The paper critically examines an unpopular line of Frege’s view on numbers in the Foundations of Arithmetic. According to this view, which analyzes numbers in terms of properties and not in terms of extensions, numbers are properties of concepts vs. properties of objects. The latter view is held by Mill and is famously criticized in the Foundations. I argue that on the property account numbers cannot only be properties of concepts but they also have to be properties of objects. My (...) main argument rests on purely metaphysical grounds. It stems from the motivation that were numbers only properties of concepts we would not have been able to explain mathematical truths about the physical world or those truths would have been miraculous. On pains that we do have mathematical truths about the physical world that are not miraculous we cannot agree with Frege’s property line about the metaphysical nature of numbers. (shrink)

Convinced that logic has a history and that its history always manages to surprise the philosophers, Claude Imbert has devoted much of her work to the study of the Stoic school and of the late-nineteenth-century German logician Gottlob Frege. In the fifth chapter of her book Pour une histoire de la logique, she examines the trajectory of Frege's awareness of what his new logic entails, in particular the way it subverts the project of Kant.

Convinced that logic has a history and that its history always manages to surprise the philosophers, Claude Imbert has devoted much of her work to the study of the Stoic school and of the late-nineteenth-century German logician Gottlob Frege. In the fifth chapter of her book Pour une histoire de la logique, she examines the trajectory of Frege's awareness of what his new logic entails, in particular the way it subverts the project of Kant.

This paper aims to determine what kind of problem Frege's famous “Julius Caesar problem” is. whether it is to be understood as the metaphysical problem of determining what kind of things abstract objects like numbers or value‐courses are, or as the epistemological problem of providing a means of recognizing these objects as the same again, or as the logical problem of providing abstract sortal concepts with a sharp delimitation in order to fulfill the law of excluded middle, or as the (...) semantic problem of fixing the referents of the corresponding abstract singular terms. It is argued that, for Frege, the Caesar problem is a bundle of related problems of which the semantic problem is the most basic one. (shrink)

This paper pursues two goals. The first is to show that Horwich's anti-primitivist version of minimalism must be rejected because, already for formal reasons, the truth-schema does not achieve a positive explication of any property of propositions. The second goal is to develop a more moderate primitivist version of minimalism according to which the truth-schema is admittedly powerless to underpin truth with something more basic but it still succeeds in giving a complete account of the necessary and sufficient conditions for (...) a proposition to be true. (shrink)

Greimann-Dirk_A-typology-of-conceptual-explications.

It is widely assumed that Russell's problems with the unity of the proposition were recurring and insoluble within the framework of the logical theory of his Principles of Mathematics. By contrast, Frege's functional analysis of thoughts (grounded in a type-theoretic distinction between concepts and objects) is commonly assumed to provide a solution to the problem or, at least, a means of avoiding the difficulty altogether. The Fregean solution is unavailable to Russell because of his commitment to the thesis that there (...) is only one ultimate ontological category. This, combined with Russell's reification of propositions, ensures that he must hold concepts and objects to be of the same logical and ontological type. In this paper I argue that, while Frege's treatment of the unity of the proposition has immediate advantages over Russell's, a deeper consideration of the philosophical underpinnings and metaphysical consequences of the two approaches reveals that Frege's supposed solution is, in fact, far from satisfactory. Russell's repudiation of the Fregean position in the Principles is, I contend, convincing and Russell's own position, despite its problems, conforms to a greater extent than Frege's with common sense and, furthermore, with certain ideas which are central to our understanding of the origins of the analytical tradition. (shrink)

Orthodoxy holds that there is a determinate fact of the matter about every arithmetical claim. Little argument has been supplied in favour of orthodoxy, and work of Field, Warren and Waxman, and others suggests that the presumption in its favour is unjustified. This paper supports orthodoxy by establishing the determinacy of arithmetic in a well-motivated modal plural logic. Recasting this result in higher-order logic reveals that even the nominalist who thinks that there are only finitely many things should think that (...) there is some sense in which arithmetic is true and determinate. (shrink)

