It is natural and important to have a formal representation of plain belief, according to which propositions are held true, or held false, or neither. (In the paper this is called a deterministic representation of epistemic states). And it is of great philosophical importance to have a dynamic account of plain belief. AGM belief revision theory seems to provide such an account, but it founders at the problem of iterated belief revision, since it can generally account only for one step (...) of revision. The paper discusses and rejects two solutions within the confines of AGM theory. It then introduces ranking functions (as I prefer to call them now; in the paper they are still called ordinal conditional functions) as the proper (and, I find, still the best) solution of the problem, proves that conditional independence w.r.t. ranking functions satisfies the so-called graphoid axioms, and proposes general rules of belief change (in close analogy to Jeffrey's generalized probabilistic conditionalization) that encompass revision and contraction as conceived in AGM theory. Indeed, the parallel to probability theory is amazing. Probability theory can profit from ranking theory as well since it is also plagued by the problem of iterated belief revision even if probability measures are conceived as Popper measures (see No. 11). Finally, the theory is compared with predecessors which are numerous and impressive, but somehow failed to explain the all-important conditional ranks in the appropriate way. (shrink)

Kant’s theory of cognition centrally builds on his conception of self-consciousness and the transcendental use of the phrase “I think”: the ability to add the phrase “I think” to a representation is a necessary condition of the ability to cognize objects. The paper argues that “I think”, rather than denoting the content of a predicative judgement, is typically an expression of the subject’s thinking. It expresses a kind of self-consciousness that, without assertively representing the subject itself, indicates that representational contents (...) are unified in a single consciousness of a single subject. Our aim is thus to develop and defend an expressivist interpretation of Kant’s “I think”. (shrink)

Conditionals somehow express conditional beliefs. However, conditional belief is a bi-propositional attitude that is generally not truth-evaluable, in contrast to unconditional belief. Therefore, this article opts for an expressivistic semantics for conditionals, grounds this semantics in the arguably most adequate account of conditional belief, that is, ranking theory, and dismisses probability theory for that purpose, because probabilities cannot represent belief. Various expressive options are then explained in terms of ranking theory, with the intention to set out a general interpretive scheme (...) that is able to account for the most variegated usage of conditionals. The Ramsey test is only the first option. Relevance is another, familiar, but little understood item, which comes in several versions. This article adds a further family of expressive options, which is able to subsume also counterfactuals and causal conditionals, and indicates at the end how this family allows for partial recovery of truth conditions for conditionals. (shrink)

Dieses Buch enthält in einer historisch-kritischen Edition die Texte, die es in seinem Hauptteil kommentiert: Das Vorwort (1893) zu Gottlob Freges Hauptwerk, den "Grundgesetzen der Arithmetik", in dem er seine fulminante Psychologismus-Kritik vorträgt; die drei von Frege selbst veröffentlichten "Logischen Untersuchungen" (1918-1923), in denen er "die Ernte [s]eines Lebens heimbringen" wollte; und schließlich ein Fragment aus seinem Nachlass, das der Entwurf zu einer vierten LU ist.

The paper takes an expressivistic perspective, i.e., it takes conditionals of all sorts to primarily express conditional beliefs. Therefore it is based on what it takes to be the best account of conditional belief, namely ranking theory. It proposes not to start looking at the bewildering linguistic phenomenology, but first to systematically study the various options of expressing features of conditional belief. Those options by far transcend the Ramsey test and include relevancies of various kinds and in particular the so-called (...) “circumstances are such that” reading, under which also all conditionals representing causal relations can be subsumed. In this way a unifying perspective on the many kinds of conditionals is offered. The final section explains the considerable extent to which truth conditions for conditionals, which may seem lost in the expressivistic or epistemic perspective, may be recovered. (shrink)

Our senses provide us with information about the world, but what exactly do they tell us? I argue that in order to optimally respond to sensory stimulations, an agent’s doxastic space may have an extra, “imaginary” dimension of possibility; perceptual experiences confer certainty on propositions in this dimension. To some extent, the resulting picture vindicates the old-fashioned empiricist idea that all empirical knowledge is based on a solid foundation of sense-datum propositions, but it avoids most of the problems traditionally associated (...) with that idea. The proposal might also explain why experiences appear to have a non-physical phenomenal character, even if the world is entirely physical. (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)

