A general survey of Frege's views on truth, the paper explores the problems in response to which Frege's distinctive view that sentences refer to truth-values develops. It also discusses his view that truth-values are objects and the so-called regress argument for the indefinability of truth. Finally, we consider, very briefly, the question whether Frege was a deflationist.

In 1880, when Oliver Wendell Holmes (later to be a Justice of the U.S. Supreme Court) criticized the logical theology of law articulated by Christopher Columbus Langdell (the first Dean of Harvard Law School), neither Holmes nor Langdell was aware of the revolution in logic that had begun, the year before, with Frege's Begriffsschrift. But there is an important element of truth in Holmes's insistence that a legal system cannot be adequately understood as a system of axioms and corollaries; and (...) this element of truth is not obviated by the more powerful logical techniques that are now available. (shrink)

Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...) structure, because they differ in the placement of the logical constants “every” and “some”. By contrast, the sentences Every girl loves some boy. and Every boy loves some girl. are thought to have the same logical form, because “girl” and “boy” are not logical constants. Thus, in order to settle questions about logical form, and ultimately about which arguments are logically valid and which sentences logically true, we must distinguish the “logical constants” of a language from its nonlogical expressions. (shrink)

In a series of papers published in the sixties and seventies, Jaakko Hintikka, drawing upon Kant’s conception, defines an argument to be analytic whenever it does not introduce new individuals into the discussion and argues that there exists a class of arguments in polyadic first-order logic that are to be synthetic according to this sense. His work has been utterly overlooked in the literature. In this paper, I claim that the value of Hintikka’s contribution has been obscured by his formalisation (...) of the original definition. Therefore, I provide (i) a brief reconstruction of the historical framework of the problem and the revolutionary import of Hintikka’s contribution, (ii) a clarification of the most complicated steps of Hintikka’s elaboration of his insight, (iii) a criticism of several features that play a fundamental role in Hintikka’s formalisation and (iv) a selection from Hintikka’s own material of some valuable suggestions towards a clear and workable formalisation. As for the pars construens, I isolate in the approach of depth-bounded first-order logics (D'Agostino et al. 2021) an alternative formalisation of the notion of syntheticity as the introduction of new individuals in the reasoning, and I show that it is not affected by the same difficulties as Hintikka’s proposal. In so doing, I hope to have contributed to the realisation of the project of rehabilitating Kant’s analytic–synthetic distinction in the context of modern first-order logic with the purpose of showing, against the logical empiricist movement, that logic is not analytic. (shrink)

This dissertation is about the structure of thought. Following Gottlob Frege, I define a thought as the sort of content relevant to determining whether an assertion is true or false. The historical component of the dissertation involves interpreting Frege’s actual views on the structure of thought. I argue that Frege did not think that a thought has a unique decomposition into its component senses, but rather the same thought can be decomposed into senses in a variety of distinct ways. I (...) extend Frege’s position and use it to develop an account of the hierarchy of senses, the senses expressed by indexicals and demonstratives, and the distinction between logical and non-logical structure. I also discuss various connections with the nature of meta-representation, our capacity for reflective judgment, some aspects of the structure of conscious experience, the way we perceive regions of space and durations of time, and our conscious awareness of our own perceptions and events of thinking. (shrink)

The task of this paper is to give a new, catholic interpretation of Leibniz’s concept of characteristica universalis. In § 2 we shall see that in different periods of his development, Leibniz defined this concept differently. He introduced it as “philosophical characteristic” in 1675, elaborated it further as characteristica universalis in 1679, and worked on it at least until 1690. Secondly, we shall see (in § 3) that in the last 130 years or so, different philosophers have advanced projects similar (...) to that of Leibniz, not always referring to him, at that. These very projects, we claim, threw some light on what Leibniz idea of characteristica universalis could be; or, in more positive sense, on how could it be reconstructed in a more workable way. Unfortunately, they failed to answer the question what exactly Leibniz’s philosophy was. Finally, despite the fact that Leibniz’s concept of characteristica universalis impressed generations of philosophers who tried to make sense of it, the result is that in the more than 300 years after it was introduced, it was never used in the scale its author dreamed of. This fact sets out the next objective which we are going to pursue in this paper: we shall try to find out (in §§ 4 and 5) how this concept can be interpreted in more practical form. (shrink)