In recent years, even some of its own practitioners have accused analytic philosophy of lacking historical awareness. My aim is to show that analytic philosophy and history are not such a mismatch after all. Against the objection that analytic philosophers have unduly ignored the past I argue that for the most part they only resist strong versions of historicism, and for good reasons. The history of philosophy is not the whole of philosophy, as extreme historicists maintain, nor is it indispensable (...) to substantive philosophizing, as mainline historicists have it, it is merely advantageous (pragmatic historicism). Against the objection that analytic histories of philosophy are inevitably anachronistic I argue that it is possible to approach past texts with a view to substantive issues and in a critical spirit (contrary to historicist relativism and to misguided interpretations of the principle of charity). Indeed, such an analytic approach makes not just for better philosophy but also for better history. (shrink)

The history of concepts is relevant in philosophy because conceptual distinctions fundamentally shape cognition. Because these conceptual distinctions are deeply entrenched in our way of thinking, we are not usually aware of this influence. How we view the world depends crucially on the concepts we have. These concepts, however, are the products of their history. Following Herbart, Gustav Teichmüller viewed philosophy as the systematic analysis and refinement of concepts. Refining concepts in such a way allows us to make new distinctions, (...) or to transform or abandon old ones. In contrast to Herbart, Teichmüller emphasized that this process presupposes detailed historical studies. This does not mean, however, that Teichmüller embraced a kind of historicism---the view that philosophy and its history are one and the same thing. On the contrary, he derogatorily referred to such a view as "historical psychology". Rather, the history of concepts in Teichmüller's sense has to be understood as a history of problems which are reflected in conceptual distinctions. This means that the history of concepts, which brings to light explicit and implicit distinctions, can be applied as a kind of hermeneutics of world views---as the basis on which we can systematically reconstruct concepts in a new light. It is the aim of this presentation to unfold such an understanding of the history of concepts in view of Teichmüller's contribution to it. (shrink)

The use of the three labels to denote the three foundational schools of the early twentieth century are now part of literature. Yet, neither their number nor the...

The paper has two parts: 1. A brief exposition of proof-theoretic semantics, not necessarily in connection to natural language. 2. A review, with a contrastive flavour, of some of the applications of PTS to NL with an indication of advantages of PTS as a theory of meaning for NL.

The paper proposes a semantic value for the logical constants (connectives and quantifiers) within the framework of proof-theoretic semantics, basic meaning on the introduction rules of a meaning conferring natural deduction proof system. The semantic value is defined based on Fregecontributions” to sentential meanings as determined by the function-argument structure as induced by a type-logical grammar. In doing so, the paper proposes a novel proof-theoretic interpretation of the semantic types, traditionally interpreted in Henkin models. The compositionality of the resulting attribution (...) of semantic values is discussed. Elsewhere, the same method was used for defining proof-theoretic meaning of subsentential phrases in a fragment of natural language. Doing the same for (the simpler and clearer case of) logic sheds more light on the proposal. (shrink)

The papers where Gerhard Gentzen introduced natural deduction and sequent calculi suggest that his conception of logic differs substantially from the now dominant views introduced by Hilbert, Gödel, Tarski, and others. Specifically, (1) the definitive features of natural deduction calculi allowed Gentzen to assert that his classical system nk is complete based purely on the sort of evidence that Hilbert called ?experimental?, and (2) the structure of the sequent calculi li and lk allowed Gentzen to conceptualize completeness as a question (...) about the relationships among a system's individual rules (as opposed to the relationship between a system as a whole and its ?semantics?). Gentzen's conception of logic is compelling in its own right. It is also of historical interest, because it allows for a better understanding of the invention of natural deduction and sequent calculi. (shrink)

In this article, I consider the possibility of interpreting Hegel’s dialectic as dialetheism. After a first basic recapitulation about the meaning of the words ‘dialetheism’ and ‘dialectic’ and a consideration of Priest’s own account of the relation between dialectical and dialetheic logic in 1989, I discuss some controversial issues, not directly considered by Priest. As a matter of fact, the reflection on paraconsistent logics and dialetheism has enormously grown in recent years. In addition, the reception of Hegel’s logic and metaphysics (...) has also impressively improved. So I suggest that the discussion about the binomial dialectic/dialetheism should be reopened, on these new bases. (shrink)

In a recent article, Harold Noonan argues that application conditions and criteria of identity are not distinct from one another. This seems to threaten the standard approach to distinguishing sortals from adjectival terms. I propose that his observation, while correct, does not have this consequence. I present a simple scheme for distinguishing sortals from adjectival terms. I also propose an amended version of the standard canonical form of criteria of identity.