Recent claims, mainly from computer scientists, concerning a largely automated and model-free data-intensive science have been countered by critical reactions from a number of philosophers of science. The debate suffers from a lack of detail in two respects, regarding the actual methods used in data-intensive science and the specific ways in which these methods presuppose theoretical assumptions. I examine two widely-used algorithms, classificatory trees and non-parametric regression, and argue that these are theory-laden in an external sense, regarding the framing of (...) research questions, but not in an internal sense concerning the causal structure of the examined phenomenon. With respect to the novelty of data-intensive science, I draw an analogy to exploratory as opposed to theory-directed experimentation. (shrink)

Kant's theory of cognition centrally builds on his conception of self‐consciousness and the transcendental use of the phrase “I think”: the ability to add the phrase “I think” to a representation is a necessary condition of the ability to cognize objects. The paper argues that “I think”, rather than denoting the content of a predicative judgement, is typically an expression of the subject's thinking. It expresses a kind of self‐consciousness that, without assertively representing the subject itself, indicates that representational contents (...) are unified in a single consciousness of a single subject. Our aim is thus to develop and defend an expressivist interpretation of Kant's “I think”. (shrink)

Eine Einfiihrung in die epistemische Logik wurde schon vor unge fahr zwei Jahrzehnten durch Jaakko Hintikka geschrieben, und auf sein "Knowledge and Belief" nimmt das vorliegende Buch nicht nur durch den Titel "Glauben, Wissen und Wahrscheinlichkeit" Bezug. Es diirfte deshalb wohl angebracht sein, wenn der Autor eines Buches, das so deutlich die Nachfolgeschaft eines anderen beansprucht, sich dafiir rechtfertigt und erklart, worin sich sein Werk von dem des Vorgangers unterscheidet. Ein wichtiger Punkt, in dem die zweite iiber die erste Einleitung (...) in die epistemische Logik hinausgeht, wird schon durch die Titel erganzung "... und Wahrscheinlichkeit" signalisiert. Wahrend Hin tikkas erkenntnistheoretische Untersuchungen sich fast ausschlieB lich auf die Bestimmung einer Wissenslogik ("episteme") konzen trierten, werden hier unter Bezugnahme auf die Theorie subjektiver Wahrscheinlichkeit zusatzlich diverse Glaubenslogiken ("doxa") ent wickelt. Insbesondere wird ein Begriff "schwachen" Glaubens im Sinne des Fiir-wahrscheinlich-Haltens vom "starken" Glaubensbe griff im Sinne festester Oberzeugungen abgegrenzt, eine Unterschei dung, die im angelsachsischen Sprachraum bei der Diskussion der Logik von "belief" straflich vernachlassigt wurde. Die genaue Aus arbeitung dieses Unterschieds, die exakte semantische Charakteri sierung der entsprechenden doxastischen Modaloperatoren, und die Suche nach vollstandigen Axiomatisierungen korrespondierender Logiken fiihrte dabei in (mathematisches) Neuland: zur Theorie klassifikatorischer Wahrscheinlichkeit. Diese erste wesentliche Wei terentwicklung von "Knowledge and Belief" konnte man durch die Formel beschreiben: von rein epistemischer Logik hin zu epistemi scher und doxastischer Logik. (shrink)

One of the main controversies of the Logic Schools of the 12th century centered on the question: What follows from the impossible? In this paper arguments for two diametrically opposed positions are examined. The author of the ‘Avranches Text’ who probably belonged to the school of the Parvipontani defended the view that from an impossible proposition everything follows (‘Ex impossibili quodlibet’). In particular he developed a proof to show that by means of so-called ‘disjunctive syllogism’ any arbitrary proposition B can (...) be logically derived from a pair of contradictory propositions A and Not-A. The author of the Ars Meliduna instead argued that nothing follows from an impossible proposition (‘ex falso nihil sequitur’). This view is supported by various counterexamples which aimed to show that the admission of impossible premises would give rise to inconsistent conclusions. Upon closer analysis these inconsistencies do not, however, have the formal structure of a real contradiction like A and Not-A, but rather the structure of two rivalling conditionals like ‘If B then A’ and ‘If B then Not-A’. Hence these counterexamples rather have to be considered as refutations of the basic principles of ‘connexive logic’. (shrink)

