Frege's essay "Der Gedanke.Eine logische Untersuchung" was first published in the Beitrage zur Philosophie des Deutschen Idealismus for 1918-1919 and is one of three related logical studies published as a complete work by Gunther Patzig entitled Logische Untersuchungen in Gottingen, 1966 .

Gottlob Frege (1848-1925) was a German logician, mathematician and philosopher who played a crucial role in the emergence of modern logic and analytic philosophy. Frege's logical works were revolutionary, and are often taken to represent the fundamental break between contemporary approaches and the older, Aristotelian tradition. He invented modern quantificational logic, and created the first fully axiomatic system for logic, which was complete in its treatment of propositional and first-order logic, and also represented the first treatment of higher-order logic. (...) In the philosophy of mathematics, he was one of the most ardent proponents of logicism, the thesis that mathematical truths are logical truths, and presented influential criticisms of rival views such as psychologism and formalism. His theory of meaning, especially his distinction between the sense and reference of linguistic expressions, was groundbreaking in semantics and the philosophy of language. He had a profound and direct influence on such thinkers as Russell, Carnap and Wittgenstein. Frege is often called the founder of modern logic, and he is sometimes even heralded as the founder of analytic philosophy. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Die Philosophische Logik Gottlob Freges. Ein Kommentar, mit den Texten des Vorworts zu Grundgesetze der Arithmetik und der Logischen Untersuchungen I–IVLeila HaaparantaWolfgang Künne. Die Philosophische Logik Gottlob Freges. Ein Kommentar, mit den Texten des Vorworts zu Grundgesetze der Arithmetik und der Logischen Untersuchungen I–IV. RoteReihe 30. Frankfurt: V. Klostermann, 2010. Pp. 840. Paper, €29.80.Frege’s thought has been a permanent point of interest among philosophers for several (...) decades. In the late sixties a few philosophers, such as Christian Thiel and Ignacio Angelelli, published studies on Frege’s logic, semantics, and metaphysics. In 1973 Michael Dummett’s work on Frege’s philosophy of language appeared, which held the stage for a long time. It presented Frege as a predecessor, even as a representative, of the analytic tradition. New approaches came up in the late 1970s and early 1980s, such as Hans Sluga’s work in 1980 and other studies, which paid special attention to Frege’s German background, where Kant played a significant role. Several scholars, including Michael Dummett, started to dig into Frege’s background. Positions varied; some studied Frege’s background in order to show that there is nothing that could help us understand his philosophical insights; others found the origins of his philosophical and logical ideas precisely in his background and philosophical environment, in such philosophers as Leibniz, Kant, Trendelenburg, and Lotze.After a few somewhat more quiet years, Frege scholarship expanded after 2000. A number of books have appeared that discuss Frege in the analytic context and also seek [End Page 507] to find more details about his philosophical sources. Wolfgang Künne’s work is a most welcome contribution to contemporary scholarship in the field. Lothar Kreiser’s Gottlob Frege: Leben—Werk—Zeit (2001) has already been available, and interpretations of Frege’s philosophy as well as editions and translations of his books contain short biographies. Still, because of its special composition, Künne’s work serves to fill a gap in the scholarship and significantly contributes to what is known about Frege’s logic and philosophy.The volume consists of three parts. First, there is an extensive biography (about 50 pages) of Frege that places Frege’s thought in its historical context and also contextualizes those of his articles that are included in the work. The main projects Frege pursued, most notably the project of logicism, receive proper attention in the first part of the volume. The four texts that are included in the volume are the Preface of the Grundgesetze der Arithmetik I (1893) and the three logical investigations that were published during Frege’s lifetime, namely “Der Gedanke” (1918), “Die Verneinung” (1919), and “Gedankengefüge” (1923), which were originally published in Beiträge zur Philosophie des deutschen Idealismus. Künne has also included a posthumously published text, “Logische Allgemeinheit,” in the volume, as that fragment, which was not written before 1923, was intended to be a fourth logical investigation. The five texts written by Frege that are included in the edition discuss topics that we would now call philosophical logic, such as meaning, reference, and truth, although they also study themes that we would include in ontology and the philosophy of mind. The title of the volume is thus sufficiently motivated.Frege’s texts take up about 100 pages of the volume, while the commentary is about 600 pages. The book also contains an appendix on Bolzano and Frege, where Künne pays attention to similarities between the two logicians and philosophers but also shows his skepticism about the thesis that Frege had read Bolzano. Apart from this position, Künne prefers to read Frege’s texts closely and inform his reader of historical and philological matters rather than take part in any heated debates concerning interpretations; his own positions become visible only indirectly, through the extensive footnotes. The work also contains a very useful bibliography and indexes of names and subjects.The book is extremely rich. If one, for example, wishes to know more about the views of Frege’s German contemporaries, about the standpoints that Russell or Wittgenstein had on Fregean topics, or about the arguments of Frege scholars, one can find... (shrink)

Gottlob Frege may be considered as the first intellectual giant in thePhilosophy of Language. He was the first to raise the issue ofmeaning by formulating an organized theory of meaning for a part ofnatural language as the theory of meaning is at the core of philosophy of language. He emphasizes that the meaning of a sentence directly depends on the meaning of its constituent parts. That is why he has to dissect the internal structure of (...) a sentence or complex expressions provided by a logical syntax, while the truth value of such sentences may be revealed by logical semantics which can be put forward by treating these sentences as a whole. (shrink)

Dieser Band enthält die vier Arbeiten Freges: Begriffsschrift, eine der arithmetischen nachgebildeten Formelsprache, 1879; Anwendungen der Begriffsschrift, 1879; Über den Briefwechsel Leibnizens und Huggens mit Papin, 1881; Über den Zweck der Begriffsschrift, 1883; Über die wissenschaftliche Berechtigung einer Begriffsschrift, 1882. Frege's research work in the field of mathematical logic is of great importance for the present-day analytic philosophy. We actually owe to Frege a great amount of basical insight and exemplary research, which set up a new standard also in other (...) fields of knowledge. As the founder of mathematical logic he severely examindes the syllogisms on which arithmetic is built up. In doing so, Frege recognized that our colloquial language is inadequate to define logic structures. His notional language corresponded to the artaivicial logical language demandes by Leibniz. Frege's achievement in the field of logic were so important, that they radiated into the domain of philosophy and influenced the development of mathematical logic decisively. (shrink)

At the turn of the century, Gottlob Frege and Edmund Husserl both participated in the discussion concerning the foundations of logic and mathematics. Since the 1960s, comparisons have been made between Frege's semantic views and Husserl's theory of intentional acts. In quite recent years, new approaches to the two philosophers' views have appeared. This collection of articles opens with the first English translation of Dagfinn Føllesdal's early classic on Husserl and Frege of 1958. The book brings together a number (...) of new contributions by well-known authors and gives a survey of recent developments in the field. It shows that Husserl's thought is coming to occupy a central role in the philosophy of logic and mathematics, as well as in the philosophy of mind and cognitive science. The work is primarily meant for philosophers, especially for those working on the problems of language, logic, mathematics, and mind. It can also be used as a textbook in advanced courses in philosophy. (shrink)

Gottlob Frege , Mathematiker und Philosoph, ist der Begründer der modernen formalen Logik. Autoren wie Bertrand Russell, Rudolf Carnap und Ludwig Wittgenstein sind von ihm ausgegangen. Die hier vorgelegten Schriften aus dem Nachlaß wurden unter dem Gesichtspunkt ausgewählt, daß das Interesse an Frege vor allem seinen Arbeiten zur logisch-semantischen Sprachanalyse gilt. Da diese Arbeiten in engem Verbund mit Themen der Erkenntnis- und Wissenschaftstheorie entstanden sind, rücken auch diese Bereiche der analytischen Philosophie in den Blick.