Kant’s theory of arithmetic is not only a central element in his theoretical philosophy but also an important contribution to the philosophy of arithmetic as such. However, modern mathematics, especially non-Euclidean geometry, has placed much pressure on Kant’s theory of mathematics. But objections against his theory of geometry do not necessarily correspond to arguments against his theory of arithmetic and algebra. The goal of this article is to show that at least some important details in Kant’s theory of arithmetic can (...) be picked up, improved by reconstruction and defended under a contemporary perspective: the theory of numbers as products of rule following construction presupposing successive synthesis in time and the theory of arithmetic equations, sentences or “formulas”—as Kant says—as synthetic a priori. In order to do so, two calculi in terms of modern mathematics are introduced which formalise Kant’s theory of addition as a form of synthetic operation. (shrink)

Kant's theory of arithmetic is not only a central element in his theoretical philosophy but also an important contribution to the philosophy of arithmetic as such. However, modern mathematics, especially non-Euclidean geometry, has placed much pressure on Kant's theory of mathematics. But objections against his theory of geometry do not necessarily correspond to arguments against his theory of arithmetic and algebra. The goal of this article is to show that at least some important details in Kant's theory of arithmetic can (...) be picked up, improved by reconstruction and defended under a contemporary perspective: the theory of numbers as products of rule following construction presupposing successive synthesis in time and the theory of arithmetic equations, sentences or "formulas"—as Kant says—as synthetic a priori. In order to do so, two calculi in terms of modern mathematics are introduced which formalise Kant's theory of addition as a form of synthetic operation. (shrink)

The paper challenges a widely held interpretation of Frege's conception of logic on which the constituent clauses of basic law V have the same sense. I argue against this interpretation by first carefully looking at the development of Frege's thoughts in Grundlagen with respect to the status of abstraction principles. In doing so, I put forth a new interpretation of Grundlagen §64 and Frege's idea of ‘recarving of content’. I then argue that there is strong evidence in Grundgesetze that Frege (...) did not hold the relevant sense-identity claim regarding basic law V. (shrink)

O presente manual tem como intenção constituir um guia para uma disciplina introdutória de filosofia da linguagem. Foi elaborado a partir da leccionação da disciplina de Filosofia da Linguagem I na Faculdade de Letras da Universidade do Porto desde 2001. A disciplina de Filosofia da Linguagem I ocupa um semestre lectivo e proporciona aos estudantes o primeiro contacto sistemático com a área da filosofia da linguagem. Pretende-se que este manual ofereça aos estudantes os instrumentos necessários não apenas para acompanhar uma (...) iniciação ao campo da filosofia da linguagem mas também para o estudo e a investigação autónomos posteriores. Para isso é percorrido um trajecto que conduz das intuições pré-teóricas acerca de linguagem, de que todos dispomos, até um conhecimento disciplinar específico, histórico e temático, da filosofia da linguagem. Em termos práticos, são considerados como precedentes da disciplina de Filosofia da Linguagem I – mesmo se, pelo existem actualmente precedências em sentido estrito – as disciplinas de Lógica I e II e de Filosofia do Conhecimento I e II. Os programas dessas disciplinas nos últimos anos estiveram presentes por trás da elaboração do manual. (shrink)

Composition as Identity is the view that an object is identical to its parts taken collectively. I elaborate and defend a theory based on this idea: composition is a kind of identity. Since this claim is best presented within a plural logic, I develop a formal system of plural logic. The principles of this system differ from the standard views on plural logic because one of my central claims is that identity is a relation which comes in a variety of (...) forms and only one of them obeys substitution unrestrictedly. I justify this departure from orthodoxy by showing some problems which result from attempts to avoid inconsistencies within plural logic by means of postulating other non-singular terms besides plural terms. Thereby, some of the main criticisms raised against Composition as Identity can be addressed. Further, I argue that the way objects are arranged is relevant with respect to the question which object they compose, i.e. to which object they are identical to. This helps to meet a second group of arguments against Composition as Identity. These arguments aim to show that identifying composite objects on the basis of the identity of their parts entails, contrary to our common sense view, that rearranging the parts of a composite object does not leave us with a different object. Moreover, it allows us to carve out the intensional aspects of Composition as Identity and to defend mereological universalism, the claim that any objects compose some object. Much of the pressure put on the latter view can be avoided by distinguishing the question whether some objects compose an object from the question what object they compose. Eventually, I conclude that Composition as Identity is a coherent and plausible position, as long as we take identity to be a more complex relation than commonly assumed. (shrink)