The paper analyzes the nature and scope of Moore’s paradox, articulates the desiderata of a successful solution and claims that psychological expressivism best meets these desiderata. After a brief discussion of prominent responses to Moore’s paradox, the paper offers a solution based on a theory of expressive acts: a Moorean utterance is absurd because the speaker expresses mental states with conflicting contents in commissive versions of the paradox and conflicting states of mind in omissive versions. The paper presents a theory (...) of expressivism for self-ascriptions of mental states. In addition, it introduces the idea of expressive denegation—the speaker’s expressing the absence of a mental state—as an analysis of negative self-ascriptions of mental states. Some of the consequences of expressivism for avowals are explored. (shrink)

This Element addresses three questions about Kant's guarantee thesis by examining the 'first addendum' of his Philosophical Sketch: how the guarantor powers interrelate, how there can be a guarantee without undermining freedom and why there is a guarantee in the first place. Kant's conception of an interplay of human and divine rational agency encompassing nature is crucial: on moral grounds, we are warranted to believe the 'world author' knew that if he were to bring about the world, the 'supreme' good (...) would come about too. Perpetual peace is the condition that enables the supreme good to be realized in history. (shrink)

Bolzano's Sätze an sich and Frege's Gedanken are obviously close relatives. The paper underlines both similarities and dissimilarities between the psychological and semantical roles assigned to structured truth-evaluable contents in Bolzano's and Frege's theories. In particular, their different accounts of propositional identity are compared, and it is argued that Dummett's recent criticism of Frege's account is grist to Bolzano's mill.

This book addresses controversies concerning the epistemological foundations of data science: Is it a genuine science? Or is data science merely some inferior practice that can at best contribute to the scientific enterprise, but cannot stand on its own? The author proposes a coherent conceptual framework with which these questions can be rigorously addressed. Readers will discover a defense of inductivism and consideration of the arguments against it: an epistemology of data science more or less by definition has to be (...) inductivist, given that data science starts with the data. As an alternative to enumerative approaches, the author endorses Federica Russo’s recent call for a variational rationale in inductive methodology. Chapters then address some of the key concepts of an inductivist methodology including causation, probability and analogy, before outlining an inductivist framework. The inductivist framework is shown to be adequate and useful for an analysis of the epistemological foundations of data science. The author points out that many aspects of the variational rationale are present in algorithms commonly used in data science. Introductions to algorithms and brief case studies of successful data science such as machine translation are included. Data science is located with reference to several crucial distinctions regarding different kinds of scientific practices, including between exploratory and theory-driven experimentation, and between phenomenological and theoretical science. Computer scientists, philosophers and data scientists of various disciplines will find this philosophical perspective and conceptual framework of great interest, especially as a starting point for further in-depth analysis of algorithms used in data science. (shrink)

The numerous modal systems between S4 and S5 are investigated from an epistemological point of view by interpreting necessity either as knowledge or as (strong) belief. It is shown that-granted some assumptions about epistemic logic for which the author has argued elsewhere-the system S4.4 may be interpreted as the logic of true belief, while S4.3.2 and S4.2 may be taken to represent epistemic logic systems for individuals who accept the scheme knowledge = true belief only for certain special instances. There (...) is strong evidence in favor of the assumption that S4.2 is the logic of knowledge. (shrink)

Recently, Bengt Hansson presented a paper about dyadic deontic logic,2 criticizing some purely axiomatic systems of dyadic deontic logic and proposing three purely semantical systems of dyadic deontic logic which he confidently called dyadic standard systems of deontic logic (DSDL1–3). Here I shall discuss the third by far most interesting system DSDL3 which is operating with preference relations. First, I shall describe this semantical system (Sections 1.1–1.3). Then I shall give an axiomatic system (Section 1.4) which is proved to be (...) correct (Section 2) and complete (Section 3) with respect to Hansson's semantics. Finally, in face of these results Hansson's semantics will be discussed from a more intuitive standpoint. After emphasizing its intuitive attractiveness (Section 4.1) I will show that two objections often discussed in connection with preference relations do not apply to it (Section 4.2 and 4.3); more precisely, I will show that the connectedness condition for preference relations can be dropped and that, in a sense, it is not necessary to compare two possible worlds differing in infinitely many respects. (What exactly is meant by this, will become clear later on.) Yet there is a third objection to Hansson's semantics which points to a real intuitive inadequacy of DSDL3. A way of removing this inadequacy, which corresponds to Hansson's own intuitions as well as to familiar metaethical views, is suggested, but not technically realized (Section 4.4). In the last section (section 4.5) I shall briefly show that DSDL3 is decidable, as expected. (shrink)