This introduction to modern work in analytic philosophy uses the example of the proper name to give a clear explanation of the logical theories of Gottlob Frege, and explain the application of his ideas to ordinary language. McCulloch then shows how meaning is rooted in the philosophy of mind and the question of intentionality, and looks at the ways in which thought can be "about" individual material objects.

This book explores the nature of meaning, primarily through readings of the work of Walter Benjamin and Ludwig Wittgenstein. Alexander Stern offers a critical analysis of Benjamin's philosophy of language, finding in it a common root with Wittgenstein's thought on language, and traces the historical foundation of both accounts of meaning to eighteenth- and nineteenth-century German philosophy. Benjamin's theory of language is notoriously dense and obscure. In elucidating it, Stern emphasizes Benjamin's attempt to reorient the Kantian project around (...) language-the medium in which knowledge is expressed-and his concern with the logical understanding of language gaining credence in the work of Bertrand Russell and Gottlob Frege. The result is a radical model of the relationship between language, experience, and the world that sees "absolutely everything" as linguistic in a broadened sense and which sees the logical or designative capacities of language as grounded in an aesthetic foundation. Wittgenstein and Benjamin are read in the book as complementary to one another, sharing comparable critiques of empiricism and comparable accounts of concept use, linguistic understanding, and the relation between experience and language. Although this similarity breaks down over Wittgenstein's account of the "experience of meaning," which is subordinated to his account of meaning as use, Stern argues that Benjamin's theory of language can productively address some unresolved issues in Wittgenstein's understanding of meaning. (shrink)

Dieser Band enthält die vier Arbeiten Freges: Begriffsschrift, eine der arithmetischen nachgebildeten Formelsprache, 1879; Anwendungen der Begriffsschrift, 1879; Über den Briefwechsel Leibnizens und Huggens mit Papin, 1881; Über den Zweck der Begriffsschrift, 1883; Über die wissenschaftliche Berechtigung einer Begriffsschrift, 1882. Frege's research work in the field of mathematical logic is of great importance for the present-day analytic philosophy. We actually owe to Frege a great amount of basical insight and exemplary research, which set up a new standard also in other (...) fields of knowledge. As the founder of mathematical logic he severely examindes the syllogisms on which arithmetic is built up. In doing so, Frege recognized that our colloquial language is inadequate to define logic structures. His notional language corresponded to the artaivicial logical language demandes by Leibniz. Frege's achievement in the field of logic were so important, that they radiated into the domain of philosophy and influenced the development of mathematical logic decisively. (shrink)

Logicism and the Philosophy of Language brings together the core works by Gottlob Frege and Bertrand Russell on logic and language. In their separate efforts to clarify mathematics through the use of logic in the late nineteenth and early twentieth century, Frege and Russell both recognized the need for rigorous and systematic semantic analysis of language. It was their turn to this style of analysis that would establish the philosophy of language as an autonomous area of inquiry. This anthology (...) gathers together these foundational writings, and frames them with an extensive historical introduction. This is a collection for anyone interested in questions about truth, meaning, reference, and logic, and in the application of formal analysis to these concepts. (shrink)

Not only can the influence of Gottlob Frege be found in contemporary work in logic, the philosophy of mathematics, and the philosophy of language, but his projects—and the very terminology he employed in pursuing those projects—are still current in contemporary philosophy. This is undoubtedly why it seems so reasonable to assume that we can read Frege' s writings as if he were one of us, speaking to our philosophical concerns in our language. In Joan Weiner's view, however, Frege's words (...) can be accurately interpreted only if we set that assumption aside. Weiner here offers a challenging new approach to the philosophy of this central figure in analytic philosophy. Weiner finds in Frege's corpus, from Begriffsschrift on, a unified project of remarkable ambition to which each of the writings in that corpus makes a distinct contribution—a project whose motivation she brings to life through a careful reading of his Foundations of Arithmetic. The Frege that Weiner brings into clear view is very different from the familiar figure. Far from having originated one of the standard positions on the nature of reference, Frege turns out not to have had positive doctrines on anything like what contemporary philosophers mean by "reference." Far from having served as a standard-bearer for those who take the realists' side of contemporary disputes with anti-realists, Frege turns out to have had no stake in either side of the controversy. Through Weiner's lens, Frege emerges as a thinker who has principled reasons for challenging the very assumptions and motivations that animate philosophers to dispute these doctrines. This lucidly written and accessible book will generate controversy among all readers with an interest in epistemology, philosophy of language, history of philosophy, and the philosophy of mathematics. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy, Psychiatry, & Psychology 9.2 (2002) 131-136 [Access article in PDF] Language, Logic, and Recovery:A Commentary on van Staden Paul Falzer and Larry Davidson Keywords: analytic philosophy, experience, Frege, ordinary language, psychosis, psychotherapy. VAN STADEN'S PAPER, "Linguistic Markers of Recovery," takes on a formidable task. As he explains it, findings from a previously conducted empirical study suggest that recovery from a psychiatric condition can be predicted by certain patterns (...) of first person pronoun usage. His current paper explains how these patterns follow the mathematical logic of Gottlob Frege. van Staden's attempt to systematize the link between language and treatment outcome shows promise. We want to support his effort by raising a few caveats about the application of foundational systems in psychiatry and psychology, particularly the advisability of employing a logical system to explain recovery from mental illness. Along the way, we will be identifying related issues that the author may elect to take up in his future work.van Staden's proposal is inspired by Frege's logical system, but the paper is, at the very least, an innovative adaptation. There are various points where we are left to wonder just how much of this proposal is really Frege's. Nevertheless, the genesis of van Staden's ideas is so dependent that one would expect a fuller account of Frege's pivotal role in the development of modern logic, how his work precipitated what is known commonly as the linguistic turn, and why a logical system that was so well received when first articulated was eclipsed so quickly by Russell's Principia (1963) and Wittgenstein's Tractatus. (1981) These issues can be addressed separately and perhaps they should, because lacking an account of how Frege's philosophy developed and evolved makes the presentation appear somewhat sketchy and incomplete.Frege is portrayed in philosophical lore as the founder of modern logic and a pioneer of the movement that later became known as analytic philosophy. Dummett (1991) regards Frege's Foundations of Arithmetic (1968) as analytical philosophy's first work (p. 111). According to Quine (1955), "All modern logic owes an incalculable debt to Frege. If anyone can be singled out as the founder of mathematical logic, it is by all odds he" (p. 158). Rorty (1967) notes that analytic philosophy's tack of construing philosophical questions as turning on language use and construction challenges the entire tradition, from Parmenides forward. However, the challenge reaches fruition not in Frege, but in works of Moore, Wittgenstein, and Austin. Rather than [End Page 131] sharing the limelight with the great analytic philosophers, Frege has become somewhat of a peripheral figure, whose contribution is usually portrayed as transitional. In some respects, analytic philosophy was moving against Frege's, and later, Russell's logical systems as it was concomitantly countering the various strands of idealism expounded principally by Bradley and McTaggart (see Hacker 1996, 5-12). Almost from the outset, Fregean logic was caught in a cross fire, and the author is obligated to tell us why we should be attending to the pristine version and not the more fully developed approaches that came soon after.Such a justification undoubtedly would begin with the dictum most central to Frege's philosophical thought, that propositions are primary. For Kemp (1998), this declaration carries two interrelated implications: Logical propositions are the real bearers of truth and falsity, and reasoning is a movement from one judgment to another (see p. 218). Frege posits that propositions are independent of mind, grammar, and language use. Knowledge and cognition are embodied in, but do not predicate, judgment. Frege adamantly rejects the notion that philosophical concepts are grounded in psychological phenomena, such as perception, sense impression, and some traditional accounts of meaning. This is the doctrine known as psychologism, and Frege abjures the suggestion that psychology can contain the sciences or adjudicate their findings (Frege 1956; for a discussion of this doctrine, see Notturno 1989; Davidson 1988; Davidson and Cosgrove 1991). The dictum that propositions are primary dispels the commonly held idea that reasoning begins with perception and proceeds... (shrink)