Philosophy becomes speculative when it raises questions about the ultimate nature of being and thought. What does it mean to be? What does it mean to think? How are being and thought related? What does it mean to ask these questions? These questions have occupied a central place in philosophy throughout history, but have led a shadow existence in twentieth-century thought, which has cut the tie between reason and these fundamental questions, leaving the questions in the twilight, and reason instrumentalised. (...) A.N. Whitehead (1861-1947), one of the founders of analytic philosophy and co-author (with Bertrand Russell) of Principia Mathematica, is one of the few contemporary thinkers to have developed an explicit speculative philosophy. Unsurprisingly, his philosophy has played a marginal role in academic debates. In this study, the methodological foundation of Whitehead’s speculative thought is reconstructed. On the basis of a systematic and historical examination of the nature of the question of being, Whiteheads ontology of the event as the passage into novelty emerges in its full scope, allowing the reader to understand why and to what extent Whitehead has walked a different path than other contemporary thinkers. His philosophy contains a conception of reason that is not alien to newness and creativity while being more than procedural or pragmatic, and a mode of understanding existence that brings out the acuteness of freedom, value and legitimacy, as well as the unity of things, of thought and nature. In order to show what is really happening in this philosophy, the received interpretation of Whitehead’s ontology is radically dismantled. The central thought, that to be means to happen, is explained in a process of reiteration and gradual clarification, examining traditional philosophical problems in metaphysics and epistemology (on topics like: nature and matter, knowledge, categorical structure, freedom and necessity, truth and meaning, modality) from its perspective. What emerges is a philosophy in which the temporality of being, when taken seriously, changes the status of familiar problems and dualisms and offers possibilities for thought, which previously did not exist. Whitehead “hears” the classical questions of philosophy in a new way. Beyond the trenches of twentieth-century philosophy, Whitehead’s speculative thinking contains many elements that will be of value to those studying the foundations of thought today and looking for new directions. In a time when the dualism of nature and man is maintained cynically in our economies and dismantled, but only in a biologistic fashion and therefore only seemingly, as a cover-up, in science and philosophy, Whitehead’s new and creative way of hearing, and answering, old questions about ultimate concerns, when understood properly, is more up to date than ever before. (shrink)

The traditional use of the expression 'pseudoproblem' is analysed in order to clarify the talk of pseudoproblems and related phenomena. The goal is to produce a philosophically serviceable terminology that stays true to its historical roots. This explicative study is inspired by and makes use of the method of logical reconstruction. Since pseudoproblems are usually expressed by pseudoquestions a formal language of questions is presented as a possible reconstruction language for alleged pseudoproblems. The study yields an informal theory of pseudoproblems (...) whose presuppositions are critically investigated right away. At least one result remains: Claims of pseudoproblemship and their refutations must not be voiced casually - they are to be relativized and need substantial interpretive effort. (shrink)

Michael Beaney ha sugerido recientemente que la distinción fregeana entre sentido y referencia fue propuesta para resolver la famosa paradoja del análisis. Casi diez años antes, Michael Dummett ya insistia en que Frege fue uno de los prirneros en buscar una soluci6n satisfactoria de esta paradoja. En esre articulo, discuto algunas sugerencias de Beaney y Dummett de cómo resolver la paradoja al estilo fregeano y tarnbién sus propias contribuciones no fregeanas al debate en torno de la corrección y de la (...) informatividad del análisis. Mi intención en esta discusión es mostrar que ninguna de ellas funciona. Concluyo con una propuesta de inspiración witttgensteiniana --el enfoque de los conceptos abiertos- para apoyar la idea de que la apelación a contertidos abiertos es la rnejor rnanera de disolver la paradoja.Michael Beaney has recently suggested that the Fregean distinction between sense and reference was proposed to solve the famous paradox of analysis. Not as recently, Michael Dummett has insisted that Frege was one of the first to look for a satisfactory solution to this paradox. In this paper, I discuss Beanry’s and Dummett’s various suggestions for solving the paradox in a Fregean style as well as their own non Fregean contributions to the debate around analysis’s correction and informativeness. My intention in this discussion is to show that none of them works. I conclude with a proposal inspired by Wittgenstein’s later work -the open concepts’ proposal- designed to support the idea that the appeal to open contents is the best way to dissolve the paradox. (shrink)