Gottlob Frege has exerted an enormous influence on the evolution of twentieth-century philosophy, yet the real significance of that influence is still very much a matter of debate. This book provides a completely new and systematic account of Frege's philosophy by focusing on its cornerstone: the theory of sense and reference. Two features distinguish this study from other books on Frege. First, sense and reference are placed absolutely at the core of Frege's work; the author shows that no adequate account (...) of the theory can avoid analysing the notion of thought that underpins it, or explaining how it has clarified our concept of judgement. Second, the theory is situated within the development of Frege's thought; the author reveals how the theory caused Frege to alter many of his fundamental views. In doing so the author presents a clearer picture of the problems the theory was intended to solve, and delineates more sharply the characteristic features of Frege's philosophy. (shrink)

This paper compares the epistemological conception of Isaac Levi with mine. We are joined in both giving a constructive answer to the relation of belief and probability, without reducing one to the other. However, our constructions differ in at least nine more or less important ways, all discussed in the paper. In particular, the paper explains the similarities and differences of Shackle's functions of potential surprise, as used by Levi, and my ranking functions in formal as well as in philosophical (...) respects. The appendix explains how ranking and probability theory can be combined in the notion of a ranked probability measure (or probabilified ranking function). (shrink)

And this paper is an attempt to say precisely how, thus addressing a philosophical problem which is commonly taken to be a serious one. It does so, however, in quite an idiosyncratic way. It is based on the account of inductive schemes I have given in (1988) and (1990a) and on the conception of causation I have presented in (1980), (1983), and (1990b), and it intends to fill one of many gaps which have been left by these papers. Still, I (...) have tried to make this paper self-contained. Section 1 explains the philosophical question this paper is about; in more general terms it asks what might be meant by objectifying epistemic states or features of them and to which extent epistemic states can be objectified. The next sections introduce the basis I rely on with formal precision and some explanation; section 2 deals with induction and section 3 with causation. Within these confines, section 4 attempts to give an explication of the relevant sense of objectification and section 5 investigates the extent to which various features of epistemic states are objectifiable. The two most salient results are roughly that the relation "A is a reason for B" cannot be objectified at all and that the relation "A is a cause of B" can be objectified only under substantial, though reasonable restrictions. What has all of this to do with probability? A lot. The paper trades on a pervasive duality between probabilistic and deterministic epistemology, between a probabilistic representation of epistemic states together with a theory of probabilistic causation and another representation of epistemic states which I call deterministic because it lends itself, in a perfectly parallel fashion, to a theory of deterministic causation. Here I explicitly deal only with the deterministic side, but the duality should pave the way for further conclusions concerning objective probabilities and statistical laws. This outlook is briefly expanded in the final section 6. (shrink)

In his paper on ‘Frege's Theory of Sense and Reference’ Saul Kripke remarks: “Like the present account, Künne stresses that for Frege times, persons, etc. can be part of the expression of the thought. However, his reading is certainly not mine in significant respects . . .”. On both counts, he is right. As regards the differences between our readings, in some respects I shall confess to having made a mistake, in several others I shall remain stubbornly unmoved. Thus I (...) shall insist on the need for distinguishing Fregean sense from linguistic (lexico-grammatical) meaning, I shall resist Kripke's function-theoretic account of ‘hybrid’ thought-expressions, and I shall deplore his transformation of Gottlob Frege into Gottrand Fressell. As regards this transformation, I shall argue that some of the main points Kripke wants to drive home do not depend on it. (shrink)

