It is Frege's third contribution that makes the point of departure for the present paper. Not merely did Frege show how to manipulate symbols more exactly; he also gave a searching account of what these symbols mean. Consider a philosophical problem that arises out of the simplest arithmetic. When we say that 5 = 2 + 3, what do we mean? Do we mean that 5 is identical with 2 + 3? But in some ways 5 and 2 + (...) 3 are obviously different. Or do we mean that 5 and 2 + 3 are equal but not identical, equality being a relation that falls short of complete identity? But in that case, some ordinary ways of speaking in mathematics must be false. Suppose a pupil is asked for the positive square root of 25. The phrasing of the question implies that there is one and only one. No doubt he may answer, '5'. But then it follows that the answer '2 + 3' is not allowable, since ex hypothesi 5 and 2 + 3, though equal, are not identical. Yet ordinarily the answer '2 + 3' would be regarded as strange but not as wrong. (shrink)

Concerns a problem posed, but not solved, by Frege in part III of his Grundgesetze. As a preliminary to defining ‘real number’, Frege attempts to analyse the notion of a quantitative domain. He was unaware of the previous attempt of Otto Holder to do this; it is remarked how much weaker Frege's assumptions were in deriving theorems than Holder's. Frege deals with groups on which there is a right‐invariant semilinear ordering, although he does not use this terminology. He is (...) uncertain whether it can be deduced that the ordering is also left‐invariant, and proves as much as possible without invoking the assumption that it is. The independence proof, due to Dr Peter Neumann, establishes that it could not be deduced. (shrink)

STEPHEN TOULMIN George Santayana used to insist that those who are ignorant of the history of thought are doomed to re-enact it. To this we can add a corollary: that those who are ignorant of the context of ideas are doom ed to misunderstand them. In a few self-contained fields such as pure mathematics, concepts and conceptual systems can perhaps be de tached from their historico-cultural situations; so that (for instance) a self-taught Ramanujan, living alone in India, mastered number theory (...) to a point at which he could make major contributions to European mathematics. But elsewhere the situation is different - and, in philosophy, inevitably so. For philosophical ideas and problems confront us like geological specimens in situ; and, in the act of prising them free from their historical and cultural locations, we can too easily forget about the matrix in which they took shape, and end by impossing on them a sculptural form of our own making. Something of this kind has happened in the case of Ludwig Wittgen stein. For his philosophical work has commonly been seen as an episode in the development, either of mathematicallogic, or oftwentieth-century British philosophy. His associations with Frege and Russell, Moore and Waismann, have over-shadowed everything else in his cultural origins and intellectual concerns. (shrink)

Edmund Husserl was one of the very first to experience the direct impact of challenging problems in set theory and his phenomenology first began to take shape while he was struggling to solve such problems. Here I study three difficulties associated with Frege's use of sets that Husserl explicitly addressed: reference to non-existent, impossible, imaginary objects; the introduction of extensions; and 'Russell's paradox'.I do so within the context of Husserl's struggle to overcome the shortcomings of set theory and to develop (...) his own theory of manifolds. I define certain issues involved and discuss how Husserl's theory of manifolds might confront them. In so doing I hope to help bring Husserl's theories about sets and manifolds out of the realm of abstract theorizing and prompt further exploration of uncharted philosophical territory rich in philosophical implications. (shrink)

For scholars of American philosophy, this anthology of essays on S. C. Pepper's works on metaphysics, aesthetics, and value theory is especially a welcome one. Also included is a reprint of a little known but valuable essay by Pepper entitled "Metaphor in Philosophy," which originally appeared in volume 3 of Phillip S. Wiener's Dictionary of the History of Ideas. In this essay, Pepper discusses his root metaphor theory in relation to Bacon and Kant, and some contemporary uses of the notion (...) of paradigm, e.g., Wittgenstein and Kuhn. Lewis E. Hahn's "The Stephen C. Pepper Papers, 1903-1972" gives an informative account of six book-length unpublished manuscripts in the Pepper Archives at the Southern Illinois University. The rest of the essays concentrate on the various aspects of Pepper's works. A few deal with aesthetic theory and its application to critical practice. Of philosophical interests are papers by Elmer H. Duncan, David B. Richardson, Robert J. Yanal, Robert L. Armstrong, and Brian Caraher, and a short essay by Charles Hartshorne and a response by Joseph H. Monast. Duncan gives a just but critical account of the neglect of Pepper's Sources of Value, and a highly appreciative appraisal of Pepper's World Hypotheses. Caraher's careful essay on the conflicting root metaphors in Frege's theory of meaning offers interesting application of Pepper's conception of formism and contextualism to problems in Frege's philosophy. A variety of problems such as the root metaphor theory, descriptive definition and aesthetic experience are discussed. Efron's long introductory essay entitled "Pepper's Continuing Value" serves its purpose well in terms of indicating Pepper's influence in non-philosophical disciplines and the problems that arise in Pepper's value theory. What is missed is a sustained critical examination of Pepper's root metaphor theory, characterization of the various world hypotheses including Pepper's own selectivism, and its relation to ethical theory. The anthology however is useful in indicating the scope of Pepper's influence and the need to examine his contributions with reference to contemporary philosophical problems.--A.S.C. (shrink)

