogether. Yet the connection between self-affection and central Critical doctrines (such as the transcendental synthesis of the imagination) marks all of these strategies as last resorts. In this paper, I seek to provide a clearer outline of the constellation of those issues which inform Kant’s discussion of self-affection. More particularly, I intend to explain the crucial role played by self-affection in the account of the transcendental conditions of perception provided late in the B Deduction. (shrink)

In the present paper, we prove the normalization theorem and the consistency of the first-order classical logic with disjunctive syllogism. First, we propose the natural deduction system SCD for classical propositional logic having rules for conjunction, implication, negation, and disjunction. The rules for disjunctive syllogism are regarded as the rules for disjunction. After we prove the normalization theorem and the consistency of SCD, we extend SCD to the system SPCD for the first-order classical logic with disjunctive syllogism. It (...) can be shown that SPCD is conservative extension to SCD. Then, the normalization theorem and the consistency of SPCD are given. (shrink)

Is it possible to give a justification of our own practice of deductive inference? The purpose of this paper is to explain what such a justification might consist in and what its purpose could be. On the conception that we are going to pursue, to give a justification for a deductive practice means to explain in terms of an intuitively satisfactory notion of validity why the inferences that conform to the practice coincide with the valid ones. That is, (...) a justification should provide an analysis of the notion of validity and show that the inferences that conform to the practice are just the ones that are valid. Moreover, a complete justification should also explain the purpose, or point, of our inferential practice. We are first going to discuss the objection that any justification of our deductive practice must use deduction and therefore be circular. Then we will consider a particular model of justificatory explanation, building on Georg Kreisel’s concept of informal rigour. Finally, in the main part of the paper, we will discuss three ideas for defining the notion of validity: (i) the classical conception according to which the notion of (bivalent) truth is taken as basic and validity is defined in terms of the preservation of truth; (ii) the constructivist idea of starting instead with the notion of (a canonical) proof (or verification) and define validity in terms of this notion; (iii) the idea of taking the notions of rational acceptance and rejection as given and define an argument to be valid just in case it is irrational to simultaneously accept its premises and reject its conclusion (or conclusions, if we allow for multiple conclusions). Building on work by Dana Scott, we show that the last conception may be viewed as being, in a certain sense, equivalent to the first one. Finally, we discuss the so-called paradox of inference and the informativeness of deductive arguments. (shrink)

Future Logic is an original, and wide-ranging treatise of formal logic. It deals with deduction and induction, of categorical and conditional propositions, involving the natural, temporal, extensional, and logical modalities. Traditional and Modern logic have covered in detail only formal deduction from actual categoricals, or from logical conditionals (conjunctives, hypotheticals, and disjunctives). Deduction from modal categoricals has also been considered, though very vaguely and roughly; whereas deduction from natural, temporal and extensional forms of conditioning has been all but totally ignored. (...) As for induction, apart from the elucidation of adductive processes (the scientific method), almost no formal work has been done. This is the first work ever to strictly formalize the inductive processes of generalization and particularization, through the novel methods of factorial analysis, factor selection and formula revision. This is the first work ever to develop a formal logic of the natural, temporal and extensional types of conditioning (as distinct from logical conditioning), including their production from modal categorical premises. Future Logic contains a great many other new discoveries, organized into a unified, consistent and empirical system, with precise definitions of the various categories and types of modality (including logical modality), and full awareness of the epistemological and ontological issues involved. Though strictly formal, it uses ordinary language, wherever symbols can be avoided. Among its other contributions: a full list of the valid modal syllogisms (which is more restrictive than previous lists); the main formalities of the logic of change (which introduces a dynamic instead of merely static approach to classification); the first formal definitions of the modal types of causality; a new theory of class logic, free of the Russell Paradox; as well as a critical review of modern metalogic. But it is impossible to list briefly all the innovations in logical science — and therefore, epistemology and ontology — this book presents; it has to be read for its scope to be appreciated. (shrink)