Introduction. PHilosophy of Language and Linguistics: The Formal Turn Piotr Stalmaszczyk Gottlob Frege, Philosophy of Language, and Predication Piotr Stalmaszczyk Philosophy, Linguistics and Semantic Interpretation Christian Bassac An Unresolved Issue: Nonsense in Natural Language and Non-Classical Logical and Semantic Systems Elzbieta Chrzanowska-Kluczewska Varieties of Context-Dependence Tadeusz Ciecierski The Logos of Semantic Structure Marie Du í, Bjørn Jespersen and Pavel Materna The Good Samaritan and the Hygienic Cook: A Cautionary Tale About Linguistic Data Chris Fox The Meaning of Multiple (...) Quantified Sentences: Where Formal Semantics Meets Psycholinguistics Justyna Grudzinska The Hybrid Theory of Reference for Proper Names Filip Kawczynski On the Nature of Statistical Language Laws Agnieszka Kulacka Vagueness and Contextualism Joanna Odrowaz-Sypniewska The Myth of Semantic Structure Jaroslav Peregrin Scalar Implicatures, Communication and Language Evolution Salvatore Pistoia Reda Semantics and Contextuality: The Case of Pia s Leaves Stefano Predelli Is Logico-Semantical Analysis of Natural Language Expressions a Translation? Jirí Raclavský Beyond the Fregean Myth: The Value of Logical Values Fabien Schang Modal Calculus of Illocutionary Logic Andrew Schumann Subjectivity in Philosophy and Linguistics Barbara Sonnenhauser Asymmetrical Semantics Mieszko Talasiewicz Truth: An Anti-realist Adequacy Condition Luca Tranchini Belief Reports: Defaults, Intentions and Scorekeeping Giacomo Turbanti On Truth in Time Bartosz Wieckowski Order William J. SUllivan Indexes. (shrink)

In this short monograph, John Horty explores the difficulties presented for Gottlob Frege's semantic theory, as well as its modern descendents, by the treatment of defined expressions. The book begins by focusing on the psychological constraints governing Frege's notion of sense, or meaning, and argues that, given these constraints, even the treatment of simple stipulative definitions led Frege to important difficulties. Horty is able to suggest ways out of these difficulties that are both philosophically and logically plausible and (...) Fregean in spirit. This discussion is then connected to a number of more familiar topics, such as indexicality and the discussion of concepts in recent theories of mind and language. In the latter part of the book, after introducing a simple semantic model of senses as procedures, Horty considers the problems that definitions present for Frege's idea that the sense of an expression should mirror its grammatical structure. The requirement can be satisfied, he argues, only if defined expressions--and incomplete expressions as well--are assigned senses of their own, rather than treated contextually. He then explores one way in which these senses might be reified within the procedural model, drawing on ideas from work in the semantics of computer programming languages. With its combination of technical semantics and history of philosophy, Horty's book tackles some of the hardest questions in the philosophy of language. It should interest philosophers, logicians, and linguists. (shrink)

The dissertation seeks to gain a comprehensive understanding of Frege's watershed work of logic, the 1879 Begriffsschrift . The treatise is the first since Aristotle's instauration of the discipline to have succeeded in completely recasting logic. Very generally stated, the dissertation aims at making explicit the conceptual origins of modern logic. To do that will require that each of the achievements of Concept-script be examined from one or more vantage points: either within the perspective of Frege's larger and guiding ambition, (...) that of providing a logical justification of arithmetic; or with respect to the horizon of modernity; or in relation to later developments in logical theory and the philosophy of language, developments stimulated, albeit not exclusively, by Frege's very work. The vantage point adopted in each case will depend on the nature of the topic and the extent to which it requires to be made explicit. One perspective will have preponderance, that of Frege's relationship to his early modern ancestors, a group that includes philosophers, scientists, and mathematicians. Since modernity is constituted in a nearly constant critical, if not polemical, relationship to the Ancients, they will also at times be drawn into the discussion. The elucidation of Frege's breakthrough work will be guided by the following thesis: Frege's attempt to justify arithmetic logically and the fine work of clarification he produced in actualizing this project; his discovery of function-theoretic logic and his fashioning of a concept-script ; and his critique of natural language and the attendant semantics developed over the course of that critique constitute an unfolding and an extension of the primacy of universal method over ontology that is the signature of modern inquiry. (shrink)

In this tutorial, the meaning of natural language is analysed along the lines proposed by Gottlob Frege and Richard Montague. In building meaning representations, we assume that the meaning of a complex expression derives from the meanings of its components. Typed logic is a convenient tool to make this process of composition explicit. Typed logic allows for the building of semantic representations for formal languages and fragments of natural language in a compositional way. The tutorial ends (...) with the discussion of an example fragment, implemented in the functional programming language Haskell Haskell Team; Jones.. (shrink)

Frege and Eucken were colleagues in the faculty of philosophy at Jena University for more than 40 years. At times they had close scientific contacts. Eucken promoted Frege's career at the university. A comparison of Eucken's writings between 1878 and 1880 with Frege's writings shows Eucken to have had an important philosophical influence on Frege's philosophical development between 1879 and 1885. In particular the classification of the Begriffsschrift in the tradition of Leibniz is influenced by Eucken. Eucken also influenced Frege's (...) choice of philosophical and logical terms. Finally, there are analogous positions concerning relations between concepts and their expressions in natural language, Frege was probably also influenced by Eucken's use of the term ?tone?. Eucken used Frege's arguments in his own fight against psychologism and empiricism. (shrink)