According to Frege, we need a criterion for recognising when different sentences express the same thought to make progress in logic. He himself hedged his own equipollence criterion with a number of provisos. In the literature on Frege, little attention has been paid to the problems these provisos raise. In this paper, I will argue that Fregeans have ignored these provisos at their peril. For without these provisos, Frege’s criterion yields wrong results; but with the provisos in place, it (...) is of no use for Frege’s purposes. This is connected to what Frege took to be the ‘greatest difficulty for philosophy’: natural language sentences don’t just express thoughts; they convey evaluations and communicative hints. Because of this, Frege’s recognition criterion for thoughts cannot be applied to them and we cannot make logical progress by ‘recognising a thought in different linguistic guises’. (shrink)

This little volume is a critical introduction to the phenomenological scene through discussion of the ideas of some of its more prominent exponents and an extensive analysis of the thought of its founder. About two thirds of the book is devoted to Husserl. It traces the evolution of Husserl's philosophy from an early interest in the psychological presuppositions of number, to the phenomenological analysis of acts of meaning, and finally to his unsuccessful attempt to construct a comprehensive system embracing the (...) presuppositions of knowledge in general. Previous acquaintance with Husserl's work is not necessary as Pivcevic gives critical expositions of the main theses of Husserl's Philosophy of Arithmetic, Logical Investigations, Ideas for a Pure Phenomenology and Phenomenological Philosophy, and The Crisis of European Sciences and Phenomenological Philosophy. He is careful to establish particular philosophic problems through reference to the views of other philosophers, and on different issues the position of Husserl is compared and contrasted to those of Frege, Brentano, Russell, Descartes, the positivists, the classical Empiricists and Kant. The presentation of Sartre's views includes brief discussions of European romanticism, Hegel, and Marx. Besides Sartre, Scheler and Heidegger are discussed to illustrate differing applications of the phenomenological method. The final chapter is a brief critique of the limitations of this method: the problem of "other egos," the marked tendency to anti-rationalism, and the failure to achieve its aim of a presupposition-less philosophy. Pivcevic is not totally sympathetic with the phenomenologists, which is perhaps what makes possible this critical exposition of their views. But at times one wishes his clear prose would follow a philosopher's thought further into its more obscure dimensions. His criticisms are often the standard, uninspired objections to what are generally accepted as unjustified excesses of existentialist thought. Nevertheless, this is an excellent introduction to phenomenology and especially valuable for its exposition of the thought of Edmund Husserl.--M. S. H. (shrink)

In the 1960s, Peter Geach and John Searle independently posed an important objection to the wide class of 'noncognitivist' metaethical views that had at that time been dominant and widely defended for a quarter of a century. The problems raised by that objection have come to be known in the literature as the Frege-Geach Problem, because of Geach's attribution of the objection to Frege's distinction between content and assertoric force, and the problem has since occupied a great deal (...) of the attention both of defenders of broadly noncognitivist views, and of their critics. In this article I explain Geach and Searle's historical objections, and put the subsequent discussion into dialectical context, paying some attention to the developments along the way and how they have enhanced our overall understanding of the problem. The article covers a lot of territory, so we will only be able to see the highlights, along the way. For further reading, see the Works Cited. (shrink)