Though the divide between reason-based and causal-explanatory approaches in psychiatry and psychopathology is old and deeply rooted, current trends involving multi-factorial explanatory models and evidence-based approaches to interpersonal psychotherapy, show that it has already been implicitly bridged. These trends require a philosophical reconsideration of how reasons can be causes. This paper contributes to that trajectory by arguing that Donald Davidson’s classic paradigm of 1963 is still a valid option.

In 1893 and 1903, two volumes of the most important of Frege’s works Grundegezte der Arithmetik were published. This period can be called the peak of Frege’s logicism. Although the subject of truth in Frege’s logical and philosophical works has been repeatedly investigated, there is a lack of studies on his view in this period, especially in Polish literature. In this article, therefore, I carry out the following research task: to collect and order Frege’s statements about truth during the period (...) of publishing the two volumes of Grundegezte der Arithmetik. I refer to the texts published during Frege’s life, published posthumously and his correspondence. Particularly noteworthy are: Grundegezte der Arithmetik and the unpublished Logik. That is why there are two separate sections dedicated to these two texts, whereas the discussions of truth from other texts are grouped thematically: the problem of antinomy, geometry, expression of generality, and others. The subject of truth appears there in relation to logic, philosophy of language, philosophy of logic, philosophy of mathematics and ontology. (shrink)

The way Frege presented the Square of Opposition in a reduced form in 1879 and 1910 can be used to develop two distinct versions of the square: The traditional square that displays inferences and a “Table of Oppositions” displaying variations of negation. This Table of Oppositions can be further simplified and thus be made more symmetrical. A brief survey of versions of the square from Aristotle to the present shows how both aspects of the square have coexisted for a very (...) long time without ever being properly distinguished. (shrink)

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 translation of both ‘bedeuten’ and ‘Bedeutung’ in Frege's works remains sufficiently problematic that some contemporary authors prefer to leave these words untranslated. Here a case is made for returning to Russell's initial choice of ‘to indicate’ and ‘indication’ as better alternatives than the more usual ‘meaning’, ‘reference’, or ‘denotation’. It is argued that this choice has the philosophical payoff that Frege's controversial doctrines concerning the semantic values of sentences and predicative expressions are rendered far more comprehensible by it, and (...) that this translational strategy fulfills the desiderata of offering a translation which is acceptable both before and after Frege introduced the distinction between sense and reference or, as this paper would have it, between the sense of an expression and what it indicates. (shrink)

This paper challenges a standard interpretation according to which Frege’s conception of logic (early and late) is at odds with the contemporary one, because on the latter’s view logic is formal, while on Frege’s view it is not, given that logic’s subject matter is reality’s most general features. I argue that Frege – in Begriffsschrift – retained the idea that logic is formal; Frege sees logic as providing the ‘logical cement’ that ties up together the contentful concepts of specific sciences, (...) not the most general truths. Finally, I discuss how Frege conceives of the application of Begriffsschrift, and of its status as a ‘lingua characteristica’. (shrink)

open journal of Philosophical Investigations (PI) is an international journal dedicated to the latest advancements in philosophy. The goal of this journal is to provide a platform for academicians all over the world to promote, share, and discuss various new issues and developments in different areas of philosophy. -/- All manuscripts to be prepared in English or Persian and are subject to a rigorous and fair peer-review process. Generally, accepted papers will appear online. The journal publishes papers including the following (...) fields: -/- · Analytic Philosophy · Ancient Greek and Roman Philosophy · Art Aesthetics · Comparative Philosophy West and Chinese · Eastern Philosophy . Islamic philosophy · Epistemology · Ethics · Hermeneutics · History of Religious Thought · History of Western Philosophy · Language Logic . (shrink)