The Logic of Causation: Definition, Induction and Deduction of Deterministic Causality is a treatise of formal logic and of aetiology. It is an original and wide-ranging investigation of the definition of causation (deterministic causality) in all its forms, and of the deduction and induction of such forms. The work was carried out in three phases over a dozen years (1998-2010), each phase introducing more sophisticated methods than the previous to solve outstanding problems. This study was intended as part of a (...) larger work on causal logic, which additionally treats volition and allied cause-effect relations (2004). The Logic of Causation deals with the main technicalities relating to reasoning about causation. Once all the deductive characteristics of causation in all its forms have been treated, and we have gained an understanding as to how it is induced, we are able to discuss more intelligently its epistemological and ontological status. In this context, past theories of causation are reviewed and evaluated (although some of the issues involved here can only be fully dealt with in a larger perspective, taking volition and other aspects of causality into consideration, as done in Volition and Allied Causal Concepts). Phase I: Macroanalysis. Starting with the paradigm of causation, its most obvious and strongest form, we can by abstraction of its defining components distinguish four genera of causation, or generic determinations, namely: complete, partial, necessary and contingent causation. When these genera and their negations are combined together in every which way, and tested for consistency, it is found that only four species of causation, or specific determinations, remain conceivable. The concept of causation thus gives rise to a number of positive and negative propositional forms, which can be studied in detail with relative ease because they are compounds of conjunctive and conditional propositions whose properties are already well known to logicians. The logical relations (oppositions) between the various determinations (and their negations) are investigated, as well as their respective implications (eductions). Thereafter, their interactions (in syllogistic reasoning) are treated in the most rigorous manner. The main question we try to answer here is: is (or when is) the cause of a cause of something itself a cause of that thing, and if so to what degree? The figures and moods of positive causative syllogism are listed exhaustively; and the resulting arguments validated or invalidated, as the case may be. In this context, a general and sure method of evaluation called ‘matricial analysis’ (macroanalysis) is introduced. Because this (initial) method is cumbersome, it is used as little as possible – the remaining cases being evaluated by means of reduction. Phase II: Microanalysis. Seeing various difficulties encountered in the first phase, and the fact that some issues were left unresolved in it, a more precise method is developed in the second phase, capable of systematically answering most outstanding questions. This improved matricial analysis (microanalysis) is based on tabular prediction of all logically conceivable combinations and permutations of conjunctions between two or more items and their negations (grand matrices). Each such possible combination is called a ‘modus’ and is assigned a permanent number within the framework concerned (for 2, 3, or more items). This allows us to identify each distinct (causative or other, positive or negative) propositional form with a number of alternative moduses. This technique greatly facilitates all work with causative and related forms, allowing us to systematically consider their eductions, oppositions, and syllogistic combinations. In fact, it constitutes a most radical approach not only to causative propositions and their derivatives, but perhaps more importantly to their constituent conditional propositions. Moreover, it is not limited to logical conditioning and causation, but is equally applicable to other modes of modality, including extensional, natural, temporal and spatial conditioning and causation. From the results obtained, we are able to settle with formal certainty most of the historically controversial issues relating to causation. Phase III: Software Assisted Analysis. The approach in the second phase was very ‘manual’ and time consuming; the third phase is intended to ‘mechanize’ much of the work involved by means of spreadsheets (to begin with). This increases reliability of calculations (though no errors were found, in fact) – but also allows for a wider scope. Indeed, we are now able to produce a larger, 4-item grand matrix, and on its basis find the moduses of causative and other forms needed to investigate 4-item syllogism. As well, now each modus can be interpreted with greater precision and causation can be more precisely defined and treated. In this latest phase, the research is brought to a successful finish! Its main ambition, to obtain a complete and reliable listing of all 3-item and 4-item causative syllogisms, being truly fulfilled. This was made technically feasible, in spite of limitations in computer software and hardware, by cutting up problems into smaller pieces. For every mood of the syllogism, it was thus possible to scan for conclusions ‘mechanically’ (using spreadsheets), testing all forms of causative and preventive conclusions. Until now, this job could only be done ‘manually’, and therefore not exhaustively and with certainty. It took over 72’000 pages of spreadsheets to generate the sought for conclusions. This is a historic breakthrough for causal logic and logic in general. Of course, not all conceivable issues are resolved. There is still some work that needs doing, notably with regard to 5-item causative syllogism. But what has been achieved solves the core problem. The method for the resolution of all outstanding issues has definitely now been found and proven. The only obstacle to solving most of them is the amount of labor needed to produce the remaining (less important) tables. As for 5-item syllogism, bigger computer resources are also needed. (shrink)

(...) However, whether we chose a weak or strong approximation, the set would not make any sense at all, if (once more) this choice would not be justified in either temporal or spatial sense or given the context of possible applicability of the set in different circumstances. This would obviously represent a dualism in itself as we would (for instance) posit and apply a full identity-equality-equivalence of x and y when applying Newtonian physics to certain observations we make (it would (...) be the case of neural correlates), and we would posit and apply a non - identity-equality-equivalence of x and y when applying Quantum mechanics to other observations. Following this dualism in and of theories, the same sate would need to be slightly modified: U2:(x~y)∪(x≈y); U3:(x~y)∩(x≈y); U4a:(x~y)⊆(x≈y) vs. U4b:(x~y)⊇(x≈y). (shrink)

Choices confront us with questions. How we act depends on our answers to those questions. So the way our beliefs guide our choices is not just a function of their informational content, but also depends systematically on the questions those beliefs address. This paper gives a precise account of the interplay between choices, questions and beliefs, and harnesses this account to obtain a principled approach to the problem of deduction. The result is a novel theory of belief-guided action that explains (...) and predicts the decisions of agents who, like ourselves, fail to be logically omniscient: that is, of agents whose beliefs may not be deductively closed, or even consistent. (Winner of the 2021 Isaac Levi Prize.). (shrink)

This paper reconsiders whether rational choice and game theory represent cases of economics imperialism. It follows the work of Uskali Maki who analyzes the significance and characteristics of disciplinary imperialism in natural science and social science. "Economics Imperialism" is a term often used to describe the increasing impact and reach of economics with respect to its encroachment on other disciplines including political science and psychology. Maki provides a framework for assessing whether the influence of one discipline on another could be (...) a case of "good imperialism" consistent with unification and greater explanatory power. The paper examines whether in the case of economics, "rational choice imperialism" is a better understanding of the question of contention. Rational choice has been used to model addiction, sex, marriage, sleep, and suicide. Applying tools offered by Maki, this paper argues that although the imperialism of rational choice over multiple disciplines provides a unified means of modeling human action, it does not demonstrably achieve deeper understanding of either individual or collective action. Furthermore, rational choice modeling may alter the human practices it analyzes if it is used in public policy. Thus although rational choice offers a means to check for deductive consistency within and among its models, it has elements suggestive of the "bad disciplinary imperialism" that Uskali provides a means to critique. (shrink)

Several recent results on the aggregation of judgments over logically connected propositions show that, under certain conditions, dictatorships are the only propositionwise aggregation functions generating fully rational (i.e., complete and consistent) collective judgments. A frequently mentioned route to avoid dictatorships is to allow incomplete collective judgments. We show that this route does not lead very far: we obtain oligarchies rather than dictatorships if instead of full rationality we merely require that collective judgments be deductively closed, arguably a minimal condition of (...) rationality, compatible even with empty judgment sets. We derive several characterizations of oligarchies and provide illustrative applications to Arrowian preference aggregation and Kasher and Rubinsteinís group identification problem. (shrink)