This long, diffuse, and intermittently quite interesting work is an attempt to explain and justify the process by which the concept of truth has been transformed in modern and contemporary philosophy from a doctrine of adequation via one of the true vision of things to that of the activity of the free subject. The main figures in this process are Descartes, Leibniz, Kant, and Hegel, although considerable space is devoted to Fichte, Schelling, Nietzsche, Husserl, Heidegger, Wittgenstein, and even K. O. (...) Apel and Hans Wagner. Despite the discussion of Wittgenstein and an odd comment or so about Frege, modern philosophy means primarily modern German philosophy; there is, however, some peripheral treatment of contemporary analytical thought. One may perhaps point to three main aspects of the author’s program. The first is his acceptance of the currently fashionable view that semantics is the orientating branch of philosophy. This thesis follows from the author’s acceptance of the historical rejection of Cartesian and Leibnizian intuition in favor of Kantian and Hegelian emphasis upon rationality as categoricity or conceptualism. The second aspect is Simon’s regular attempt to assimilate semantics into the doctrine of reflection. Hence the emphasis upon concepts shifts from that of objects to a second-order reflection upon the nature of conceptual thinking. The third aspect is in many ways the most comprehensive; at least Simon’s book culminates in its articulation. This is the attempt to assimilate the doctrine of reflection into a conception of freedom as a doctrine of both Recht and communication. I found especially valuable the emphasis upon the contribution of the subject to "objective" conceptions of meaning and truth. There are very good pages on the modern doctrine of intuition and the changing role assigned to imagination. The regular emphasis placed by Simon on negation as determination, and hence upon negation of negation as a crucial element even within non-dialectical logic, is also valuable. I was less persuaded by the treatment of intersubjectivity as an expression of a hermeneutics of communication within the context of a doctrine of individual rights. This Fichtean revision of Habermas and Apel may be the latest chapter in German academic philosophy of the traditional stream, but it does not follow even on Simon’s quasi-Hegelian principles that the text is sound. The deepest problem facing the author is to prevent the concept of truth from dissolving altogether into subjective reflection upon the limitations of objective definitions of truth. Stated somewhat differently, the author fails to persuade this reader that truth is actually the consensus of the community. Whatever the "positivist" deficiencies of Descartes and Leibniz, they do provide us with a concept of truth that is not easily mistaken for ideology.—S.R. (shrink)

Analytical Thomism is a recent label for a newer kind of approach to the philosophical and natural theology of St Thomas Aquinas. It illuminates the meaning of Aquinas's work for contemporary problems by drawing on the resources of contemporary Anglo-Saxon analytical philosophy, the work of Frege, Wittgenstein, and Kripke proving particularly significant. This book expands the discourse in contemporary debate, exploring crucial philosophical, theological and ethical issues such as: metaphysics and epistemology, the nature of God, personhood, action and meta-ethics. All (...) those interested in the thought of St Thomas Aquinas, and more generally contemporary Catholic scholarship, problems in philosophy of religion, and contemporary metaphysics, will find this collection an invaluable resource. (shrink)

I argue that Frege's so-called "concept 'horse' problem" is not one problem but many. When these different sub-problems are distinguished, some emerge as more tractable than others. I argue that, contrary to a widespread scholarly assumption originating with Peter Geach, there is scant evidence that Frege engaged with the general problem of the inexpressibility of logical category distinctions in writings available to Wittgenstein. In consequence, Geach is mistaken in his claim that in the Tractatus Wittgenstein simply accepts (...) from Frege certain lessons about the inexpressibility of logical category distinctions and the say-show distinction. In truth, Wittgenstein drew his own morals about these matters, quite possibly as the result of reflecting on how the general problem of the inexpressibility of logical category distinctions arises in Frege's writings , but also, quite possibly, by discerning certain glimmerings of these doctrines in the writings of Russell. (shrink)

This critical analytical review examines the ways in which realism can be justified in epistemology and philosophy of science and which are presented in the collection of papers “Perspectives of Realism in Modern Philosophy” (M., 2017). The exposition of areas in which the authors of this book study the problems of realism, as well as those arguments in its defense that they offer, is given. A criticism of these arguments is presented, according to which all of them are not able (...) to convince an antirealist to abandon their views in favor of realism. The question of whether realists and anti-realists have the same object of discussion and what could become a common ground for them is explored. The author suggests that an appeal to language can become such a common ground and reproduces Frege’s argument against skeptics and idealists as a possible methodological justification for realism. (shrink)