This book is about whether reference to an individual is the essential feature of a proper name -- a widely held view -- or whether referring to an individual is simply a contingent feature. Three questions need resolving, then. First, whether all names in particular contexts are themselves referring devices. Second, whether recognizing names types and the consequent issue of their ambiguity can be resolved simply by distinguishing between name types and tokens thereof. Last, whether names are ever referential in (...) the way Kripke and others have convincingly argued. The answer to first two questions is negative. The answer to third is a qualified "yes." I explain the theory that allows for these answers in the manuscript, as well as addressing other issues such as: the problem of fictional names; descriptive names; empty names; what an act of naming consists of; an account of ontological commitment; and the data that suggests that names are predicates. (shrink)

Since the appearance of Dummett’s monumental monograph in the early seventies of the last century there have been two interpretative traditions of reading Frege, one contradicting the other: the platonistic (or realistic) interpretation and the holistic (rationalistic) one. In this article, as a kind of intermediation, I firstly point out some pragmatic aspects of Frege’s work. Secondly, and more ambitiously, I outline the controversy between the most influential theories of truth (the correspondence, coherence, redundancy and pragmatic theory) in the light (...) of Frege’s philosophy. After all it was the concept of truth that Frege himself identified as the main objective of logic. (shrink)

The Linda paradox is a key topic in current debates on the rationality of human reasoning and its limitations. We present a novel analysis of this paradox, based on the notion of verisimilitude as studied in the philosophy of science. The comparison with an alternative analysis based on probabilistic confirmation suggests how to overcome some problems of our account by introducing an adequately defined notion of verisimilitudinarian confirmation.

این‌ نوشتار به گزارش و بررسی یکی از مهم‌ترین دیدگاه‌ها در رد وجود محمولی، یعنی بحث اشاره‌پذیری/‌ اشاره‌ناپذیری، می‌پردازد. همچنین نشان می‌دهد اغلب ادعاهای زیر از قوت چندانی برخوردار نیستند: 1. وجود مطلقاً محمول نیست؛ 2. وجود محمول منطقی نیست؛ و حتی، از جهاتی، این ادعای معتدل‌تر که می‌گوید: 3. گرچه وجود به‌صورت موضوع ـ محمولی محمول منطقی نیست، می‌توان آن را محمول منطقی به‌شمار آورد. برای این منظور دیدگاه برگزیده به کمک تساوی وجود و اشاره‌پذیری، تحلیلی از وجود محمولی (...) در فلسفة اسلامی ارائه می‌کند و نشان می‌دهد در دو بحث نخست دیدگاه مطرح در فلسفه و منطق دورة اسلامی قابل دفاع و تقویت است و در بحث سوم نیز دیدگاه‌های رقیب در تحلیل منطقی، بر فلسفه و منطق دورة اسلامی ترجیحی ندارند. همچنین، این جستار، با اصلاح‌ مبنای فلسفة اسلامی، اشاره‌پذیری معدوم به اشارة عقلی تبعی و غیر مستقیم را می‌پذیرد. (shrink)

When I talk about the objects of belief I do not mean, e.g., the sun to which my thought that the sun will rise tomorrow refers; I do not mean the objects we think about. I take objects rather in a general philosophical sense; they simply are the bearers of properties and the relata of relations. I am thus concerned with the objects that are related by the belief relation „_a_ believes that _p_“. In this scheme „ _a _“ represents (...) a person or an epistemic subject; but I am not going to discuss what a person is. „ _p _“ or „that _p _“ represents an object, namely the object of belief; and I am going to discuss what this is. In other words, I am interested in belief contents – to use a less neutral, narrower and equally unclear term. (shrink)