The founder of modern logic and grandfather of analytic philosophy was 70 years old when he published his paper 'Der Gedanke' (The Thought ) in 1918. This essay contains some of Gottlob Frege's deepest and most provocative reflections on the concept of truth, and it will play a prominent role in my lectures. The plan for my lectures is as follows. What is it that is (primarily) true or false? 'Thoughts', is Frege's answer. In §1, I shall explain and defend (...) this answer. In §2, I shall briefly consider his enthymematic argument for the conclusion that the word 'true' resists any attempt at defining it. In §3, I shall discuss his thesis that the thought that things are thus and so is identical with the thought that it is true that things are thus and so. The reasons we are offered for this thesis will be found wanting. In §4, I shall comment extensively on Frege's claim that, in a non-formal language like the one I am currently trying to speak, we can say whatever we want to say without ever using the word 'true' or any of its synonyms. I will reject the propositional-redundancy claim, endorse the assertive-redundancy claim and deny the connection Frege ascribes to them. In his classic 1892 paper 'Über Sinn und Bedeutung' (On Sense and Signification) Frege argues that truth-values are objects. In §5, I shall scrutinize his argument. In §6, I will show that in Frege's ideography (Begriffsschrift) truth, far from being redundant, is omnipresent. The final §7 is again on truth-bearers, this time as a topic in the theory of intentionality and in metaphysics. In the course of discussing Frege's views on the objecthood, the objectivity of thoughts and the timelessness of truth(s), I will plead for a somewhat mitigated Platonism. (shrink)

The paper is motivated by the need of accounting for the practical syllogism as a piece of defeasible reasoning. To meet the need, the paper first refers to ranking theory as an account of defeasible descriptive reasoning. It then argues that two kinds of ought need to be distinguished, purely normative and fact-regarding obligations. It continues arguing that both kinds of ought can be iteratively revised and should hence be represented by ranking functions, too, just as iteratively revisable beliefs. Its (...) central proposal will then be that the fact-regarding normative ranking function must be conceived as the sum of a purely normative ranking function and an epistemic ranking function. The distinctions defends this proposal with a comparative discussion of some critical examples and some other distinctions made in the literature. It gives a more rigorous justification of this proposal. Finally, it starts developing the logic of purely normative and of fact-regarding normative defeasible reasoning, points to the difficulties of completing the logic of the fact-regarding side, but reaches the initial aim of accounting for the defeasible nature of the practical syllogism. (shrink)

The paper focuses on interpreting ceteris paribus conditions as normal conditions. After discussing six basic problems for the explication of normal conditions and seven interpretations that do not well solve those problems I turn to what I call the epistemic account. According to it the normal is, roughly, the not unexpected. This is developed into a rigorous constructive account of normal conditions, which makes essential use of ranking theory and in particular allows to explain the phenomenon of multiply exceptional conditions. (...) Finally, this static account is extended to a schematic dynamic model of how we may learn about those normal and exceptional conditions. (shrink)

Elaborating on the substantial parallels between Molina’s and Kant’s attempts to reconcile human freedom with divine foreknowledge and natural causal determinism respectively, my aim is to establish a proper historical connection as well. Leibniz is shown to be the crucial mediator in two respects: (i) Kant knew Molina’s account of divine knowledge in general in its Leibnizian version through Baumgarten’s Metaphysica. In this work, scientia media plays no role in the explication as to how God knows absolute future contingents. (ii) (...) In the Critique of Practical Reason Kant resorted to doctrines similar to Molina’s in his criticism of Leibniz’s alternative explication which drew on complete concepts of monads. (shrink)

This paper attempts to develop a projectivistic understanding of chance or objective probability or partial determination. It does so by critically examining David Lewis’ philosophy of probability and his defense of Humean Supervenience, building thereupon the constructive projectivistic alternative, which will basically be a suitable reinterpretation of de Finetti’s position. Any treatment of the topic must show how it extends to natural necessity or deterministic laws or full determination in perfect parallel. The paper indicates at the end how this demand (...) can be met. (shrink)

As the paper explains, it is crucial to epistemology in general and to the theory of causation in particular to investigate the properties of conditional independence as completely as possible. The paper summarizes the most important results concerning conditional independence with respect to two important representations of epistemic states, namely (strictly positive) probability measures and natural conditional (or disbelief or ranking) functions. It finally adds some new observations.