This study explores the phenomenon of the so-called “third reading” of propositional attitude reports. This reading, which was originally explored in the dissertation of J. Fodor (1973) and has since become one of the significant problems in the formal semantics of natural languages, differs from the more well-known de re and de dicto readings by being an intermediate case. If the de re interpretation can be referred to as transparent specific, and the de dicto interpretation as opaque non-specific, then the (...) third reading is transparent non-specific. Fodor's standard solution has been the subject of much discussion in the literature and has given rise to a series of widely accepted counterexamples that are thought to demonstrate the limitations of Fodor's solution. At the same time, alternative approaches to the explication of these readings also suffer from formal shortcomings (for example, some of them did not satisfy the requirement of meaning compositionality, which is a basic requirement in formal semantic literature). This study points out that the analysis of all complex cases of the third reading did not fully take into account their syntactic structure. This remained unnoticed due to the ellipsis in many of these cases. It is shown that a restoration of the ellided syntactic structure makes it possible to analyze all hard cases as basic ones using the classical standard analysis proposed by Fodor supplemented by the principles of admissibility of substitution of L-equivalent expressions in intensional contexts (known since G. Frege and R. Carnap). In the final part of the work, it is demonstrated how exactly the main complex cases of the “third reading” are explicated in terms of the standard approach. (shrink)

Mark Eli Kalderon has argued for a fictionalist variant of non-cognitivism. On his view, what the Frege–Geach problem shows is that standard non-cognitivism proceeds uncritically from claims about use to claims about meaning; if non-cognitivism's claims were solely about use it would be on safe ground as far as the Frege–Geach problem is concerned. I argue that Kalderon's diagnosis is mistaken: the problem concerns the non-cognitivist's account of the use of moral sentences too.

The author tries to read ontology out of existence by means of a series of linguistic recommendations. His presiding assumption is that all ontological disagreements are matters of linguistic reference. His dominant claim is that quantification has wrongly been thought to imply existence. His strategy rests on the success of his claim that Kant's reasons for holding that "exist" is a logical and not a real predicate is the precursor of Frege's account of existence as a second rather than a (...) first order predicate. His conclusion is that all of the traditional problems which have dominated ontological inquiry can be dissolved once it has been shown, first, that the vehicles of reference which have historically been associated with ontological claims are linguistically dispensable and secondly, that what have been taken to be names or definite descriptions are really second order predicates. Both names and definite descriptions can be translated without remainder into second order predicates. Predicates do not denote because they are not names. The problems of ontology are not really problems at all because their traditional formulations are ill formed. Ontology is a linguistic repugnancy. (shrink)

Frege's Grundgesetze was one of the 19th century forerunners to contemporary set theory which was plagued by the Russell paradox. In recent years, it has been shown that subsystems of the Grundgesetze formed by restricting the comprehension schema are consistent. One aim of this paper is to ascertain how much set theory can be developed within these consistent fragments of the Grundgesetze, and our main theorem shows that there is a model of a fragment of the Grundgesetze which defines a (...) model of all the axioms of Zermelo-Fraenkel set theory with the exception of the power set axiom. The proof of this result appeals to G\"odel's constructible universe of sets, which G\"odel famously used to show the relative consistency of the continuum hypothesis. More specifically, our proofs appeal to Kripke and Platek's idea of the projectum within the constructible universe as well as to a weak version of uniformization (which does not involve knowledge of Jensen's fine structure theory). The axioms of the Grundgesetze are examples of abstraction principles, and the other primary aim of this paper is to articulate a sufficient condition for the consistency of abstraction principles with limited amounts of comprehension. As an application, we resolve an analogue of the joint consistency problem in the predicative setting. (shrink)

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)

According to an influential variety of the representational view of perceptual experience—the singular content view—the contents of perceptual experiences include singular propositions partly composed of the particular physical object a given experience is about or of. The singular content view faces well-known difficulties accommodating hallucinations; I maintain that there is also an analogue of Frege's puzzle that poses a significant problem for this view. In fact, I believe that this puzzle presents difficulties for the theory that are unique to (...) perception in that strategies that have been developed to respond to Frege's puzzle in the case of belief cannot be employed successfully in the case of perception. Ultimately, I maintain that this perceptual analogue of Frege's puzzle provides a compelling reason to reject the singular content view of perceptual experience. (shrink)

This is an opinionated overview of the Frege-Geach problem, in both its historical and contemporary guises. Covers Higher-order Attitude approaches, Tree-tying, Gibbard-style solutions, and Schroeder's recent A-type expressivist solution.