David Hilbert's finitistic standpoint is a conception of elementary number theory designed to answer the intuitionist doubts regarding the security and certainty of mathematics. Hilbert was unfortunately not exact in delineating what that viewpoint was, and Hilbert himself changed his usage of the term through the 1920s and 30s. The purpose of this paper is to outline what the main problems are in understanding Hilbert and Bernays on this issue, based on some publications by them which have so far received (...) little attention, and on a number of philosophical reconstructions of the viewpoint (in particular, by Hand, Kitcher, and Tait). (shrink)

In this paper we reconstruct an argument, based on the observations of David Lewis and Jaegwon Kim, according to which, given that identities are necessary, they cannot be grounded; and given that they cannot be grounded, they cannot be explained either. We argue against two key premises of this argument. Furthermore, we present two counterexamples, in the form of two alleged sets of cases of explanation of identities. This argument against the explanation of identities is instrumental for a wider discussion (...) about the nature of explanation itself, in relation with other notions of recent philosophical interest such as grounding. (shrink)

Megethology is the second-order theory of the part-whole relation developed by David Lewis, and it is obtained by combining plural quantification with classical extensional mereology. It can express some hypotheses about the size of the domain such as that there are inaccessibly many atoms. This will prove enough to get the orthodox set theory. Then, megethology is a possible foundation for mathematics. This paper is an introduction to megethology.

Resumen Como es muy conocido, Frege afirmó que la expresión ‘el concepto caballo’ se refiere a un objeto y no a un concepto. En este artículo, en primer lugar, mostramos cómo hay algunos barruntos de esta paradoja en textos anteriores a 1891. En segundo lugar, revisamos algunos argumentos que defienden que con el término ‘el concepto caballo’ Frege se refería a la extensión del mencionado concepto. Por último, sostendremos que, aun cuando el concepto caballo sea dicha extensión, es muy poco (...) lo que sabemos de su naturaleza. Esto último se debe a la forma fragmentaria en que Frege introduce las extensiones de concepto en los Grundgesetze y en ensayos previos.As is well known, Frege stated that the expression ‘the concept horse’ refers to an object and not to a concept. In this article we firstly show how there are some hints of this paradox in texts prior to 1891. Secondly we review some arguments given in the literature to hold that with ‘the concept horse’ Frege referred to the extension of the mentioned concept. Finally, we argue that, even if the concept horse is such an extension, we still know very little about its nature, given the fragmentary way in which Frege introduces the extensions of concepts in Grundgesetze and in previous essays. (shrink)

In this talk I present the main results from Anta (2021), namely, that the theoretical division between Boltzmannian and Gibbsian statistical mechanics should be understood as a separation in the epistemic capabilities of this physical discipline. In particular, while from the Boltzmannian framework one can generate powerful explanations of thermal processes by appealing to their microdynamics, from the Gibbsian framework one can predict observable values in a computationally effective way. Finally, I argue that this statistical mechanical schism contradicts the Hempelian (...) (1958) thesis that the predictive power of a scientific theory is directly proportional to its explanatory potential, and vice versa. (shrink)

My starting point is that discussions in philosophy about the ontology of technical artifacts ought to be informed by classificatory practices in engineering. Hence, the heuristic value of the natural-artificial distinction in engineering counts against arguments which favour abandoning the distinction in metaphysics. In this chapter, I present the philosophical equipment needed to analyse classificatory practices and then present a case study of engineering practice using these theoretical tools. More in particular, I make use of the Collectivist Account of Technical (...) Artifacts (CAT) according to which there are different classificatory practices for natural, artificial, and social objects. I demonstrate that in the community studied, artificial kinds are marked by distinctive classificatory practices. The presence of these distinctive classificatory practices in engineering with regard to artificial kinds should inform discussions about the ontology of technical artifacts just as the distinctive classificatory practices in natural science inform discussions about natural kinds. (shrink)