Analytic philosophy is based on the assumption that our world is a world grasped in terms of (this or another) language and that the question of the character of any entity is closely connected with the question of the linguistic grasp of that entity. The father of this philosophical trend was Gottlob Frege: he showed the way to capture the semantic aspect of language in a systematic way without resorting into psychologism; he also showed that logical analysis can be (...) an extremely powerful tool for capturing meaning. Frege's teaching was further developed by Bertrand Russell, Rudolf Carnap, Ludwig Wittgenstein, Willard Van Quine and other philosophers. This philosophy, in connection with which the term linguistic turn is also often mentioned, is characterized by viewing language as a means of picturing the world and truth as the correspondence between statement and reality. Whereas some of the analytic philosophers (Carnap, Alfred Tarski) understood the relation between language and the world as a matter of a better or worse adaptation of the structure of language to the autonomous structure of the world, others (Wittgenstein, Quine, Nelson Goodman) realized that the structure of the world is always a matter of the language we use approaching the world. (shrink)

The volume honours Eva Picardi – her philosophical views and interests, as well as her teaching – collecting eighteen essays, some by former students of hers, some by colleagues with whom she discussed and interacted. The themes of the volume encompass topics ranging from foundational and historical issues in the philosophy of language and the philosophy of logic and mathematics, as well as issues related to the recent debates on rationality, naturalism and the contextual aspects of meaning. The volume (...) is split into three sections: one on Gottlob Frege’s work – in philosophy of language and logic –, taking into account also its historical dimension; one on Donald’s Davidson’s work; and one on the contextualism-literalism dispute about meaning and on naturalist research programmes such as Chomsky’s. (shrink)

Keith A. Coleman Department of Philosophy, February 2008 University of Kansas A traditional problem concerning the meaning or logical content of statements of identity received its modern formulation in Gottlob Frege's "On Sense and Reference." Identity is taken either as a relation between objects or a relation between terms. If identity is interpreted as a relation between objects, then identity statements seem to be of little value since everything is clearly identical to itself. Assertions of identity are thought (...) to convey significant information, but it is hard to see how they can on this interpretation. If identity is instead interpreted as a relation between terms, then identity statements still seem to be of little value since apparently they only convey a linguistic pronouncement to use certain terms interchangeably. Assertions of identity do not appear to be about the use of language, but, on this understanding of identity, they evidently are. I examine the nature of the problem and the advantages and disadvantages of each one of the two approaches to interpreting the content of identity statements. I then investigate two approaches for solving the problem from the perspective of identity as a relation between objects. The first of these represents the account provided by Gottlob Frege, and the second represents the account provided by Saul Kripke. I conclude that neither one of these accounts finally solves the problem of identity in its entirety. I then examine Michael Lockwood's approach to resolving the problem of identity based on the idea of identity as a relation between terms. I discuss and critically evaluate Lockwood's account together with a modified version of that account. After arguing for the inadequacy of the views examined as ultimate solutions to the problem of identity, I end by suggesting a strategy prompted by treating identity as indiscernibility. (shrink)

This new book offers a comprehensive and accessible introduction to Frege's remarkable philosophical work, examining the main areas of his writings and demonstrating the connections between them. Frege's main contribution to philosophy spans philosophical logic, the theory of meaning, mathematical logic and the philosophy of mathematics. The book clearly explains and assesses Frege's work in these areas, systematically examining his major concepts, and revealing the links between them. The emphasis is on Frege's highly influential work in philosophical logic and (...) the theory of meaning, including the features of his logic, his conceptions of object, concept and function, and his seminal distinction between sense and reference. Frege will be invaluable for students of the philosophy of language, philosophical logic, and analytic philosophy. (shrink)

This entry introduces the reader to the main ideas in Frege's philosophy of logic, mathematics, and language.

Western (deductive) logic originated in Greek antiquity. It found its first expression in those works of the great philosopher Aristotle (384–322 BC) which have come to be known as the Organon, i.e., ‘instrument’. Aristotle’s logic, also known as syllogistics, was unsystematically concerned with patterns of reasoning and argumentation. It remained in this rudimentary state relatively unchanged and unchallenged until the second half of the nineteenth century. At that time, logic underwent a period of unprecedented reform and modernization, due in large (...) part to the German mathematician Gottlob Frege (1848– 1925) It thus became more and more a mathematical endeavor of studying the structure and peculiarities of artificial, formal languages. In this new form, logic gave rise in the twentieth century to disciplines such as theoretical informatics and programming languages, and transformed our lives through computation, information processing, and the Internet. A formal language consists, in effect, of a particular alphabet and some precise rules of forming, and transforming, strings over this alphabet. There exist several types of formal languages analyzed in logic. Depending on their structure, they are called first-order languages, second-order languages, and so on. Today a logic is considered a theory of such a language and is, correspondingly, referred to as a first-order logic, a second-order logic, and so on. In this chapter, we shall outline a first-order logic as a paragon of deductive logic. Its full name is: “Classical, first-order predicate logic with identity”. What all these expressions mean exactly, will become clear below. The logic we shall study first is termed classical logic because the idea to create such an instrument, or ‘organon’, is rooted in Greek antiquity. Owing to its origin, it is based on three time-honored Aristotelian doctrines. For these and several other reasons that we shall discuss later in this chapter, it is also called a logic of the Aristotelian style, or an Aristotelian logic for short. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:356 BOOK REVIEWS The Logical Basis of Metaphysics. By MICHAEL DUMMETT; The William James Lectures, 1976. Cambridge, Mass.: Harvard University Press, 1991. Pp. xi + 355. $34.95 (cloth). Michael Dummett, who is Wykeham Professor of Logic at Oxford, represents an influential force in contemporary analytical philosophy. In the tradition of Gottlob Frege and Ludwig Wittgenstein, Dum· mett has contributed significant works in philosophy of language (theory of (...) class='Hi'>meaning) and intuitionistic logic as well as in current metaphysics, liberated from the neopositivistic imprisonment. Dummett's newest book has a self-explanatory title and is based on the William James Lectures which he delivered at Harvard University in 1976. As he explains in his Preface (1989), the publication of these lectures, however delayed and edited, should show the importance of the theory of meaning " for its more glamorous relative, metaphysics." Dummett is known as the leading proponent of "anti-realism "-a position endorsed, for instance, by Hilary Putnam-and the book under review amply demonstrates his views on this current controversial issue. Various " anti-realists," Dummett contends, share their rejection of the prin· ciple of bivalence (according to which every proposition is determinately either true or false) and of the related law of the excluded middle. Such rejections require the acceptance of " stricter canons of valid deductive reasoning" (p. 11), which, in turn, demand tightened and clarified concepts of meaning and truth or, in Wittgenstein's phrase, "a clear view of the working of our language." (p. 13). What one needs, in short, is a good theory of meaning which will " determine the correct logic " of a language and also settle various metaphysical controversies with regard to the nature of physical reality, time, mind, mathematics, etc. Dummett understands such theory of meaning as the key part of the philosophy of thought that has been so much stimulated by Frege's theory of sense and reference. Dummett's methodology de· mands therefore the following order: a good theory of meaning leading to " correct " logic, which in turn helps to settle metaphysical controversies. He aspires to show " how the choice between different logics arises at the level of the theory of meaning" (p. 18) and makes no apologies for using in this process a highly technical conceptual apparatus of mathematical logic. By his own admission, Dummett does not want to raise classical metaphysical questions of God, free will, and immortality, but "others almost equally profound" yet requiring a "painfully slow pace of advance" (p. 19). In spite of such declarations Dummett touches upon the problem of BOOK REVIEWS 357 God's omniscience: if, determinately, one of two possibilities holds, then God must know which of the two possibilities it is. Yet this example is utilized by Dummett not because of its theological impact (which he seems to take for granted) hut for the service it can provide in clarifying the problem of hivalence. At the very end of the last chapter, entitled ".Realism and the Theory of Meaning," Dummett concludes that the premise which expresses God's omniscience does not entail that God knows whether any given proposition is true or false nor does such a premise entail that the proposition is either true or false. Allegedly, an additional premise is needed asserting the truth or the falsehood of the proposition in question (whichever the case) " in order to deduce from his omniscience that he knows, in the sense stated, whether it is true or false" (p. 351). This anti-realistic position is thus based on the rejection of classical, two-valued logic and on the endorsement of intuitionistic logic, developed by the Dutch mathematician Brouwer and his followers, including Dummett himself (see his Elements of Intuitwnism, published in 1977 by Oxford Clarendon Press). According to this logic, if a statement is true only if we are able to prove it (to provide or construct evidence for it, etc.), then " there is no ground to assume every statement to he either true or false" (p. 9). Dummett claims that intuitionistic logic is supported by a verificationist meaningtheory which gets a large share of his attention. In the verificationist theory of meaning, " the meaning of a statement is determined by what we acknowledge as grounds... (shrink)