Blackburn has outlined a formal account for moral expressivism, and we argued that the moral Frege-Geach problem can be solved formally by appending two rules for the boo-operator which are missing from his account. We then extended Blackburn’s formal account to generate a similar solution to the problem in modal context and showed that the validity of the modal argument can be preserved too in modal expressivism. However, the higher-order element endorsed by Blackburn does not seem necessary for (...) solving the Frege-Geach problem. Nor is his extension from moral expressivism to modal expressivism tenable, since the latter violates its own ontological constraint. A general moral is drawn on the basis on three observations made in evaluating Blackburn’s expressivism. (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)

In their recent article ‘Resolving Frege’s other Puzzle’ Eric Snyder, Richard Samuels, and Stewart Shapiro defend a semantic type-shifting solution to Frege’s other Puzzle and criticize my own cognitive type-shifting solution. In this article I respond to their criticism and in turn point to several problems with their preferred solution. In particular, I argue that they conflate semantic function and semantic value, and that their proposal is neither based on general semantic type-shifting principles nor adequate to the data.

One of the remarkable results of Frege’s Logicism is Frege’s Theorem, which holds that one can derive the main truths of Peano arithmetic from Hume’s Principle (HP) without using Frege’s Basic Law V. This result was rediscovered by the Neo-Fregeans and their allies. However, when applied in developing a more advanced theory of mathematics, their fundamental principles—the abstraction principles—incur some problems, e.g., that of inflation. This paper finds alternative paths for such inquiry in extensionalism and object theory.

Neo-logicism is, not least in the light of Frege’s logicist programme, an important topic in the current philosophy of mathematics. In this essay, I critically discuss a number of issues that I consider to be relevant for both Frege’s logicism and neo-logicism. I begin with a brief introduction into Wright’s neo-Fregean project and mention the main objections that he faces. In Sect. 2, I discuss the Julius Caesar problem and its possible Fregean and neo-Fregean solution. In Sect. (...) 3, I raise what I take to be a central objection to the position of neo-logicism. In Sect. 4, I attempt to clarify how we should understand Frege’s stipulation that the two sides of an abstraction principle qua contextual definition of a term-forming operator shall be “gleichbedeutend”. In Sect. 5, I consider the options that Frege might have had to establish the analyticity of Hume’s Principle: The number that belongs to the concept F is equal to the number that belongs to the concept G if and only if F and G are equinumerous. Section 6 is devoted to Frege’s two criteria of thought identity. In Sects. 7 and 8, I defend the position of the neo-logicist against an alleged “knock-down argument”. In Sect. 9, I comment on Frege’s description of abstraction in Grundlagen, §64 and the use of the terms “recarving” and “reconceptualization” in the relevant literature on Fregean abstraction and neo-logicism. I argue that Fregean abstraction has nothing to do with the recarving of a sentence content or its decomposition in different ways. I conclude with remarks on global logicism versus local logicisms. (shrink)

In a series of articles dating from 1903 to 1906, Frege criticizes Hilbert’s methodology of proving the independence and consistency of various fragments of Euclidean geometry in his Foundations of Geometry. In the final part of the last article, Frege makes his own proposal as to how the independence of genuine axioms should be proved. Frege contends that independence proofs require the development of a ‘new science’ with its own basic truths. This paper aims to provide a reconstruction of this (...) New Science that meets modern standards and to examine possible problems surrounding Frege’s original proposal. The paper is organized as follows: the first two sections summarize the main points of the Frege–Hilbert controversy and discuss some issues surrounding the problem of independence proofs. Section 3 contains an informal presentation of Frege’s proposal. In section 4 a more detailed reconstruction of Frege’s New Science is set out while section 5 examines what is left out. The concluding section is devoted to a discussion of Frege’s strategy and its significance from a broader perspective. (shrink)

The paper focuses on Gottlob Frege’s so called Context Principle (CP hereafter), which counts as one of the most controversial points of his philosophy. Due to its importance and centrality in Frege’s thought, a detailed discussion of the principle requires a detailed analysis of almost all aspects of his philosophy. Obviously, such a task cannot be successfully accomplished here. Thus I limit myself to address only two questions concerning the CP: what role does the principle play (in Grundlagen) (...) and how can we interpret it. Addressing the first problem is required in order to address the second. Most authors interpreted CP from the perspective of Frege’s later distinction between sense and reference, which I will call the ‘semantic interpretation’. Although I accept this perspective as valuable and important, I will initially inverse the action and I will try to approach CP, and generally Grundlagen, in a more natural way, contextually, namely setting them in the initial logicist plan of the Begriffschrift. Finally, I will try to provide an interpretation concerning the alleged conflict between CP and Frege’s compositionality thesis such that they could coherently stay together. (shrink)