Joan Weiner has argued that Frege’s definitions of numbers constitute linguistic stipulations that carry no ontological commitment: they don’t present numbers as pre-existing objects. This paper offers a critical discussion of this view, showing that it is vitiated by serious exegetical errors and that it saddles Frege’s project with insuperable substantive difficulties. It is first demonstrated that Weiner misrepresents the Fregean notions of so-called Foundations-content, and of sense, reference, and truth. The discussion then focuses on the role of definitions in (...) Frege’s work, demonstrating that they cannot be understood as mere linguistic stipulations, since they have an ontological aim. The paper concludes with stressing both the epistemological and the ontological aspects of Frege’s project, and their crucial interdependence. (shrink)

An overview of what Frege accomplishes in Part II of Grundgesetze, which contains proofs of axioms for arithmetic and several additional results concerning the finite, the infinite, and the relationship between these notions. One might think of this paper as an extremely compressed form of Part II of my book Reading Frege's Grundgesetze.

A speculative investigation of how Frege's logical views change between Begriffsschrift and Grundgesetze and how this might have affected the formal development of logicism.

The two main features of this thesis are (i) an account of contextualized (context indexed) counterfactuals, and (ii) a non-vacuist account of counterpossibles. Experience tells us that the truth of the counterfactual is contingent on what is meant by the antecedent, which in turn rests on what context is assumed to underlie its reading (intended meaning). On most conditional analyses, only the world of evaluation and the antecedent determine which worlds are relevant to determining the truth of a conditional, and (...) consequently what its truth value is. But that results in the underlying context being fixed, when evaluating distinct counterfactuals with the same antecedent on any single occasion, even when the context underlying the evaluation of each counterfactual may vary. Alternative approaches go some of the way toward resolving this inadequacy by appealing to a difference in the consequents associated with counterfactuals with the same antecedent. That is, in addition to the world of evaluation and the antecedent, the consequent contributes to the counterfactual’s evaluation. But these alternative approaches nevertheless give a single, determinate truth value to any single conditional (same antecedent and consequent), despite the possibility that this value may vary with context. My reply to these shortcomings (chapter 4) takes the form of an analysis of a language that makes appropriate explicit access to the intended context available. That is, I give an account of a contextualized counterfactual of the form ‘In context C: If it were the case that … , then it would be the case that …’. Although my proposal is largely based on Lewis’ (1973, 1981) analyses of counterfactuals (the logic VW and its ordering semantics), it does not require that any particular logic of counterfactuals should serve as its basis – rather, it is a general prescription for contextualizing a conditional language. The advantage of working with ordering semantics stems from existing results (which I apply and develop) concerning the properties of ordering frames that facilitate fashioning and implementing a notion of contextual information preservation. Analyses of counterfactuals, such as Lewis’ (1973), that cash out the truth of counterfactuals in terms of the corresponding material conditional’s truth at possible worlds result in all counterpossibles being evaluated as vacuously true. This is because antecedents of counterpossibles are not true at any possible world, by definition. Such vacuist analyses have already been identified and challenged by a number of authors. I join this critical front, and drawing on existing proposals, I develop an impossible world semantics for a non-vacuist account of counterpossibles (chapter 5), by modifying the same system and semantics that serve the basis of the contextualized account offered in chapter 4, i.e. Lewis’ (1986) ordering semantics for the logic VW. I critically evaluate the advantages and disadvantages of key conditions on the ordering of worlds on the extended domain and show that there is a sense in which all of Lewis’ analysis of mere counterfactuals can be preserved, whilst offering an analysis of counterpossibles that meets our intuitions. The first part of chapter 1 consists of an outline of the usefulness of impossible worlds across philosophical analyses and logic. That outline in conjunction with a critical evaluation of Lewis’ logical arguments in favour of vacuism in chapter 2, and his marvellous mountain argument against impossible worlds in chapter 3, serves to motivate and justify the impossible world semantics for counterpossibles proposed in chapter 5. The second part of chapter 1 discusses the limitations that various conditional logics face when tasked to give an adequate treatment of the influence of context. That introductory discussion in conjunction with an overview of conditional logics and their various semantics in chapter 2 – which includes an in-depth exposition of Stalnaker-Lewis similarity semantics for counterfactuals – serves as the motivation and conceptual basis for the contextualized account of counterfactuals proposed in chapter 4. (shrink)