Agents are often assumed to have degrees of belief (“credences”) and also binary beliefs (“beliefs simpliciter”). How are these related to each other? A much-discussed answer asserts that it is rational to believe a proposition if and only if one has a high enough degree of belief in it. But this answer runs into the “lottery paradox”: the set of believed propositions may violate the key rationality conditions of consistency and deductive closure. In earlier work, we showed that (...) this problem generalizes: there exists no local function from degrees of belief to binary beliefs that satisfies some minimal conditions of rationality and non-triviality. “Locality” means that the binary belief in each proposition depends only on the degree of belief in that proposition, not on the degrees of belief in others. One might think that the impossibility can be avoided by dropping the assumption that binary beliefs are a function of degrees of belief. We prove that, even if we drop the “functionality” restriction, there still exists no local relation between degrees of belief and binary beliefs that satisfies some minimal conditions. Thus functionality is not the source of the impossibility; its source is the condition of locality. If there is any non-trivial relation between degrees of belief and binary beliefs at all, it must be a “holistic” one. We explore several concrete forms this “holistic” relation could take. (shrink)

In this paper we prove the completeness of three logical systems I LI, IL2 and IL3. IL1 deals solely with identities {a = b), and its deductions are the direct deductions constructed with the three traditional rules: (T) from a = b and b = c infer a = c, (S) from a = b infer b = a and (A) infer a = a(from anything). IL2 deals solely with identities and inidentities {a ± b) and its deductions include both (...) the direct and the indirect deductions constructed with the three traditional rules. IL3 is a hybrid of IL1 and IL2: its deductions are all direct as in IL1 but it deals with identities and inidentities as in IL2. IL1 and IL2 have a high degree of naturalness. Although the hybrid system IL3 was constructed as an artifact useful in the mathematical study of IL1 and IL2, it nevertheless has some intrinsically interesting aspects. The main motivation for describing and studying such simple systems is pedagogical. In teaching beginning logic one would like to present a system of logic which has the following properties. First, it exemplifies the main ideas of logic: implication, deduction, non-implication, counterargument(or countermodel), logical truth, self-contradiction, consistency,satisfiability, etc. Second, it exemplifies the usual general metaprinciples of logic: contraposition and transitivity of implication, cut laws, completeness,soundness, etc. Third, it is simple enough to be thoroughly grasped by beginners. Fourth, it is obvious enough so that its rules do not appear to be arbitrary or purely conventional. Fifth, it does not invite confusions which must be unlearned later. Sixth, it involves a minimum of presuppositions which are no longer accepted in mainstream contemporary logic. (shrink)

ABSTRACT: An introduction to Stoic logic. Stoic logic can in many respects be regarded as a fore-runner of modern propositional logic. I discuss: 1. the Stoic notion of sayables or meanings (lekta); the Stoic assertibles (axiomata) and their similarities and differences to modern propositions; the time-dependency of their truth; 2.-3. assertibles with demonstratives and quantified assertibles and their truth-conditions; truth-functionality of negations and conjunctions; non-truth-functionality of disjunctions and conditionals; language regimentation and ‘bracketing’ devices; Stoic basic principles of propositional logic; 4. (...) Stoic modal logic; 5. Stoic theory of arguments: two premisses requirement; validity and soundness; 6. Stoic syllogistic or theory of formally valid arguments: a reconstruction of the Stoic deductive system, which consisted of accounts of five types of indemonstrable syllogisms, which function as nullary argumental rules that identify indemonstrables or axioms of the system, and four deductive rules (themata) by which certain complex arguments can be reduced to indemonstrables and thus shown to be formally valid themselves; 7. arguments that were considered as non-syllogistically valid (subsyllogistic and unmethodically concluding arguments). Their validity was explained by recourse to formally valid arguments. (shrink)

Abduction* is the genus with deduction and induction as species. Modus tollens is backward reasoning as an unknown proposition is inferred from a known proposition. Reductio ad absurdum is abductive because the conclusion is inferred by deriving a contradiction from an assumption. Inductive reasoning from effect to cause is also backward reasoning. But abduction* consists of forward reasoning as well. The generic structure of abductive* argumentation is universal among all cultures, occupations and disciplines.

Mathematical instrumentalism construes some parts of mathematics, typically the abstract ones, as an instrument for establishing statements in other parts of mathematics, typically the elementary ones. Gödel’s second incompleteness theorem seems to show that one cannot prove the consistency of all of mathematics from within elementary mathematics. It is therefore generally thought to defeat instrumentalisms that insist on a proof of the consistency of abstract mathematics from within the elementary portion. This article argues that though some versions of (...) mathematical instrumentalism are defeated by Gödel’s theorem, not all are. By considering inductive reasons in mathematics, we show that some mathematical instrumentalisms survive the theorem. (shrink)

El trabajo consiste en una elucidación de los elementos que conforman el concepto de pena natural (poena naturalis) en el Derecho penal. Se puede caracterizar la pena natural como el daño o sufrimiento que recae sobre el autor de un delito, producto de la comisión del mismo, que debe ser descontado de la pena legal que ha de aplicársele. Si bien existe un mínimo acuerdo sobre esto, tanto en la jurisprudencia como en la doctrina penal se observan serios desacuerdos acerca (...) de los requisitos que se deben cumplir para reconocer que se está frente a una pena natural. Para elucidar los elementos, se utilizará el constructivismo conceptual de Ronald Dworkin, a fin de describir el desacuerdo y sus implicancias, reconocer los elementos principales de la pena natural y justificarlos bajo su mejor luz moral. ABSTRACT This study focuses on the clarification of the conceptual elements of poena naturalis in criminal law settings. The poena naturalis is the damage or suffering that falls on the convict for its commission. This damage must be deducted from the poena forensis to be applied. Although there is a minimum agreement about the concept of poena naturalis, in the jurisprudence and among legal scholars, there are serious disagreements about the elements of poena naturalis. To elucidate the elements, I will adopt Ronald Dworkin’s conceptual constructivism to describe the disagreement and its implications. At last, I will justify the main elements of the poena naturalis by their best moral light. (shrink)