Analogical reasoning addresses the question how evidence from various phenomena can be combined and made relevant for theory development and prediction. In the first part of my contribution, I review some influential accounts of analogical reasoning, both historical and contemporary, focusing in particular on Keynes, Carnap, Hesse, and more recently Bartha. In the second part, I sketch a general framework. To this purpose, a distinction between a predictive and a conceptual type of analogical reasoning is introduced. I then take up (...) a common intuition according to which analogical inferences hold if the differences between source and target concern only irrelevant circumstances. I attempt to make this idea more precise by addressing possible objections and in particular by specifying a notion of causal irrelevance based on difference making in homogeneous contexts. (shrink)

Diese Arbeit stellt Freges Denken in seiner Entwicklung von den Anfängen bis zum Auftreten des Widerspruch dar. Ausführlich behandelt sind die Begriffsschrift, die Erläuterungsschriften dazu, die Grundlagen der Arithmetik sowie die Texte im Übergang zu den Grundgesetzen der Arithmetik, ein- schließlich der klassischen Aufsätze Funktion und Begriff, Über Sinn und Bedeutung und Über Begriff und Gegenstand. Die Texte werden nach Chronologie und Stellung zueinander präzise aufgeschlüsselt; auch die zeitgenössischen Rezensionen und Freges wissenschaftliches Umfeld werden berücksichtigt. Freges Werk wird dadurch in (...) seiner beeindruckenden Zielstrebigkeit, Geschlossenheit und Tiefe sichtbar. Sein Zentrum ist die radikale Neufassung der Logik, ausgehend von der Grundunterscheidung von Begriff und Gegenstand, die zunächst eher unauffällig über die Zerfällung des Urteils in Funktion und Argument eingeführt und mit f(a) notiert wird. Zusammen mit der Einführung einer (Quantoren-)Notation, um die Allgemeinheit der Einsetzungen auf beiden Positionen einzuschränken, übertrifft Freges Logik die traditionelle, alle zeitgenössischen und etliche spätere an Präzision und Ausdruckskraft. Eben die grundsätzliche Trennung von Begriff und Gegenstand erweist sich aber für sein wissenschaftliches Hauptanliegen, die Ableitung der Arithmetik aus der Logik, als schwerwiegendes, letztlich nicht zu überwindendes Hindernis. Es gelingt ihm nicht, die Zahlen als „logische Gegenstände“ überzeugend einzuführen, und so zeigt er wider Willen die wesentliche Verschiedenheit von Logik und Arithmetik auf. (shrink)

First, ranking functions are argued to be superior to AGM belief revision theory in two crucial respects. Second, it is shown how ranking functions are uniquely reflected in iterated belief change. More precisely, conditions on threefold contractions are specified which suffice for representing contractions by a ranking function uniquely up to multiplication by a positive integer. Thus, an important advantage AGM theory seemed to have over ranking functions proves to be spurious.

The core idea of the ontological proof is to show that the concept of existence is somehow contained in the concept of God, and that therefore God’s existence can be logically derived—without any further assumptions about the external world—from the very idea, or definition, of God. Now, G.W. Leibniz has argued repeatedly that the traditional versions of the ontological proof are not fully conclusive, because they rest on the tacit assumption that the concept of God is possible, i.e. free from (...) contradiction. A complete proof will rather have to consist of two parts. First, a proof of premiseGod is possible. Second, a demonstration of the “remarkable proposition”If God is possible, then God exists. The present contribution investigates an interesting paper in which Leibniz tries to prove proposition. It will be argued that the underlying idea of God as a necessary being has to be interpreted with the help of a distinguished predicate letter ‘E’ as follows:\\). Proposition which Leibniz considered as “the best fruit of the entire logic” can then be formalized as follows:\) \rightarrow \, E)\). At first sight, Leibniz’s proof appears to be formally correct; but a closer examination reveals an ambiguity in his use of the modal notions. According to, the possibility of the necessary being has to be understood in the sense of something which possibly exists. However, in other places of his proof, Leibniz interprets the assumption that the necessary being is impossible in the diverging sense of something which involves a contradiction. Furthermore, Leibniz believes that an »impossible thing«, y, is such that contradictory propositions like \\) and \\) might both be true of y. It will be argued that the latter assumption is incompatible with Leibniz’s general views about logic and that the crucial proof is better reinterpreted as dealing with the necessity, possibility, and impossibility of concepts rather than of objects. In this case, the counterpart of turns out to be a theorem of Leibniz’s second order logic of concepts; but in order to obtain a full demonstration of the existence of God, the counterpart of, i.e. the self-consistency of the concept of a necessary being, remains to be proven. (shrink)