Adrian Moore develops a helpful distinction between good and bad metaphysics. Employing this distinction, I argue, first, that some contemporary metaphysical theories might be ‘bad’, insofar as they employ, unreflectively, concepts akin to Kant’s Ideas of reason. Second, I investigate the difficulty Kant himself has with explaining our craving for bad metaphysics. Third, I raise some problems for Kant’s doctrine of ‘transcendental cognition’, which rests on the difficult assumption that Ideas have objective reality. I conclude that, while Kant has given (...) us means to combat certain bad metaphysics, his own philosophy is not entirely free of it either. (shrink)

In his late fragment, ‘Sources of Knowledge of Mathematics and Natural Sciences’ Frege laments the tendency to confuse functions with objects and says, ‘It is here that the tendency of language by its use of the definite article to stamp as an object what is a function and hence a non-object, proves itself to be the source of inaccurate and misleading expressions and also of errors of thought. Probably most of the impurities that contaminate the logical source of knowledge have (...) their origins in this.’ This paper applies Frege’s logical insights to a series of influential modal arguments for the existence of souls or minds, in order to demonstrate that they hinge on the error of treating functions as objects. Related arguments have also resulted in the claim that identity statements are necessary, and that apparent identities ‘really’ involve relations of constitution. Here it is argued that once we recognise that all these arguments involve the assimilation of objects and concepts (which Frege identifies with functions) they can be seen to be defective. (shrink)

Well over a century after its introduction, Frege's two-dimensional Begriffsschrift notation is still considered mainly a curiosity that stands out more for its clumsiness than anything else. This paper focuses mainly on the propositional fragment of the Begriffsschrift, because it embodies the characteristic features that distinguish it from other expressively equivalent notations. In the first part, I argue for the perspicuity and readability of the Begriffsschrift by discussing several idiosyncrasies of the notation, which allow an easy conversion of logically equivalent (...) formulas, and presenting the notation's close connection to syntax trees. In the second part, Frege's considerations regarding the design principles underlying the Begriffsschrift are presented. Frege was quite explicit about these in his replies to early criticisms and unfavorable comparisons with Boole's notation for propositional logic. This discussion reveals that the Begriffsschrift is in fact a well thought-out and carefully crafted notation that intentionally exploits the possibilities afforded by the two-dimensional medium of writing like none other. (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 paper offers a survey of four key moments in which symbolisms for quantification were first introduced: §§11–2 of Frege’s Begriffsschrift ; Peirce’s ‘Algebra of Logic’ ; Peano’s ‘St...

Despite the often false impression that the analytic philosophy as an anti-metaphysical movement has nothing to do with metaphysics, there can be found good reasons to grant the metaphysical dispositions of analytic philosophers, and thereby, to minimize the anti-metaphysical nature of analytic philosophy in its all phases. Since analytic philosophy is a historical movement the main nature of which developed through several stages, the very kinds of metaphysical dispositions within each one of its various stages can be easily portrayed. In (...) the meantime, logical realism as the early stage of analytic philosophy contains plenty of metaphysical dispositions. Undoubtedly, one cannot say that analytic philosophy in this period was not committed to metaphysical theses about the plurality of entities, the ultimate nature of reality and the logical structure of the world. In this paper, then, after giving a relatively complete explanation of the logical realism, we claimed that although logical realists rejected the traditional speculative metaphysics of their predecessors, they also replaced it by the metaphysics of logic that pursues the metaphysical aims, this time, by logical means. So, we portrayed this kind of metaphysics as Bolzano’s Semantic Platonism, Frege’s and Russell’s Pluralistic Platonism, Russell’s Pluralistic Atomism, and Wittgenstein’s logical atomism. (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.