This paper is concerned with the construction of theories of software systems yielding adequate predictions of their target systems’ computations. It is first argued that mathematical theories of programs are not able to provide predictions that are consistent with observed executions. Empirical theories of software systems are here introduced semantically, in terms of a hierarchy of computational models that are supplied by formal methods and testing techniques in computer science. Both deductive top-down and inductive bottom-up approaches in the discovery (...) of semantic software theories are refused to argue in favour of the abductive process of hypothesising and refining models at each level in the hierarchy, until they become satisfactorily predictive. Empirical theories of computational systems are required to be modular, as modular are most software verification and testing activities. We argue that logic relations must be thereby defined among models representing different modules in a semantic theory of a modular software system. We exclude that scientific structuralism is able to define module relations needed in software modular theories. The algebraic Theory of Institutions is finally introduced to specify the logic structure of modular semantic theories of computational systems. (shrink)

Putnam, Hilary FPhilosophy of logic. Harper Essays in Philosophy. Harper Torchbooks, No. TB 1544. Harper & Row, Publishers, New York-London, 1971. v+76 pp. The author of this book has made highly regarded contributions to mathematics, to philosophy of logic and to philosophy of science, and in this book he brings his ideas in these three areas to bear on the traditional philosophic problem of materialism versus (objective) idealism. The book assumes that contemporary science (mathematical and physical) is largely correct as (...) far as it goes, or at least that it is rational to believe in it. The main thesis of the book is that consistent acceptance of contemporary science requires the acceptance of some sort of Platonistic idealism affirming the existence of abstract, non-temporal, non-material, non-mental entities (numbers,scientific laws, mathematical formulas, etc.). The author is thus in direct opposition to the extreme materialism which had dominated philosophy of science in the first three quarters of this century. the book can be especially recommended to the scientifically literate, general reader whose acquaintance with these areas is limited to the earlier literature of when it had been assumed that empiricistic materialism was the only philosophy compatible with a scientific outlook. To this group the book presents an eye-opening challenge fulfilling the author’s intention of “shaking up preconceptions and stimulating further discussion”. (shrink)

Recent work in formal semantics suggests that the language system includes not only a structure building device, as standardly assumed, but also a natural deductive system which can determine when expressions have trivial truth-conditions (e.g., are logically true/false) and mark them as unacceptable. This hypothesis, called the `logicality of language', accounts for many acceptability patterns, including systematic restrictions on the distribution of quantifiers. To deal with apparent counter-examples consisting of acceptable tautologies and contradictions, the logicality of language is often (...) paired with an additional assumption according to which logical forms are radically underspecified: i.e., the language system can see functional terms but is `blind' to open class terms to the extent that different tokens of the same term are treated as if independent. This conception of logical form has profound implications: it suggests an extreme version of the modularity of language, and can only be paired with non-classical---indeed quite exotic---kinds of deductive systems. The aim of this paper is to show that we can pair the logicality of language with a different and ultimately more traditional account of logical form. This framework accounts for the basic acceptability patterns which motivated the logicality of language, can explain why some tautologies and contradictions are acceptable, and makes better predictions in key cases. As a result, we can pursue versions of the logicality of language in frameworks compatible with the view that the language system is not radically modular vis-a-vis its open class terms and employs a deductive system that is basically classical. (shrink)

In this article, I will provide a critical overview of the form of non-deductive reasoning commonly known as “Inference to the Best Explanation” (IBE). Roughly speaking, according to IBE, we ought to infer the hypothesis that provides the best explanation of our evidence. In section 2, I survey some contemporary formulations of IBE and highlight some of its putative applications. In section 3, I distinguish IBE from C.S. Peirce’s notion of abduction. After underlining some of the essential elements of (...) IBE, the rest of the entry is organized around an examination of various problems that IBE confronts, along with some extant attempts to address these problems. In section 4, I consider the question of when a fact requires an explanation, since presumably IBE applies only in cases where some explanation is called for. In section 5, I consider the difficult question of how we ought to understand IBE in light of the fact that among philosophers, there is significant disagreement about what constitutes an explanation. In section 6, I consider different strategies for justifying the truth-conduciveness of the explanatory virtues, e.g., simplicity, unification, scope, etc., criteria which play an indispensable role in any given application of IBE. In section 7, I survey some of the most recent literature on IBE, much of which consists of investigations of the status of IBE from the standpoint of the Bayesian philosophy of science. (shrink)