The book is a collection of papers and aims to unify the questions of syntax and semantics of language, which are included in logic, philosophy and ontology of language. The leading motif of the presented selection of works is the differentiation between linguistic tokens (material, concrete objects) and linguistic types (ideal, abstract objects) following two philosophical trends: nominalism (concretism) and Platonizing version of realism. The opening article under the title “The Dual Ontological Nature of Language Signs and the Problem of (...) Their Mutual Relations” provides a broad introduction into the problem area connected with this differentiation, while the logic-formal characteristics of the distinction are framed in the work entitled “On the Type-Token Relationships” (Chapter 1). The basic part of the book deals with issues relating to syntax (Chapters 2-4) and semantics of language (Chapters 5-6), as well as pertaining to syntactic-semantic pragmatic questions (Chapters 7-13). Throughout the book, language, categorial language, is characterized syntactically as generated by classical categorial grammar (Chapter 2) and formalized on two opposing levels: as language of expression-tokens (level of tokens) and language of expression-types (level of types). The author’s considerations contained in Chapters 2 and 4 lead to the important philosophical conclusion that in formal-logical syntactic studies on language the assumption that expression-types constitute the primary language layer while expression-tokens make the secondary one, can be neglected; thus, this speaks in favour of the opposing standpoint—the concretistic one—in the ontology of language syntax. In the works “Meaning and Interpretations”, Parts I and II (Chapters 5 and 6), it is underlined, however, that such semantic concepts as: meaning, denotation and interpretation are defined on the types level, yet their formal definitions require making use of notions of the tokens level. The semantic notions introduced in the above-mentioned articles are also used in the following works of the present selection, under the titles: “Three Principles of Compositionality” and “On Metaknowledge and Truth” (Chapters 7 and 8). They formalize two principles of compositionality that are well known in the literature on the subject, deriving from Frege, i.e. those of meaning and of denotation; they are related to the syntactic principle of compositionality which was introduced by the author. All the three principles are, at the same time, three conditions of homomorphism of categorial language algebra into three kinds of non-standard models of language (one syntactic and two semantic ones: intensional and extensional), which allows introducing three definitions of truthfulness into these models. The next two works in the collection, entitled: “On Language Adequacy” and “What is the Sense in Logic and Philosophy of Language” (Chapters 9 and 10) concern adequacy of categorial language syntax along with its dual semantics: intensional and extensional, and categorial compatibility of any of its syntactic categories with two corresponding semantic categories: intensional and extensional, based on the compatibility the syntactic category of each language expression with the ontological category assigned to its denotatum. The well-known problem of categorial compatibility for first-order quantifiers finds its solution in the paper “Categories of First-Order Quantifiers” (Chapter 11). In the work “Logic and Ontology of Language” (Chapter 12), being in a sense a summary of the considerations presented in the preceding chapters of the book, language is treated as an ontological being, characterized in compliance with the logical conception of language proposed by Ajdukiewicz. Application—like throughout the book—of tools of classical logic and set theory has resulted in emergence of a general formal logical theory of syntax, semantics and pragmatics of language, which takes into account duality in the understanding of linguistic expressions as tokens (concretes) and types (abstract objects). In terms that take into account a functional approach to language itself, there comes out an ontological neutrality of logic with respect to existential assumptions relating to the ontological nature of linguistic expressions and their extra-linguistic ontological counterparts. The issues connected with applying logic while explaining the manner of using linguistic tokens and linguistic types to determine notions of language communication are raised and illustrated in the last chapter of the work, bearing the title “A Logical Conceptualization of Knowledge on the Notion of Language Communication”. (shrink)

Forthcoming in Darren Bradley (ed.), Carnap and Contemporary Philosophy. -/- This paper is centered on Carnap’s views on rationality. More specifically, much of the focus is on a puzzle regarding Carnap’s view on rationality that Florian Steinberger has recently discussed. Not only is Steinberger’s discussion of significant intrinsic interest: his discussion also raises general questions about Carnap interpretation. As I have discussed in earlier work, there are two very different ways of interpreting Carnap’s talk of “frameworks” – and, relatedly, different (...) ways of interpreting Carnap’s principle of tolerance. Carnap can be interpreted as either a relativist or as what I call a language pluralist. Steinberger’s puzzle arises given the relativist interpretation; I believe the language pluralist interpretation is correct. Most of the discussion will concern the correct interpretation of Carnap, and what this means for Steinberger’s puzzle. While I will not here mount a full defense of the language pluralist interpretation, I will pause to discuss Vera Flocke’s recent criticism of it. Towards the end, I will describe a puzzle regarding rationality different from Steinberger’s. The puzzle that I describe does arise already for the language pluralist. (shrink)

This programmatic paper is an attempt to connect some worries in the philosophy of language with some traditional views in artificial intelligence. After a short introduction to the notion of context in philosophy (§1), starting from the inventor of mathematical logic, Gottlob Frege, I list three debates in the philosophy of language where the solution is strongly undecided: §2 treats the debate between holism and molecularism; §3 describes the debate on the boundaries between semantics and pragmatics; §4 hints at (...) a solution of the debate between explicit and implicit view of incomplete descriptions. These debates may be considered case studies on what is happening to the notion of context in philosophy in the first two decades of XXI century; they push us to look for a unifying framework in which to frame those worries: I propose to shift the attention towards a representation of the basic abilities required to navigate across contexts (§5). In the conclusion, I use some suggestions from computer sciences as a contribution towards a better definition of what is meant by “pragmatic competence”, strictly connected to the philosophical enterprise (§6). (shrink)