This paper argues against the claim that Frege is committed to an infinite hierarchy of senses. Carnap and Kripke, along with many others, argue the contrary; I expose where all such arguments go astray. Invariably these arguments assume (without citation) that Frege holds that sense and reference are always distinct. This is the fulcrum upon which the hierarchy is hoisted. The counter to this assumption is based on two important but neglected passages. The locution ‘indirect sense’ has no ontological significance (...) for Frege. It was just a ‘short expression’ (his term) to indicate that the customary relation between sign, sense, and reference is suspended in what he called the exception case of indirect context. Once the hierarchy is abandoned, the alleged problem of just what indirect sense is, as well as questions as to why Frege said so little about it and why he did not examine iterative indirect contexts are resolved. Of course, with no hierarchy, Davidson’s “unlearnability argument” turns out to be a non-starter. Some objections to my interpretation are considered and answered. Additionally, comparisons to Dummett’s one-level view of sense, which is similar to mine are made, as well as to some two-level views (Parsons and Skiba). (shrink)

This paper provides a new approach to a family of outstanding logical and semantical puzzles, the most famous being Frege's puzzle. The three main reductionist theories of propositions (the possible-worlds theory, the propositional-function theory, the propositional-complex theory) are shown to be vulnerable to Benacerraf-style problems, difficulties involving modality, and other problems. The nonreductionist algebraic theory avoids these problems and allows us to identify the elusive nondescriptive, non-metalinguistic, necessary propositions responsible for the indicated family of puzzles. The algebraic approach is also (...) used to defend antiexistentialism against existentialist prejudices. The paper closes with a suggestion about how this theory of content might enable us to give purely semantic (as opposed to pragmatic) solutions to the puzzles based on a novel formulation of the principle of compositionality. (shrink)

I shall discuss some of the issues concerning a notorious doctrine of Frege that sentences are names of truth-values. I am interested in a problem raised by Kripke that the doctrine obscures the distinction between judgeable and unjudgeable contents. I shall present what I take to be Frege’s account of judgeable content: a proper expression of a judgeable content is susceptible to an analysis into a predicate and an argument-word, where a predicate is understood as a concept-word used (...) to attribute a certain property to the referent of the argument-word. In the light of this analysis, I shall argue that the doctrine does not obscure the distinction. The problem will also be discussed within the formal context of Grundgesetze. A new light will be shed on his rather peculiar conception of the symbol ‘ ${\boldsymbol \vdash}$’. (shrink)

In this dissertation I explore Frege’s conception of truth. In particular I defend the thesis that Frege in his mature career takes truth to be an object, i.e., the True qua the reference of true sentences. In the literature on truth Frege has been usually taken to be a truth deflationist or a truth primitivist. Indeed Frege leaves a number of comments that sound like typical deflationist claims and his famous indefinability argument is the most discussed argument for primitivism. (...) However, Frege is neither a deflationist nor a primitivist. His deflationist remarks and the indefinability argument are rather his arguments that truth is an object. -/- For Frege judging—and its verbal counterpart asserting—is always acknowledging the truth of a truth-bearer. Thus, if truth is an object for him, his conception of judgment ought to also be adjusted accordingly. Indeed Frege shows how we can understand judgment qua acknowledgment of truth if truth is an object. Specifically, judging that p is identifying the True with the reference of ‘p’ non-judgmentally, i.e., without judging that p is identical with the reference of ‘p’. Frege’s conception of judgment impacts his conception of knowledge because the act of judging is that of producing knowledge. In a nutshell our act of judging and the knowledge we produce by it are epistemically grounded in our objectual knowledge of the True. If we take this point into account, we can develop a new reading of Frege’s claim that logic is the science of truth. -/- The suggested reading of Frege’s conception of truth and related notions can make a contribution to contemporary philosophical problems. First, Frege’s conception of judgment can cope with Peter Hanks’s recent criticisms of the Fregean picture of judgment in general. Secondly, his conception of assertion can explain the connection between truth and assertion in a novel way. Lastly, Frege’s conception of knowledge can be developed into a new theory of knowledge where objectual knowledge is more fundamental than propositional knowledge. (shrink)