In this paper, I develop a quasi-transcendental argument to justify Kant’s infamous claim “man is evil by nature.” The cornerstone of my reconstruction lies in drawing a systematic distinction between the seemingly identical concepts of “evil disposition” (böseGesinnung) and “propensity to evil” (Hang zumBösen). The former, I argue, Kant reserves to describe the fundamental moral outlook of a single individual; the latter, the moral orientation of the whole species. Moreover, the appellative “evil” ranges over two different types of moral failure: (...) while an “evil disposition” is a failure to realize the good (i.e., to adopt the motive of duty as limiting condition for all one’s desires), an “evil propensity” is a failure to realize the highest good (i.e., to engage in the collective project of transforming the legal order into an ethical community). This correlation between units of moral analysis and types of obligation suggests a way to offer a deduction of the universal propensity on behalf of Kant. It consists in tracing the source of radical evil to the same subjective necessity that gives rise to the doctrine of the highest good. For, at the basis of Kant’s two doctrines lies the same natural dialectic between happiness and morality. While the highest good brings about the critically acceptable resolution of this dialectic, the propensity to evil perpetuates and aggravates it. Instead of connecting happiness and morality in an objective relation, the human will subordinatesmorality to the pursuit of happiness according to the subjective order of association. If this reading is correct, it would explain why prior attempts at a transcendental deduction have failed: interpreters have looked for the key to the deduction in the body of Kant’s text, where it is not to be found, for it is tucked, instead, in the Preface to the first edition. (shrink)

Bilateralists hold that the meanings of the connectives are determined by rules of inference for their use in deductive reasoning with asserted and denied formulas. This paper presents two bilateral connectives comparable to Prior's tonk, for which, unlike for tonk, there are reduction steps for the removal of maximal formulas arising from introducing and eliminating formulas with those connectives as main operators. Adding either of them to bilateral classical logic results in an incoherent system. One way around this problem (...) is to count formulas as maximal that are the conclusion of reductio and major premise of an elimination rule and to require their removability from deductions. The main part of the paper consists in a proof of a normalisation theorem for bilateral logic. The closing sections address philosophical concerns whether the proof provides a satisfactory solution to the problem at hand and confronts bilateralists with the dilemma that a bilateral notion of stability sits uneasily with the core bilateral thesis. (shrink)

John D. Norton is responsible for a number of influential views in contemporary philosophy of science. This paper will discuss two of them. The material theory of induction claims that inductive arguments are ultimately justified by their material features, not their formal features. Thus, while a deductive argument can be valid irrespective of the content of the propositions that make up the argument, an inductive argument about, say, apples, will be justified (or not) depending on facts about apples. The (...) argument view of thought experiments claims that thought experiments are arguments, and that they function epistemically however arguments do. These two views have generated a great deal of discussion, although there hasn’t been much written about their combination. I argue that despite some interesting harmonies, there is a serious tension between them. I consider several options for easing this tension, before suggesting a set of changes to the argument view that I take to be consistent with Norton’s fundamental philosophical commitments, and which retain what seems intuitively correct about the argument view. These changes require that we move away from a unitary epistemology of thought experiments and towards a more pluralist position. (shrink)

Recent work in formal semantics suggests that the language system includes not only a structure building device, as standardly assumed, but also a natural deductive system which can determine when expressions have trivial truth‐conditions (e.g., are logically true/false) and mark them as unacceptable. This hypothesis, called the ‘logicality of language’, accounts for many acceptability patterns, including systematic restrictions on the distribution of quantifiers. To deal with apparent counter‐examples consisting of acceptable tautologies and contradictions, the logicality of language is often (...) paired with an additional assumption according to which logical forms are radically underspecified: i.e., the language system can see functional terms but is ‘blind’ to open class terms to the extent that different tokens of the same term are treated as if independent. This conception of logical form has profound implications: it suggests an extreme version of the modularity of language, and can only be paired with non‐classical—indeed quite exotic—kinds of deductive systems. The aim of this paper is to show that we can pair the logicality of language with a different and ultimately more traditional account of logical form. This framework accounts for the basic acceptability patterns which motivated the logicality of language, can explain why some tautologies and contradictions are acceptable, and makes better predictions in key cases. As a result, we can pursue versions of the logicality of language in frameworks compatible with the view that the language system is not radically modular vis‐á‐vis its open class terms and employs a deductive system that is basically classical. (shrink)

Biology –in its simplest definition– is a natural science that studies the living things. Philosophy of Biology, on the other hand, is the whole of conceptual analysis, synthesis and deductions that filters the scientific information being produced by biology, especially those of ‘life’ and ‘evolution’. In this study, the importance of the philosophy-science view of the famous philosopher Teoman Duralı, who passed away a year ago, will be mentioned in terms of contemporary biology and philosophy of biology. In doing this, (...) first of all, the historical relationship between the philosophy of biology and the philosophy of science will be revealed. Then having in consideration of the scope of the philosophy of biology, its relationship to the pure biology and to the history of biology will be mentioned. Then, Duralı’s philosophy-science view will be examined in terms of meaning and cause-effect relationships, thus both his contribution to the philosophy of biology literature in Turkish and his position will be pointed out. In conclusion, the use of the term biophilosophy, which concerns and connects two separate-but-adjoint flowing rivers ‘the philosophy’ and ‘the biology’, will be mentioned by pointing out why ‘biology for philosophy’ and why ‘philosophy for biology’ are important reciprocally. Finally, a declaration consisting a list of ten proposed items will be put forth. (shrink)

Epistemologists have recently proposed a number of norms governing rational inquiry. My aim in this paper is to unify and explain recently proposed norms of inquiry by developing a general account of the conditions under which inquiries are rational, analogous to theories such as evidentialism and reliabilism for rational belief. I begin with a reason-responsiveness conception of rationality as responding correctly to possessed normative reasons. I extend this account with a series of claims about the normative reasons for inquiry that (...) we possess. I apply the account to shed light on two classes of norms that have featured prominently in recent discussions: norms of clutter avoidance forbidding agents from engaging in trivial inquiries, and norms of logical non-omniscience governing properties such as the deductive closure and consistency of an agent's belief state. I conclude with a discussion of the sense in which norms of inquiry should be regarded as epistemic norms. (shrink)