Analytic philosophy, a dominant tradition of twentieth-century philosophy, can be informatively cast as the outgrowth of the investigations of logic and language of Gottlob Frege, Bertrand Russell, and Ludwig Wittgenstein, and in the next generation, of Rudolf Carnap and W.V. Quine. As such, it is a specific historical development, one that featured subtle dialectical interactions among its propounders, interactions that have been reflected or reenacted in later developments. Whatever its heritage, contemporary analytic philosophy continues to use investigations of language (...) and thought to get at fundamental issues at the heart of philosophy: truth, meaning, and knowledge. (shrink)

One of Gottlob Frege’s most original contributions to logic and philosophy was his logical notation, his ‘Begriffsschrift’. While long criticized, dismissed, or simply ignored, the recent secondary literature contains some helpful re-evaluations and partial defenses of it. These rely largely on technical, pragmatic, or cognitive-psychological considerations. In this paper, we reconsider Frege’s own reasons for valuing his notation highly. We argue that there is a further semiotic dimension, one that matters epistemologically. This dimension becomes evident once one takes seriously, (...) partly also literally, some striking visual metaphors Frege uses. The result is an interpretation highlighting a side of Frege’s position that is not widely known. It involves his views about the indispensable role that language, or sign systems more generally, play for human thought, and especially, for logic and mathematics. More particularly and as we read Frege, a good logical notation allows for expressing conceptual/inferential relations in a ‘visually inscribed’, thus ‘perspicuous’ way, and this leads to a special kind of ‘insight’ in mathematics. Or as we elaborate this point further, it involves a kind of articulation and understanding hardly possible without it. Frege designed his Begriffsschrift with that specific goal in mind. (shrink)

Freges Werk eröffnete und leitete den Prozeß der Emanzipation der Logik von der ontologisch fundierten zur autarken, von allen nicht-logischen Voraussetzungen losgelösten Logik der Zeichen. Unmittelbaren Aufschluß über den Beginn dieser neuen Epoche gibt Freges Briefwechsel mit den führenden Theoretikern und Philosophen seiner Zeit. Kern des Bandes ist seine Korrespondenz mit Hilbert (über die Grundlagen der Geometrie), mit Husserl (über Sprachphilosophie) und mit Russell (über Logik).

Gottlob Frege is not only the father of contemporary mathematical logic and the philosophy of logic, but — as advocated by others, especially M. Dummett – he is, above all, the founder of contemporary research in logic and the philosophy of language. The categories and concepts introduced by Frege were assimilated by philosophers studying language and inspired further detailed analyses. It seems impossible to overestimate the role of Frege’s theory, despite the fact that his objectives — setting a logical (...) basis for mathematics, undoing the psychologizing of logic, building a clear and accurate language for logic and science — differ from the ones set out by contemporary explorers of language. (shrink)

In the paper, various notions of the logical semiotic sense of linguistic expressions – namely, syntactic and semantic, intensional and extensional – are considered and formalised on the basis of a formal-logical conception of any language L characterised categorially in the spirit of certain Husserl's ideas of pure grammar, Leśniewski-Ajdukiewicz's theory of syntactic/semantic categories and, in accordance with Frege's ontological canons, Bocheński's and some of Suszko's ideas of language adequacy of expressions of L. The adequacy ensures their unambiguous syntactic and (...) semantic senses and mutual, syntactic and semantic correspondence guaranteed by the acceptance of a postulate of categorial compatibility of syntactic and semantic (extensional and intensional) categories of expressions of L. This postulate defines the unification of these three logical senses. There are three principles of compositionality which follow from this postulate: one syntactic and two semantic ones already known to Frege. They are treated as conditions of homomorphism of partial algebra of L into algebraic models of L: syntactic, intensional and extensional. In the paper, they are applied to some expressions with quantifiers. Language adequacy connected with the logical senses described in the logical conception of language L is, obviously, an idealisation. The syntactic and semantic unambiguity of its expressions is not, of course, a feature of natural languages, but every syntactically and semantically ambiguous expression of such languages may be treated as a schema representing all of its interpretations that are unambiguous expressions. (shrink)

The problem of existence is reputed to be one of the oldest and most intractable of philosophy: What do we mean when we say that something exists or, even more challengingly, that something does not exist? Intuitively, it seems that we all have a firm grip upon what we are saying. But how should we explain the difference–if there is any–between statements about existence and other, garden-variety predicative statements? What is the difference between saying that something exists and saying, for (...) instance, that something is red, heavy, soft, etc.? These questions provide the focus of the present study. In the first part, this study addresses those authors that have been most effective and influential at widening the gap between statements about existence and garden-variety predicative statements. These are David Hume, Immanuel Kant, Franz Brentano, and Gottlob Frege. According to this family of approaches, existence becomes something very different from a property of objects. In the second part, this study turns to more recent attempts that have moved in the opposite direction by trying to reduce existence to a–more or less–plain property of objects. The philosophers that are going to be discussed here are Alexius Meinong, Richard Routley, Terence Parsons, William Rapaport, Edward Zalta, and Graham Priest. Between the first and the second part, an extensive chapter is dedicated to the approaches to existence developed under the heading of free logics. Finally, the third part of this study develops a deflationist account of existence: We should abandon the assumption shared by all accounts discussed in this study, namely that the notion of existence adds something to the content of a statement. To the contrary, we should think of existence as a redundant notion. The advantage of this strategy is that it does not make it contradictory to say that something does not exist – a frequent upshot of the approaches discussed in the first part. At the same time, this strategy avoids the epicycles common to the approaches discussed in the second part, which are strictly linked to the reduction of existence to a property of objects. (shrink)

In his “Begriffsschrift, a Formalized Language of Pure Thought Modelled upon the Language of Arithmetic,” published in 1879, Frege attributes his approach to Leibniz’ idea of a “lingua characteristica.” And it can be said that, in the field of logic and the foundations of mathematics, he indeed achieved the realization of the essential aspects of Leibniz’ program.

In this exciting new collection, a distinguished international group of philosophers contribute new essays on central issues in philosophy of language and logic, in honor of Michael Dummett, one of the most influential philosophers of the late twentieth century. The essays are focused on areas particularly associated with Professor Dummett. Five are contributions to the philosophy of language, addressing in particular the nature of truth and meaning and the relation between language and thought. Two contributors discuss time, in particular (...) the reality of the past. The last four essays focus on Frege and the philosophy of mathematics. The volume represents some of the best work in contemporary analytical philosophy. (shrink)

Gottlob Frege is one of the founding figures of analytic philosophy, whose contributions to logic, philosophical semantics, philosophy of language, and philosophy of mathematics set the agenda for future generations of theorists in these and related areas. Dale Jacquette's lively and incisive biography charts Frege's life from its beginnings in small-town north Germany, through his student days in Jena, to his development as an enduringly influential thinker. Along the way Jacquette considers Frege's ground-breaking Begriffschrift, in which he formulated his (...) 'ideal logical language', his magisterial Grundgesetze der Arithmetik, and his complex relation to thinkers including Husserl and especially Russell, whose Paradox had such drastic implications for Frege's logicism. Jacquette concludes with a thoughtful assessment of Frege's legacy. His rich and informative biography will appeal to all who are interested in Frege's philosophy. (shrink)