Hybrid expressivists claim to solve the Frege-Geach problem by offloading the explanation of the logico-semantic properties of moral sentences onto beliefs that are components of hybrid states they express. We argue that this strategy is undermined by one of hybrid expressivism’s own commitments: that the truth of the belief-component is neither necessary nor sufficient for the truth of the hybrid state it composes. We articulate a new approach. Instead of explaining head-on what it is for, say, a pair of (...) moral sentences to be inconsistent, expressivists should “sidestep” and explain what it is _to think that_ a pair of moral sentences is inconsistent. To think so is to think they cannot both be true – a modal notion. Since expressivists have given accounts of such modals, we illustrate how sentences like ‘“lying is wrong” and “lying is not wrong” are inconsistent’ express sensible – and rationally compelling – states of mind. (shrink)

This paper examines four arguments in support of Frege's theory of incomplete entities, the heart of his semantics and ontology. Two of these arguments are based upon Frege's contributions to the foundations of mathematics. These are shown to be question-begging. Two are based upon Frege's solution to the problem of the relation of language to thought and reality. They are metaphysical in nature and they force Frege to maintain a theory of types. The latter puts his theory of incomplete (...) entities in the paradoxical position of maintaining that it is no theory at all. Moreover, his metaphysics rules out well-known suggestions for avoiding this difficulty. (shrink)

I resolve the major challenge to an Expressivist theory of the meaning of normative discourse: the Frege–Geach Problem. Drawing on considerations from the semantics of directive language (e.g., imperatives), I argue that, although certain forms of Expressivism (like Gibbard’s) do run into at least one version of the Problem, it is reasonably clear that there is a version of Expressivism that does not.

Frege believes that the content of declarative sentences divides into a thought and its ‘colouring’, perhaps combined with assertoric force. He further thinks it is important to separate the thought from its colouring. To do this, a criterion which determines sameness of sense between sentences must be deployed. But Frege provides three criteria for this task, each of which adjudicate on different grounds. In this article, rather than expand on criticisms levelled at two of the criteria offered, the author focuses (...) on the most promising candidate. As it stands, this criterion has problems, but not insuperable ones. He suggests an adjusted criterion that relies on the epistemic notion of triviality. He recommends this criterion as both harmonious with Frege’s broader thought and preferable to alternatives offered. The moral is that Frege individuates thoughts by deploying an epistemic concept, and this is the only suitable way for him to do so. (shrink)

En este articulo relaciono dos asuntos que no se relacionan comunmente en la literatura sobre Frege: el argumento de Frege sobre la interpretacion de las oraciones de identidad y su problema de referirse a las funciones. Primero expongo el argumento y concluyo que es plausible. Luego caracterizo las relaciones semanticas que el argumento le permite introducir. A continuacion trato el problema antes mencionado y muestro corno afecta a la semantica de Frege: esas relaciones semanticas se vuelven innominables y, por tanto, (...) su seolantica resulta ser inexpresable. Finalmente considero una solucion posible a este probierna.In this paper, I relate two items not commonly related in the literature on Frege: Frege’s argument on the interpretation of identity statements and his problem of referring to functions. First, I expound the argument and conclude that it is sound. Second, I characterize the semantical relations which the argument allows him to introduce. In what follows, I deal with the above mentioned problem and show how it affects Frege’s semantics: those semantical relations become unnameable and, therefore, his semantics turns out to be unexpressible. I consider a possible solution of this problem. (shrink)

In his logical foundation of arithmetic, Frege faced the problem that the semantic interpretation of his system does not determine the reference of the abstract terms completely. The contextual definition of number, for instance, does not decide whether the number 5 is identical to Julius Caesar. In a late writing, Quine claimed that the indeterminacy of reference established by Frege’s Caesar problem is a special case of the indeterminacy established by his proxy-function argument. The present paper aims (...) to show that Frege’s Caesar problem does not really support the conclusions that Quine draws from the proxy-function argument. On the contrary, it reveals that Quine’s argument is a non sequitur: it does not establish that there are alternative interpretations of our terms that are equally correct, but only that these terms are ambiguous. The latter kind of referential indeterminacy implies that almost all sentences of our overall theory of the world are either false or neither true nor false, because they contain definite descriptions whose uniqueness presupposition is not fulfilled. The proxy-function argument must therefore be regarded as a reductio ad absurdum of Quine’s behaviorist premise that the reference of terms is determined only by our linguistic behavior. (shrink)