The Knower paradox purports to place surprising a priori limitations on what we can know. According to orthodoxy, it shows that we need to abandon one of three plausible and widely-held ideas: that knowledge is factive, that we can know that knowledge is factive, and that we can use logical/mathematical reasoning to extend our knowledge via very weak single-premise closure principles. I argue that classical logic, not any of these epistemic principles, is the culprit. I develop a consistent theory validating (...) all these principles by combining Hartry Field's theory of truth with a modal enrichment developed for a different purpose by Michael Caie. The only casualty is classical logic: the theory avoids paradox by using a weaker-than-classical K3 logic. I then assess the philosophical merits of this approach. I argue that, unlike the traditional semantic paradoxes involving extensional notions like truth, its plausibility depends on the way in which sentences are referred to--whether in natural languages via direct sentential reference, or in mathematical theories via indirect sentential reference by Gödel coding. In particular, I argue that from the perspective of natural language, my non-classical treatment of knowledge as a predicate is plausible, while from the perspective of mathematical theories, its plausibility depends on unresolved questions about the limits of our idealized deductive capacities. (shrink)

I describe three extant attempts to identify the global external symmetries within a Humean framework with theorems of some or other deductive systematization of the world, respectively, the best system, a meta-best system and a maximally simple system. Each has merits, but also serious flaws. Instead, I propose a view of global external symmetries as consequences of the structure of Humean-consistent world-making relations.

In this paper, I propose a solution to a notorious puzzle that lies at the heart of Kant’s Critique of Judgment. The puzzle arises because Kant asserts two apparently conflicting claims: (1) F→J: A judgment of beauty is aesthetic, i.e., grounded in feeling. (2) J→F: A judgment of beauty could not be based on and must ground the feeling of pleasure in the beautiful. I argue that (1) and (2) are consistent. Kant’s text indicates that he distinguishes two feelings: the (...) feeling of the harmony of the cognitive faculties that is the ground of judgments of beauty (F1 → J), and the feeling of pleasure that is its consequence (J → F2). I develop and defend a view of Kant’s account of the structure of judgments of beauty that incorporates this crucial distinction. Next, I argue that my view resolves another long-standing problem for Kant’s “Deduction” of judgments of beauty: it allows him to claim that the harmony of the faculties is a condition of judgment in general without implying, absurdly, that all judgments are pleasurable. (shrink)

This paper assesses the role of the Refutation of Idealism within the Critique of Pure Reason, as well as its relation to the treatment of idealism in the First Edition and to transcendental idealism more generally. It is argued that the Refutation is consistent with the Fourth Paralogism and that it can be considered as an extension of the Transcendental Deduction. While the Deduction, considered on its own, constitutes a 'regressive argument', the Refutation allows us to turn the Transcendental Analytic (...) into a 'progressive argument' that proceeds by the synthetic method. (shrink)

We defend hylomorphism against Maegan Fairchild’s purported proof of its inconsistency. We provide a deduction of a contradiction from SH+, which is the combination of “simple hylomorphism” and an innocuous premise. We show that the deduction, reminiscent of Russell’s Paradox, is proof-theoretically valid in classical higher-order logic and invokes an impredicatively defined property. We provide a proof that SH+ is nevertheless consistent in a free higher-order logic. It is shown that the unrestricted comprehension principle of property abstraction on which the (...) purported proof of inconsistency relies is analogous to naïve unrestricted set-theoretic comprehension. We conclude that logic imposes a restriction on property comprehension, a restriction that is satisfied by the ramified theory of types. By extension, our observations constitute defenses of theories that are structurally similar to SH+, such as the theory of singular propositions, against similar purported disproofs. (shrink)

A framing effect occurs when an agent's choices are not invariant under changes in the way a decision problem is presented, e.g. changes in the way options are described (violation of description invariance) or preferences are elicited (violation of procedure invariance). Here we identify those rationality violations that underlie framing effects. We attribute to the agent a sequential decision process in which a “target” proposition and several “background” propositions are considered. We suggest that the agent exhibits a framing effect if (...) and only if two conditions are met. First, different presentations of the decision problem lead the agent to consider the propositions in a different order (the empirical condition). Second, different such “decision paths” lead to different decisions on the target proposition (the logical condition). The second condition holds when the agent's initial dispositions on the propositions are “implicitly inconsistent,” which may be caused by violations of “deductive closure.” Our account is consistent with some observations made by psychologists and provides a unified framework for explaining violations of description and procedure invariance. (shrink)

The article proceeds upon the assumption that the beliefs and degrees of belief of rational agents satisfy a number of constraints, including: consistency and deductive closure for belief sets, conformity to the axioms of probability for degrees of belief, and the Lockean Thesis concerning the relationship between belief and degree of belief. Assuming that the beliefs and degrees of belief of both individuals and collectives satisfy the preceding three constraints, I discuss what further constraints may be imposed on (...) the aggregation of beliefs and degrees of belief. Some possibility and impossibility results are presented. The possibility results suggest that the three proposed rationality constraints are compatible with reasonable aggregation procedures for belief and degree of belief. (shrink)

Contemporary Humeans treat laws of nature as statements of exceptionless regularities that function as the axioms of the best deductive system. Such ‘Best System Accounts’ marry realism about laws with a denial of necessary connections among events. I argue that Hume’s predecessor, George Berkeley, offers a more sophisticated conception of laws, equally consistent with the absence of powers or necessary connections among events in the natural world. On this view, laws are not statements of regularities but the most general (...) rules God follows in producing the world. Pace most commentators, I argue that Berkeley’s view is neither instrumentalist nor reductionist. More important, the Berkeleyan Best System can solve some of the problems afflicting its Humean rivals, including the problems of theory choice and Nancy Cartwright’s ‘facticity’ dilemma. Some of these solutions are available in the contemporary context, without any appeal to God. Berkeley’s account deserves to be taken seriously in its own right. (shrink)