In a notoriously obscure passage in Metaphysics 7.1 Aristotle claims that substance is primary in time. The only concrete literal interpretation suggested so far of this controversial claim is in terms of existing before and after in time. I argue that this interpretation faces serious problems. I then present a novel literal interpretation, in terms of being an appropriate subject of temporal predications, that is immune to these problems and strongly supported by philosophical and contextual considerations.

The paper attempts to rationalize cooperation in the one-shot prisoners' dilemma (PD). It starts by introducing (and preliminarily investigating) a new kind of equilibrium (differing from Aumann's correlated equilibria) according to which the players' actions may be correlated (sect. 2). In PD the Pareto-optimal among these equilibria is joint cooperation. Since these equilibria seem to contradict causal preconceptions, the paper continues with a standard analysis of the causal structure of decision situations (sect. 3). The analysis then raises to a reflexive (...) point of view according to which the agent integrates his own present and future decision situations into the causal picture of his situation (sect. 4). This reflexive structure is first applied to the toxin puzzle and then to Newcomb's problem, showing a way to rationalize drinking the toxin and taking only one box with-out assuming causal mystery (sect. 5). The latter result is finally extended to a rationalization of cooperation in PD (sect. 6). (shrink)

There is a tacit assumption that interpretation comes naturally, that human beings live by constantly interpreting. In this sense, we might even rephrase Descartes by saying: We interpret, therefore we are. While such a basic human disposition makes interpretation appear to come naturally, the forms it takes, however, do not. In this work, Iser offers a fresh approach by formulating an "anatomy of interpretation" through which we can understand the act of interpretation in its many different manifestations. For Iser, there (...) are several different genres of interpretation, all of which are acts of translation designed to transpose something into something else. Perhaps the most obvious example of interpretation involves canonical texts, such as the Rabbinical exegesis of the Torah or Samuel Johnson's reading of Shakespeare. But what happens when the matter that one seeks to interpret consists not of a text but of a welter of fragments, as in the study of history, or when something is hidden, as in the practice of psychoanalysis, or is as complex as a culture or system? Iser details how, in each of these cases, the space that is opened up by interpretation is negotiated in a different way, thus concluding that interpretation always depends on what it seeks to translate. For students of philosophy, literary and critical theory, anthropology, and cultural history, Iser's elucidation of the mechanics by which we translate and understand, as well as his assessment of the anthropological roots of our drive to make meaning, will undoubtedly serve as a revelation. (shrink)

Truth is a stable, epistemically unconstrained property of propositions, and the concept of truth admits of a non-reductive explanation: that, in a nutshell, is the view for which I argued in Conceptions of Truth. In this paper I try to explain that explanation in a more detailed and, hopefully, more perspicuous way than I did in Ch. 6.2 of the book and to defend its use of sentential quantification against some of the criticisms it has has come in for.

The systems Kα of transfinite cumulative types up to α are extended to systems K∞α that include a natural infinitary inference rule, the so-called limit rule. For countable α a semantic completeness theorem for K∞α is proved by the method of reduction trees, and it is shown that every model of K∞α is equivalent to a cumulative hierarchy of sets. This is used to show that several axiomatic first-order set theories can be interpreted in K∞α, for suitable α.

It is well known that in his logical writings Leibniz typically disregarded the operation of disjunction, confining himself to the theory of conjunction ajid negation. Now, while this fact has been interpreted by Couturat and others as indicating a serious incompleteness of the Leibnizian calculus, it is shown in this paper that actually Leibniz's conjunction-negation logic, with 'est Ens', i. e. 'is possible' as an additional logical operator, is provably equivalent to Boolean algebra. Moreover, already in the Generales Inquisitiones of (...) 1686 Leibniz had established all basic principles that are necessary for a complete axiomatization of "Boolean" algebra. In this sense Leibniz should be acknowledged as the true inventor of the algebra of sets. (shrink)