In print, the central objection to expressivism has been the Frege–Geach problem. Yet most cognitivists seem to be motivated by “deeper” worries, ones they have spent comparatively little time pursuing in print. Part of the explanation for this mismatch between motivation and rhetoric is likely that those deeper worries are largely metaphysical. Since expressivism is not a metaphysical view, it can be hard to see how to mount a relevant attack. The strategy in this chapter is to introduce claims (...) about thought and language, rather than metaphysics, that represent common intuitions about normative objectivity. It then argues that popular forms of expressivism cannot accommodate these claims if they are to solve the negation problem—an aspect of Frege–Geach. If successful, this shows that expressivism really does have a problem accommodating normative objectivity. But, significantly, it does so without requiring any assumptions about what expressivist metaphysics look like. (shrink)

Frege’s writings contain arguments for the thesis (i) that a thought expressed by a sentence S is a structured object whose composition pictures the composition of S, and for the thesis (ii) that a thought is an unstructured object. I will argue that Frege’s reasons for both (i) and (ii) are strong. Frege’s explanation of the difference in sense between logically equivalent sentences rests on assumption (i), while Frege’s claim that the same thought can be decomposed (...) differently makes (ii) plausible. Thoughts are supposed to do work that requires that they be structured and work that requires that they be unstructured. But this cannot be! While the standard response to this problem is to reject either (i) or (ii), I propose a charitable repair in the spirit of Frege’s theory that accepts both. The key idea can be found in Frege’s Basic Laws of Arithmetic(BL, GGA). Frege argues that the thought expressed by a sentence is determined by the truth-conditions that can be derived from the semantic axioms for the sentence constituents. The fact that the same axiomatic truth-condition can be derived in different ways from different semantic axioms suggests a Fregean solution of the dilemma: A thought is a type that is instantiated by all sequences of senses (decomposed thoughts) that have the same axiomatic truth-conditions. This allows for multiple decomposability of the same thought (for different decomposed thoughts can have the same axiomatic truth-conditions) and for a notion of containment (the decomposed thought contains those senses whose semantic axioms are needed in the derivation of the truth-conditions). My proposal combines the virtues of (i) and (ii) without inheriting their vices. (shrink)

The ex ante Pareto principle has an intuitive pull, and it has been a principle of central importance since Harsanyi’s defence of utilitarianism. The principle has been used to criticize and refine a range of positions in welfare economics, including egalitarianism and prioritarianism. But this principle faces a serious problem. I have argued elsewhere :303-323 2017) that the concept of ex ante Pareto superiority is not well defined, because its application in a choice situation concerning a fixed population can (...) depend on how the members of that population are designated. I show in this paper that in almost all cases of policy choice, there will be numerous sets of rival designators for the same fixed population. I explore two ways that we might complete the definition of ex ante Pareto superiority. I call these the ‘supervaluationist’ reading and the ‘subvaluationist’ reading. I reject the subvaluationist reading as uncharitable, and argue that the supervaluationist reading is the most promising interpretation of the ex ante Pareto principle. I end by exploring some of the implications of this principle for prioritarianism and egalitarianism. (shrink)

Expressivists, such as Blackburn, analyse sentences such as 'S thinks that it ought to be the case that p' as S hoorays that p'. A problem is that the former sentence can be negated in three different ways, but the latter in only two. The distinction between refusing to accept a moral judgement and accepting its negation therefore cannot be accounted for. This is shown to undermine Blackburn's solution to the Frege-Geach problem.

What is mathematics about? And if it is about some sort of mathematical reality, how can we have access to it? This is the problem raised by Plato, which still today is the subject of lively philosophical disputes. This book traces the history of the problem, from its origins to its contemporary treatment. It discusses the answers given by Aristotle, Proclus and Kant, through Frege's and Russell's versions of logicism, Hilbert's formalism, Gödel's platonism, up to the the current (...) debate on Benacerraf's dilemma and the indispensability argument. Through the considerations of themes in the philosophy of language, ontology, and the philosophy of science, the book aims at offering an historically-informed introduction to the philosophy of mathematics, approached through the lenses of its most fundamental problem. (shrink)

This paper is about belief ascriptions and problems that arise for a Fregean theory.