"By looking at Frege's lectures on logic through the eyes of the young Carnap, this book casts new light on the history of logic and analytic philosophy. As two introductory essays by Gottfried Gabriel and by Erich H. Reck and Steve Awodey explain, Carnap's notes allow us to better understand Frege's deep influence on Carnap and analytic philosophy, as well as the broader philosophical matrix from which both continental and analytic styles of thought emerged in the 20th century."--BOOK JACKET.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Philosophical Analysis in the Twentieth CenturyA. P. MartinichScott Soames. Philosophical Analysis in the Twentieth Century. Vol. 1, The Dawn of Analysis. Pp. xix + 411. Vol. 2, The Age of Meaning. Pp. xxii + 479. Princeton: Princeton University Press, 2003. Cloth, $35.00, each volume.This two-volume work treats Anglo-American analytic philosophy from 1900 to roughly 1970. This means that the views of Michael Dummett, John Rawls and others (...) are not treated. Soames explains the omission in an epilogue to the second volume. Too much good philosophy on too many topics has been done recently—much of it using technical devices—to allow him or anyone else, to master more than a few parts. That seems right to me.The first volume consists of five parts: One: G. E. Moore on Ethics, Epistemology, and Philosophical Analysis; Two: Bertrand Russell on Logical and Linguistic Analysis; Three: Ludwig Wittgenstein's Tractatus; and Four: Logical Positivism, Emotivism, and Ethics; and Five: The Post-Positivist Perspective of the Early W. V. Quine. The great figure associated with twentieth-century analytic philosophy who is missing from Volume 1, Gottlob Frege, Soames omits, because Frege's "concerns were, on the whole, more specialized and technical than the others, and for many years this limited his influence" (1:xiii n. 1). The second volume consists of seven parts: One: Ludwig Wittgenstein's Philosophical Investigations; Two: Classics of Ordinary Language Philosophy: Truth, Goodness, the Mind, and Analysis; Three: More Classics of Ordinary Language Philosophy: The Response to Radical Skepticism; Four: Paul Grice and the End of Ordinary Language Philosophy; Five: The Philosophical Naturalism of Willard Van Orman Quine; Six: Donald Davidson on Truth and Meaning; Seven: Saul Kripke on Naming and Necessity.What does twentieth-century analytic philosophy come to? Soames thinks its "two most important achievements" are (i) the recognition that philosophical speculation must be grounded in pre-philosophical thought, and (ii) the success achieved in understanding, and separating one from another, the fundamental methodological notions of logical consequence, logical truth, necessary truth, and apriori truth" (1:xi; see also 1:298-99 and 2:252). He admirably succeeds in making the case for these judgments, although many philosophers will think that these two together do not amount to a great deal, considering all the effort expended by analytic philosophers. I think that analytic philosophy has done more; it has given philosophers many techniques for attacking conceptual problems, a great deal of information about the structure and nature of language, and has decisively refuted various theses that were once thought attractive and even obviously true. In any case, those who think that analytic philosophy, especially conceptual analysis, accomplished nothing are, I think, refuted by these volumes. In his discussion of G. E. Moore's article, "A Defense of Common Sense," Soames explains what he takes to be the first great result of analytic philosophy. Moore showed that the beliefs of common sense should often be accepted "with more confidence" than any philosophical beliefs or propositions that conflict with them, and in these cases cannot be overthrown by philosophical beliefs. For example, "The skeptic assumes that we can be certain about what knowledge is before we decide whether what we all ordinarily take to be paradigmatic cases of knowledge really are genuine" [End Page 125] (23, entire sentence is bold in the original). (Soames uses boldface type to mark all of the significant propositions discussed in the book, a nice pedagogical device.)In his discussion of Bertrand Russell's theory of descriptions, Soames gives the impression that linguistic interests primarily motivated Russell. I think the motivation was primarily ontological. Russell wanted to justify ridding philosophy of nonexistent entities. The doctrines of Wittgenstein's Tractatus Logico-Philosophicus and Logical Positivism were two ways in which philosophical analysis developed. For Soames, what is most important in the Tractatus is the theory of names, and he holds, I believe, the minority belief (which I share) that properties are reducible to configurations of objects (1:206-6). What is most important in Logical Positivism is the verification theory of meaning. Strongly verifiable sentences "were supposed to be those the truth of which could, in principle, be completely established... (shrink)

Most areas of philosopher Edmund Husserl’s thought have been explored, but his views on logic, mathematics, and semantics have been largely ignored. These essays offer an alternative to discussions of the philosophy of contemporary mathematics. The book covers areas of disagreement between Husserl and Gottlob Frege, the father of analytical philosophy, and explores new perspectives seen in their work.

An outstanding philosopher-logician, Gottlob Frege's work has received much attention in recent years. In the pursuit of Frege's main goal to solidify the foundations of mathematics and scientific work, Frege conceived a comprehensive philosophy of language and developed the main thesis of logicism, that mathematics is reducible to logic. This book contains essays covering a large range of issues related to Frege that will be of great interest to philosophers working on these issues. This volume represents an important addition (...) to the study of Frege. This book contains essays from some of the most important contemporary philosophers investigating Frege's ideas. Treating issues of contemporary interest, this book discusses topics either in a Fregean spirit or in dialogue with Frege's original views. The wide implications of Frege's views are evident in the variety of topics presented in this volume, from the Frege fundamentals to innovative interpretations that break new ground in the study of Frege. Key papers concern the ontological status of propositions and concepts, recent attempts to improve on the semantics of singular terms, the question of how to construe the content of concept-expressions, and other themes within the common grounds in which ontology and philosophical semantics intersect. (shrink)

Frege's conception of the logical categories has vexed commentators for decades. In this dissertation, I argue that it revolves around two forms of internality. The first is the internality of its use in the expression of judgment to the sign. A proper understanding of that internality reveals how Frege's philosophical logic cannot be fit into the framework given by the contemporary syntax/semantics distinction. The second is the internality that obtains between the way in which Begriffsschrift signs stratify into different categories, (...) on the one hand, and the way in which the realm of Bedeutungen stratifies into logical categories, on the other hand. A proper understanding of this internality reveals how Frege's conception of the relation between language and the world is neither a form of realism nor a form of linguistic idealism. To come to understand Frege's conception of the logical categories, is to come to understand both these forms of internality by coming to understand how they hang together. (shrink)

This chapter contains sections titled: Gottlob Frege Bertrand Russell H.P. Grice Donald Davidson Truth theories of meaning Use Theories of Meaning Thinking in Language Two‐level Theories of Reference The Social Construction of Meaning Kripke's Wittgenstein.

Analytic philosophy has been perhaps the most successful philosophical movement of the twentieth century. While there is no one doctrine that defines it, one of the most salient features of analytic philosophy is its reliance on contemporary logic, the logic that had its origin in the works of George Boole and Gottlob Frege and others in the mid‐to‐late nineteenth century. Boolean algebra, the heart of Boole's contributions to logic, has also come to represent a cornerstone of modern computing. Frege (...) had broad philosophical interests, and his writings on the nature of logical form, meaning and truth remain the subject of intense theoretical discussion, especially in the analytic tradition. Frege's works, and the powerful new logical calculi developed at the end of the nineteenth century, influenced many of its most seminal figures, such as Bertrand Russell, Ludwig Wittgenstein and Rudolf Carnap. (shrink)

This volume contains all of Frege's extant unpublished writings on philosophy and logic other than his correspondence, written at various stages of his career.