A paradox about sets of properties is presented. The paradox, which invokes an impredicatively defined property, is formalized in a free third-order logic with lambda-abstraction, through a classically proof-theoretically valid deduction of a contradiction from a single premise to the effect that every property has a unit set. Something like a model is offered to establish that the premise is, although classically inconsistent, nevertheless consistent, so that the paradox discredits the logic employed. A resolution through the ramified theory of types (...) is considered. Finally, a general scheme that generates a family of analogous paradoxes and a generally applicable resolution are proposed. (shrink)

ABSTRACT: In antiquity we encounter a distinction of two types of hypothetical syllogisms. One type are the ‘mixed hypothetical syllogisms’. The other type is the one to which the present paper is devoted. These arguments went by the name of ‘wholly hypothetical syllogisms’. They were thought to make up a self-contained system of valid arguments. Their paradigm case consists of two conditionals as premisses, and a third as conclusion. Their presentation, either schematically or by example, varies in different authors. For (...) instance, we find ‘If (it is) A, (it is) B; if (it is) B, (it is) C; therefore, if (it is) A, (it is) C’. The main contentious point about these arguments is what the ancients thought their logical form was. Are A, B, C schematic letters for terms or propositions? Is ‘is’, where it occurs, predicative, existential, or veridical? That is, should ‘A esti’ be translated as ‘it is an A’, ‘A exists’, ‘As exist’ or ‘It is true/the case that A’? If A, B, C are term letters, and ‘is’ is predicative, are the conditionals quantified propositions or do they contain designators? If one cannot answer these questions, one can hardly claim to know what sort of arguments the wholly hypothetical syllogisms were. In fact, all the above-mentioned possibilities have been taken to describe them correctly. In this paper I argue that it would be mistaken to assume that in antiquity there was one prevalent understanding of the logical form of these arguments - even if the ancients thought they were all talking about the same kind of argument. Rather, there was a complex development in their understanding, starting from a term-logical conception and leading to a propositional-logical one. I trace this development from Aristotle to Philoponus and set out the deductive system on which the logic of the wholly hypothetical syllogisms was grounded. (shrink)

This paper aims to flesh out the celebrated notion of reflective equilibrium within a probabilistic framework for epistemic rationality. On the account developed here, an agent's attitudes are in reflective equilibrium when there is a certain sort of harmony between the agent's credences, on the one hand, and what the agent accepts, on the other hand. Somewhat more precisely, reflective equilibrium is taken to consist in the agent accepting, or being prepared to accept, all and only claims that follow from (...) a maximally comprehensive theory that is more probable than any other such theory. Drawing on previous work, the paper shows that when an agent is in reflective equilibrium in this sense, the set of claims they accept or are prepared to accept is bound to be logically consistent and closed under logical implication. The paper also argues that this account can explain various features of philosophical argumentation in which the notion of reflective equilibrium features centrally, such as the emphasis on evaluating philosophical theories holistically rather than in a piecemeal fashion. (shrink)

In solving judgment aggregation problems, groups often face constraints. Many decision problems can be modelled in terms the acceptance or rejection of certain propositions in a language, and constraints as propositions that the decisions should be consistent with. For example, court judgments in breach-of-contract cases should be consistent with the constraint that action and obligation are necessary and sufficient for liability; judgments on how to rank several options in an order of preference with the constraint of transitivity; and judgments on (...) budget items with budgetary constraints. Often more or less demanding constraints on decisions are imaginable. For instance, in preference ranking problems, the transitivity constraint is often contrasted with the weaker acyclicity constraint. In this paper, we make constraints explicit in judgment aggregation by relativizing the rationality conditions of consistency and deductive closure to a constraint set, whose variation yields more or less strong notions of rationality. We review several general results on judgment aggregation in light of such constraints. (shrink)

In the first book of the Prior Analytics, Aristotle sets out, for the first time in Greek philosophy, a logical system. It consists of a deductive system (I.4-22), meta-logical results (I.23-26), and a method for finding and giving deductions (I.27-29) that can apply in “any art or science whatsoever” (I.30). After this, Aristotle compares this method with Plato’s method of division, a procedure designed to find essences of natural kinds through systematic classification. This critical comparison in APr I.31 raises (...) an interpretive puzzle: how can Aristotle reasonably juxtapose two methods that differ so much in their aims and approach? What can be gained by doing so? Previous interpreters have failed to show how this comparison is legitimate or what important point Aristotle is making. The goal of this paper is to resolve the puzzle. In resolving this puzzle we not only learn more about the relationship be- tween division and the syllogistic in Aristotle. We will also learn something about the motivation for the syllogistic itself, by seeing the role that it plays in his philosophy of science. (shrink)

John Maynard Keynes’s A Treatise on Probability is the seminal text for the logical interpretation of probability. According to his analysis, probabilities are evidential relations between a hypothesis and some evidence, just like the relations of deductive logic. While some philosophers had suggested similar ideas prior to Keynes, it was not until his Treatise that the logical interpretation of probability was advocated in a clear, systematic and rigorous way. I trace Keynes’s influence in the philosophy of probability through a (...) heterogeneous sample of thinkers who adopted his interpretation. This sample consists of Frederick C. Benenson, Roy Harrod, Donald C. Williams, Henry E. Kyburg and David Stove. The ideas of Keynes prove to be adaptable to their diverse theories of probability. My discussion indicates both the robustness of Keynes’s probability theory and the importance of its influence on the philosophers whom I describe. I also discuss the Problem of the Priors. I argue that none of those I discuss have obviously improved on Keynes’s theory with respect to this issue. (shrink)