Contributing to the debate between referentialist and predicativist accounts of the semantics of proper names, this paper partly endorses a recent trend to reject unitary accounts of their semantics. It does so by restoring a Fregean version of the variety of use account. It criticizes alternative variety of use accounts for not clearly distinguishing pragmatic, syntactic, and semantic issues and argues that, once these are distinguished, the necessity of accepting that names have a variety of uses, and are sometimes logical (...) singular terms and at others logical predicates shows that Frege’s claim, that we should recognize that names have both reference and sense, is vindicated. (shrink)

By way of a close reading of Boole and Frege’s solutions to the same logical problem, we highlight an underappreciated aspect of Boole’s work—and of its difference with Frege’s better-known approach—which we believe sheds light on the concepts of ‘calculus’ and ‘mechanization’ and on their history. Boole has a clear notion of a logical problem; for him, the whole point of a logical calculus is to enable systematic and goal-directed solution methods for such problems. Frege’s Begriffsschrift, on the other hand, (...) is a visual tool to scrutinize concepts and inferences, and is a calculus only in the thin sense that every possible transition between sentences is fully and unambiguously specified in advance. While Frege’s outlook has dominated much of philosophical thinking about logical symbolism, we believe there is value—particularly in light of recent interest in the role of notations in mathematics and logic—in reviving Boole’s idea of an intrinsic link between, as he put it, a ‘calculus’ and a ‘directive method’ to solve problems. (shrink)

The unique relation between logic and truth is crucial for understanding Fregean conception of logic. Frege has an insight that the nature of logic resides in the “truth“, which he finally locates in the assertoric-force of a sentence. Though Frege admits that assertoric-force is ineffable in ordinary language, he coins in his conceptual notation for such a force a much-disputed sign, i.e., judgment-stroke. In this paper, I will try to demonstrate that judgment-stroke is not adequate for the task its inventor (...) has assigned to it. Accordingly, it is misconceived and inconducive to clarify Frege’s vague insight into the protorelation. The mistake of judgment-stroke for the sign of assertoric-force has its root in Frege’s ignorance of the significant difference between “judgment” and assertion”, which will be elucidated at length in the light of Husserl’s theory of “doxic-modification“. In the end, based on a further elucidation of the activity of assertion, I will advance a tentative interpretation of the vague insight Frege has concerning the protorelation. (shrink)

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)

In this paper, based on a critical analysis of ideas of Frege, Quine and Prior, we show how Lambda Calculus and Hilbert’s Epsilon Calculus are useful to give us a good understanding of Platonic objects.

This two-part paper reviews a scholarly debate on an alleged tension in Frege ’s philosophy of logic. In Section 1 of Part I, I discuss Frege ’s view that logic is concerned with establishing norms for correct thinking and is therefore a normative science. In Section 2, I explore a different understanding of the role of logic that Frege seems to advance: logic is constitutive of the very possibility of thought, because it sets forth necessary conditions for thought. Hence, the (...) tension the view according to which logic is normative for thought seems to be incompatible with the idea that abiding by the laws of logic forms a precondition for thought. In Section 1 of Part II, I survey a number of interpretations of Frege ’s conception of logic that deal with this question. I show that they are for the most part either normative readings or constitutive readings. Finally, in Section 2, I adjudicate the debate and aim at reconciling the normative and the constitutive strands in Frege ’s conception of logic. (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)

Frege's philosophical writings, including the “logistic project,” acquire a new insight by being confronted with Kant's criticism and Wittgenstein's logical and grammatical investigations. Between these two points a non-formalist history of logic is just taking shape, a history emphasizing the Greek and Kantian inheritance and its aftermath. It allows us to understand the radical change in rationality introduced by Gottlob Frege's syntax. This syntax put an end to Greek categorization and opened the way to the multiplicity of expressions producing their (...) own intelligibility. This article is based on more technical analyses of Frege which Claude Imbert has previously offered in other writings. (shrink)