This guide accompanies the following article: ‘Logic and Divine Simplicity’. Philosophy Compass 6/4 : pp. 282–294, doi: Author’s IntroductionFirst‐order formalizations of classical theistic doctrines are increasingly used in contemporary work in philosophy of religion and philosophical theology, as a means for clarifying the conceptual structure of the doctrines and their role in inferential procedures. But there are a variety of different ways in which such doctrines have been formalized, each representing the doctrines as having different conceptual structures. Moreover, the adequacy (...) of such formalizations as such has, at least with respect to some classes of doctrines, been disputed. One reason for disputing their adequacy derives from the conceptual impact of classical theism’s doctrine of divine simplicity.Author RecommendsFrege, Gottlob ‘Begriffsschrift: a formula language of pure thought,’ trans. Michael Beany, in The Frege Reader, ed. Beany. Oxford: Blackwell, pp. 47–78. The preface contains interesting remarks about the purpose of formalization as understood by the chief pioneer of modern formal logic. These remarks are also connected by Frege to his views on the relation between thought and language more generally.Russell, Bertrand, and Whitehead, A.N. Principia Mathematica, Vol. I. Cambridge: Cambridge University Press.The preface and first section of the long introduction contain remarks on the purpose and advantages of formalization. Chapter 1 of the introduction contains what is probably one of the first formalizations ever of a theistic doctrine, and is given in terms of a definite description analysis.Suppes, Patrick ‘The Desirability of Formalization in Science,’The Journal of Philosophy, Vol. 65, No. 20, pp. 651–64.Clear and concise discussion of some of the advantages of formalization in philosophical inquiry, written by a prominent contemporary American philosopher‐logician.Nieznański, Edward ‘The Beginnings of Formalization in Theology,’ in Advances in Scientific Philosophy: Essays in Honour of Paul Weingartner, eds. Gerhard Schurz and Gregory J.W. Dorn. Amsterdam and Atlanta, GA: Ropodi, pp. 551–9.A valuable paper that narrates, among other things, the programme of formalizing theistic doctrines that emerged in Poland in the 1920s under the influence of the Lvov‐Warsaw School. Various examples of formalizations are also given.Quine, W.V.O. Mathematical Logic. Cambridge, MA: Harvard University Press.In Section 27 of this classic study, Quine offers a formalization of theistic doctrines which seeks to avoid the difficulties of earlier formalizations by means of a subtle extensional singleton set analysis. The proposal has not won many adherents, but is worthy of careful study nonetheless.Woleński, Jan ‘Theism, Fideism, Atheism, Agnosticism,’ in Logic, Ethics and All That Jazz: Essays in Honour of Jordan Howard Sobel, eds. Lars‐Göran Johansson, Jan Österberg, and Rysiek Sliwinski. Uppsala: Uppsala Philosophical Studies, pp. 387–400.A concise but lucid survey of some attempts to formalize theistic doctrines and some problems besetting these attempts. Woleński also proposes his own method of formalization, which could be described as a simplified version of Quine’s method in Mathematical Logic.Bocheński, Joseph The Logic of Religion. New York: New York University Press.The first book‐length treatment of the relation between modern logic and theism. It covers much ground, and remains very readable.Alston, William P. ‘Religious Language and Verificationism,’ in The Rationality of Theism, eds. Paul Moser and Paul Copan. London: Routledge, pp. 17–34.Identifies some problems with attempts at articulating theistic doctrines by means of subject‐predicate language. Highly relevant to formalizations of theistic doctrines, even though this topic is not dealt with explicitly.Kraal, Anders ‘Logic and Divine Simplicity,’Philosophy Compass.Offers a survey of three main methods of formalizing theistic doctrines, and of some variants of these methods. Argues that certain formalizations of theistic doctrines are bound to be rejected as conceptually inadequate by all who understand the doctrines at hand within the framework provided by the traditional doctrine of divine simplicity.Sample Syllabus Week I: The Idea of Formalization and the Project of Formalizing Theistic Doctrines Reading:Frege, Gottlob ‘Begriffsschrift: a formula language of pure thought,’ trans. Michael Beany, in The Frege Reader, ed. Beany. Oxford: Blackwell, pp. 47–78. Russell, Bertrand, and Whitehead, A.N. Principia Mathematica, Vol. I. Cambridge: Cambridge University Press. Suppes, Patrick ‘The Desirability of Formalization in Science,’The Journal of Philosophy, Vol. 65, No. 20, pp. 651–64.Nieznański, Edward ‘The Beginnings of Formalization in Theology,’ in Advances in Scientific Philosophy: Essays in Honour of Paul Weingartner, eds. Gerhard Schurz and Gregory J.W. Dorn. Amsterdam and Atlanta, GA: Ropodi, pp. 551–9. Week II: Formalizing Theistic Doctrines: Three Alternative Methods Reading:Woleński, Jan ‘Theism, Fideism, Atheism, Agnosticism,’ in Logic, Ethics and All That Jazz: Essays in Honour of Jordan Howard Sobel, eds. Lars‐Göran Johansson, Jan Österberg, and Rysiek Sliwinski. Uppsala: Uppsala Philosophical Studies, pp. 387–400.Russell, Bertrand, and Whitehead, A.N. Principia Mathematica, Vol. I. Cambridge: Cambridge University Press. Quine, W.V.O. Mathematical Logic. Cambridge, MA: Harvard University Press. Week III: Arguments for and Against Some Formalizations of Theistic Doctrines Reading:Bocheński, Joseph The Logic of Religion. New York: New York University Press. Kraal, Anders ‘Logic and Divine Simplicity,’Philosophy Compass, Vol. 6, No. 4, pp. 282–94.Focus Questions1 What do Frege, Russell and Whitehead, and Suppes understand the purpose or purposes of logical formalization to be, and why do they think formalization can achieve these purposes?2 Woleński sketches some simple ways of formalizing theistic doctrines such as ‘God exists’ or ‘God is almighty’ in terms of 1‐place predicates which he subsequently abandons in favour of other methods. What reasons lead him to abandon these more simple methods of formalization?3 What are the advantages of the definite description formalization of theistic doctrines offered by Russell and Whitehead?4 Quine offers a subtle formalization of the theistic doctrine ‘God exists’ in terms of singleton sets. What problems are Quine’s formalization intended to accommodate, and how does it seek to accommodate them?5 Which relative merits or demerits are there in Bocheński’s and Kraal’s respective arguments for and against the adequacy of certain formalizations of theistic doctrines? (shrink)

Pieranna Garavaso and Nicla Vassallo investigate Gottlob Frege's largely unexplored notion of thinking to provide insight into the roles of language in expressing thoughts and in fostering the development of human knowledge. The analysis will benefit studies of epistemology, logic, philosophy of mind, psychology, and philosophy of language.