In this article, I explore the compatibility of inference to the best explanation (IBE) with several influential models and accounts of scientific explanation. First, I explore the different conceptions of IBE and limit my discussion to two: the heuristic conception and the objective Bayesian conception. Next, I discuss five models of scientific explanation with regard to each model’s compatibility with IBE. I argue that Kitcher’s unificationist account supports IBE; Railton’s deductive–nomological–probabilistic model, Salmon’s statistical-relevance model, and van Fraassen’s erotetic account (...) are incompatible with IBE; and Salmon’s causal–mechanical model is merely consistent with IBE. In short, many influential models of scientific explanation do not support IBE. I end by outlining three possible conclusions to draw: (1) either philosophers of science or defenders of IBE have seriously misconstrued the concept of explanation, (2) philosophers of science and defenders of IBE do not use the term ‘explanation’ univocally, and (3) the ampliative conception of IBE, which is compatible with any model of scientific explanation, deserves a closer look. (shrink)

ACTION-THEORETICALLY EXPLANATORY INTERPRETATIONS AS A MEANS OF SEMANTIC MEANING ANALYSIS The article first develops a general procedure for semantic meaning analysis in difficult cases where the meaning is very uncertain. The procedure consists of searching for one or more possible hypothetical causal explanations of the text, these explanations containing, among other things, the semantic intention of the author, his subjective reasons for this meaning and for the writing down of the text, but also the path of transmission of the text (...) from the writing down to the respective present text version. These hypothetical explanations (interpretations) are deductive-nomological or probabilistic, therefore presuppose corresponding general law hypotheses. If there is only one possible (hypothetical) explanation of the text at hand, this hypothetical explanation is also true. Very often, however, there are several possible explanations. In this case, the probabilities of these possible explanations must be determined; these probabilities then carry over to the individual hypotheses in the explanation (according to Bayes' law). This general procedure of meaning analysis is used in the second part of the article to reconstruct two famous interpretations (by Wapnewski and Hahn) of a poem by Walther von der Vogelweide ("Nemt, frowe, disen kranz"). -/- GERMAN ABSTRACT In dem Artikel wird zunächst ein allgemeines Verfahren zur semantischen Bedeutungsanalyse in schwierigen Fällen entwickelt, in denen die Bedeutung sehr unsicher ist. Das Verfahren besteht darin, daß eine oder mehrere mögliche hypothetische kausale Erklärungen des Textes gesucht werden, wobei diese Erklärungen u.a. die semantische Intention des Autors enthalten, seine subjektiven Gründe für diese Bedeutung und für die Niederschrift des Textes, aber auch den Weg der Tradierung des Textes von der Niederschrift bis zur jeweils vorliegenden Textversion. Diese hypothetischen Erklärungen (Deutungen) sind deduktiv-nomologisch oder probabilistisch, setzen deshalb entsprechende allgemeine Gesetzeshypothesen voraus. Wenn es nur eine mögliche (hypothetische) Erklärung des vorliegenden Textes gibt, ist diese hypothetische Erklärung auch wahr. Sehr häufig gibt es aber mehrere mögliche Erklärungen. In diesem Fall müssen die Wahrscheinlichkeiten dieser möglichen Erklärungen bestimmt werden; diese Wahrscheinlichkeiten übertragen sich dann auch auf die einzelnen Hypothesen in der Erklärung (nach dem Bayesschen Gesetz). Dieses allgemeine Verfahren der Bedeutungsanalyse wird im zweiten Teil des Artikels zur Rekonstruktion zweier berühmter Interpretationen (von Wapnewski und Hahn) eines Gedichts von Walther von der Vogelweide („Nemt, frowe, disen kranz“) verwendet. (shrink)

Logical inferentialism maintains that the formal rules of inference fix the meanings of the logical terms. The categoricity problem points out to the fact that the standard formalizations of classical logic do not uniquely determine the intended meanings of its logical terms, i.e., these formalizations are not categorical. This means that there are different interpretations of the logical terms that are consistent with the relation of logical derivability in a logical calculus. In the case of the quantificational logic, the categoricity (...) problem is generated by the finite nature of the standard calculi and one direction in which it can be solved is to strengthen the deductive systems by adding infinite rules (such as the ω-rule), i.e., to construct a full formalization. Another main direction is to provide a natural semantics for the standard rules of inference, i.e., a semantics for which these rules are categorical. My aim in this paper is to analyze some recent approaches for solving the categoricity problem and to argue that a logical inferentialist should accept the infinite rules of inference for the first order quantifiers, since our use of the expressions “all” and “there is” leads us beyond the concrete and finite reasoning, and human beings do sometimes employ infinite rules of inference in their reasoning. (shrink)

Judgment-aggregation theory has always focused on the attainment of rational collective judgments. But so far, rationality has been understood in static terms: as coherence of judgments at a given time, defined as consistency, completeness, and/or deductive closure. This paper asks whether collective judgments can be dynamically rational, so that they change rationally in response to new information. Formally, a judgment aggregation rule is dynamically rational with respect to a given revision operator if, whenever all individuals revise their judgments (...) in light of some information (a learnt proposition), then the new aggregate judgments are the old ones revised in light of this information, i.e., aggregation and revision commute. We prove an impossibility theorem: if the propositions on the agenda are non-trivially connected, no judgment aggregation rule with standard properties is dynamically rational with respect to any revision operator satisfying some basic conditions on revision. Our theorem is the dynamic-rationality counterpart of some well-known impossibility theorems for static rationality. We also explore how dynamic rationality might be achieved by relaxing some of the conditions on the aggregation rule and/or the revision operator. Notably, premise-based aggregation rules are dynamically rational with respect to so-called premise-based revision operators. (shrink)